0.003 * [progress]: [Phase 1 of 3] Setting up.
0.003 * * * [progress]: [1/2] Preparing points
0.257 * * * [progress]: [2/2] Setting up program.
0.263 * [progress]: [Phase 2 of 3] Improving.
0.263 * * * * [progress]: [ 1 / 1 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
0.264 * [simplify]: Simplifying:
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
0.264 * * [simplify]: iteration 1: (13 enodes)
0.273 * * [simplify]: iteration 2: (57 enodes)
0.295 * * [simplify]: iteration 3: (102 enodes)
0.334 * * [simplify]: iteration 4: (189 enodes)
0.389 * * [simplify]: iteration 5: (375 enodes)
0.555 * * [simplify]: iteration 6: (937 enodes)
1.483 * * [simplify]: Extracting #0: cost 1 inf + 0
1.483 * * [simplify]: Extracting #1: cost 60 inf + 0
1.484 * * [simplify]: Extracting #2: cost 219 inf + 1
1.485 * * [simplify]: Extracting #3: cost 277 inf + 210
1.492 * * [simplify]: Extracting #4: cost 283 inf + 2300
1.499 * * [simplify]: Extracting #5: cost 183 inf + 26485
1.530 * * [simplify]: Extracting #6: cost 74 inf + 97550
1.570 * * [simplify]: Extracting #7: cost 0 inf + 165315
1.641 * * [simplify]: Extracting #8: cost 0 inf + 165195
1.686 * [simplify]: Simplified to:
  (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))
1.698 * * [progress]: iteration 1 / 4
1.698 * * * [progress]: picking best candidate
1.710 * * * * [pick]: Picked  #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))>
1.710 * * * [progress]: localizing error
1.751 * * * [progress]: generating rewritten candidates
1.751 * * * * [progress]: [ 1 / 3 ] rewriting at (2 1)
1.763 * * * * [progress]: [ 2 / 3 ] rewriting at (2 1 1)
1.782 * * * * [progress]: [ 3 / 3 ] rewriting at (2)
1.796 * * * [progress]: generating series expansions
1.796 * * * * [progress]: [ 1 / 3 ] generating series at (2 1)
1.797 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) into (pow (* 2 (* n PI)) (* 1/2 (- 1 k)))
1.797 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in (n k) around 0
1.797 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
1.797 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
1.797 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
1.797 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
1.797 * [taylor]: Taking taylor expansion of 1/2 in k
1.797 * [backup-simplify]: Simplify 1/2 into 1/2
1.797 * [taylor]: Taking taylor expansion of (- 1 k) in k
1.797 * [taylor]: Taking taylor expansion of 1 in k
1.797 * [backup-simplify]: Simplify 1 into 1
1.797 * [taylor]: Taking taylor expansion of k in k
1.797 * [backup-simplify]: Simplify 0 into 0
1.797 * [backup-simplify]: Simplify 1 into 1
1.797 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
1.797 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
1.797 * [taylor]: Taking taylor expansion of 2 in k
1.797 * [backup-simplify]: Simplify 2 into 2
1.797 * [taylor]: Taking taylor expansion of (* n PI) in k
1.797 * [taylor]: Taking taylor expansion of n in k
1.797 * [backup-simplify]: Simplify n into n
1.797 * [taylor]: Taking taylor expansion of PI in k
1.797 * [backup-simplify]: Simplify PI into PI
1.797 * [backup-simplify]: Simplify (* n PI) into (* n PI)
1.797 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
1.797 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
1.797 * [backup-simplify]: Simplify (- 0) into 0
1.798 * [backup-simplify]: Simplify (+ 1 0) into 1
1.798 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
1.798 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
1.798 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
1.798 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
1.798 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
1.798 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
1.798 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
1.798 * [taylor]: Taking taylor expansion of 1/2 in n
1.798 * [backup-simplify]: Simplify 1/2 into 1/2
1.798 * [taylor]: Taking taylor expansion of (- 1 k) in n
1.798 * [taylor]: Taking taylor expansion of 1 in n
1.798 * [backup-simplify]: Simplify 1 into 1
1.798 * [taylor]: Taking taylor expansion of k in n
1.798 * [backup-simplify]: Simplify k into k
1.798 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
1.798 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
1.798 * [taylor]: Taking taylor expansion of 2 in n
1.799 * [backup-simplify]: Simplify 2 into 2
1.799 * [taylor]: Taking taylor expansion of (* n PI) in n
1.799 * [taylor]: Taking taylor expansion of n in n
1.799 * [backup-simplify]: Simplify 0 into 0
1.799 * [backup-simplify]: Simplify 1 into 1
1.799 * [taylor]: Taking taylor expansion of PI in n
1.799 * [backup-simplify]: Simplify PI into PI
1.799 * [backup-simplify]: Simplify (* 0 PI) into 0
1.799 * [backup-simplify]: Simplify (* 2 0) into 0
1.800 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
1.801 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
1.802 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
1.802 * [backup-simplify]: Simplify (- k) into (- k)
1.802 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
1.802 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
1.803 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
1.803 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
1.804 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
1.804 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
1.804 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
1.804 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
1.804 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
1.804 * [taylor]: Taking taylor expansion of 1/2 in n
1.804 * [backup-simplify]: Simplify 1/2 into 1/2
1.804 * [taylor]: Taking taylor expansion of (- 1 k) in n
1.804 * [taylor]: Taking taylor expansion of 1 in n
1.804 * [backup-simplify]: Simplify 1 into 1
1.804 * [taylor]: Taking taylor expansion of k in n
1.804 * [backup-simplify]: Simplify k into k
1.804 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
1.804 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
1.804 * [taylor]: Taking taylor expansion of 2 in n
1.804 * [backup-simplify]: Simplify 2 into 2
1.804 * [taylor]: Taking taylor expansion of (* n PI) in n
1.804 * [taylor]: Taking taylor expansion of n in n
1.804 * [backup-simplify]: Simplify 0 into 0
1.804 * [backup-simplify]: Simplify 1 into 1
1.804 * [taylor]: Taking taylor expansion of PI in n
1.804 * [backup-simplify]: Simplify PI into PI
1.805 * [backup-simplify]: Simplify (* 0 PI) into 0
1.805 * [backup-simplify]: Simplify (* 2 0) into 0
1.806 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
1.807 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
1.807 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
1.807 * [backup-simplify]: Simplify (- k) into (- k)
1.808 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
1.808 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
1.809 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
1.809 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
1.810 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
1.810 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) in k
1.810 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) in k
1.810 * [taylor]: Taking taylor expansion of 1/2 in k
1.810 * [backup-simplify]: Simplify 1/2 into 1/2
1.810 * [taylor]: Taking taylor expansion of (* (- 1 k) (+ (log n) (log (* 2 PI)))) in k
1.810 * [taylor]: Taking taylor expansion of (- 1 k) in k
1.810 * [taylor]: Taking taylor expansion of 1 in k
1.810 * [backup-simplify]: Simplify 1 into 1
1.810 * [taylor]: Taking taylor expansion of k in k
1.810 * [backup-simplify]: Simplify 0 into 0
1.810 * [backup-simplify]: Simplify 1 into 1
1.810 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
1.810 * [taylor]: Taking taylor expansion of (log n) in k
1.810 * [taylor]: Taking taylor expansion of n in k
1.810 * [backup-simplify]: Simplify n into n
1.810 * [backup-simplify]: Simplify (log n) into (log n)
1.810 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
1.810 * [taylor]: Taking taylor expansion of (* 2 PI) in k
1.810 * [taylor]: Taking taylor expansion of 2 in k
1.810 * [backup-simplify]: Simplify 2 into 2
1.810 * [taylor]: Taking taylor expansion of PI in k
1.810 * [backup-simplify]: Simplify PI into PI
1.811 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
1.811 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
1.811 * [backup-simplify]: Simplify (- 0) into 0
1.812 * [backup-simplify]: Simplify (+ 1 0) into 1
1.813 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
1.814 * [backup-simplify]: Simplify (* 1 (+ (log n) (log (* 2 PI)))) into (+ (log n) (log (* 2 PI)))
1.815 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
1.816 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
1.817 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
1.818 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
1.819 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
1.821 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
1.821 * [backup-simplify]: Simplify (- 0) into 0
1.822 * [backup-simplify]: Simplify (+ 0 0) into 0
1.822 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 k))) into 0
1.823 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
1.824 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
1.825 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0
1.825 * [taylor]: Taking taylor expansion of 0 in k
1.825 * [backup-simplify]: Simplify 0 into 0
1.825 * [backup-simplify]: Simplify 0 into 0
1.826 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
1.826 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
1.827 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
1.828 * [backup-simplify]: Simplify (+ 0 0) into 0
1.828 * [backup-simplify]: Simplify (- 1) into -1
1.828 * [backup-simplify]: Simplify (+ 0 -1) into -1
1.829 * [backup-simplify]: Simplify (+ (* 1 0) (* -1 (+ (log n) (log (* 2 PI))))) into (- (+ (log (* 2 PI)) (log n)))
1.833 * [backup-simplify]: Simplify (+ (* 1/2 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))))
1.835 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
1.837 * [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)))))))
1.837 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
1.838 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
1.840 * [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
1.840 * [backup-simplify]: Simplify (- 0) into 0
1.841 * [backup-simplify]: Simplify (+ 0 0) into 0
1.841 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0
1.842 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
1.843 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
1.845 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
1.845 * [taylor]: Taking taylor expansion of 0 in k
1.845 * [backup-simplify]: Simplify 0 into 0
1.845 * [backup-simplify]: Simplify 0 into 0
1.845 * [backup-simplify]: Simplify 0 into 0
1.846 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
1.846 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) 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
1.849 * [backup-simplify]: Simplify (+ 0 0) into 0
1.849 * [backup-simplify]: Simplify (- 0) into 0
1.849 * [backup-simplify]: Simplify (+ 0 0) into 0
1.850 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
1.852 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
1.854 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 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)))))
1.858 * [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)))))
1.869 * [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)))))
1.870 * [backup-simplify]: Simplify (pow (* (/ 1 n) (* 2 PI)) (* (- 1 (/ 1 k)) 1/2)) into (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k))))
1.870 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in (n k) around 0
1.870 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
1.870 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
1.870 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
1.870 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
1.870 * [taylor]: Taking taylor expansion of 1/2 in k
1.870 * [backup-simplify]: Simplify 1/2 into 1/2
1.870 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
1.870 * [taylor]: Taking taylor expansion of 1 in k
1.870 * [backup-simplify]: Simplify 1 into 1
1.870 * [taylor]: Taking taylor expansion of (/ 1 k) in k
1.870 * [taylor]: Taking taylor expansion of k in k
1.870 * [backup-simplify]: Simplify 0 into 0
1.870 * [backup-simplify]: Simplify 1 into 1
1.871 * [backup-simplify]: Simplify (/ 1 1) into 1
1.871 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
1.871 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
1.871 * [taylor]: Taking taylor expansion of 2 in k
1.871 * [backup-simplify]: Simplify 2 into 2
1.871 * [taylor]: Taking taylor expansion of (/ PI n) in k
1.871 * [taylor]: Taking taylor expansion of PI in k
1.871 * [backup-simplify]: Simplify PI into PI
1.871 * [taylor]: Taking taylor expansion of n in k
1.871 * [backup-simplify]: Simplify n into n
1.871 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
1.871 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
1.871 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
1.872 * [backup-simplify]: Simplify (- 1) into -1
1.872 * [backup-simplify]: Simplify (+ 0 -1) into -1
1.873 * [backup-simplify]: Simplify (* 1/2 -1) 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 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
1.873 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
1.873 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
1.873 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
1.873 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 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 (/ 1 k)) in n
1.873 * [taylor]: Taking taylor expansion of 1 in n
1.873 * [backup-simplify]: Simplify 1 into 1
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
1.874 * [backup-simplify]: Simplify 0 into 0
1.874 * [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))
1.876 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
1.876 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
1.876 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
1.877 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
1.878 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
1.879 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
1.879 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
1.880 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
1.880 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
1.880 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
1.880 * [taylor]: Taking taylor expansion of 1/2 in n
1.880 * [backup-simplify]: Simplify 1/2 into 1/2
1.880 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
1.880 * [taylor]: Taking taylor expansion of 1 in n
1.880 * [backup-simplify]: Simplify 1 into 1
1.880 * [taylor]: Taking taylor expansion of (/ 1 k) in n
1.880 * [taylor]: Taking taylor expansion of k in n
1.880 * [backup-simplify]: Simplify k into k
1.880 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
1.880 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
1.880 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
1.880 * [taylor]: Taking taylor expansion of 2 in n
1.880 * [backup-simplify]: Simplify 2 into 2
1.880 * [taylor]: Taking taylor expansion of (/ PI n) in n
1.880 * [taylor]: Taking taylor expansion of PI in n
1.880 * [backup-simplify]: Simplify PI into PI
1.880 * [taylor]: Taking taylor expansion of n in n
1.880 * [backup-simplify]: Simplify 0 into 0
1.880 * [backup-simplify]: Simplify 1 into 1
1.881 * [backup-simplify]: Simplify (/ PI 1) into PI
1.881 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
1.882 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
1.882 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
1.882 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
1.882 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
1.884 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
1.885 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
1.886 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
1.886 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k
1.886 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 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 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k
1.886 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
1.886 * [taylor]: Taking taylor expansion of 1 in k
1.886 * [backup-simplify]: Simplify 1 into 1
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
1.888 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
1.889 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
1.889 * [taylor]: Taking taylor expansion of (log n) in k
1.889 * [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) into -1
1.890 * [backup-simplify]: Simplify (+ 0 -1) into -1
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 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n)))
1.892 * [backup-simplify]: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n)))
1.893 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
1.894 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
1.894 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
1.895 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
1.896 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
1.896 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
1.896 * [backup-simplify]: Simplify (- 0) into 0
1.896 * [backup-simplify]: Simplify (+ 0 0) into 0
1.897 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 (/ 1 k)))) into 0
1.897 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
1.898 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
1.899 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
1.899 * [taylor]: Taking taylor expansion of 0 in k
1.899 * [backup-simplify]: Simplify 0 into 0
1.899 * [backup-simplify]: Simplify 0 into 0
1.900 * [backup-simplify]: Simplify 0 into 0
1.900 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.901 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
1.902 * [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
1.903 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
1.903 * [backup-simplify]: Simplify (- 0) into 0
1.903 * [backup-simplify]: Simplify (+ 0 0) into 0
1.904 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0
1.904 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
1.905 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
1.907 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
1.907 * [taylor]: Taking taylor expansion of 0 in k
1.907 * [backup-simplify]: Simplify 0 into 0
1.907 * [backup-simplify]: Simplify 0 into 0
1.907 * [backup-simplify]: Simplify 0 into 0
1.907 * [backup-simplify]: Simplify 0 into 0
1.907 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.908 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
1.911 * [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
1.911 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 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 (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) 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 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
1.916 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 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
1.916 * [taylor]: Taking taylor expansion of 0 in k
1.916 * [backup-simplify]: Simplify 0 into 0
1.916 * [backup-simplify]: Simplify 0 into 0
1.917 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
1.918 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) (* 2 PI)) (* (- 1 (/ 1 (- k))) 1/2)) into (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1)))
1.918 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in (n k) around 0
1.918 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
1.918 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
1.918 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
1.918 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
1.918 * [taylor]: Taking taylor expansion of 1/2 in k
1.918 * [backup-simplify]: Simplify 1/2 into 1/2
1.918 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
1.918 * [taylor]: Taking taylor expansion of (/ 1 k) in k
1.918 * [taylor]: Taking taylor expansion of k in k
1.918 * [backup-simplify]: Simplify 0 into 0
1.918 * [backup-simplify]: Simplify 1 into 1
1.918 * [backup-simplify]: Simplify (/ 1 1) into 1
1.918 * [taylor]: Taking taylor expansion of 1 in k
1.918 * [backup-simplify]: Simplify 1 into 1
1.918 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
1.918 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
1.918 * [taylor]: Taking taylor expansion of -2 in k
1.918 * [backup-simplify]: Simplify -2 into -2
1.918 * [taylor]: Taking taylor expansion of (/ PI n) in k
1.918 * [taylor]: Taking taylor expansion of PI in k
1.918 * [backup-simplify]: Simplify PI into PI
1.918 * [taylor]: Taking taylor expansion of n in k
1.918 * [backup-simplify]: Simplify n into n
1.918 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
1.919 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
1.919 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
1.919 * [backup-simplify]: Simplify (+ 1 0) into 1
1.919 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
1.919 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
1.919 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
1.919 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
1.919 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
1.919 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
1.919 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
1.919 * [taylor]: Taking taylor expansion of 1/2 in n
1.919 * [backup-simplify]: Simplify 1/2 into 1/2
1.919 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
1.919 * [taylor]: Taking taylor expansion of (/ 1 k) in n
1.919 * [taylor]: Taking taylor expansion of k in n
1.919 * [backup-simplify]: Simplify k into k
1.920 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
1.920 * [taylor]: Taking taylor expansion of 1 in n
1.920 * [backup-simplify]: Simplify 1 into 1
1.920 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
1.920 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
1.920 * [taylor]: Taking taylor expansion of -2 in n
1.920 * [backup-simplify]: Simplify -2 into -2
1.920 * [taylor]: Taking taylor expansion of (/ PI n) in n
1.920 * [taylor]: Taking taylor expansion of PI in n
1.920 * [backup-simplify]: Simplify PI into PI
1.920 * [taylor]: Taking taylor expansion of n in n
1.920 * [backup-simplify]: Simplify 0 into 0
1.920 * [backup-simplify]: Simplify 1 into 1
1.920 * [backup-simplify]: Simplify (/ PI 1) into PI
1.920 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
1.921 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
1.921 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
1.921 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
1.922 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
1.922 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
1.923 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
1.923 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
1.923 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
1.923 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
1.923 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
1.923 * [taylor]: Taking taylor expansion of 1/2 in n
1.923 * [backup-simplify]: Simplify 1/2 into 1/2
1.923 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
1.923 * [taylor]: Taking taylor expansion of (/ 1 k) in n
1.923 * [taylor]: Taking taylor expansion of k in n
1.923 * [backup-simplify]: Simplify k into k
1.923 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
1.923 * [taylor]: Taking taylor expansion of 1 in n
1.923 * [backup-simplify]: Simplify 1 into 1
1.923 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
1.923 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
1.923 * [taylor]: Taking taylor expansion of -2 in n
1.923 * [backup-simplify]: Simplify -2 into -2
1.923 * [taylor]: Taking taylor expansion of (/ PI n) in n
1.923 * [taylor]: Taking taylor expansion of PI in n
1.923 * [backup-simplify]: Simplify PI into PI
1.923 * [taylor]: Taking taylor expansion of n in n
1.923 * [backup-simplify]: Simplify 0 into 0
1.924 * [backup-simplify]: Simplify 1 into 1
1.924 * [backup-simplify]: Simplify (/ PI 1) into PI
1.924 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
1.925 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
1.925 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
1.925 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
1.927 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
1.928 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
1.929 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
1.929 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k
1.929 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) in k
1.929 * [taylor]: Taking taylor expansion of 1/2 in k
1.929 * [backup-simplify]: Simplify 1/2 into 1/2
1.929 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) in k
1.929 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
1.929 * [taylor]: Taking taylor expansion of (/ 1 k) in k
1.929 * [taylor]: Taking taylor expansion of k in k
1.929 * [backup-simplify]: Simplify 0 into 0
1.929 * [backup-simplify]: Simplify 1 into 1
1.930 * [backup-simplify]: Simplify (/ 1 1) into 1
1.930 * [taylor]: Taking taylor expansion of 1 in k
1.930 * [backup-simplify]: Simplify 1 into 1
1.930 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
1.930 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
1.930 * [taylor]: Taking taylor expansion of (* -2 PI) in k
1.930 * [taylor]: Taking taylor expansion of -2 in k
1.930 * [backup-simplify]: Simplify -2 into -2
1.930 * [taylor]: Taking taylor expansion of PI in k
1.930 * [backup-simplify]: Simplify PI into PI
1.931 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
1.932 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
1.932 * [taylor]: Taking taylor expansion of (log n) in k
1.932 * [taylor]: Taking taylor expansion of n in k
1.932 * [backup-simplify]: Simplify n into n
1.932 * [backup-simplify]: Simplify (log n) into (log n)
1.932 * [backup-simplify]: Simplify (+ 1 0) into 1
1.932 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
1.933 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
1.934 * [backup-simplify]: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n))
1.935 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
1.936 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
1.938 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
1.944 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
1.945 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
1.947 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
1.948 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
1.948 * [backup-simplify]: Simplify (+ 0 0) into 0
1.949 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (/ 1 k) 1))) into 0
1.949 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
1.950 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
1.951 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
1.951 * [taylor]: Taking taylor expansion of 0 in k
1.951 * [backup-simplify]: Simplify 0 into 0
1.951 * [backup-simplify]: Simplify 0 into 0
1.951 * [backup-simplify]: Simplify 0 into 0
1.952 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.953 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
1.955 * [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
1.955 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
1.955 * [backup-simplify]: Simplify (+ 0 0) into 0
1.955 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0
1.956 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
1.957 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
1.959 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
1.959 * [taylor]: Taking taylor expansion of 0 in k
1.959 * [backup-simplify]: Simplify 0 into 0
1.959 * [backup-simplify]: Simplify 0 into 0
1.959 * [backup-simplify]: Simplify 0 into 0
1.959 * [backup-simplify]: Simplify 0 into 0
1.959 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.960 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
1.963 * [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
1.963 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
1.964 * [backup-simplify]: Simplify (+ 0 0) into 0
1.965 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1))))) into 0
1.965 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
1.967 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
1.968 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
1.968 * [taylor]: Taking taylor expansion of 0 in k
1.968 * [backup-simplify]: Simplify 0 into 0
1.968 * [backup-simplify]: Simplify 0 into 0
1.969 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
1.969 * * * * [progress]: [ 2 / 3 ] generating series at (2 1 1)
1.969 * [backup-simplify]: Simplify (* n (* 2 PI)) into (* 2 (* n PI))
1.969 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
1.969 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
1.969 * [taylor]: Taking taylor expansion of 2 in n
1.969 * [backup-simplify]: Simplify 2 into 2
1.969 * [taylor]: Taking taylor expansion of (* n PI) in n
1.970 * [taylor]: Taking taylor expansion of n in n
1.970 * [backup-simplify]: Simplify 0 into 0
1.970 * [backup-simplify]: Simplify 1 into 1
1.970 * [taylor]: Taking taylor expansion of PI in n
1.970 * [backup-simplify]: Simplify PI into PI
1.970 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
1.970 * [taylor]: Taking taylor expansion of 2 in n
1.970 * [backup-simplify]: Simplify 2 into 2
1.970 * [taylor]: Taking taylor expansion of (* n PI) in n
1.970 * [taylor]: Taking taylor expansion of n in n
1.970 * [backup-simplify]: Simplify 0 into 0
1.970 * [backup-simplify]: Simplify 1 into 1
1.970 * [taylor]: Taking taylor expansion of PI in n
1.970 * [backup-simplify]: Simplify PI into PI
1.970 * [backup-simplify]: Simplify (* 0 PI) into 0
1.970 * [backup-simplify]: Simplify (* 2 0) into 0
1.970 * [backup-simplify]: Simplify 0 into 0
1.971 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
1.972 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
1.972 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
1.973 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
1.974 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
1.974 * [backup-simplify]: Simplify 0 into 0
1.974 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
1.975 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
1.975 * [backup-simplify]: Simplify 0 into 0
1.976 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
1.977 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
1.977 * [backup-simplify]: Simplify 0 into 0
1.979 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
1.980 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
1.980 * [backup-simplify]: Simplify 0 into 0
1.982 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
1.985 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
1.985 * [backup-simplify]: Simplify 0 into 0
1.987 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
1.989 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
1.989 * [backup-simplify]: Simplify 0 into 0
1.990 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
1.990 * [backup-simplify]: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n))
1.990 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
1.991 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
1.991 * [taylor]: Taking taylor expansion of 2 in n
1.991 * [backup-simplify]: Simplify 2 into 2
1.991 * [taylor]: Taking taylor expansion of (/ PI n) in n
1.991 * [taylor]: Taking taylor expansion of PI in n
1.991 * [backup-simplify]: Simplify PI into PI
1.991 * [taylor]: Taking taylor expansion of n in n
1.991 * [backup-simplify]: Simplify 0 into 0
1.991 * [backup-simplify]: Simplify 1 into 1
1.991 * [backup-simplify]: Simplify (/ PI 1) into PI
1.991 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
1.991 * [taylor]: Taking taylor expansion of 2 in n
1.991 * [backup-simplify]: Simplify 2 into 2
1.991 * [taylor]: Taking taylor expansion of (/ PI n) in n
1.991 * [taylor]: Taking taylor expansion of PI in n
1.991 * [backup-simplify]: Simplify PI into PI
1.991 * [taylor]: Taking taylor expansion of n in n
1.991 * [backup-simplify]: Simplify 0 into 0
1.992 * [backup-simplify]: Simplify 1 into 1
1.992 * [backup-simplify]: Simplify (/ PI 1) into PI
1.993 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
1.993 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
1.994 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
1.995 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
1.995 * [backup-simplify]: Simplify 0 into 0
1.996 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.997 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
1.997 * [backup-simplify]: Simplify 0 into 0
1.998 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.000 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
2.000 * [backup-simplify]: Simplify 0 into 0
2.001 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.002 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
2.002 * [backup-simplify]: Simplify 0 into 0
2.003 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.005 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
2.005 * [backup-simplify]: Simplify 0 into 0
2.006 * [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
2.008 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
2.008 * [backup-simplify]: Simplify 0 into 0
2.009 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
2.009 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* 2 PI)) into (* -2 (/ PI n))
2.009 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
2.009 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
2.009 * [taylor]: Taking taylor expansion of -2 in n
2.010 * [backup-simplify]: Simplify -2 into -2
2.010 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.010 * [taylor]: Taking taylor expansion of PI in n
2.010 * [backup-simplify]: Simplify PI into PI
2.010 * [taylor]: Taking taylor expansion of n in n
2.010 * [backup-simplify]: Simplify 0 into 0
2.010 * [backup-simplify]: Simplify 1 into 1
2.010 * [backup-simplify]: Simplify (/ PI 1) into PI
2.010 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
2.010 * [taylor]: Taking taylor expansion of -2 in n
2.010 * [backup-simplify]: Simplify -2 into -2
2.010 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.010 * [taylor]: Taking taylor expansion of PI in n
2.010 * [backup-simplify]: Simplify PI into PI
2.010 * [taylor]: Taking taylor expansion of n in n
2.010 * [backup-simplify]: Simplify 0 into 0
2.010 * [backup-simplify]: Simplify 1 into 1
2.011 * [backup-simplify]: Simplify (/ PI 1) into PI
2.012 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
2.012 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
2.013 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
2.014 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
2.014 * [backup-simplify]: Simplify 0 into 0
2.015 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.016 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
2.016 * [backup-simplify]: Simplify 0 into 0
2.017 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.017 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
2.017 * [backup-simplify]: Simplify 0 into 0
2.018 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.019 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
2.019 * [backup-simplify]: Simplify 0 into 0
2.019 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.021 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
2.021 * [backup-simplify]: Simplify 0 into 0
2.022 * [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
2.023 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
2.023 * [backup-simplify]: Simplify 0 into 0
2.023 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
2.023 * * * * [progress]: [ 3 / 3 ] generating series at (2)
2.023 * [backup-simplify]: Simplify (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)) into (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k)))
2.024 * [approximate]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in (n k) around 0
2.024 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k
2.024 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
2.024 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
2.024 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
2.024 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
2.024 * [taylor]: Taking taylor expansion of 1/2 in k
2.024 * [backup-simplify]: Simplify 1/2 into 1/2
2.024 * [taylor]: Taking taylor expansion of (- 1 k) in k
2.024 * [taylor]: Taking taylor expansion of 1 in k
2.024 * [backup-simplify]: Simplify 1 into 1
2.024 * [taylor]: Taking taylor expansion of k in k
2.024 * [backup-simplify]: Simplify 0 into 0
2.024 * [backup-simplify]: Simplify 1 into 1
2.024 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
2.024 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
2.024 * [taylor]: Taking taylor expansion of 2 in k
2.024 * [backup-simplify]: Simplify 2 into 2
2.024 * [taylor]: Taking taylor expansion of (* n PI) in k
2.024 * [taylor]: Taking taylor expansion of n in k
2.024 * [backup-simplify]: Simplify n into n
2.024 * [taylor]: Taking taylor expansion of PI in k
2.024 * [backup-simplify]: Simplify PI into PI
2.024 * [backup-simplify]: Simplify (* n PI) into (* n PI)
2.024 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
2.024 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
2.024 * [backup-simplify]: Simplify (- 0) into 0
2.025 * [backup-simplify]: Simplify (+ 1 0) into 1
2.025 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
2.025 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
2.025 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
2.025 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
2.025 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.025 * [taylor]: Taking taylor expansion of k in k
2.025 * [backup-simplify]: Simplify 0 into 0
2.025 * [backup-simplify]: Simplify 1 into 1
2.025 * [backup-simplify]: Simplify (/ 1 1) into 1
2.026 * [backup-simplify]: Simplify (sqrt 0) into 0
2.026 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
2.027 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in n
2.027 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
2.027 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
2.027 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
2.027 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
2.027 * [taylor]: Taking taylor expansion of 1/2 in n
2.027 * [backup-simplify]: Simplify 1/2 into 1/2
2.027 * [taylor]: Taking taylor expansion of (- 1 k) in n
2.027 * [taylor]: Taking taylor expansion of 1 in n
2.027 * [backup-simplify]: Simplify 1 into 1
2.027 * [taylor]: Taking taylor expansion of k in n
2.027 * [backup-simplify]: Simplify k into k
2.027 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
2.027 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
2.027 * [taylor]: Taking taylor expansion of 2 in n
2.027 * [backup-simplify]: Simplify 2 into 2
2.027 * [taylor]: Taking taylor expansion of (* n PI) in n
2.027 * [taylor]: Taking taylor expansion of n in n
2.027 * [backup-simplify]: Simplify 0 into 0
2.027 * [backup-simplify]: Simplify 1 into 1
2.027 * [taylor]: Taking taylor expansion of PI in n
2.027 * [backup-simplify]: Simplify PI into PI
2.027 * [backup-simplify]: Simplify (* 0 PI) into 0
2.027 * [backup-simplify]: Simplify (* 2 0) into 0
2.028 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
2.029 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
2.030 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
2.030 * [backup-simplify]: Simplify (- k) into (- k)
2.030 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
2.030 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
2.031 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
2.032 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
2.032 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
2.032 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
2.032 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.032 * [taylor]: Taking taylor expansion of k in n
2.032 * [backup-simplify]: Simplify k into k
2.032 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.032 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
2.032 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
2.033 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
2.033 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in n
2.033 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
2.033 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
2.033 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
2.033 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
2.033 * [taylor]: Taking taylor expansion of 1/2 in n
2.033 * [backup-simplify]: Simplify 1/2 into 1/2
2.033 * [taylor]: Taking taylor expansion of (- 1 k) in n
2.033 * [taylor]: Taking taylor expansion of 1 in n
2.033 * [backup-simplify]: Simplify 1 into 1
2.033 * [taylor]: Taking taylor expansion of k in n
2.033 * [backup-simplify]: Simplify k into k
2.033 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
2.033 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
2.033 * [taylor]: Taking taylor expansion of 2 in n
2.033 * [backup-simplify]: Simplify 2 into 2
2.033 * [taylor]: Taking taylor expansion of (* n PI) in n
2.033 * [taylor]: Taking taylor expansion of n in n
2.033 * [backup-simplify]: Simplify 0 into 0
2.033 * [backup-simplify]: Simplify 1 into 1
2.033 * [taylor]: Taking taylor expansion of PI in n
2.033 * [backup-simplify]: Simplify PI into PI
2.033 * [backup-simplify]: Simplify (* 0 PI) into 0
2.034 * [backup-simplify]: Simplify (* 2 0) into 0
2.035 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
2.035 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
2.036 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
2.036 * [backup-simplify]: Simplify (- k) into (- k)
2.036 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
2.036 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
2.037 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
2.038 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
2.038 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
2.038 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
2.038 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.038 * [taylor]: Taking taylor expansion of k in n
2.039 * [backup-simplify]: Simplify k into k
2.039 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.039 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
2.039 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
2.039 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
2.039 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (sqrt (/ 1 k))) into (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (sqrt (/ 1 k)))
2.039 * [taylor]: Taking taylor expansion of (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (sqrt (/ 1 k))) in k
2.040 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) in k
2.040 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) in k
2.040 * [taylor]: Taking taylor expansion of 1/2 in k
2.040 * [backup-simplify]: Simplify 1/2 into 1/2
2.040 * [taylor]: Taking taylor expansion of (* (- 1 k) (+ (log n) (log (* 2 PI)))) in k
2.040 * [taylor]: Taking taylor expansion of (- 1 k) in k
2.040 * [taylor]: Taking taylor expansion of 1 in k
2.040 * [backup-simplify]: Simplify 1 into 1
2.040 * [taylor]: Taking taylor expansion of k in k
2.040 * [backup-simplify]: Simplify 0 into 0
2.040 * [backup-simplify]: Simplify 1 into 1
2.040 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
2.040 * [taylor]: Taking taylor expansion of (log n) in k
2.040 * [taylor]: Taking taylor expansion of n in k
2.040 * [backup-simplify]: Simplify n into n
2.040 * [backup-simplify]: Simplify (log n) into (log n)
2.040 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
2.040 * [taylor]: Taking taylor expansion of (* 2 PI) in k
2.040 * [taylor]: Taking taylor expansion of 2 in k
2.040 * [backup-simplify]: Simplify 2 into 2
2.040 * [taylor]: Taking taylor expansion of PI in k
2.040 * [backup-simplify]: Simplify PI into PI
2.040 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
2.041 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
2.041 * [backup-simplify]: Simplify (- 0) into 0
2.041 * [backup-simplify]: Simplify (+ 1 0) into 1
2.042 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
2.042 * [backup-simplify]: Simplify (* 1 (+ (log n) (log (* 2 PI)))) into (+ (log n) (log (* 2 PI)))
2.043 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
2.044 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
2.044 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
2.044 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.044 * [taylor]: Taking taylor expansion of k in k
2.044 * [backup-simplify]: Simplify 0 into 0
2.044 * [backup-simplify]: Simplify 1 into 1
2.044 * [backup-simplify]: Simplify (/ 1 1) into 1
2.044 * [backup-simplify]: Simplify (sqrt 0) into 0
2.045 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
2.046 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) into 0
2.046 * [backup-simplify]: Simplify 0 into 0
2.046 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
2.047 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
2.048 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
2.048 * [backup-simplify]: Simplify (- 0) into 0
2.049 * [backup-simplify]: Simplify (+ 0 0) into 0
2.049 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 k))) into 0
2.050 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
2.050 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
2.057 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0
2.058 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 0) (* 0 (sqrt (/ 1 k)))) into 0
2.058 * [taylor]: Taking taylor expansion of 0 in k
2.058 * [backup-simplify]: Simplify 0 into 0
2.059 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
2.060 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
2.062 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
2.063 * [backup-simplify]: Simplify (+ 0 0) into 0
2.063 * [backup-simplify]: Simplify (- 1) into -1
2.063 * [backup-simplify]: Simplify (+ 0 -1) into -1
2.065 * [backup-simplify]: Simplify (+ (* 1 0) (* -1 (+ (log n) (log (* 2 PI))))) into (- (+ (log (* 2 PI)) (log n)))
2.067 * [backup-simplify]: Simplify (+ (* 1/2 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))))
2.070 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
2.074 * [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)))))))
2.075 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
2.076 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.076 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0
2.078 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
2.079 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
2.081 * [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
2.081 * [backup-simplify]: Simplify (- 0) into 0
2.082 * [backup-simplify]: Simplify (+ 0 0) into 0
2.082 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0
2.083 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
2.084 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
2.085 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
2.086 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k))))) into 0
2.086 * [taylor]: Taking taylor expansion of 0 in k
2.086 * [backup-simplify]: Simplify 0 into 0
2.086 * [backup-simplify]: Simplify 0 into 0
2.087 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
2.089 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
2.090 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
2.090 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
2.092 * [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
2.092 * [backup-simplify]: Simplify (+ 0 0) into 0
2.092 * [backup-simplify]: Simplify (- 0) into 0
2.093 * [backup-simplify]: Simplify (+ 0 0) into 0
2.094 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
2.095 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
2.097 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 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)))))
2.103 * [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))))))))
2.106 * [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))))))))
2.106 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.106 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0
2.107 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
2.108 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
2.114 * [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
2.114 * [backup-simplify]: Simplify (- 0) into 0
2.115 * [backup-simplify]: Simplify (+ 0 0) into 0
2.116 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 k))))) into 0
2.118 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
2.119 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
2.122 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
2.124 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k)))))) into 0
2.124 * [taylor]: Taking taylor expansion of 0 in k
2.124 * [backup-simplify]: Simplify 0 into 0
2.124 * [backup-simplify]: Simplify 0 into 0
2.124 * [backup-simplify]: Simplify 0 into 0
2.125 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.127 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
2.129 * [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
2.129 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
2.132 * [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
2.133 * [backup-simplify]: Simplify (+ 0 0) into 0
2.133 * [backup-simplify]: Simplify (- 0) into 0
2.133 * [backup-simplify]: Simplify (+ 0 0) into 0
2.135 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
2.136 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
2.140 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 3) 6)) (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 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)))))))
2.150 * [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))))))))))))))
2.164 * [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))))))))))))))
2.183 * [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))))))))))))))))))))))
2.184 * [backup-simplify]: Simplify (/ (pow (* (/ 1 n) (* 2 PI)) (* (- 1 (/ 1 k)) 1/2)) (sqrt (/ 1 k))) into (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k))
2.184 * [approximate]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in (n k) around 0
2.184 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k
2.184 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
2.184 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
2.184 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
2.184 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
2.184 * [taylor]: Taking taylor expansion of 1/2 in k
2.184 * [backup-simplify]: Simplify 1/2 into 1/2
2.184 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
2.184 * [taylor]: Taking taylor expansion of 1 in k
2.184 * [backup-simplify]: Simplify 1 into 1
2.184 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.184 * [taylor]: Taking taylor expansion of k in k
2.184 * [backup-simplify]: Simplify 0 into 0
2.184 * [backup-simplify]: Simplify 1 into 1
2.184 * [backup-simplify]: Simplify (/ 1 1) into 1
2.184 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
2.184 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
2.185 * [taylor]: Taking taylor expansion of 2 in k
2.185 * [backup-simplify]: Simplify 2 into 2
2.185 * [taylor]: Taking taylor expansion of (/ PI n) in k
2.185 * [taylor]: Taking taylor expansion of PI in k
2.185 * [backup-simplify]: Simplify PI into PI
2.185 * [taylor]: Taking taylor expansion of n in k
2.185 * [backup-simplify]: Simplify n into n
2.185 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
2.185 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
2.185 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
2.185 * [backup-simplify]: Simplify (- 1) into -1
2.186 * [backup-simplify]: Simplify (+ 0 -1) into -1
2.186 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
2.186 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
2.187 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
2.187 * [taylor]: Taking taylor expansion of (sqrt k) in k
2.187 * [taylor]: Taking taylor expansion of k in k
2.187 * [backup-simplify]: Simplify 0 into 0
2.187 * [backup-simplify]: Simplify 1 into 1
2.187 * [backup-simplify]: Simplify (sqrt 0) into 0
2.189 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
2.189 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in n
2.189 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
2.189 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
2.189 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
2.189 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
2.189 * [taylor]: Taking taylor expansion of 1/2 in n
2.189 * [backup-simplify]: Simplify 1/2 into 1/2
2.189 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
2.189 * [taylor]: Taking taylor expansion of 1 in n
2.189 * [backup-simplify]: Simplify 1 into 1
2.189 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.189 * [taylor]: Taking taylor expansion of k in n
2.189 * [backup-simplify]: Simplify k into k
2.189 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.189 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
2.189 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
2.189 * [taylor]: Taking taylor expansion of 2 in n
2.189 * [backup-simplify]: Simplify 2 into 2
2.189 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.189 * [taylor]: Taking taylor expansion of PI in n
2.189 * [backup-simplify]: Simplify PI into PI
2.189 * [taylor]: Taking taylor expansion of n in n
2.189 * [backup-simplify]: Simplify 0 into 0
2.189 * [backup-simplify]: Simplify 1 into 1
2.190 * [backup-simplify]: Simplify (/ PI 1) into PI
2.190 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
2.191 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
2.191 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
2.191 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
2.192 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
2.193 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
2.194 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
2.195 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
2.195 * [taylor]: Taking taylor expansion of (sqrt k) in n
2.195 * [taylor]: Taking taylor expansion of k in n
2.195 * [backup-simplify]: Simplify k into k
2.196 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
2.196 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
2.196 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in n
2.196 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
2.196 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
2.196 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
2.196 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
2.196 * [taylor]: Taking taylor expansion of 1/2 in n
2.196 * [backup-simplify]: Simplify 1/2 into 1/2
2.196 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
2.196 * [taylor]: Taking taylor expansion of 1 in n
2.196 * [backup-simplify]: Simplify 1 into 1
2.196 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.196 * [taylor]: Taking taylor expansion of k in n
2.196 * [backup-simplify]: Simplify k into k
2.196 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.196 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
2.196 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
2.196 * [taylor]: Taking taylor expansion of 2 in n
2.196 * [backup-simplify]: Simplify 2 into 2
2.196 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.196 * [taylor]: Taking taylor expansion of PI in n
2.196 * [backup-simplify]: Simplify PI into PI
2.196 * [taylor]: Taking taylor expansion of n in n
2.196 * [backup-simplify]: Simplify 0 into 0
2.196 * [backup-simplify]: Simplify 1 into 1
2.197 * [backup-simplify]: Simplify (/ PI 1) into PI
2.197 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
2.198 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
2.199 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
2.199 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
2.199 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
2.200 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
2.201 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
2.203 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
2.203 * [taylor]: Taking taylor expansion of (sqrt k) in n
2.203 * [taylor]: Taking taylor expansion of k in n
2.203 * [backup-simplify]: Simplify k into k
2.203 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
2.203 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
2.204 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) into (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k))
2.204 * [taylor]: Taking taylor expansion of (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) in k
2.204 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k
2.204 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k
2.204 * [taylor]: Taking taylor expansion of 1/2 in k
2.204 * [backup-simplify]: Simplify 1/2 into 1/2
2.204 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k
2.204 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
2.204 * [taylor]: Taking taylor expansion of 1 in k
2.204 * [backup-simplify]: Simplify 1 into 1
2.205 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.205 * [taylor]: Taking taylor expansion of k in k
2.205 * [backup-simplify]: Simplify 0 into 0
2.205 * [backup-simplify]: Simplify 1 into 1
2.205 * [backup-simplify]: Simplify (/ 1 1) into 1
2.205 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
2.205 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
2.205 * [taylor]: Taking taylor expansion of (* 2 PI) in k
2.205 * [taylor]: Taking taylor expansion of 2 in k
2.205 * [backup-simplify]: Simplify 2 into 2
2.205 * [taylor]: Taking taylor expansion of PI in k
2.205 * [backup-simplify]: Simplify PI into PI
2.206 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
2.207 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
2.207 * [taylor]: Taking taylor expansion of (log n) in k
2.207 * [taylor]: Taking taylor expansion of n in k
2.207 * [backup-simplify]: Simplify n into n
2.207 * [backup-simplify]: Simplify (log n) into (log n)
2.207 * [backup-simplify]: Simplify (- 1) into -1
2.208 * [backup-simplify]: Simplify (+ 0 -1) into -1
2.208 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
2.209 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
2.210 * [backup-simplify]: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n)))
2.211 * [backup-simplify]: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n)))
2.212 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
2.212 * [taylor]: Taking taylor expansion of (sqrt k) in k
2.212 * [taylor]: Taking taylor expansion of k in k
2.212 * [backup-simplify]: Simplify 0 into 0
2.212 * [backup-simplify]: Simplify 1 into 1
2.212 * [backup-simplify]: Simplify (sqrt 0) into 0
2.213 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
2.214 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 0) into 0
2.214 * [backup-simplify]: Simplify 0 into 0
2.214 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
2.215 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
2.216 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
2.216 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
2.216 * [backup-simplify]: Simplify (- 0) into 0
2.217 * [backup-simplify]: Simplify (+ 0 0) into 0
2.217 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 (/ 1 k)))) into 0
2.218 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
2.219 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
2.220 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
2.220 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 0) (* 0 (sqrt k))) into 0
2.220 * [taylor]: Taking taylor expansion of 0 in k
2.220 * [backup-simplify]: Simplify 0 into 0
2.220 * [backup-simplify]: Simplify 0 into 0
2.221 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
2.222 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
2.223 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
2.223 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.224 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
2.225 * [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
2.226 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.226 * [backup-simplify]: Simplify (- 0) into 0
2.226 * [backup-simplify]: Simplify (+ 0 0) into 0
2.227 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0
2.227 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
2.228 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
2.230 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
2.231 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (sqrt k)))) into 0
2.231 * [taylor]: Taking taylor expansion of 0 in k
2.231 * [backup-simplify]: Simplify 0 into 0
2.231 * [backup-simplify]: Simplify 0 into 0
2.231 * [backup-simplify]: Simplify 0 into 0
2.232 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
2.234 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
2.234 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
2.235 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
2.235 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.236 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
2.239 * [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
2.239 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.239 * [backup-simplify]: Simplify (- 0) into 0
2.240 * [backup-simplify]: Simplify (+ 0 0) into 0
2.241 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0
2.242 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
2.244 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
2.247 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 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
2.249 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt k))))) into 0
2.249 * [taylor]: Taking taylor expansion of 0 in k
2.249 * [backup-simplify]: Simplify 0 into 0
2.249 * [backup-simplify]: Simplify 0 into 0
2.249 * [backup-simplify]: Simplify 0 into 0
2.250 * [backup-simplify]: Simplify 0 into 0
2.254 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
2.256 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
2.257 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
2.259 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3))))))))
2.260 * [backup-simplify]: Simplify (/ (pow (* (/ 1 (- n)) (* 2 PI)) (* (- 1 (/ 1 (- k))) 1/2)) (sqrt (/ 1 (- k)))) into (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k)))
2.260 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in (n k) around 0
2.260 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in k
2.260 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
2.260 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
2.260 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
2.260 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
2.260 * [taylor]: Taking taylor expansion of 1/2 in k
2.260 * [backup-simplify]: Simplify 1/2 into 1/2
2.260 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
2.260 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.260 * [taylor]: Taking taylor expansion of k in k
2.260 * [backup-simplify]: Simplify 0 into 0
2.260 * [backup-simplify]: Simplify 1 into 1
2.260 * [backup-simplify]: Simplify (/ 1 1) into 1
2.260 * [taylor]: Taking taylor expansion of 1 in k
2.260 * [backup-simplify]: Simplify 1 into 1
2.260 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
2.260 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
2.260 * [taylor]: Taking taylor expansion of -2 in k
2.260 * [backup-simplify]: Simplify -2 into -2
2.260 * [taylor]: Taking taylor expansion of (/ PI n) in k
2.261 * [taylor]: Taking taylor expansion of PI in k
2.261 * [backup-simplify]: Simplify PI into PI
2.261 * [taylor]: Taking taylor expansion of n in k
2.261 * [backup-simplify]: Simplify n into n
2.261 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
2.261 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
2.261 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
2.261 * [backup-simplify]: Simplify (+ 1 0) into 1
2.261 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
2.261 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
2.261 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
2.261 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
2.261 * [taylor]: Taking taylor expansion of (/ -1 k) in k
2.261 * [taylor]: Taking taylor expansion of -1 in k
2.261 * [backup-simplify]: Simplify -1 into -1
2.262 * [taylor]: Taking taylor expansion of k in k
2.262 * [backup-simplify]: Simplify 0 into 0
2.262 * [backup-simplify]: Simplify 1 into 1
2.262 * [backup-simplify]: Simplify (/ -1 1) into -1
2.262 * [backup-simplify]: Simplify (sqrt 0) into 0
2.263 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
2.263 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))
2.263 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in n
2.263 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
2.263 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
2.263 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
2.263 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
2.263 * [taylor]: Taking taylor expansion of 1/2 in n
2.263 * [backup-simplify]: Simplify 1/2 into 1/2
2.263 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
2.263 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.263 * [taylor]: Taking taylor expansion of k in n
2.263 * [backup-simplify]: Simplify k into k
2.263 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.263 * [taylor]: Taking taylor expansion of 1 in n
2.263 * [backup-simplify]: Simplify 1 into 1
2.263 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
2.263 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
2.263 * [taylor]: Taking taylor expansion of -2 in n
2.263 * [backup-simplify]: Simplify -2 into -2
2.263 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.263 * [taylor]: Taking taylor expansion of PI in n
2.263 * [backup-simplify]: Simplify PI into PI
2.263 * [taylor]: Taking taylor expansion of n in n
2.263 * [backup-simplify]: Simplify 0 into 0
2.263 * [backup-simplify]: Simplify 1 into 1
2.264 * [backup-simplify]: Simplify (/ PI 1) into PI
2.264 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
2.265 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
2.265 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
2.265 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
2.266 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
2.266 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
2.267 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
2.267 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
2.267 * [taylor]: Taking taylor expansion of (/ -1 k) in n
2.267 * [taylor]: Taking taylor expansion of -1 in n
2.267 * [backup-simplify]: Simplify -1 into -1
2.267 * [taylor]: Taking taylor expansion of k in n
2.267 * [backup-simplify]: Simplify k into k
2.267 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
2.267 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
2.267 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
2.267 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
2.268 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))
2.268 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in n
2.268 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
2.268 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
2.268 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
2.268 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
2.268 * [taylor]: Taking taylor expansion of 1/2 in n
2.268 * [backup-simplify]: Simplify 1/2 into 1/2
2.268 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
2.268 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.268 * [taylor]: Taking taylor expansion of k in n
2.268 * [backup-simplify]: Simplify k into k
2.268 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.268 * [taylor]: Taking taylor expansion of 1 in n
2.268 * [backup-simplify]: Simplify 1 into 1
2.268 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
2.268 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
2.268 * [taylor]: Taking taylor expansion of -2 in n
2.268 * [backup-simplify]: Simplify -2 into -2
2.268 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.268 * [taylor]: Taking taylor expansion of PI in n
2.268 * [backup-simplify]: Simplify PI into PI
2.268 * [taylor]: Taking taylor expansion of n in n
2.268 * [backup-simplify]: Simplify 0 into 0
2.268 * [backup-simplify]: Simplify 1 into 1
2.272 * [backup-simplify]: Simplify (/ PI 1) into PI
2.273 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
2.274 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
2.274 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
2.274 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
2.275 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
2.275 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
2.276 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
2.276 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
2.276 * [taylor]: Taking taylor expansion of (/ -1 k) in n
2.276 * [taylor]: Taking taylor expansion of -1 in n
2.276 * [backup-simplify]: Simplify -1 into -1
2.276 * [taylor]: Taking taylor expansion of k in n
2.276 * [backup-simplify]: Simplify k into k
2.276 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
2.276 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
2.276 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
2.276 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
2.277 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))
2.277 * [taylor]: Taking taylor expansion of (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) in k
2.277 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k
2.277 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) in k
2.277 * [taylor]: Taking taylor expansion of 1/2 in k
2.277 * [backup-simplify]: Simplify 1/2 into 1/2
2.277 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) in k
2.277 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
2.277 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.277 * [taylor]: Taking taylor expansion of k in k
2.277 * [backup-simplify]: Simplify 0 into 0
2.277 * [backup-simplify]: Simplify 1 into 1
2.278 * [backup-simplify]: Simplify (/ 1 1) into 1
2.278 * [taylor]: Taking taylor expansion of 1 in k
2.278 * [backup-simplify]: Simplify 1 into 1
2.278 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
2.278 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
2.278 * [taylor]: Taking taylor expansion of (* -2 PI) in k
2.278 * [taylor]: Taking taylor expansion of -2 in k
2.278 * [backup-simplify]: Simplify -2 into -2
2.278 * [taylor]: Taking taylor expansion of PI in k
2.278 * [backup-simplify]: Simplify PI into PI
2.278 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
2.279 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
2.279 * [taylor]: Taking taylor expansion of (log n) in k
2.279 * [taylor]: Taking taylor expansion of n in k
2.279 * [backup-simplify]: Simplify n into n
2.279 * [backup-simplify]: Simplify (log n) into (log n)
2.279 * [backup-simplify]: Simplify (+ 1 0) into 1
2.279 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
2.280 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
2.280 * [backup-simplify]: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n))
2.281 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
2.282 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
2.282 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
2.282 * [taylor]: Taking taylor expansion of (/ -1 k) in k
2.282 * [taylor]: Taking taylor expansion of -1 in k
2.282 * [backup-simplify]: Simplify -1 into -1
2.282 * [taylor]: Taking taylor expansion of k in k
2.282 * [backup-simplify]: Simplify 0 into 0
2.282 * [backup-simplify]: Simplify 1 into 1
2.282 * [backup-simplify]: Simplify (/ -1 1) into -1
2.282 * [backup-simplify]: Simplify (sqrt 0) into 0
2.283 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
2.284 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))
2.285 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))
2.285 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
2.286 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
2.287 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
2.287 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
2.287 * [backup-simplify]: Simplify (+ 0 0) into 0
2.287 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (/ 1 k) 1))) into 0
2.288 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
2.289 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
2.290 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
2.291 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0
2.291 * [taylor]: Taking taylor expansion of 0 in k
2.291 * [backup-simplify]: Simplify 0 into 0
2.291 * [backup-simplify]: Simplify 0 into 0
2.291 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
2.293 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
2.294 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
2.295 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
2.296 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.296 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
2.298 * [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
2.298 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.298 * [backup-simplify]: Simplify (+ 0 0) into 0
2.299 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0
2.300 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
2.301 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
2.302 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
2.302 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.303 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0
2.304 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0
2.304 * [taylor]: Taking taylor expansion of 0 in k
2.304 * [backup-simplify]: Simplify 0 into 0
2.304 * [backup-simplify]: Simplify 0 into 0
2.304 * [backup-simplify]: Simplify 0 into 0
2.304 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.307 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
2.310 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
2.311 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
2.316 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))))))))
2.316 * * * [progress]: simplifying candidates
2.316 * * * * [progress]: [ 1 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (+ (log n) (+ (log 2) (log PI))) (* (- 1 k) 1/2))) (sqrt k)))>
2.316 * * * * [progress]: [ 2 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (+ (log n) (log (* 2 PI))) (* (- 1 k) 1/2))) (sqrt k)))>
2.316 * * * * [progress]: [ 3 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (log (* n (* 2 PI))) (* (- 1 k) 1/2))) (sqrt k)))>
2.316 * * * * [progress]: [ 4 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (log (* n (* 2 PI))) (* (- 1 k) 1/2))) (sqrt k)))>
2.316 * * * * [progress]: [ 5 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (* 1 (* (- 1 k) 1/2))) (sqrt k)))>
2.316 * * * * [progress]: [ 6 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (* 1 (* (- 1 k) 1/2))) (sqrt k)))>
2.316 * * * * [progress]: [ 7 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (* 1 (* (- 1 k) 1/2))) (sqrt k)))>
2.316 * * * * [progress]: [ 8 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (- 1 k)) 1/2) (sqrt k)))>
2.316 * * * * [progress]: [ 9 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow n (* (- 1 k) 1/2)) (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt k)))>
2.316 * * * * [progress]: [ 10 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) 1) (sqrt k)))>
2.317 * * * * [progress]: [ 11 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (exp (log (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt k)))>
2.317 * * * * [progress]: [ 12 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (log (exp (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt k)))>
2.317 * * * * [progress]: [ 13 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))) (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt k)))>
2.317 * * * * [progress]: [ 14 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (cbrt (* (* (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt k)))>
2.317 * * * * [progress]: [ 15 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (* (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt k)))>
2.317 * * * * [progress]: [ 16 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (* 1 (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt k)))>
2.317 * * * * [progress]: [ 17 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2)) (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2))) (sqrt k)))>
2.317 * * * * [progress]: [ 18 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (posit16->real (real->posit16 (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt k)))>
2.317 * * * * [progress]: [ 19 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) 1) (* (- 1 k) 1/2)) (sqrt k)))>
2.317 * * * * [progress]: [ 20 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) 1) (* (- 1 k) 1/2)) (sqrt k)))>
2.317 * * * * [progress]: [ 21 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) 1) (* (- 1 k) 1/2)) (sqrt k)))>
2.317 * * * * [progress]: [ 22 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (+ (log n) (+ (log 2) (log PI)))) (* (- 1 k) 1/2)) (sqrt k)))>
2.317 * * * * [progress]: [ 23 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (+ (log n) (log (* 2 PI)))) (* (- 1 k) 1/2)) (sqrt k)))>
2.317 * * * * [progress]: [ 24 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (log (* n (* 2 PI)))) (* (- 1 k) 1/2)) (sqrt k)))>
2.317 * * * * [progress]: [ 25 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (pow (log (exp (* n (* 2 PI)))) (* (- 1 k) 1/2)) (sqrt k)))>
2.318 * * * * [progress]: [ 26 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (pow (cbrt (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))) (* (- 1 k) 1/2)) (sqrt k)))>
2.318 * * * * [progress]: [ 27 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (pow (cbrt (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))) (* (- 1 k) 1/2)) (sqrt k)))>
2.318 * * * * [progress]: [ 28 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI)))) (cbrt (* n (* 2 PI)))) (* (- 1 k) 1/2)) (sqrt k)))>
2.318 * * * * [progress]: [ 29 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (pow (cbrt (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))) (* (- 1 k) 1/2)) (sqrt k)))>
2.318 * * * * [progress]: [ 30 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (sqrt (* n (* 2 PI))) (sqrt (* n (* 2 PI)))) (* (- 1 k) 1/2)) (sqrt k)))>
2.318 * * * * [progress]: [ 31 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 1 (* n (* 2 PI))) (* (- 1 k) 1/2)) (sqrt k)))>
2.318 * * * * [progress]: [ 32 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* n 2) PI) (* (- 1 k) 1/2)) (sqrt k)))>
2.318 * * * * [progress]: [ 33 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (cbrt n) (cbrt n)) (* (cbrt n) (* 2 PI))) (* (- 1 k) 1/2)) (sqrt k)))>
2.318 * * * * [progress]: [ 34 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (sqrt n) (* (sqrt n) (* 2 PI))) (* (- 1 k) 1/2)) (sqrt k)))>
2.318 * * * * [progress]: [ 35 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 1 (* n (* 2 PI))) (* (- 1 k) 1/2)) (sqrt k)))>
2.318 * * * * [progress]: [ 36 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (pow (posit16->real (real->posit16 (* n (* 2 PI)))) (* (- 1 k) 1/2)) (sqrt k)))>
2.318 * * * * [progress]: [ 37 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* 2 PI) n) (* (- 1 k) 1/2)) (sqrt k)))>
2.318 * * * * [progress]: [ 38 / 104 ] simplifiying candidate #<alt (λ (k n) (pow (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)) 1))>
2.318 * * * * [progress]: [ 39 / 104 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (+ (log n) (+ (log 2) (log PI))) (* (- 1 k) 1/2)) (log (sqrt k)))))>
2.318 * * * * [progress]: [ 40 / 104 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (+ (log n) (log (* 2 PI))) (* (- 1 k) 1/2)) (log (sqrt k)))))>
2.318 * * * * [progress]: [ 41 / 104 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (log (* n (* 2 PI))) (* (- 1 k) 1/2)) (log (sqrt k)))))>
2.319 * * * * [progress]: [ 42 / 104 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (log (* n (* 2 PI))) (* (- 1 k) 1/2)) (log (sqrt k)))))>
2.319 * * * * [progress]: [ 43 / 104 ] simplifiying candidate #<alt (λ (k n) (exp (- (log (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (log (sqrt k)))))>
2.319 * * * * [progress]: [ 44 / 104 ] simplifiying candidate #<alt (λ (k n) (exp (log (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))))>
2.319 * * * * [progress]: [ 45 / 104 ] simplifiying candidate #<alt (λ (k n) (log (exp (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))))>
2.319 * * * * [progress]: [ 46 / 104 ] simplifiying candidate #<alt (λ (k n) (cbrt (/ (* (* (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (* (* (sqrt k) (sqrt k)) (sqrt k)))))>
2.319 * * * * [progress]: [ 47 / 104 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (cbrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))) (cbrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))))>
2.319 * * * * [progress]: [ 48 / 104 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)) (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))))>
2.319 * * * * [progress]: [ 49 / 104 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))))>
2.319 * * * * [progress]: [ 50 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (- (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (- (sqrt k))))>
2.319 * * * * [progress]: [ 51 / 104 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (* (- 1 k) 1/2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (cbrt (sqrt k)))))>
2.319 * * * * [progress]: [ 52 / 104 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (* (- 1 k) 1/2)) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt (cbrt k)))))>
2.319 * * * * [progress]: [ 53 / 104 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (* (- 1 k) 1/2)) (sqrt (sqrt k))) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt (sqrt k)))))>
2.319 * * * * [progress]: [ 54 / 104 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (* (- 1 k) 1/2)) (sqrt 1)) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))>
2.319 * * * * [progress]: [ 55 / 104 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (* (- 1 k) 1/2)) (sqrt (sqrt k))) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt (sqrt k)))))>
2.320 * * * * [progress]: [ 56 / 104 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (* (- 1 k) 1/2)) 1) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))>
2.320 * * * * [progress]: [ 57 / 104 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (cbrt (sqrt k)))))>
2.320 * * * * [progress]: [ 58 / 104 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt (cbrt k)))))>
2.320 * * * * [progress]: [ 59 / 104 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt (sqrt k))) (/ (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt (sqrt k)))))>
2.320 * * * * [progress]: [ 60 / 104 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt 1)) (/ (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt k))))>
2.320 * * * * [progress]: [ 61 / 104 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt (sqrt k))) (/ (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt (sqrt k)))))>
2.320 * * * * [progress]: [ 62 / 104 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))) 1) (/ (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt k))))>
2.320 * * * * [progress]: [ 63 / 104 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (cbrt (sqrt k)))))>
2.320 * * * * [progress]: [ 64 / 104 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt (cbrt k)))))>
2.320 * * * * [progress]: [ 65 / 104 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt (sqrt k))) (/ (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt (sqrt k)))))>
2.320 * * * * [progress]: [ 66 / 104 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt 1)) (/ (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt k))))>
2.320 * * * * [progress]: [ 67 / 104 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt (sqrt k))) (/ (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt (sqrt k)))))>
2.320 * * * * [progress]: [ 68 / 104 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) 1) (/ (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt k))))>
2.320 * * * * [progress]: [ 69 / 104 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (cbrt (sqrt k)))))>
2.321 * * * * [progress]: [ 70 / 104 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt (cbrt k)))))>
2.321 * * * * [progress]: [ 71 / 104 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt (sqrt k)))))>
2.321 * * * * [progress]: [ 72 / 104 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt 1)) (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))))>
2.321 * * * * [progress]: [ 73 / 104 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt (sqrt k)))))>
2.321 * * * * [progress]: [ 74 / 104 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 1) (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))))>
2.321 * * * * [progress]: [ 75 / 104 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2)) (cbrt (sqrt k)))))>
2.321 * * * * [progress]: [ 76 / 104 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2)) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2)) (sqrt (cbrt k)))))>
2.321 * * * * [progress]: [ 77 / 104 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2)) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2)) (sqrt (sqrt k)))))>
2.321 * * * * [progress]: [ 78 / 104 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2)) (sqrt 1)) (/ (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2)) (sqrt k))))>
2.321 * * * * [progress]: [ 79 / 104 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2)) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2)) (sqrt (sqrt k)))))>
2.321 * * * * [progress]: [ 80 / 104 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2)) 1) (/ (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2)) (sqrt k))))>
2.321 * * * * [progress]: [ 81 / 104 ] simplifiying candidate #<alt (λ (k n) (* 1 (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))))>
2.321 * * * * [progress]: [ 82 / 104 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (/ 1 (sqrt k))))>
2.321 * * * * [progress]: [ 83 / 104 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))))>
2.321 * * * * [progress]: [ 84 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k))))>
2.322 * * * * [progress]: [ 85 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt (* (cbrt k) (cbrt k)))) (sqrt (cbrt k))))>
2.322 * * * * [progress]: [ 86 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt (sqrt k))) (sqrt (sqrt k))))>
2.322 * * * * [progress]: [ 87 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt 1)) (sqrt k)))>
2.322 * * * * [progress]: [ 88 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt (sqrt k))) (sqrt (sqrt k))))>
2.322 * * * * [progress]: [ 89 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) 1) (sqrt k)))>
2.322 * * * * [progress]: [ 90 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (pow n (* (- 1 k) 1/2)) (/ (sqrt k) (pow (* 2 PI) (* (- 1 k) 1/2)))))>
2.322 * * * * [progress]: [ 91 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (* (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))) (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))))))>
2.322 * * * * [progress]: [ 92 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))))))>
2.322 * * * * [progress]: [ 93 / 104 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))))>
2.322 * * * * [progress]: [ 94 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2)) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2)))))>
2.322 * * * * [progress]: [ 95 / 104 ] simplifiying candidate #<alt (λ (k n) (posit16->real (real->posit16 (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))))>
2.322 * * * * [progress]: [ 96 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (- (+ (* 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))))) (sqrt k)))>
2.322 * * * * [progress]: [ 97 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (sqrt k)))>
2.322 * * * * [progress]: [ 98 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (sqrt k)))>
2.322 * * * * [progress]: [ 99 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (* (- 1 k) 1/2)) (sqrt k)))>
2.323 * * * * [progress]: [ 100 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (* (- 1 k) 1/2)) (sqrt k)))>
2.323 * * * * [progress]: [ 101 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (* (- 1 k) 1/2)) (sqrt k)))>
2.323 * * * * [progress]: [ 102 / 104 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +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)))))))))))))))))))))))>
2.323 * * * * [progress]: [ 103 / 104 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3)))))))))>
2.323 * * * * [progress]: [ 104 / 104 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))))))))))>
2.325 * [simplify]: Simplifying:
  (* (+ (log n) (+ (log 2) (log PI))) (* (- 1 k) 1/2))
  (* (+ (log n) (log (* 2 PI))) (* (- 1 k) 1/2))
  (* (log (* n (* 2 PI))) (* (- 1 k) 1/2))
  (* (log (* n (* 2 PI))) (* (- 1 k) 1/2))
  (* 1 (* (- 1 k) 1/2))
  (* 1 (* (- 1 k) 1/2))
  (* 1 (* (- 1 k) 1/2))
  (pow (* n (* 2 PI)) (- 1 k))
  (pow n (* (- 1 k) 1/2))
  (pow (* 2 PI) (* (- 1 k) 1/2))
  (log (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))
  (exp (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))
  (* (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))))
  (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))
  (* (* (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))
  (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))
  (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))
  (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2))
  (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2))
  (real->posit16 (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))
  (* 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)))
  (- (* (+ (log n) (+ (log 2) (log PI))) (* (- 1 k) 1/2)) (log (sqrt k)))
  (- (* (+ (log n) (log (* 2 PI))) (* (- 1 k) 1/2)) (log (sqrt k)))
  (- (* (log (* n (* 2 PI))) (* (- 1 k) 1/2)) (log (sqrt k)))
  (- (* (log (* n (* 2 PI))) (* (- 1 k) 1/2)) (log (sqrt k)))
  (- (log (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (log (sqrt k)))
  (log (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))
  (exp (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))
  (/ (* (* (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
  (* (cbrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (cbrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))))
  (cbrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))
  (* (* (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)) (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))
  (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))
  (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))
  (- (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))
  (- (sqrt k))
  (/ (pow n (* (- 1 k) 1/2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (cbrt (sqrt k)))
  (/ (pow n (* (- 1 k) 1/2)) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt (cbrt k)))
  (/ (pow n (* (- 1 k) 1/2)) (sqrt (sqrt k)))
  (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt (sqrt k)))
  (/ (pow n (* (- 1 k) 1/2)) (sqrt 1))
  (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))
  (/ (pow n (* (- 1 k) 1/2)) (sqrt (sqrt k)))
  (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt (sqrt k)))
  (/ (pow n (* (- 1 k) 1/2)) 1)
  (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))
  (/ (* (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (cbrt (sqrt k)))
  (/ (* (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt (* (cbrt k) (cbrt k))))
  (/ (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt (cbrt k)))
  (/ (* (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt (sqrt k)))
  (/ (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt (sqrt k)))
  (/ (* (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt 1))
  (/ (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt k))
  (/ (* (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt (sqrt k)))
  (/ (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt (sqrt k)))
  (/ (* (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))) 1)
  (/ (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt k))
  (/ (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (cbrt (sqrt k)))
  (/ (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt (* (cbrt k) (cbrt k))))
  (/ (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt (cbrt k)))
  (/ (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt 1))
  (/ (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt k))
  (/ (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) 1)
  (/ (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt k))
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (cbrt (sqrt k)))
  (/ 1 (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt (sqrt k)))
  (/ 1 (sqrt 1))
  (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt (sqrt k)))
  (/ 1 1)
  (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))
  (/ (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2)) (cbrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2)) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2)) (sqrt (cbrt k)))
  (/ (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2)) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2)) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2)) (sqrt 1))
  (/ (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2)) (sqrt k))
  (/ (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2)) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2)) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2)) 1)
  (/ (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2)) (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))
  (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt 1))
  (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) 1)
  (/ (sqrt k) (pow (* 2 PI) (* (- 1 k) 1/2)))
  (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))))
  (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))))
  (/ (sqrt k) (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))
  (/ (sqrt k) (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2)))
  (real->posit16 (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))
  (- (+ (* 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)))))
  (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
  (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (- (+ (* +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))))))))))))))))))))))
  (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3))))))))
  (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))))))))
2.330 * * [simplify]: iteration 1: (239 enodes)
2.453 * * [simplify]: iteration 2: (1017 enodes)
2.822 * * [simplify]: Extracting #0: cost 82 inf + 0
2.822 * * [simplify]: Extracting #1: cost 369 inf + 1
2.825 * * [simplify]: Extracting #2: cost 598 inf + 10298
2.843 * * [simplify]: Extracting #3: cost 482 inf + 86599
2.877 * * [simplify]: Extracting #4: cost 275 inf + 195662
2.932 * * [simplify]: Extracting #5: cost 169 inf + 249507
2.991 * * [simplify]: Extracting #6: cost 134 inf + 284603
3.067 * * [simplify]: Extracting #7: cost 54 inf + 339415
3.157 * * [simplify]: Extracting #8: cost 10 inf + 374683
3.258 * * [simplify]: Extracting #9: cost 2 inf + 379546
3.380 * * [simplify]: Extracting #10: cost 0 inf + 380902
3.523 * * [simplify]: Extracting #11: cost 0 inf + 380822
3.668 * [simplify]: Simplified to:
  (* (log (* n (* PI 2))) (* (- 1 k) 1/2))
  (* (log (* n (* PI 2))) (* (- 1 k) 1/2))
  (* (log (* n (* PI 2))) (* (- 1 k) 1/2))
  (* (log (* n (* PI 2))) (* (- 1 k) 1/2))
  (* (- 1 k) 1/2)
  (* (- 1 k) 1/2)
  (* (- 1 k) 1/2)
  (pow (* n (* PI 2)) (- 1 k))
  (pow n (* (- 1 k) 1/2))
  (pow (* PI 2) (* (- 1 k) 1/2))
  (* (log (* n (* PI 2))) (* (- 1 k) 1/2))
  (exp (pow (* n (* PI 2)) (/ (- 1 k) 2)))
  (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))))
  (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))
  (pow (pow (* n (* PI 2)) (/ (- 1 k) 2)) 3)
  (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))
  (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))
  (pow (* n (* PI 2)) (/ (- 1 k) 4))
  (pow (* n (* PI 2)) (/ (- 1 k) 4))
  (real->posit16 (pow (* n (* PI 2)) (/ (- 1 k) 2)))
  (* n (* PI 2))
  (* n (* PI 2))
  (log (* n (* PI 2)))
  (log (* n (* PI 2)))
  (log (* n (* PI 2)))
  (* (exp (* PI n)) (exp (* PI n)))
  (* (* (* n (* PI 2)) (* n (* PI 2))) (* n (* PI 2)))
  (* (* (* n (* PI 2)) (* n (* PI 2))) (* n (* PI 2)))
  (* (cbrt (* n (* PI 2))) (cbrt (* n (* PI 2))))
  (cbrt (* n (* PI 2)))
  (* (* (* n (* PI 2)) (* n (* PI 2))) (* n (* PI 2)))
  (sqrt (* n (* PI 2)))
  (sqrt (* n (* PI 2)))
  (* n 2)
  (* 2 (* PI (cbrt n)))
  (* (sqrt n) (* PI 2))
  (* n (* PI 2))
  (real->posit16 (* n (* PI 2)))
  (- (* (log (* n (* PI 2))) (* (- 1 k) 1/2)) (log (sqrt k)))
  (- (* (log (* n (* PI 2))) (* (- 1 k) 1/2)) (log (sqrt k)))
  (- (* (log (* n (* PI 2))) (* (- 1 k) 1/2)) (log (sqrt k)))
  (- (* (log (* n (* PI 2))) (* (- 1 k) 1/2)) (log (sqrt k)))
  (- (* (log (* n (* PI 2))) (* (- 1 k) 1/2)) (log (sqrt k)))
  (- (* (log (* n (* PI 2))) (* (- 1 k) 1/2)) (log (sqrt k)))
  (exp (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))
  (/ (/ (pow (pow (* n (* PI 2)) (/ (- 1 k) 2)) 3) k) (sqrt k))
  (* (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))
  (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))
  (/ (* (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)) (* (pow (* n (* PI 2)) (/ (- 1 k) 2)) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) (sqrt k))
  (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))
  (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))
  (- (pow (* n (* PI 2)) (/ (- 1 k) 2)))
  (- (sqrt k))
  (/ (pow n (* (- 1 k) 1/2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* PI 2) (* (- 1 k) 1/2)) (cbrt (sqrt k)))
  (/ (pow n (* (- 1 k) 1/2)) (fabs (cbrt k)))
  (/ (pow (* PI 2) (* (- 1 k) 1/2)) (sqrt (cbrt k)))
  (/ (pow n (* (- 1 k) 1/2)) (sqrt (sqrt k)))
  (/ (pow (* PI 2) (* (- 1 k) 1/2)) (sqrt (sqrt k)))
  (pow n (* (- 1 k) 1/2))
  (/ (pow (* PI 2) (* (- 1 k) 1/2)) (sqrt k))
  (/ (pow n (* (- 1 k) 1/2)) (sqrt (sqrt k)))
  (/ (pow (* PI 2) (* (- 1 k) 1/2)) (sqrt (sqrt k)))
  (pow n (* (- 1 k) 1/2))
  (/ (pow (* PI 2) (* (- 1 k) 1/2)) (sqrt k))
  (* (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (sqrt k))) (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (sqrt k))))
  (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (sqrt k)))
  (* (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (fabs (cbrt k))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))))
  (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (cbrt k)))
  (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt (sqrt k)))
  (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))))
  (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k))
  (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt (sqrt k)))
  (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))))
  (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k))
  (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (sqrt k)))
  (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (fabs (cbrt k)))
  (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (cbrt k)))
  (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))
  (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k))
  (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))
  (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k))
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (cbrt (sqrt k)))
  (/ 1 (fabs (cbrt k)))
  (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  1
  (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  1
  (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))
  (/ (/ (pow (* n (* PI 2)) (/ (- 1 k) 4)) (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ (pow (* n (* PI 2)) (/ (- 1 k) 4)) (cbrt (sqrt k)))
  (/ (pow (* n (* PI 2)) (/ (- 1 k) 4)) (fabs (cbrt k)))
  (/ (pow (* n (* PI 2)) (/ (- 1 k) 4)) (sqrt (cbrt k)))
  (/ (pow (* n (* PI 2)) (/ (- 1 k) 4)) (sqrt (sqrt k)))
  (/ (pow (* n (* PI 2)) (/ (- 1 k) 4)) (sqrt (sqrt k)))
  (pow (* n (* PI 2)) (/ (- 1 k) 4))
  (/ (pow (* n (* PI 2)) (/ (- 1 k) 4)) (sqrt k))
  (/ (pow (* n (* PI 2)) (/ (- 1 k) 4)) (sqrt (sqrt k)))
  (/ (pow (* n (* PI 2)) (/ (- 1 k) 4)) (sqrt (sqrt k)))
  (pow (* n (* PI 2)) (/ (- 1 k) 4))
  (/ (pow (* n (* PI 2)) (/ (- 1 k) 4)) (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) (pow (* n (* PI 2)) (/ (- 1 k) 2)))
  (/ (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (fabs (cbrt k)))
  (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (pow (* n (* PI 2)) (/ (- 1 k) 2))
  (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (pow (* n (* PI 2)) (/ (- 1 k) 2))
  (/ (sqrt k) (pow (* PI 2) (* (- 1 k) 1/2)))
  (/ (sqrt k) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))))
  (/ (sqrt k) (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))))
  (/ (sqrt k) (pow (* n (* PI 2)) (/ (- 1 k) 2)))
  (/ (sqrt k) (pow (* n (* PI 2)) (/ (- 1 k) 4)))
  (real->posit16 (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))
  (- (+ (+ (* (* (* (log (* PI 2)) 1/4) (* (exp (* 1/2 (log (* n (* PI 2))))) (log n))) (* k k)) (* (* (exp (* 1/2 (log (* n (* PI 2))))) 1/8) (* (* (log n) k) (* (log n) k)))) (+ (exp (* 1/2 (log (* n (* PI 2))))) (* (* (log (* PI 2)) (log (* PI 2))) (* (* (exp (* 1/2 (log (* n (* PI 2))))) (* k k)) 1/8)))) (* (* k (+ (* (exp (* 1/2 (log (* n (* PI 2))))) (log n)) (* (exp (* 1/2 (log (* n (* PI 2))))) (log (* PI 2))))) 1/2))
  (exp (* (log (* n (* PI 2))) (* (- 1 k) 1/2)))
  (exp (* (- (log (* PI -2)) (log (/ -1 n))) (* (- 1 k) 1/2)))
  (* n (* PI 2))
  (* n (* PI 2))
  (* n (* PI 2))
  (- (* (- +nan.0) (* (* (log (* PI 2)) (* (* k k) (log n))) (exp (* 1/2 (log (* n (* PI 2))))))) (+ (* (* (log (* PI 2)) (* (exp (* 1/2 (log (* n (* PI 2))))) (* k k))) (- +nan.0)) (+ (- (* +nan.0 (* (* (* (log n) k) (* (log n) k)) (exp (* 1/2 (log (* n (* PI 2))))))) (* +nan.0 (* (exp (* 1/2 (log (* n (* PI 2))))) k))) (+ (- (* (exp (* 1/2 (log (* n (* PI 2))))) +nan.0) (* (* (* (log (* PI 2)) (log (* PI 2))) (* (exp (* 1/2 (log (* n (* PI 2))))) (* k k))) +nan.0)) (- (* (* (exp (* 1/2 (log (* n (* PI 2))))) (log n)) (* (* k k) +nan.0)) (- (* (exp (* 1/2 (log (* n (* PI 2))))) (* (* k k) +nan.0)) (- (* (* (log (* PI 2)) +nan.0) (* (exp (* 1/2 (log (* n (* PI 2))))) k)) (* +nan.0 (* (* (exp (* 1/2 (log (* n (* PI 2))))) (log n)) k)))))))))
  (+ (* +nan.0 (- (/ (exp (* (log (* n (* PI 2))) (* (- 1 k) 1/2))) (* k k)) (/ (/ (exp (* (log (* n (* PI 2))) (* (- 1 k) 1/2))) k) (* k k)))) (* (- +nan.0) (/ (exp (* (log (* n (* PI 2))) (* (- 1 k) 1/2))) k)))
  (+ (- (/ (exp (* (- (log (* PI -2)) (log (/ -1 n))) (* (- 1 k) 1/2))) (/ k +nan.0))) (* +nan.0 (- (/ (exp (* (- (log (* PI -2)) (log (/ -1 n))) (* (- 1 k) 1/2))) (* k k)) (exp (* (- (log (* PI -2)) (log (/ -1 n))) (* (- 1 k) 1/2))))))
3.679 * * * [progress]: adding candidates to table
4.815 * * [progress]: iteration 2 / 4
4.815 * * * [progress]: picking best candidate
4.879 * * * * [pick]: Picked  #<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))))>
4.879 * * * [progress]: localizing error
4.914 * * * [progress]: generating rewritten candidates
4.914 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 1 1)
4.939 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1 1)
4.965 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1 1 1)
4.977 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1 1 1)
4.993 * * * [progress]: generating series expansions
4.993 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 1 1)
4.994 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) into (pow (* 2 (* n PI)) (* 1/2 (- 1 k)))
4.994 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in (n k) around 0
4.994 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
4.994 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
4.994 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
4.994 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
4.994 * [taylor]: Taking taylor expansion of 1/2 in k
4.994 * [backup-simplify]: Simplify 1/2 into 1/2
4.994 * [taylor]: Taking taylor expansion of (- 1 k) in k
4.994 * [taylor]: Taking taylor expansion of 1 in k
4.994 * [backup-simplify]: Simplify 1 into 1
4.994 * [taylor]: Taking taylor expansion of k in k
4.994 * [backup-simplify]: Simplify 0 into 0
4.994 * [backup-simplify]: Simplify 1 into 1
4.994 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
4.994 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
4.994 * [taylor]: Taking taylor expansion of 2 in k
4.994 * [backup-simplify]: Simplify 2 into 2
4.994 * [taylor]: Taking taylor expansion of (* n PI) in k
4.994 * [taylor]: Taking taylor expansion of n in k
4.994 * [backup-simplify]: Simplify n into n
4.994 * [taylor]: Taking taylor expansion of PI in k
4.994 * [backup-simplify]: Simplify PI into PI
4.994 * [backup-simplify]: Simplify (* n PI) into (* n PI)
4.994 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
4.995 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
4.995 * [backup-simplify]: Simplify (- 0) into 0
4.995 * [backup-simplify]: Simplify (+ 1 0) into 1
4.996 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
4.996 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
4.996 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
4.996 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
4.996 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
4.996 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
4.996 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
4.996 * [taylor]: Taking taylor expansion of 1/2 in n
4.996 * [backup-simplify]: Simplify 1/2 into 1/2
4.996 * [taylor]: Taking taylor expansion of (- 1 k) in n
4.996 * [taylor]: Taking taylor expansion of 1 in n
4.996 * [backup-simplify]: Simplify 1 into 1
4.996 * [taylor]: Taking taylor expansion of k in n
4.997 * [backup-simplify]: Simplify k into k
4.997 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
4.997 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
4.997 * [taylor]: Taking taylor expansion of 2 in n
4.997 * [backup-simplify]: Simplify 2 into 2
4.997 * [taylor]: Taking taylor expansion of (* n PI) in n
4.997 * [taylor]: Taking taylor expansion of n in n
4.997 * [backup-simplify]: Simplify 0 into 0
4.997 * [backup-simplify]: Simplify 1 into 1
4.997 * [taylor]: Taking taylor expansion of PI in n
4.997 * [backup-simplify]: Simplify PI into PI
4.997 * [backup-simplify]: Simplify (* 0 PI) into 0
4.998 * [backup-simplify]: Simplify (* 2 0) into 0
4.999 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.001 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
5.002 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.002 * [backup-simplify]: Simplify (- k) into (- k)
5.002 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
5.002 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
5.004 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
5.005 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
5.006 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
5.006 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
5.006 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
5.006 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
5.006 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
5.006 * [taylor]: Taking taylor expansion of 1/2 in n
5.006 * [backup-simplify]: Simplify 1/2 into 1/2
5.006 * [taylor]: Taking taylor expansion of (- 1 k) in n
5.006 * [taylor]: Taking taylor expansion of 1 in n
5.006 * [backup-simplify]: Simplify 1 into 1
5.006 * [taylor]: Taking taylor expansion of k in n
5.006 * [backup-simplify]: Simplify k into k
5.006 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
5.006 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
5.006 * [taylor]: Taking taylor expansion of 2 in n
5.006 * [backup-simplify]: Simplify 2 into 2
5.006 * [taylor]: Taking taylor expansion of (* n PI) in n
5.006 * [taylor]: Taking taylor expansion of n in n
5.007 * [backup-simplify]: Simplify 0 into 0
5.007 * [backup-simplify]: Simplify 1 into 1
5.007 * [taylor]: Taking taylor expansion of PI in n
5.007 * [backup-simplify]: Simplify PI into PI
5.007 * [backup-simplify]: Simplify (* 0 PI) into 0
5.007 * [backup-simplify]: Simplify (* 2 0) into 0
5.009 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.010 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
5.011 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.012 * [backup-simplify]: Simplify (- k) into (- k)
5.012 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
5.012 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
5.013 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
5.014 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
5.016 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
5.016 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) in k
5.016 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) in k
5.016 * [taylor]: Taking taylor expansion of 1/2 in k
5.016 * [backup-simplify]: Simplify 1/2 into 1/2
5.016 * [taylor]: Taking taylor expansion of (* (- 1 k) (+ (log n) (log (* 2 PI)))) in k
5.016 * [taylor]: Taking taylor expansion of (- 1 k) in k
5.016 * [taylor]: Taking taylor expansion of 1 in k
5.016 * [backup-simplify]: Simplify 1 into 1
5.016 * [taylor]: Taking taylor expansion of k in k
5.016 * [backup-simplify]: Simplify 0 into 0
5.016 * [backup-simplify]: Simplify 1 into 1
5.016 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
5.016 * [taylor]: Taking taylor expansion of (log n) in k
5.016 * [taylor]: Taking taylor expansion of n in k
5.016 * [backup-simplify]: Simplify n into n
5.016 * [backup-simplify]: Simplify (log n) into (log n)
5.016 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
5.016 * [taylor]: Taking taylor expansion of (* 2 PI) in k
5.016 * [taylor]: Taking taylor expansion of 2 in k
5.016 * [backup-simplify]: Simplify 2 into 2
5.016 * [taylor]: Taking taylor expansion of PI in k
5.016 * [backup-simplify]: Simplify PI into PI
5.017 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.018 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.018 * [backup-simplify]: Simplify (- 0) into 0
5.019 * [backup-simplify]: Simplify (+ 1 0) into 1
5.020 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
5.021 * [backup-simplify]: Simplify (* 1 (+ (log n) (log (* 2 PI)))) into (+ (log n) (log (* 2 PI)))
5.022 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
5.023 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
5.024 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
5.025 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
5.026 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
5.028 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
5.029 * [backup-simplify]: Simplify (- 0) into 0
5.029 * [backup-simplify]: Simplify (+ 0 0) into 0
5.030 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 k))) into 0
5.031 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
5.032 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
5.033 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0
5.033 * [taylor]: Taking taylor expansion of 0 in k
5.033 * [backup-simplify]: Simplify 0 into 0
5.033 * [backup-simplify]: Simplify 0 into 0
5.034 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
5.034 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
5.035 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
5.036 * [backup-simplify]: Simplify (+ 0 0) into 0
5.036 * [backup-simplify]: Simplify (- 1) into -1
5.036 * [backup-simplify]: Simplify (+ 0 -1) into -1
5.037 * [backup-simplify]: Simplify (+ (* 1 0) (* -1 (+ (log n) (log (* 2 PI))))) into (- (+ (log (* 2 PI)) (log n)))
5.038 * [backup-simplify]: Simplify (+ (* 1/2 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))))
5.040 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
5.045 * [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)))))))
5.046 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
5.047 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
5.049 * [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
5.049 * [backup-simplify]: Simplify (- 0) into 0
5.049 * [backup-simplify]: Simplify (+ 0 0) into 0
5.050 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0
5.051 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
5.052 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
5.053 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
5.053 * [taylor]: Taking taylor expansion of 0 in k
5.053 * [backup-simplify]: Simplify 0 into 0
5.053 * [backup-simplify]: Simplify 0 into 0
5.053 * [backup-simplify]: Simplify 0 into 0
5.054 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
5.055 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
5.056 * [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
5.057 * [backup-simplify]: Simplify (+ 0 0) into 0
5.057 * [backup-simplify]: Simplify (- 0) into 0
5.057 * [backup-simplify]: Simplify (+ 0 0) into 0
5.058 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
5.060 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
5.064 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 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)))))
5.069 * [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)))))
5.078 * [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)))))
5.079 * [backup-simplify]: Simplify (pow (* (/ 1 n) (* 2 PI)) (* (- 1 (/ 1 k)) 1/2)) into (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k))))
5.079 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in (n k) around 0
5.079 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
5.079 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
5.079 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
5.079 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
5.079 * [taylor]: Taking taylor expansion of 1/2 in k
5.079 * [backup-simplify]: Simplify 1/2 into 1/2
5.079 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
5.079 * [taylor]: Taking taylor expansion of 1 in k
5.079 * [backup-simplify]: Simplify 1 into 1
5.079 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.079 * [taylor]: Taking taylor expansion of k in k
5.079 * [backup-simplify]: Simplify 0 into 0
5.079 * [backup-simplify]: Simplify 1 into 1
5.080 * [backup-simplify]: Simplify (/ 1 1) into 1
5.080 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
5.080 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
5.080 * [taylor]: Taking taylor expansion of 2 in k
5.080 * [backup-simplify]: Simplify 2 into 2
5.080 * [taylor]: Taking taylor expansion of (/ PI n) in k
5.080 * [taylor]: Taking taylor expansion of PI in k
5.080 * [backup-simplify]: Simplify PI into PI
5.080 * [taylor]: Taking taylor expansion of n in k
5.080 * [backup-simplify]: Simplify n into n
5.080 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
5.080 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
5.080 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
5.081 * [backup-simplify]: Simplify (- 1) into -1
5.081 * [backup-simplify]: Simplify (+ 0 -1) into -1
5.081 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
5.082 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
5.082 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
5.082 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
5.082 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
5.082 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
5.082 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
5.082 * [taylor]: Taking taylor expansion of 1/2 in n
5.082 * [backup-simplify]: Simplify 1/2 into 1/2
5.082 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
5.082 * [taylor]: Taking taylor expansion of 1 in n
5.082 * [backup-simplify]: Simplify 1 into 1
5.082 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.082 * [taylor]: Taking taylor expansion of k in n
5.082 * [backup-simplify]: Simplify k into k
5.082 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.082 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
5.082 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
5.082 * [taylor]: Taking taylor expansion of 2 in n
5.082 * [backup-simplify]: Simplify 2 into 2
5.082 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.082 * [taylor]: Taking taylor expansion of PI in n
5.082 * [backup-simplify]: Simplify PI into PI
5.082 * [taylor]: Taking taylor expansion of n in n
5.082 * [backup-simplify]: Simplify 0 into 0
5.082 * [backup-simplify]: Simplify 1 into 1
5.083 * [backup-simplify]: Simplify (/ PI 1) into PI
5.083 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.084 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.085 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
5.085 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
5.085 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
5.086 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.087 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
5.088 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
5.088 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
5.088 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
5.089 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
5.089 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
5.089 * [taylor]: Taking taylor expansion of 1/2 in n
5.089 * [backup-simplify]: Simplify 1/2 into 1/2
5.089 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
5.089 * [taylor]: Taking taylor expansion of 1 in n
5.089 * [backup-simplify]: Simplify 1 into 1
5.089 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.089 * [taylor]: Taking taylor expansion of k in n
5.089 * [backup-simplify]: Simplify k into k
5.089 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.089 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
5.089 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
5.089 * [taylor]: Taking taylor expansion of 2 in n
5.089 * [backup-simplify]: Simplify 2 into 2
5.089 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.089 * [taylor]: Taking taylor expansion of PI in n
5.089 * [backup-simplify]: Simplify PI into PI
5.089 * [taylor]: Taking taylor expansion of n in n
5.089 * [backup-simplify]: Simplify 0 into 0
5.089 * [backup-simplify]: Simplify 1 into 1
5.090 * [backup-simplify]: Simplify (/ PI 1) into PI
5.090 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.091 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.091 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
5.091 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
5.091 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
5.093 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.094 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
5.095 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
5.095 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k
5.095 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k
5.095 * [taylor]: Taking taylor expansion of 1/2 in k
5.095 * [backup-simplify]: Simplify 1/2 into 1/2
5.095 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k
5.095 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
5.095 * [taylor]: Taking taylor expansion of 1 in k
5.095 * [backup-simplify]: Simplify 1 into 1
5.095 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.095 * [taylor]: Taking taylor expansion of k in k
5.096 * [backup-simplify]: Simplify 0 into 0
5.096 * [backup-simplify]: Simplify 1 into 1
5.096 * [backup-simplify]: Simplify (/ 1 1) into 1
5.096 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
5.096 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
5.096 * [taylor]: Taking taylor expansion of (* 2 PI) in k
5.096 * [taylor]: Taking taylor expansion of 2 in k
5.096 * [backup-simplify]: Simplify 2 into 2
5.096 * [taylor]: Taking taylor expansion of PI in k
5.096 * [backup-simplify]: Simplify PI into PI
5.096 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.097 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.097 * [taylor]: Taking taylor expansion of (log n) in k
5.097 * [taylor]: Taking taylor expansion of n in k
5.097 * [backup-simplify]: Simplify n into n
5.097 * [backup-simplify]: Simplify (log n) into (log n)
5.097 * [backup-simplify]: Simplify (- 1) into -1
5.097 * [backup-simplify]: Simplify (+ 0 -1) into -1
5.098 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
5.098 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
5.099 * [backup-simplify]: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n)))
5.099 * [backup-simplify]: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n)))
5.100 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
5.101 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
5.101 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
5.102 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
5.103 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
5.103 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
5.103 * [backup-simplify]: Simplify (- 0) into 0
5.103 * [backup-simplify]: Simplify (+ 0 0) into 0
5.104 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 (/ 1 k)))) into 0
5.104 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.105 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
5.106 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
5.106 * [taylor]: Taking taylor expansion of 0 in k
5.106 * [backup-simplify]: Simplify 0 into 0
5.106 * [backup-simplify]: Simplify 0 into 0
5.106 * [backup-simplify]: Simplify 0 into 0
5.107 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.107 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
5.109 * [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
5.109 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
5.110 * [backup-simplify]: Simplify (- 0) into 0
5.110 * [backup-simplify]: Simplify (+ 0 0) into 0
5.110 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0
5.111 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.112 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
5.113 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
5.114 * [taylor]: Taking taylor expansion of 0 in k
5.114 * [backup-simplify]: Simplify 0 into 0
5.114 * [backup-simplify]: Simplify 0 into 0
5.114 * [backup-simplify]: Simplify 0 into 0
5.114 * [backup-simplify]: Simplify 0 into 0
5.114 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.115 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
5.118 * [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
5.118 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
5.119 * [backup-simplify]: Simplify (- 0) into 0
5.119 * [backup-simplify]: Simplify (+ 0 0) into 0
5.120 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0
5.121 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.122 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
5.123 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 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
5.124 * [taylor]: Taking taylor expansion of 0 in k
5.124 * [backup-simplify]: Simplify 0 into 0
5.124 * [backup-simplify]: Simplify 0 into 0
5.124 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
5.125 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) (* 2 PI)) (* (- 1 (/ 1 (- k))) 1/2)) into (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1)))
5.125 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in (n k) around 0
5.125 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
5.125 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
5.125 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
5.125 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
5.125 * [taylor]: Taking taylor expansion of 1/2 in k
5.125 * [backup-simplify]: Simplify 1/2 into 1/2
5.125 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
5.125 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.125 * [taylor]: Taking taylor expansion of k in k
5.125 * [backup-simplify]: Simplify 0 into 0
5.125 * [backup-simplify]: Simplify 1 into 1
5.125 * [backup-simplify]: Simplify (/ 1 1) into 1
5.125 * [taylor]: Taking taylor expansion of 1 in k
5.125 * [backup-simplify]: Simplify 1 into 1
5.125 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
5.125 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
5.125 * [taylor]: Taking taylor expansion of -2 in k
5.125 * [backup-simplify]: Simplify -2 into -2
5.125 * [taylor]: Taking taylor expansion of (/ PI n) in k
5.125 * [taylor]: Taking taylor expansion of PI in k
5.125 * [backup-simplify]: Simplify PI into PI
5.125 * [taylor]: Taking taylor expansion of n in k
5.125 * [backup-simplify]: Simplify n into n
5.125 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
5.125 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
5.126 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
5.126 * [backup-simplify]: Simplify (+ 1 0) into 1
5.126 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
5.126 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
5.126 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
5.126 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
5.126 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
5.126 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
5.126 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
5.126 * [taylor]: Taking taylor expansion of 1/2 in n
5.126 * [backup-simplify]: Simplify 1/2 into 1/2
5.126 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
5.126 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.126 * [taylor]: Taking taylor expansion of k in n
5.126 * [backup-simplify]: Simplify k into k
5.126 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.126 * [taylor]: Taking taylor expansion of 1 in n
5.126 * [backup-simplify]: Simplify 1 into 1
5.127 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
5.127 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
5.127 * [taylor]: Taking taylor expansion of -2 in n
5.127 * [backup-simplify]: Simplify -2 into -2
5.127 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.127 * [taylor]: Taking taylor expansion of PI in n
5.127 * [backup-simplify]: Simplify PI into PI
5.127 * [taylor]: Taking taylor expansion of n in n
5.127 * [backup-simplify]: Simplify 0 into 0
5.127 * [backup-simplify]: Simplify 1 into 1
5.127 * [backup-simplify]: Simplify (/ PI 1) into PI
5.127 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
5.128 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
5.128 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
5.128 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
5.129 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.130 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
5.132 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
5.132 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
5.132 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
5.132 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
5.132 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
5.132 * [taylor]: Taking taylor expansion of 1/2 in n
5.132 * [backup-simplify]: Simplify 1/2 into 1/2
5.132 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
5.132 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.132 * [taylor]: Taking taylor expansion of k in n
5.132 * [backup-simplify]: Simplify k into k
5.132 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.132 * [taylor]: Taking taylor expansion of 1 in n
5.132 * [backup-simplify]: Simplify 1 into 1
5.132 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
5.132 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
5.132 * [taylor]: Taking taylor expansion of -2 in n
5.132 * [backup-simplify]: Simplify -2 into -2
5.132 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.132 * [taylor]: Taking taylor expansion of PI in n
5.132 * [backup-simplify]: Simplify PI into PI
5.132 * [taylor]: Taking taylor expansion of n in n
5.132 * [backup-simplify]: Simplify 0 into 0
5.132 * [backup-simplify]: Simplify 1 into 1
5.133 * [backup-simplify]: Simplify (/ PI 1) into PI
5.133 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
5.134 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
5.134 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
5.134 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
5.136 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.137 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
5.138 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
5.138 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k
5.139 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) in k
5.139 * [taylor]: Taking taylor expansion of 1/2 in k
5.139 * [backup-simplify]: Simplify 1/2 into 1/2
5.139 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) in k
5.139 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
5.139 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.139 * [taylor]: Taking taylor expansion of k in k
5.139 * [backup-simplify]: Simplify 0 into 0
5.139 * [backup-simplify]: Simplify 1 into 1
5.139 * [backup-simplify]: Simplify (/ 1 1) into 1
5.139 * [taylor]: Taking taylor expansion of 1 in k
5.139 * [backup-simplify]: Simplify 1 into 1
5.139 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
5.139 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
5.139 * [taylor]: Taking taylor expansion of (* -2 PI) in k
5.139 * [taylor]: Taking taylor expansion of -2 in k
5.139 * [backup-simplify]: Simplify -2 into -2
5.139 * [taylor]: Taking taylor expansion of PI in k
5.139 * [backup-simplify]: Simplify PI into PI
5.140 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
5.141 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
5.141 * [taylor]: Taking taylor expansion of (log n) in k
5.141 * [taylor]: Taking taylor expansion of n in k
5.141 * [backup-simplify]: Simplify n into n
5.141 * [backup-simplify]: Simplify (log n) into (log n)
5.141 * [backup-simplify]: Simplify (+ 1 0) into 1
5.141 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
5.142 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
5.143 * [backup-simplify]: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n))
5.145 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
5.146 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
5.147 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
5.148 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
5.149 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
5.150 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
5.151 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
5.151 * [backup-simplify]: Simplify (+ 0 0) into 0
5.151 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (/ 1 k) 1))) into 0
5.153 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.154 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
5.161 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
5.161 * [taylor]: Taking taylor expansion of 0 in k
5.161 * [backup-simplify]: Simplify 0 into 0
5.162 * [backup-simplify]: Simplify 0 into 0
5.162 * [backup-simplify]: Simplify 0 into 0
5.163 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.164 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
5.167 * [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
5.168 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
5.168 * [backup-simplify]: Simplify (+ 0 0) into 0
5.169 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0
5.170 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.172 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
5.174 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
5.175 * [taylor]: Taking taylor expansion of 0 in k
5.175 * [backup-simplify]: Simplify 0 into 0
5.175 * [backup-simplify]: Simplify 0 into 0
5.175 * [backup-simplify]: Simplify 0 into 0
5.175 * [backup-simplify]: Simplify 0 into 0
5.176 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.177 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
5.183 * [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
5.183 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
5.184 * [backup-simplify]: Simplify (+ 0 0) into 0
5.185 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1))))) into 0
5.187 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.189 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
5.191 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
5.191 * [taylor]: Taking taylor expansion of 0 in k
5.191 * [backup-simplify]: Simplify 0 into 0
5.192 * [backup-simplify]: Simplify 0 into 0
5.193 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
5.193 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1 1)
5.193 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) into (pow (* 2 (* n PI)) (* 1/2 (- 1 k)))
5.193 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in (n k) around 0
5.194 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
5.194 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
5.194 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
5.194 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
5.194 * [taylor]: Taking taylor expansion of 1/2 in k
5.194 * [backup-simplify]: Simplify 1/2 into 1/2
5.194 * [taylor]: Taking taylor expansion of (- 1 k) in k
5.194 * [taylor]: Taking taylor expansion of 1 in k
5.194 * [backup-simplify]: Simplify 1 into 1
5.194 * [taylor]: Taking taylor expansion of k in k
5.194 * [backup-simplify]: Simplify 0 into 0
5.194 * [backup-simplify]: Simplify 1 into 1
5.194 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
5.194 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
5.194 * [taylor]: Taking taylor expansion of 2 in k
5.194 * [backup-simplify]: Simplify 2 into 2
5.194 * [taylor]: Taking taylor expansion of (* n PI) in k
5.194 * [taylor]: Taking taylor expansion of n in k
5.194 * [backup-simplify]: Simplify n into n
5.194 * [taylor]: Taking taylor expansion of PI in k
5.194 * [backup-simplify]: Simplify PI into PI
5.194 * [backup-simplify]: Simplify (* n PI) into (* n PI)
5.194 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
5.194 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
5.195 * [backup-simplify]: Simplify (- 0) into 0
5.195 * [backup-simplify]: Simplify (+ 1 0) into 1
5.195 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
5.196 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
5.196 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
5.196 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
5.196 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
5.196 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
5.196 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
5.196 * [taylor]: Taking taylor expansion of 1/2 in n
5.196 * [backup-simplify]: Simplify 1/2 into 1/2
5.196 * [taylor]: Taking taylor expansion of (- 1 k) in n
5.196 * [taylor]: Taking taylor expansion of 1 in n
5.196 * [backup-simplify]: Simplify 1 into 1
5.196 * [taylor]: Taking taylor expansion of k in n
5.196 * [backup-simplify]: Simplify k into k
5.196 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
5.196 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
5.196 * [taylor]: Taking taylor expansion of 2 in n
5.196 * [backup-simplify]: Simplify 2 into 2
5.196 * [taylor]: Taking taylor expansion of (* n PI) in n
5.197 * [taylor]: Taking taylor expansion of n in n
5.197 * [backup-simplify]: Simplify 0 into 0
5.197 * [backup-simplify]: Simplify 1 into 1
5.197 * [taylor]: Taking taylor expansion of PI in n
5.197 * [backup-simplify]: Simplify PI into PI
5.197 * [backup-simplify]: Simplify (* 0 PI) into 0
5.198 * [backup-simplify]: Simplify (* 2 0) into 0
5.199 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.201 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
5.201 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.202 * [backup-simplify]: Simplify (- k) into (- k)
5.202 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
5.202 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
5.203 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
5.204 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
5.205 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
5.205 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
5.205 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
5.205 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
5.205 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
5.205 * [taylor]: Taking taylor expansion of 1/2 in n
5.205 * [backup-simplify]: Simplify 1/2 into 1/2
5.205 * [taylor]: Taking taylor expansion of (- 1 k) in n
5.206 * [taylor]: Taking taylor expansion of 1 in n
5.206 * [backup-simplify]: Simplify 1 into 1
5.206 * [taylor]: Taking taylor expansion of k in n
5.206 * [backup-simplify]: Simplify k into k
5.206 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
5.206 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
5.206 * [taylor]: Taking taylor expansion of 2 in n
5.206 * [backup-simplify]: Simplify 2 into 2
5.206 * [taylor]: Taking taylor expansion of (* n PI) in n
5.206 * [taylor]: Taking taylor expansion of n in n
5.206 * [backup-simplify]: Simplify 0 into 0
5.206 * [backup-simplify]: Simplify 1 into 1
5.206 * [taylor]: Taking taylor expansion of PI in n
5.206 * [backup-simplify]: Simplify PI into PI
5.206 * [backup-simplify]: Simplify (* 0 PI) into 0
5.207 * [backup-simplify]: Simplify (* 2 0) into 0
5.208 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.210 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
5.211 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.211 * [backup-simplify]: Simplify (- k) into (- k)
5.211 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
5.211 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
5.212 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
5.214 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
5.215 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
5.215 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) in k
5.215 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) in k
5.215 * [taylor]: Taking taylor expansion of 1/2 in k
5.215 * [backup-simplify]: Simplify 1/2 into 1/2
5.215 * [taylor]: Taking taylor expansion of (* (- 1 k) (+ (log n) (log (* 2 PI)))) in k
5.215 * [taylor]: Taking taylor expansion of (- 1 k) in k
5.215 * [taylor]: Taking taylor expansion of 1 in k
5.215 * [backup-simplify]: Simplify 1 into 1
5.215 * [taylor]: Taking taylor expansion of k in k
5.215 * [backup-simplify]: Simplify 0 into 0
5.215 * [backup-simplify]: Simplify 1 into 1
5.215 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
5.215 * [taylor]: Taking taylor expansion of (log n) in k
5.215 * [taylor]: Taking taylor expansion of n in k
5.215 * [backup-simplify]: Simplify n into n
5.215 * [backup-simplify]: Simplify (log n) into (log n)
5.215 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
5.215 * [taylor]: Taking taylor expansion of (* 2 PI) in k
5.215 * [taylor]: Taking taylor expansion of 2 in k
5.215 * [backup-simplify]: Simplify 2 into 2
5.215 * [taylor]: Taking taylor expansion of PI in k
5.215 * [backup-simplify]: Simplify PI into PI
5.216 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.217 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.217 * [backup-simplify]: Simplify (- 0) into 0
5.217 * [backup-simplify]: Simplify (+ 1 0) into 1
5.218 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
5.219 * [backup-simplify]: Simplify (* 1 (+ (log n) (log (* 2 PI)))) into (+ (log n) (log (* 2 PI)))
5.221 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
5.222 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
5.223 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
5.224 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
5.225 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
5.226 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
5.227 * [backup-simplify]: Simplify (- 0) into 0
5.227 * [backup-simplify]: Simplify (+ 0 0) into 0
5.228 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 k))) into 0
5.229 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
5.229 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
5.230 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0
5.230 * [taylor]: Taking taylor expansion of 0 in k
5.230 * [backup-simplify]: Simplify 0 into 0
5.230 * [backup-simplify]: Simplify 0 into 0
5.231 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
5.232 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
5.232 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
5.233 * [backup-simplify]: Simplify (+ 0 0) into 0
5.233 * [backup-simplify]: Simplify (- 1) into -1
5.233 * [backup-simplify]: Simplify (+ 0 -1) into -1
5.234 * [backup-simplify]: Simplify (+ (* 1 0) (* -1 (+ (log n) (log (* 2 PI))))) into (- (+ (log (* 2 PI)) (log n)))
5.235 * [backup-simplify]: Simplify (+ (* 1/2 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))))
5.237 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
5.239 * [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)))))))
5.240 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
5.240 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
5.242 * [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
5.242 * [backup-simplify]: Simplify (- 0) into 0
5.242 * [backup-simplify]: Simplify (+ 0 0) into 0
5.243 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0
5.244 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
5.245 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
5.246 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
5.246 * [taylor]: Taking taylor expansion of 0 in k
5.246 * [backup-simplify]: Simplify 0 into 0
5.246 * [backup-simplify]: Simplify 0 into 0
5.246 * [backup-simplify]: Simplify 0 into 0
5.247 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
5.248 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
5.250 * [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
5.250 * [backup-simplify]: Simplify (+ 0 0) into 0
5.250 * [backup-simplify]: Simplify (- 0) into 0
5.251 * [backup-simplify]: Simplify (+ 0 0) into 0
5.252 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
5.253 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
5.255 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 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)))))
5.258 * [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)))))
5.267 * [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)))))
5.267 * [backup-simplify]: Simplify (pow (* (/ 1 n) (* 2 PI)) (* (- 1 (/ 1 k)) 1/2)) into (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k))))
5.267 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in (n k) around 0
5.267 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
5.267 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
5.267 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
5.268 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
5.268 * [taylor]: Taking taylor expansion of 1/2 in k
5.268 * [backup-simplify]: Simplify 1/2 into 1/2
5.268 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
5.268 * [taylor]: Taking taylor expansion of 1 in k
5.268 * [backup-simplify]: Simplify 1 into 1
5.268 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.268 * [taylor]: Taking taylor expansion of k in k
5.268 * [backup-simplify]: Simplify 0 into 0
5.268 * [backup-simplify]: Simplify 1 into 1
5.268 * [backup-simplify]: Simplify (/ 1 1) into 1
5.268 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
5.268 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
5.268 * [taylor]: Taking taylor expansion of 2 in k
5.268 * [backup-simplify]: Simplify 2 into 2
5.268 * [taylor]: Taking taylor expansion of (/ PI n) in k
5.268 * [taylor]: Taking taylor expansion of PI in k
5.268 * [backup-simplify]: Simplify PI into PI
5.268 * [taylor]: Taking taylor expansion of n in k
5.268 * [backup-simplify]: Simplify n into n
5.268 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
5.269 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
5.269 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
5.269 * [backup-simplify]: Simplify (- 1) into -1
5.269 * [backup-simplify]: Simplify (+ 0 -1) into -1
5.270 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
5.270 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
5.270 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
5.270 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
5.270 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
5.270 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
5.270 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
5.270 * [taylor]: Taking taylor expansion of 1/2 in n
5.270 * [backup-simplify]: Simplify 1/2 into 1/2
5.270 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
5.270 * [taylor]: Taking taylor expansion of 1 in n
5.270 * [backup-simplify]: Simplify 1 into 1
5.270 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.270 * [taylor]: Taking taylor expansion of k in n
5.271 * [backup-simplify]: Simplify k into k
5.271 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.271 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
5.271 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
5.271 * [taylor]: Taking taylor expansion of 2 in n
5.271 * [backup-simplify]: Simplify 2 into 2
5.271 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.271 * [taylor]: Taking taylor expansion of PI in n
5.271 * [backup-simplify]: Simplify PI into PI
5.271 * [taylor]: Taking taylor expansion of n in n
5.271 * [backup-simplify]: Simplify 0 into 0
5.271 * [backup-simplify]: Simplify 1 into 1
5.271 * [backup-simplify]: Simplify (/ PI 1) into PI
5.272 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.273 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.273 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
5.273 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
5.273 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
5.274 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.276 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
5.277 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
5.277 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
5.277 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
5.277 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
5.277 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
5.277 * [taylor]: Taking taylor expansion of 1/2 in n
5.277 * [backup-simplify]: Simplify 1/2 into 1/2
5.277 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
5.277 * [taylor]: Taking taylor expansion of 1 in n
5.277 * [backup-simplify]: Simplify 1 into 1
5.277 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.277 * [taylor]: Taking taylor expansion of k in n
5.277 * [backup-simplify]: Simplify k into k
5.277 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.277 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
5.277 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
5.277 * [taylor]: Taking taylor expansion of 2 in n
5.277 * [backup-simplify]: Simplify 2 into 2
5.277 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.277 * [taylor]: Taking taylor expansion of PI in n
5.277 * [backup-simplify]: Simplify PI into PI
5.277 * [taylor]: Taking taylor expansion of n in n
5.277 * [backup-simplify]: Simplify 0 into 0
5.277 * [backup-simplify]: Simplify 1 into 1
5.278 * [backup-simplify]: Simplify (/ PI 1) into PI
5.284 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.285 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.286 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
5.286 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
5.286 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
5.287 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.289 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
5.290 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
5.290 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k
5.290 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k
5.290 * [taylor]: Taking taylor expansion of 1/2 in k
5.290 * [backup-simplify]: Simplify 1/2 into 1/2
5.290 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k
5.290 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
5.290 * [taylor]: Taking taylor expansion of 1 in k
5.290 * [backup-simplify]: Simplify 1 into 1
5.290 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.290 * [taylor]: Taking taylor expansion of k in k
5.290 * [backup-simplify]: Simplify 0 into 0
5.291 * [backup-simplify]: Simplify 1 into 1
5.291 * [backup-simplify]: Simplify (/ 1 1) into 1
5.291 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
5.291 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
5.291 * [taylor]: Taking taylor expansion of (* 2 PI) in k
5.291 * [taylor]: Taking taylor expansion of 2 in k
5.291 * [backup-simplify]: Simplify 2 into 2
5.291 * [taylor]: Taking taylor expansion of PI in k
5.291 * [backup-simplify]: Simplify PI into PI
5.292 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.293 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.293 * [taylor]: Taking taylor expansion of (log n) in k
5.293 * [taylor]: Taking taylor expansion of n in k
5.293 * [backup-simplify]: Simplify n into n
5.293 * [backup-simplify]: Simplify (log n) into (log n)
5.293 * [backup-simplify]: Simplify (- 1) into -1
5.294 * [backup-simplify]: Simplify (+ 0 -1) into -1
5.294 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
5.295 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
5.296 * [backup-simplify]: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n)))
5.296 * [backup-simplify]: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n)))
5.297 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
5.298 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
5.298 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
5.299 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
5.300 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
5.300 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
5.300 * [backup-simplify]: Simplify (- 0) into 0
5.300 * [backup-simplify]: Simplify (+ 0 0) into 0
5.301 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 (/ 1 k)))) into 0
5.301 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.302 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
5.304 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
5.304 * [taylor]: Taking taylor expansion of 0 in k
5.304 * [backup-simplify]: Simplify 0 into 0
5.304 * [backup-simplify]: Simplify 0 into 0
5.304 * [backup-simplify]: Simplify 0 into 0
5.304 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.305 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
5.308 * [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
5.308 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
5.309 * [backup-simplify]: Simplify (- 0) into 0
5.309 * [backup-simplify]: Simplify (+ 0 0) into 0
5.310 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0
5.311 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.313 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
5.315 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
5.315 * [taylor]: Taking taylor expansion of 0 in k
5.315 * [backup-simplify]: Simplify 0 into 0
5.315 * [backup-simplify]: Simplify 0 into 0
5.315 * [backup-simplify]: Simplify 0 into 0
5.315 * [backup-simplify]: Simplify 0 into 0
5.316 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.317 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
5.322 * [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
5.322 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
5.323 * [backup-simplify]: Simplify (- 0) into 0
5.323 * [backup-simplify]: Simplify (+ 0 0) into 0
5.325 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0
5.326 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.328 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
5.330 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 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
5.330 * [taylor]: Taking taylor expansion of 0 in k
5.330 * [backup-simplify]: Simplify 0 into 0
5.330 * [backup-simplify]: Simplify 0 into 0
5.331 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
5.332 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) (* 2 PI)) (* (- 1 (/ 1 (- k))) 1/2)) into (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1)))
5.332 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in (n k) around 0
5.332 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
5.332 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
5.332 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
5.332 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
5.332 * [taylor]: Taking taylor expansion of 1/2 in k
5.332 * [backup-simplify]: Simplify 1/2 into 1/2
5.332 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
5.332 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.332 * [taylor]: Taking taylor expansion of k in k
5.332 * [backup-simplify]: Simplify 0 into 0
5.332 * [backup-simplify]: Simplify 1 into 1
5.332 * [backup-simplify]: Simplify (/ 1 1) into 1
5.332 * [taylor]: Taking taylor expansion of 1 in k
5.332 * [backup-simplify]: Simplify 1 into 1
5.333 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
5.333 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
5.333 * [taylor]: Taking taylor expansion of -2 in k
5.333 * [backup-simplify]: Simplify -2 into -2
5.333 * [taylor]: Taking taylor expansion of (/ PI n) in k
5.333 * [taylor]: Taking taylor expansion of PI in k
5.333 * [backup-simplify]: Simplify PI into PI
5.333 * [taylor]: Taking taylor expansion of n in k
5.333 * [backup-simplify]: Simplify n into n
5.333 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
5.333 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
5.333 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
5.333 * [backup-simplify]: Simplify (+ 1 0) into 1
5.334 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
5.334 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
5.334 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
5.334 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
5.334 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
5.334 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
5.334 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
5.334 * [taylor]: Taking taylor expansion of 1/2 in n
5.334 * [backup-simplify]: Simplify 1/2 into 1/2
5.334 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
5.334 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.334 * [taylor]: Taking taylor expansion of k in n
5.334 * [backup-simplify]: Simplify k into k
5.334 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.334 * [taylor]: Taking taylor expansion of 1 in n
5.334 * [backup-simplify]: Simplify 1 into 1
5.334 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
5.334 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
5.334 * [taylor]: Taking taylor expansion of -2 in n
5.334 * [backup-simplify]: Simplify -2 into -2
5.334 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.334 * [taylor]: Taking taylor expansion of PI in n
5.334 * [backup-simplify]: Simplify PI into PI
5.334 * [taylor]: Taking taylor expansion of n in n
5.335 * [backup-simplify]: Simplify 0 into 0
5.335 * [backup-simplify]: Simplify 1 into 1
5.335 * [backup-simplify]: Simplify (/ PI 1) into PI
5.335 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
5.336 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
5.336 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
5.336 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
5.338 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.339 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
5.340 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
5.340 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
5.340 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
5.340 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
5.340 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
5.340 * [taylor]: Taking taylor expansion of 1/2 in n
5.340 * [backup-simplify]: Simplify 1/2 into 1/2
5.340 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
5.340 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.340 * [taylor]: Taking taylor expansion of k in n
5.340 * [backup-simplify]: Simplify k into k
5.340 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.340 * [taylor]: Taking taylor expansion of 1 in n
5.340 * [backup-simplify]: Simplify 1 into 1
5.340 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
5.340 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
5.340 * [taylor]: Taking taylor expansion of -2 in n
5.340 * [backup-simplify]: Simplify -2 into -2
5.340 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.340 * [taylor]: Taking taylor expansion of PI in n
5.340 * [backup-simplify]: Simplify PI into PI
5.340 * [taylor]: Taking taylor expansion of n in n
5.340 * [backup-simplify]: Simplify 0 into 0
5.340 * [backup-simplify]: Simplify 1 into 1
5.341 * [backup-simplify]: Simplify (/ PI 1) into PI
5.341 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
5.342 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
5.342 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
5.342 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
5.344 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.345 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
5.346 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
5.346 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k
5.346 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) in k
5.346 * [taylor]: Taking taylor expansion of 1/2 in k
5.346 * [backup-simplify]: Simplify 1/2 into 1/2
5.346 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) in k
5.346 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
5.346 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.346 * [taylor]: Taking taylor expansion of k in k
5.346 * [backup-simplify]: Simplify 0 into 0
5.346 * [backup-simplify]: Simplify 1 into 1
5.346 * [backup-simplify]: Simplify (/ 1 1) into 1
5.346 * [taylor]: Taking taylor expansion of 1 in k
5.346 * [backup-simplify]: Simplify 1 into 1
5.346 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
5.346 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
5.346 * [taylor]: Taking taylor expansion of (* -2 PI) in k
5.346 * [taylor]: Taking taylor expansion of -2 in k
5.347 * [backup-simplify]: Simplify -2 into -2
5.347 * [taylor]: Taking taylor expansion of PI in k
5.347 * [backup-simplify]: Simplify PI into PI
5.347 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
5.348 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
5.348 * [taylor]: Taking taylor expansion of (log n) in k
5.348 * [taylor]: Taking taylor expansion of n in k
5.348 * [backup-simplify]: Simplify n into n
5.348 * [backup-simplify]: Simplify (log n) into (log n)
5.348 * [backup-simplify]: Simplify (+ 1 0) into 1
5.348 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
5.349 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
5.350 * [backup-simplify]: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n))
5.351 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
5.352 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
5.353 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
5.354 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
5.355 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
5.356 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
5.357 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
5.357 * [backup-simplify]: Simplify (+ 0 0) into 0
5.357 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (/ 1 k) 1))) into 0
5.359 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.360 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
5.362 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
5.362 * [taylor]: Taking taylor expansion of 0 in k
5.362 * [backup-simplify]: Simplify 0 into 0
5.362 * [backup-simplify]: Simplify 0 into 0
5.362 * [backup-simplify]: Simplify 0 into 0
5.363 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.364 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
5.367 * [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
5.368 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
5.368 * [backup-simplify]: Simplify (+ 0 0) into 0
5.369 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0
5.370 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.372 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
5.374 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
5.374 * [taylor]: Taking taylor expansion of 0 in k
5.374 * [backup-simplify]: Simplify 0 into 0
5.374 * [backup-simplify]: Simplify 0 into 0
5.374 * [backup-simplify]: Simplify 0 into 0
5.374 * [backup-simplify]: Simplify 0 into 0
5.375 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.376 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
5.382 * [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
5.382 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
5.383 * [backup-simplify]: Simplify (+ 0 0) into 0
5.384 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1))))) into 0
5.386 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.387 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
5.390 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
5.390 * [taylor]: Taking taylor expansion of 0 in k
5.390 * [backup-simplify]: Simplify 0 into 0
5.390 * [backup-simplify]: Simplify 0 into 0
5.391 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
5.391 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1 1 1)
5.392 * [backup-simplify]: Simplify (* n (* 2 PI)) into (* 2 (* n PI))
5.392 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
5.392 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
5.392 * [taylor]: Taking taylor expansion of 2 in n
5.392 * [backup-simplify]: Simplify 2 into 2
5.392 * [taylor]: Taking taylor expansion of (* n PI) in n
5.392 * [taylor]: Taking taylor expansion of n in n
5.392 * [backup-simplify]: Simplify 0 into 0
5.392 * [backup-simplify]: Simplify 1 into 1
5.392 * [taylor]: Taking taylor expansion of PI in n
5.392 * [backup-simplify]: Simplify PI into PI
5.392 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
5.392 * [taylor]: Taking taylor expansion of 2 in n
5.392 * [backup-simplify]: Simplify 2 into 2
5.392 * [taylor]: Taking taylor expansion of (* n PI) in n
5.392 * [taylor]: Taking taylor expansion of n in n
5.392 * [backup-simplify]: Simplify 0 into 0
5.392 * [backup-simplify]: Simplify 1 into 1
5.392 * [taylor]: Taking taylor expansion of PI in n
5.392 * [backup-simplify]: Simplify PI into PI
5.393 * [backup-simplify]: Simplify (* 0 PI) into 0
5.393 * [backup-simplify]: Simplify (* 2 0) into 0
5.393 * [backup-simplify]: Simplify 0 into 0
5.394 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.396 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
5.396 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.397 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
5.398 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
5.398 * [backup-simplify]: Simplify 0 into 0
5.399 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
5.400 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
5.400 * [backup-simplify]: Simplify 0 into 0
5.401 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
5.403 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
5.403 * [backup-simplify]: Simplify 0 into 0
5.404 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
5.405 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
5.405 * [backup-simplify]: Simplify 0 into 0
5.407 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
5.408 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
5.409 * [backup-simplify]: Simplify 0 into 0
5.410 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
5.412 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
5.412 * [backup-simplify]: Simplify 0 into 0
5.418 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
5.419 * [backup-simplify]: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n))
5.419 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
5.419 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
5.419 * [taylor]: Taking taylor expansion of 2 in n
5.419 * [backup-simplify]: Simplify 2 into 2
5.419 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.419 * [taylor]: Taking taylor expansion of PI in n
5.419 * [backup-simplify]: Simplify PI into PI
5.419 * [taylor]: Taking taylor expansion of n in n
5.419 * [backup-simplify]: Simplify 0 into 0
5.419 * [backup-simplify]: Simplify 1 into 1
5.420 * [backup-simplify]: Simplify (/ PI 1) into PI
5.420 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
5.420 * [taylor]: Taking taylor expansion of 2 in n
5.420 * [backup-simplify]: Simplify 2 into 2
5.420 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.420 * [taylor]: Taking taylor expansion of PI in n
5.420 * [backup-simplify]: Simplify PI into PI
5.420 * [taylor]: Taking taylor expansion of n in n
5.420 * [backup-simplify]: Simplify 0 into 0
5.420 * [backup-simplify]: Simplify 1 into 1
5.420 * [backup-simplify]: Simplify (/ PI 1) into PI
5.421 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.421 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.422 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
5.423 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
5.423 * [backup-simplify]: Simplify 0 into 0
5.424 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.425 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
5.425 * [backup-simplify]: Simplify 0 into 0
5.426 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.427 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
5.427 * [backup-simplify]: Simplify 0 into 0
5.429 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.429 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
5.429 * [backup-simplify]: Simplify 0 into 0
5.430 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.431 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
5.431 * [backup-simplify]: Simplify 0 into 0
5.431 * [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
5.432 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
5.432 * [backup-simplify]: Simplify 0 into 0
5.433 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
5.433 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* 2 PI)) into (* -2 (/ PI n))
5.433 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
5.433 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
5.433 * [taylor]: Taking taylor expansion of -2 in n
5.433 * [backup-simplify]: Simplify -2 into -2
5.433 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.433 * [taylor]: Taking taylor expansion of PI in n
5.433 * [backup-simplify]: Simplify PI into PI
5.433 * [taylor]: Taking taylor expansion of n in n
5.433 * [backup-simplify]: Simplify 0 into 0
5.433 * [backup-simplify]: Simplify 1 into 1
5.434 * [backup-simplify]: Simplify (/ PI 1) into PI
5.434 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
5.434 * [taylor]: Taking taylor expansion of -2 in n
5.434 * [backup-simplify]: Simplify -2 into -2
5.434 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.434 * [taylor]: Taking taylor expansion of PI in n
5.434 * [backup-simplify]: Simplify PI into PI
5.434 * [taylor]: Taking taylor expansion of n in n
5.434 * [backup-simplify]: Simplify 0 into 0
5.434 * [backup-simplify]: Simplify 1 into 1
5.434 * [backup-simplify]: Simplify (/ PI 1) into PI
5.434 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
5.435 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
5.435 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
5.436 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
5.436 * [backup-simplify]: Simplify 0 into 0
5.436 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.437 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
5.437 * [backup-simplify]: Simplify 0 into 0
5.438 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.438 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
5.438 * [backup-simplify]: Simplify 0 into 0
5.439 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.440 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
5.440 * [backup-simplify]: Simplify 0 into 0
5.440 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.441 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
5.441 * [backup-simplify]: Simplify 0 into 0
5.442 * [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
5.443 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
5.443 * [backup-simplify]: Simplify 0 into 0
5.443 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
5.443 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1 1 1)
5.443 * [backup-simplify]: Simplify (* n (* 2 PI)) into (* 2 (* n PI))
5.443 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
5.443 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
5.443 * [taylor]: Taking taylor expansion of 2 in n
5.443 * [backup-simplify]: Simplify 2 into 2
5.443 * [taylor]: Taking taylor expansion of (* n PI) in n
5.443 * [taylor]: Taking taylor expansion of n in n
5.444 * [backup-simplify]: Simplify 0 into 0
5.444 * [backup-simplify]: Simplify 1 into 1
5.444 * [taylor]: Taking taylor expansion of PI in n
5.444 * [backup-simplify]: Simplify PI into PI
5.444 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
5.444 * [taylor]: Taking taylor expansion of 2 in n
5.444 * [backup-simplify]: Simplify 2 into 2
5.444 * [taylor]: Taking taylor expansion of (* n PI) in n
5.444 * [taylor]: Taking taylor expansion of n in n
5.444 * [backup-simplify]: Simplify 0 into 0
5.444 * [backup-simplify]: Simplify 1 into 1
5.444 * [taylor]: Taking taylor expansion of PI in n
5.444 * [backup-simplify]: Simplify PI into PI
5.444 * [backup-simplify]: Simplify (* 0 PI) into 0
5.444 * [backup-simplify]: Simplify (* 2 0) into 0
5.444 * [backup-simplify]: Simplify 0 into 0
5.445 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.446 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
5.446 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.447 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
5.448 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
5.448 * [backup-simplify]: Simplify 0 into 0
5.449 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
5.450 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
5.450 * [backup-simplify]: Simplify 0 into 0
5.452 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
5.453 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
5.453 * [backup-simplify]: Simplify 0 into 0
5.455 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
5.457 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
5.457 * [backup-simplify]: Simplify 0 into 0
5.458 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
5.460 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
5.460 * [backup-simplify]: Simplify 0 into 0
5.462 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
5.464 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
5.464 * [backup-simplify]: Simplify 0 into 0
5.465 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
5.465 * [backup-simplify]: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n))
5.465 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
5.465 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
5.466 * [taylor]: Taking taylor expansion of 2 in n
5.466 * [backup-simplify]: Simplify 2 into 2
5.466 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.466 * [taylor]: Taking taylor expansion of PI in n
5.466 * [backup-simplify]: Simplify PI into PI
5.466 * [taylor]: Taking taylor expansion of n in n
5.466 * [backup-simplify]: Simplify 0 into 0
5.466 * [backup-simplify]: Simplify 1 into 1
5.466 * [backup-simplify]: Simplify (/ PI 1) into PI
5.466 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
5.466 * [taylor]: Taking taylor expansion of 2 in n
5.466 * [backup-simplify]: Simplify 2 into 2
5.466 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.466 * [taylor]: Taking taylor expansion of PI in n
5.466 * [backup-simplify]: Simplify PI into PI
5.466 * [taylor]: Taking taylor expansion of n in n
5.466 * [backup-simplify]: Simplify 0 into 0
5.466 * [backup-simplify]: Simplify 1 into 1
5.467 * [backup-simplify]: Simplify (/ PI 1) into PI
5.467 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.468 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.469 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
5.469 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
5.470 * [backup-simplify]: Simplify 0 into 0
5.471 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.472 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
5.472 * [backup-simplify]: Simplify 0 into 0
5.473 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.474 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
5.474 * [backup-simplify]: Simplify 0 into 0
5.475 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.477 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
5.477 * [backup-simplify]: Simplify 0 into 0
5.478 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.479 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
5.479 * [backup-simplify]: Simplify 0 into 0
5.481 * [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
5.483 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
5.483 * [backup-simplify]: Simplify 0 into 0
5.483 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
5.484 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* 2 PI)) into (* -2 (/ PI n))
5.484 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
5.484 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
5.484 * [taylor]: Taking taylor expansion of -2 in n
5.484 * [backup-simplify]: Simplify -2 into -2
5.484 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.484 * [taylor]: Taking taylor expansion of PI in n
5.484 * [backup-simplify]: Simplify PI into PI
5.484 * [taylor]: Taking taylor expansion of n in n
5.484 * [backup-simplify]: Simplify 0 into 0
5.484 * [backup-simplify]: Simplify 1 into 1
5.484 * [backup-simplify]: Simplify (/ PI 1) into PI
5.485 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
5.485 * [taylor]: Taking taylor expansion of -2 in n
5.485 * [backup-simplify]: Simplify -2 into -2
5.485 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.485 * [taylor]: Taking taylor expansion of PI in n
5.485 * [backup-simplify]: Simplify PI into PI
5.485 * [taylor]: Taking taylor expansion of n in n
5.485 * [backup-simplify]: Simplify 0 into 0
5.485 * [backup-simplify]: Simplify 1 into 1
5.485 * [backup-simplify]: Simplify (/ PI 1) into PI
5.486 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
5.486 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
5.487 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
5.488 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
5.488 * [backup-simplify]: Simplify 0 into 0
5.489 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.490 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
5.490 * [backup-simplify]: Simplify 0 into 0
5.491 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.492 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
5.492 * [backup-simplify]: Simplify 0 into 0
5.493 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.495 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
5.495 * [backup-simplify]: Simplify 0 into 0
5.496 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.497 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
5.497 * [backup-simplify]: Simplify 0 into 0
5.499 * [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
5.500 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
5.500 * [backup-simplify]: Simplify 0 into 0
5.500 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
5.501 * * * [progress]: simplifying candidates
5.501 * * * * [progress]: [ 1 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (exp (* (+ (log n) (+ (log 2) (log PI))) (* (- 1 k) 1/2))) (sqrt k)))))>
5.501 * * * * [progress]: [ 2 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (exp (* (+ (log n) (log (* 2 PI))) (* (- 1 k) 1/2))) (sqrt k)))))>
5.501 * * * * [progress]: [ 3 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (exp (* (log (* n (* 2 PI))) (* (- 1 k) 1/2))) (sqrt k)))))>
5.501 * * * * [progress]: [ 4 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (exp (* (log (* n (* 2 PI))) (* (- 1 k) 1/2))) (sqrt k)))))>
5.501 * * * * [progress]: [ 5 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (* 1 (* (- 1 k) 1/2))) (sqrt k)))))>
5.501 * * * * [progress]: [ 6 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (* 1 (* (- 1 k) 1/2))) (sqrt k)))))>
5.501 * * * * [progress]: [ 7 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (* 1 (* (- 1 k) 1/2))) (sqrt k)))))>
5.501 * * * * [progress]: [ 8 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (pow (pow (* n (* 2 PI)) (- 1 k)) 1/2) (sqrt k)))))>
5.501 * * * * [progress]: [ 9 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (* (pow n (* (- 1 k) 1/2)) (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt k)))))>
5.501 * * * * [progress]: [ 10 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (pow (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) 1) (sqrt k)))))>
5.501 * * * * [progress]: [ 11 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (exp (log (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt k)))))>
5.501 * * * * [progress]: [ 12 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (log (exp (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt k)))))>
5.501 * * * * [progress]: [ 13 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (* (* (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))) (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt k)))))>
5.501 * * * * [progress]: [ 14 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (cbrt (* (* (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt k)))))>
5.501 * * * * [progress]: [ 15 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (* (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt k)))))>
5.501 * * * * [progress]: [ 16 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (* 1 (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt k)))))>
5.501 * * * * [progress]: [ 17 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (* (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2)) (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2))) (sqrt k)))))>
5.501 * * * * [progress]: [ 18 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (posit16->real (real->posit16 (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt k)))))>
5.501 * * * * [progress]: [ 19 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (exp (* (+ (log n) (+ (log 2) (log PI))) (* (- 1 k) 1/2))) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))))>
5.501 * * * * [progress]: [ 20 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (exp (* (+ (log n) (log (* 2 PI))) (* (- 1 k) 1/2))) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))))>
5.501 * * * * [progress]: [ 21 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (exp (* (log (* n (* 2 PI))) (* (- 1 k) 1/2))) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))))>
5.501 * * * * [progress]: [ 22 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (exp (* (log (* n (* 2 PI))) (* (- 1 k) 1/2))) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))))>
5.502 * * * * [progress]: [ 23 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (* 1 (* (- 1 k) 1/2))) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))))>
5.502 * * * * [progress]: [ 24 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (* 1 (* (- 1 k) 1/2))) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))))>
5.502 * * * * [progress]: [ 25 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (* 1 (* (- 1 k) 1/2))) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))))>
5.502 * * * * [progress]: [ 26 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (pow (* n (* 2 PI)) (- 1 k)) 1/2) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))))>
5.502 * * * * [progress]: [ 27 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (* (pow n (* (- 1 k) 1/2)) (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))))>
5.502 * * * * [progress]: [ 28 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) 1) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))))>
5.502 * * * * [progress]: [ 29 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (exp (log (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))))>
5.502 * * * * [progress]: [ 30 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (log (exp (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))))>
5.502 * * * * [progress]: [ 31 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (* (* (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))) (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))))>
5.502 * * * * [progress]: [ 32 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (cbrt (* (* (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))))>
5.502 * * * * [progress]: [ 33 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (* (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))))>
5.502 * * * * [progress]: [ 34 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (* 1 (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))))>
5.502 * * * * [progress]: [ 35 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (* (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2)) (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2))) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))))>
5.502 * * * * [progress]: [ 36 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (posit16->real (real->posit16 (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))))>
5.502 * * * * [progress]: [ 37 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (pow (pow (* n (* 2 PI)) 1) (* (- 1 k) 1/2)) (sqrt k)))))>
5.502 * * * * [progress]: [ 38 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (pow (pow (* n (* 2 PI)) 1) (* (- 1 k) 1/2)) (sqrt k)))))>
5.502 * * * * [progress]: [ 39 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (pow (pow (* n (* 2 PI)) 1) (* (- 1 k) 1/2)) (sqrt k)))))>
5.502 * * * * [progress]: [ 40 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (pow (exp (+ (log n) (+ (log 2) (log PI)))) (* (- 1 k) 1/2)) (sqrt k)))))>
5.502 * * * * [progress]: [ 41 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (pow (exp (+ (log n) (log (* 2 PI)))) (* (- 1 k) 1/2)) (sqrt k)))))>
5.502 * * * * [progress]: [ 42 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (pow (exp (log (* n (* 2 PI)))) (* (- 1 k) 1/2)) (sqrt k)))))>
5.502 * * * * [progress]: [ 43 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (pow (log (exp (* n (* 2 PI)))) (* (- 1 k) 1/2)) (sqrt k)))))>
5.502 * * * * [progress]: [ 44 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (pow (cbrt (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))) (* (- 1 k) 1/2)) (sqrt k)))))>
5.502 * * * * [progress]: [ 45 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (pow (cbrt (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))) (* (- 1 k) 1/2)) (sqrt k)))))>
5.502 * * * * [progress]: [ 46 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (pow (* (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI)))) (cbrt (* n (* 2 PI)))) (* (- 1 k) 1/2)) (sqrt k)))))>
5.503 * * * * [progress]: [ 47 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (pow (cbrt (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))) (* (- 1 k) 1/2)) (sqrt k)))))>
5.503 * * * * [progress]: [ 48 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (pow (* (sqrt (* n (* 2 PI))) (sqrt (* n (* 2 PI)))) (* (- 1 k) 1/2)) (sqrt k)))))>
5.503 * * * * [progress]: [ 49 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (pow (* 1 (* n (* 2 PI))) (* (- 1 k) 1/2)) (sqrt k)))))>
5.503 * * * * [progress]: [ 50 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (* (- 1 k) 1/2)) (sqrt k)))))>
5.503 * * * * [progress]: [ 51 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (pow (* (* (cbrt n) (cbrt n)) (* (cbrt n) (* 2 PI))) (* (- 1 k) 1/2)) (sqrt k)))))>
5.503 * * * * [progress]: [ 52 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (pow (* (sqrt n) (* (sqrt n) (* 2 PI))) (* (- 1 k) 1/2)) (sqrt k)))))>
5.503 * * * * [progress]: [ 53 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (pow (* 1 (* n (* 2 PI))) (* (- 1 k) 1/2)) (sqrt k)))))>
5.503 * * * * [progress]: [ 54 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (pow (posit16->real (real->posit16 (* n (* 2 PI)))) (* (- 1 k) 1/2)) (sqrt k)))))>
5.503 * * * * [progress]: [ 55 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (pow (* (* 2 PI) n) (* (- 1 k) 1/2)) (sqrt k)))))>
5.503 * * * * [progress]: [ 56 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (pow (* n (* 2 PI)) 1) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))))>
5.503 * * * * [progress]: [ 57 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (pow (* n (* 2 PI)) 1) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))))>
5.503 * * * * [progress]: [ 58 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (pow (* n (* 2 PI)) 1) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))))>
5.503 * * * * [progress]: [ 59 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (exp (+ (log n) (+ (log 2) (log PI)))) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))))>
5.503 * * * * [progress]: [ 60 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (exp (+ (log n) (log (* 2 PI)))) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))))>
5.503 * * * * [progress]: [ 61 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (exp (log (* n (* 2 PI)))) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))))>
5.503 * * * * [progress]: [ 62 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (log (exp (* n (* 2 PI)))) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))))>
5.503 * * * * [progress]: [ 63 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (cbrt (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))))>
5.503 * * * * [progress]: [ 64 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (cbrt (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))))>
5.503 * * * * [progress]: [ 65 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI)))) (cbrt (* n (* 2 PI)))) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))))>
5.503 * * * * [progress]: [ 66 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (cbrt (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))))>
5.503 * * * * [progress]: [ 67 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (sqrt (* n (* 2 PI))) (sqrt (* n (* 2 PI)))) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))))>
5.503 * * * * [progress]: [ 68 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* 1 (* n (* 2 PI))) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))))>
5.503 * * * * [progress]: [ 69 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))))>
5.503 * * * * [progress]: [ 70 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* (cbrt n) (cbrt n)) (* (cbrt n) (* 2 PI))) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))))>
5.504 * * * * [progress]: [ 71 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (sqrt n) (* (sqrt n) (* 2 PI))) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))))>
5.504 * * * * [progress]: [ 72 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* 1 (* n (* 2 PI))) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))))>
5.504 * * * * [progress]: [ 73 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (posit16->real (real->posit16 (* n (* 2 PI)))) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))))>
5.504 * * * * [progress]: [ 74 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* 2 PI) n) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))))>
5.504 * * * * [progress]: [ 75 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (- (+ (* 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))))) (sqrt k)))))>
5.504 * * * * [progress]: [ 76 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (sqrt k)))))>
5.504 * * * * [progress]: [ 77 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (sqrt k)))))>
5.504 * * * * [progress]: [ 78 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (- (+ (* 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))))) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))))>
5.504 * * * * [progress]: [ 79 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))))>
5.504 * * * * [progress]: [ 80 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))))>
5.504 * * * * [progress]: [ 81 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (pow (* 2 (* n PI)) (* (- 1 k) 1/2)) (sqrt k)))))>
5.504 * * * * [progress]: [ 82 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (pow (* 2 (* n PI)) (* (- 1 k) 1/2)) (sqrt k)))))>
5.504 * * * * [progress]: [ 83 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (pow (* 2 (* n PI)) (* (- 1 k) 1/2)) (sqrt k)))))>
5.504 * * * * [progress]: [ 84 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* 2 (* n PI)) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))))>
5.504 * * * * [progress]: [ 85 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* 2 (* n PI)) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))))>
5.504 * * * * [progress]: [ 86 / 86 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* 2 (* n PI)) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))))>
5.505 * [simplify]: Simplifying:
  (* (+ (log n) (+ (log 2) (log PI))) (* (- 1 k) 1/2))
  (* (+ (log n) (log (* 2 PI))) (* (- 1 k) 1/2))
  (* (log (* n (* 2 PI))) (* (- 1 k) 1/2))
  (* (log (* n (* 2 PI))) (* (- 1 k) 1/2))
  (* 1 (* (- 1 k) 1/2))
  (* 1 (* (- 1 k) 1/2))
  (* 1 (* (- 1 k) 1/2))
  (pow (* n (* 2 PI)) (- 1 k))
  (pow n (* (- 1 k) 1/2))
  (pow (* 2 PI) (* (- 1 k) 1/2))
  (log (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))
  (exp (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))
  (* (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))))
  (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))
  (* (* (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))
  (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))
  (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))
  (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2))
  (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2))
  (real->posit16 (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))
  (* (+ (log n) (+ (log 2) (log PI))) (* (- 1 k) 1/2))
  (* (+ (log n) (log (* 2 PI))) (* (- 1 k) 1/2))
  (* (log (* n (* 2 PI))) (* (- 1 k) 1/2))
  (* (log (* n (* 2 PI))) (* (- 1 k) 1/2))
  (* 1 (* (- 1 k) 1/2))
  (* 1 (* (- 1 k) 1/2))
  (* 1 (* (- 1 k) 1/2))
  (pow (* n (* 2 PI)) (- 1 k))
  (pow n (* (- 1 k) 1/2))
  (pow (* 2 PI) (* (- 1 k) 1/2))
  (log (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))
  (exp (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))
  (* (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))))
  (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))
  (* (* (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))
  (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))
  (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))
  (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2))
  (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2))
  (real->posit16 (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))
  (* 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)))
  (* 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)))
  (- (+ (* 1/4 (* (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)))))
  (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
  (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
  (- (+ (* 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)))))
  (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
  (exp (* 1/2 (* (- 1 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))
5.506 * * [simplify]: iteration 1: (105 enodes)
5.546 * * [simplify]: iteration 2: (480 enodes)
5.703 * * [simplify]: iteration 3: (1226 enodes)
6.828 * * [simplify]: Extracting #0: cost 26 inf + 0
6.829 * * [simplify]: Extracting #1: cost 316 inf + 0
6.836 * * [simplify]: Extracting #2: cost 825 inf + 5079
6.868 * * [simplify]: Extracting #3: cost 930 inf + 43453
6.935 * * [simplify]: Extracting #4: cost 471 inf + 174552
7.045 * * [simplify]: Extracting #5: cost 138 inf + 302312
7.165 * * [simplify]: Extracting #6: cost 89 inf + 321518
7.276 * * [simplify]: Extracting #7: cost 25 inf + 341701
7.417 * * [simplify]: Extracting #8: cost 1 inf + 349148
7.553 * * [simplify]: Extracting #9: cost 0 inf + 349233
7.654 * [simplify]: Simplified to:
  (* (- 1/2 (/ k 2)) (log (* n (* PI 2))))
  (* (- 1/2 (/ k 2)) (log (* n (* PI 2))))
  (* (- 1/2 (/ k 2)) (log (* n (* PI 2))))
  (* (- 1/2 (/ k 2)) (log (* n (* PI 2))))
  (* (- 1 k) 1/2)
  (* (- 1 k) 1/2)
  (* (- 1 k) 1/2)
  (exp (* (log (* n (* PI 2))) (- 1 k)))
  (pow n (* (- 1 k) 1/2))
  (pow (* PI 2) (* (- 1 k) 1/2))
  (* (- 1/2 (/ k 2)) (log (* n (* PI 2))))
  (exp (exp (* (- 1/2 (/ k 2)) (log (* n (* PI 2))))))
  (* (cbrt (exp (* (- 1/2 (/ k 2)) (log (* n (* PI 2)))))) (cbrt (exp (* (- 1/2 (/ k 2)) (log (* n (* PI 2)))))))
  (cbrt (exp (* (- 1/2 (/ k 2)) (log (* n (* PI 2))))))
  (* (exp (* (- 1 k) (* 1/2 (log (* n (* PI 2)))))) (exp (* (log (* n (* PI 2))) (- 1 k))))
  (sqrt (exp (* (- 1/2 (/ k 2)) (log (* n (* PI 2))))))
  (sqrt (exp (* (- 1/2 (/ k 2)) (log (* n (* PI 2))))))
  (pow (* n (* PI 2)) (/ (- 1 k) 4))
  (pow (* n (* PI 2)) (/ (- 1 k) 4))
  (real->posit16 (exp (* (- 1/2 (/ k 2)) (log (* n (* PI 2))))))
  (* (- 1/2 (/ k 2)) (log (* n (* PI 2))))
  (* (- 1/2 (/ k 2)) (log (* n (* PI 2))))
  (* (- 1/2 (/ k 2)) (log (* n (* PI 2))))
  (* (- 1/2 (/ k 2)) (log (* n (* PI 2))))
  (* (- 1 k) 1/2)
  (* (- 1 k) 1/2)
  (* (- 1 k) 1/2)
  (exp (* (log (* n (* PI 2))) (- 1 k)))
  (pow n (* (- 1 k) 1/2))
  (pow (* PI 2) (* (- 1 k) 1/2))
  (* (- 1/2 (/ k 2)) (log (* n (* PI 2))))
  (exp (exp (* (- 1/2 (/ k 2)) (log (* n (* PI 2))))))
  (* (cbrt (exp (* (- 1/2 (/ k 2)) (log (* n (* PI 2)))))) (cbrt (exp (* (- 1/2 (/ k 2)) (log (* n (* PI 2)))))))
  (cbrt (exp (* (- 1/2 (/ k 2)) (log (* n (* PI 2))))))
  (* (exp (* (- 1 k) (* 1/2 (log (* n (* PI 2)))))) (exp (* (log (* n (* PI 2))) (- 1 k))))
  (sqrt (exp (* (- 1/2 (/ k 2)) (log (* n (* PI 2))))))
  (sqrt (exp (* (- 1/2 (/ k 2)) (log (* n (* PI 2))))))
  (pow (* n (* PI 2)) (/ (- 1 k) 4))
  (pow (* n (* PI 2)) (/ (- 1 k) 4))
  (real->posit16 (exp (* (- 1/2 (/ k 2)) (log (* n (* PI 2))))))
  (* n (* PI 2))
  (* n (* PI 2))
  (log (* n (* PI 2)))
  (log (* n (* PI 2)))
  (log (* n (* PI 2)))
  (* (exp (* PI n)) (exp (* PI n)))
  (* (* (* n (* PI 2)) (* n (* PI 2))) (* n (* PI 2)))
  (* (* (* n (* PI 2)) (* n (* PI 2))) (* n (* PI 2)))
  (* (cbrt (* n (* PI 2))) (cbrt (* n (* PI 2))))
  (cbrt (* n (* PI 2)))
  (* (* (* n (* PI 2)) (* n (* PI 2))) (* n (* PI 2)))
  (sqrt (* n (* PI 2)))
  (sqrt (* n (* PI 2)))
  (* n 2)
  (* (* (cbrt n) 2) PI)
  (* (sqrt n) (* PI 2))
  (* n (* PI 2))
  (real->posit16 (* n (* PI 2)))
  (* n (* PI 2))
  (* n (* PI 2))
  (log (* n (* PI 2)))
  (log (* n (* PI 2)))
  (log (* n (* PI 2)))
  (* (exp (* PI n)) (exp (* PI n)))
  (* (* (* n (* PI 2)) (* n (* PI 2))) (* n (* PI 2)))
  (* (* (* n (* PI 2)) (* n (* PI 2))) (* n (* PI 2)))
  (* (cbrt (* n (* PI 2))) (cbrt (* n (* PI 2))))
  (cbrt (* n (* PI 2)))
  (* (* (* n (* PI 2)) (* n (* PI 2))) (* n (* PI 2)))
  (sqrt (* n (* PI 2)))
  (sqrt (* n (* PI 2)))
  (* n 2)
  (* (* (cbrt n) 2) PI)
  (* (sqrt n) (* PI 2))
  (* n (* PI 2))
  (real->posit16 (* n (* PI 2)))
  (+ (+ (+ (* (* (* k k) 1/8) (+ (* (* (sqrt (* n (* PI 2))) (log n)) (log n)) (* (log (* PI 2)) (* (sqrt (* n (* PI 2))) (log (* PI 2)))))) (sqrt (* n (* PI 2)))) (+ (* (* (* 1/4 (log (* PI 2))) (* (* (sqrt (* n (* PI 2))) (log n)) k)) k) (* -1/2 (* (* (sqrt (* n (* PI 2))) (log n)) k)))) (* (* k (* (sqrt (* n (* PI 2))) (log (* PI 2)))) -1/2))
  (exp (* (- 1/2 (/ k 2)) (log (* n (* PI 2)))))
  (sqrt (exp (* (- (log (* PI -2)) (log (/ -1 n))) (- 1 k))))
  (+ (+ (+ (* (* (* k k) 1/8) (+ (* (* (sqrt (* n (* PI 2))) (log n)) (log n)) (* (log (* PI 2)) (* (sqrt (* n (* PI 2))) (log (* PI 2)))))) (sqrt (* n (* PI 2)))) (+ (* (* (* 1/4 (log (* PI 2))) (* (* (sqrt (* n (* PI 2))) (log n)) k)) k) (* -1/2 (* (* (sqrt (* n (* PI 2))) (log n)) k)))) (* (* k (* (sqrt (* n (* PI 2))) (log (* PI 2)))) -1/2))
  (exp (* (- 1/2 (/ k 2)) (log (* n (* PI 2)))))
  (sqrt (exp (* (- (log (* PI -2)) (log (/ -1 n))) (- 1 k))))
  (* n (* PI 2))
  (* n (* PI 2))
  (* n (* PI 2))
  (* n (* PI 2))
  (* n (* PI 2))
  (* n (* PI 2))
7.665 * * * [progress]: adding candidates to table
8.915 * * [progress]: iteration 3 / 4
8.915 * * * [progress]: picking best candidate
8.986 * * * * [pick]: Picked  #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))>
8.986 * * * [progress]: localizing error
9.042 * * * [progress]: generating rewritten candidates
9.042 * * * * [progress]: [ 1 / 4 ] rewriting at (2 1)
9.049 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1)
9.061 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2)
9.078 * * * * [progress]: [ 4 / 4 ] rewriting at (2)
9.118 * * * [progress]: generating series expansions
9.118 * * * * [progress]: [ 1 / 4 ] generating series at (2 1)
9.118 * [backup-simplify]: Simplify (pow n (* (- 1 k) 1/2)) into (pow n (* 1/2 (- 1 k)))
9.119 * [approximate]: Taking taylor expansion of (pow n (* 1/2 (- 1 k))) in (n k) around 0
9.119 * [taylor]: Taking taylor expansion of (pow n (* 1/2 (- 1 k))) in k
9.119 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log n))) in k
9.119 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log n)) in k
9.119 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
9.119 * [taylor]: Taking taylor expansion of 1/2 in k
9.119 * [backup-simplify]: Simplify 1/2 into 1/2
9.119 * [taylor]: Taking taylor expansion of (- 1 k) in k
9.119 * [taylor]: Taking taylor expansion of 1 in k
9.119 * [backup-simplify]: Simplify 1 into 1
9.119 * [taylor]: Taking taylor expansion of k in k
9.119 * [backup-simplify]: Simplify 0 into 0
9.119 * [backup-simplify]: Simplify 1 into 1
9.119 * [taylor]: Taking taylor expansion of (log n) in k
9.119 * [taylor]: Taking taylor expansion of n in k
9.119 * [backup-simplify]: Simplify n into n
9.119 * [backup-simplify]: Simplify (log n) into (log n)
9.120 * [backup-simplify]: Simplify (- 0) into 0
9.120 * [backup-simplify]: Simplify (+ 1 0) into 1
9.121 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
9.121 * [backup-simplify]: Simplify (* 1/2 (log n)) into (* 1/2 (log n))
9.121 * [backup-simplify]: Simplify (exp (* 1/2 (log n))) into (pow n 1/2)
9.121 * [taylor]: Taking taylor expansion of (pow n (* 1/2 (- 1 k))) in n
9.121 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log n))) in n
9.121 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log n)) in n
9.121 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
9.121 * [taylor]: Taking taylor expansion of 1/2 in n
9.121 * [backup-simplify]: Simplify 1/2 into 1/2
9.121 * [taylor]: Taking taylor expansion of (- 1 k) in n
9.121 * [taylor]: Taking taylor expansion of 1 in n
9.121 * [backup-simplify]: Simplify 1 into 1
9.121 * [taylor]: Taking taylor expansion of k in n
9.121 * [backup-simplify]: Simplify k into k
9.121 * [taylor]: Taking taylor expansion of (log n) in n
9.121 * [taylor]: Taking taylor expansion of n in n
9.121 * [backup-simplify]: Simplify 0 into 0
9.121 * [backup-simplify]: Simplify 1 into 1
9.122 * [backup-simplify]: Simplify (log 1) into 0
9.122 * [backup-simplify]: Simplify (- k) into (- k)
9.122 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
9.122 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
9.123 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
9.123 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (log n)) into (* 1/2 (* (- 1 k) (log n)))
9.123 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (log n)))) into (exp (* 1/2 (* (- 1 k) (log n))))
9.123 * [taylor]: Taking taylor expansion of (pow n (* 1/2 (- 1 k))) in n
9.123 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log n))) in n
9.123 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log n)) in n
9.123 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
9.123 * [taylor]: Taking taylor expansion of 1/2 in n
9.123 * [backup-simplify]: Simplify 1/2 into 1/2
9.123 * [taylor]: Taking taylor expansion of (- 1 k) in n
9.123 * [taylor]: Taking taylor expansion of 1 in n
9.123 * [backup-simplify]: Simplify 1 into 1
9.123 * [taylor]: Taking taylor expansion of k in n
9.123 * [backup-simplify]: Simplify k into k
9.123 * [taylor]: Taking taylor expansion of (log n) in n
9.123 * [taylor]: Taking taylor expansion of n in n
9.123 * [backup-simplify]: Simplify 0 into 0
9.123 * [backup-simplify]: Simplify 1 into 1
9.124 * [backup-simplify]: Simplify (log 1) into 0
9.124 * [backup-simplify]: Simplify (- k) into (- k)
9.124 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
9.124 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
9.124 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
9.124 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (log n)) into (* 1/2 (* (- 1 k) (log n)))
9.124 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (log n)))) into (exp (* 1/2 (* (- 1 k) (log n))))
9.125 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (log n)))) in k
9.125 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 k) (log n))) in k
9.125 * [taylor]: Taking taylor expansion of 1/2 in k
9.125 * [backup-simplify]: Simplify 1/2 into 1/2
9.125 * [taylor]: Taking taylor expansion of (* (- 1 k) (log n)) in k
9.125 * [taylor]: Taking taylor expansion of (- 1 k) in k
9.125 * [taylor]: Taking taylor expansion of 1 in k
9.125 * [backup-simplify]: Simplify 1 into 1
9.125 * [taylor]: Taking taylor expansion of k in k
9.125 * [backup-simplify]: Simplify 0 into 0
9.125 * [backup-simplify]: Simplify 1 into 1
9.125 * [taylor]: Taking taylor expansion of (log n) in k
9.125 * [taylor]: Taking taylor expansion of n in k
9.125 * [backup-simplify]: Simplify n into n
9.125 * [backup-simplify]: Simplify (log n) into (log n)
9.125 * [backup-simplify]: Simplify (- 0) into 0
9.126 * [backup-simplify]: Simplify (+ 1 0) into 1
9.126 * [backup-simplify]: Simplify (* 1 (log n)) into (log n)
9.126 * [backup-simplify]: Simplify (* 1/2 (log n)) into (* 1/2 (log n))
9.126 * [backup-simplify]: Simplify (exp (* 1/2 (log n))) into (pow n 1/2)
9.126 * [backup-simplify]: Simplify (pow n 1/2) into (pow n 1/2)
9.128 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0
9.128 * [backup-simplify]: Simplify (- 0) into 0
9.128 * [backup-simplify]: Simplify (+ 0 0) into 0
9.129 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 k))) into 0
9.129 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
9.129 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (log n))) into 0
9.130 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
9.130 * [taylor]: Taking taylor expansion of 0 in k
9.130 * [backup-simplify]: Simplify 0 into 0
9.130 * [backup-simplify]: Simplify 0 into 0
9.131 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
9.132 * [backup-simplify]: Simplify (- 1) into -1
9.132 * [backup-simplify]: Simplify (+ 0 -1) into -1
9.133 * [backup-simplify]: Simplify (+ (* 1 0) (* -1 (log n))) into (- (log n))
9.133 * [backup-simplify]: Simplify (+ (* 1/2 (- (log n))) (* 0 (log n))) into (- (* 1/2 (log n)))
9.133 * [backup-simplify]: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 1) 1)))) into (* -1/2 (* (sqrt n) (log n)))
9.133 * [backup-simplify]: Simplify (* -1/2 (* (sqrt n) (log n))) into (* -1/2 (* (sqrt n) (log n)))
9.136 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0
9.137 * [backup-simplify]: Simplify (- 0) into 0
9.137 * [backup-simplify]: Simplify (+ 0 0) into 0
9.138 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0
9.139 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
9.139 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (log n)))) into 0
9.141 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
9.141 * [taylor]: Taking taylor expansion of 0 in k
9.141 * [backup-simplify]: Simplify 0 into 0
9.141 * [backup-simplify]: Simplify 0 into 0
9.141 * [backup-simplify]: Simplify 0 into 0
9.147 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
9.148 * [backup-simplify]: Simplify (- 0) into 0
9.148 * [backup-simplify]: Simplify (+ 0 0) into 0
9.149 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (log n)))) into 0
9.150 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (log n))) (* 0 (log n)))) into 0
9.151 * [backup-simplify]: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt n) (pow (log n) 2)))
9.151 * [backup-simplify]: Simplify (* 1/8 (* (sqrt n) (pow (log n) 2))) into (* 1/8 (* (sqrt n) (pow (log n) 2)))
9.152 * [backup-simplify]: Simplify (+ (* (* 1/8 (* (sqrt n) (pow (log n) 2))) (pow (* k 1) 2)) (+ (* (* -1/2 (* (sqrt n) (log n))) (* k 1)) (pow n 1/2))) into (- (+ (pow n 1/2) (* 1/8 (* (sqrt n) (* (pow (log n) 2) (pow k 2))))) (* 1/2 (* (sqrt n) (* (log n) k))))
9.152 * [backup-simplify]: Simplify (pow (/ 1 n) (* (- 1 (/ 1 k)) 1/2)) into (pow (/ 1 n) (* 1/2 (- 1 (/ 1 k))))
9.152 * [approximate]: Taking taylor expansion of (pow (/ 1 n) (* 1/2 (- 1 (/ 1 k)))) in (n k) around 0
9.152 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (* 1/2 (- 1 (/ 1 k)))) in k
9.152 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (/ 1 n)))) in k
9.152 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (/ 1 n))) in k
9.152 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
9.152 * [taylor]: Taking taylor expansion of 1/2 in k
9.152 * [backup-simplify]: Simplify 1/2 into 1/2
9.152 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
9.152 * [taylor]: Taking taylor expansion of 1 in k
9.152 * [backup-simplify]: Simplify 1 into 1
9.152 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.152 * [taylor]: Taking taylor expansion of k in k
9.152 * [backup-simplify]: Simplify 0 into 0
9.152 * [backup-simplify]: Simplify 1 into 1
9.153 * [backup-simplify]: Simplify (/ 1 1) into 1
9.153 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in k
9.153 * [taylor]: Taking taylor expansion of (/ 1 n) in k
9.153 * [taylor]: Taking taylor expansion of n in k
9.153 * [backup-simplify]: Simplify n into n
9.153 * [backup-simplify]: Simplify (/ 1 n) into (/ 1 n)
9.153 * [backup-simplify]: Simplify (log (/ 1 n)) into (log (/ 1 n))
9.153 * [backup-simplify]: Simplify (- 1) into -1
9.154 * [backup-simplify]: Simplify (+ 0 -1) into -1
9.155 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
9.155 * [backup-simplify]: Simplify (* -1/2 (log (/ 1 n))) into (* -1/2 (log (/ 1 n)))
9.155 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (/ 1 n)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (/ 1 n)))))
9.155 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (* 1/2 (- 1 (/ 1 k)))) in n
9.155 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (/ 1 n)))) in n
9.155 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (/ 1 n))) in n
9.155 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
9.155 * [taylor]: Taking taylor expansion of 1/2 in n
9.155 * [backup-simplify]: Simplify 1/2 into 1/2
9.155 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
9.155 * [taylor]: Taking taylor expansion of 1 in n
9.155 * [backup-simplify]: Simplify 1 into 1
9.155 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.155 * [taylor]: Taking taylor expansion of k in n
9.155 * [backup-simplify]: Simplify k into k
9.155 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.155 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n
9.155 * [taylor]: Taking taylor expansion of (/ 1 n) in n
9.155 * [taylor]: Taking taylor expansion of n in n
9.155 * [backup-simplify]: Simplify 0 into 0
9.155 * [backup-simplify]: Simplify 1 into 1
9.156 * [backup-simplify]: Simplify (/ 1 1) into 1
9.156 * [backup-simplify]: Simplify (log 1) into 0
9.156 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
9.156 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
9.156 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
9.157 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n))
9.157 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log n))) into (* -1/2 (* (- 1 (/ 1 k)) (log n)))
9.157 * [backup-simplify]: Simplify (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) into (exp (* -1/2 (* (- 1 (/ 1 k)) (log n))))
9.157 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (* 1/2 (- 1 (/ 1 k)))) in n
9.157 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (/ 1 n)))) in n
9.157 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (/ 1 n))) in n
9.157 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
9.157 * [taylor]: Taking taylor expansion of 1/2 in n
9.157 * [backup-simplify]: Simplify 1/2 into 1/2
9.157 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
9.157 * [taylor]: Taking taylor expansion of 1 in n
9.157 * [backup-simplify]: Simplify 1 into 1
9.157 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.157 * [taylor]: Taking taylor expansion of k in n
9.158 * [backup-simplify]: Simplify k into k
9.158 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.158 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n
9.158 * [taylor]: Taking taylor expansion of (/ 1 n) in n
9.158 * [taylor]: Taking taylor expansion of n in n
9.158 * [backup-simplify]: Simplify 0 into 0
9.158 * [backup-simplify]: Simplify 1 into 1
9.158 * [backup-simplify]: Simplify (/ 1 1) into 1
9.158 * [backup-simplify]: Simplify (log 1) into 0
9.159 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
9.159 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
9.159 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
9.159 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n))
9.159 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log n))) into (* -1/2 (* (- 1 (/ 1 k)) (log n)))
9.159 * [backup-simplify]: Simplify (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) into (exp (* -1/2 (* (- 1 (/ 1 k)) (log n))))
9.160 * [taylor]: Taking taylor expansion of (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) in k
9.160 * [taylor]: Taking taylor expansion of (* -1/2 (* (- 1 (/ 1 k)) (log n))) in k
9.160 * [taylor]: Taking taylor expansion of -1/2 in k
9.160 * [backup-simplify]: Simplify -1/2 into -1/2
9.160 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log n)) in k
9.160 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
9.160 * [taylor]: Taking taylor expansion of 1 in k
9.160 * [backup-simplify]: Simplify 1 into 1
9.160 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.160 * [taylor]: Taking taylor expansion of k in k
9.160 * [backup-simplify]: Simplify 0 into 0
9.160 * [backup-simplify]: Simplify 1 into 1
9.160 * [backup-simplify]: Simplify (/ 1 1) into 1
9.160 * [taylor]: Taking taylor expansion of (log n) in k
9.160 * [taylor]: Taking taylor expansion of n in k
9.160 * [backup-simplify]: Simplify n into n
9.160 * [backup-simplify]: Simplify (log n) into (log n)
9.161 * [backup-simplify]: Simplify (- 1) into -1
9.161 * [backup-simplify]: Simplify (+ 0 -1) into -1
9.161 * [backup-simplify]: Simplify (* -1 (log n)) into (* -1 (log n))
9.161 * [backup-simplify]: Simplify (* -1/2 (* -1 (log n))) into (* 1/2 (log n))
9.162 * [backup-simplify]: Simplify (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) into (exp (* -1/2 (* (- 1 (/ 1 k)) (log n))))
9.162 * [backup-simplify]: Simplify (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) into (exp (* -1/2 (* (- 1 (/ 1 k)) (log n))))
9.163 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
9.164 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0
9.164 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
9.164 * [backup-simplify]: Simplify (- 0) into 0
9.165 * [backup-simplify]: Simplify (+ 0 0) into 0
9.165 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 (/ 1 k)))) into 0
9.166 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n))
9.166 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log n)))) into 0
9.167 * [backup-simplify]: Simplify (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
9.167 * [taylor]: Taking taylor expansion of 0 in k
9.167 * [backup-simplify]: Simplify 0 into 0
9.167 * [backup-simplify]: Simplify 0 into 0
9.167 * [backup-simplify]: Simplify 0 into 0
9.168 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.171 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0
9.171 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
9.171 * [backup-simplify]: Simplify (- 0) into 0
9.172 * [backup-simplify]: Simplify (+ 0 0) into 0
9.172 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0
9.173 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n))
9.173 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log n))))) into 0
9.175 * [backup-simplify]: Simplify (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
9.175 * [taylor]: Taking taylor expansion of 0 in k
9.175 * [backup-simplify]: Simplify 0 into 0
9.175 * [backup-simplify]: Simplify 0 into 0
9.175 * [backup-simplify]: Simplify 0 into 0
9.175 * [backup-simplify]: Simplify 0 into 0
9.176 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.181 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0
9.181 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
9.182 * [backup-simplify]: Simplify (- 0) into 0
9.182 * [backup-simplify]: Simplify (+ 0 0) into 0
9.183 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0
9.184 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n))
9.185 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0
9.186 * [backup-simplify]: Simplify (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
9.186 * [taylor]: Taking taylor expansion of 0 in k
9.186 * [backup-simplify]: Simplify 0 into 0
9.186 * [backup-simplify]: Simplify 0 into 0
9.187 * [backup-simplify]: Simplify (exp (* -1/2 (* (- 1 (/ 1 (/ 1 k))) (log (/ 1 n))))) into (exp (* -1/2 (* (- 1 k) (log (/ 1 n)))))
9.187 * [backup-simplify]: Simplify (pow (/ 1 (- n)) (* (- 1 (/ 1 (- k))) 1/2)) into (pow (/ -1 n) (* 1/2 (+ (/ 1 k) 1)))
9.187 * [approximate]: Taking taylor expansion of (pow (/ -1 n) (* 1/2 (+ (/ 1 k) 1))) in (n k) around 0
9.187 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (* 1/2 (+ (/ 1 k) 1))) in k
9.187 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (/ -1 n)))) in k
9.187 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (/ -1 n))) in k
9.187 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
9.187 * [taylor]: Taking taylor expansion of 1/2 in k
9.187 * [backup-simplify]: Simplify 1/2 into 1/2
9.187 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
9.187 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.187 * [taylor]: Taking taylor expansion of k in k
9.187 * [backup-simplify]: Simplify 0 into 0
9.187 * [backup-simplify]: Simplify 1 into 1
9.188 * [backup-simplify]: Simplify (/ 1 1) into 1
9.188 * [taylor]: Taking taylor expansion of 1 in k
9.188 * [backup-simplify]: Simplify 1 into 1
9.188 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in k
9.188 * [taylor]: Taking taylor expansion of (/ -1 n) in k
9.188 * [taylor]: Taking taylor expansion of -1 in k
9.188 * [backup-simplify]: Simplify -1 into -1
9.188 * [taylor]: Taking taylor expansion of n in k
9.188 * [backup-simplify]: Simplify n into n
9.188 * [backup-simplify]: Simplify (/ -1 n) into (/ -1 n)
9.188 * [backup-simplify]: Simplify (log (/ -1 n)) into (log (/ -1 n))
9.188 * [backup-simplify]: Simplify (+ 1 0) into 1
9.189 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
9.189 * [backup-simplify]: Simplify (* 1/2 (log (/ -1 n))) into (* 1/2 (log (/ -1 n)))
9.189 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (/ -1 n)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (/ -1 n)))))
9.189 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (* 1/2 (+ (/ 1 k) 1))) in n
9.189 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (/ -1 n)))) in n
9.189 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (/ -1 n))) in n
9.189 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
9.189 * [taylor]: Taking taylor expansion of 1/2 in n
9.189 * [backup-simplify]: Simplify 1/2 into 1/2
9.189 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
9.189 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.189 * [taylor]: Taking taylor expansion of k in n
9.189 * [backup-simplify]: Simplify k into k
9.189 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.189 * [taylor]: Taking taylor expansion of 1 in n
9.190 * [backup-simplify]: Simplify 1 into 1
9.190 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n
9.190 * [taylor]: Taking taylor expansion of (/ -1 n) in n
9.190 * [taylor]: Taking taylor expansion of -1 in n
9.190 * [backup-simplify]: Simplify -1 into -1
9.190 * [taylor]: Taking taylor expansion of n in n
9.190 * [backup-simplify]: Simplify 0 into 0
9.190 * [backup-simplify]: Simplify 1 into 1
9.190 * [backup-simplify]: Simplify (/ -1 1) into -1
9.190 * [backup-simplify]: Simplify (log -1) into (log -1)
9.191 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
9.191 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
9.191 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n))
9.192 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log -1) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))
9.192 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))
9.193 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (* 1/2 (+ (/ 1 k) 1))) in n
9.193 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (/ -1 n)))) in n
9.193 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (/ -1 n))) in n
9.193 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
9.193 * [taylor]: Taking taylor expansion of 1/2 in n
9.193 * [backup-simplify]: Simplify 1/2 into 1/2
9.193 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
9.193 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.193 * [taylor]: Taking taylor expansion of k in n
9.193 * [backup-simplify]: Simplify k into k
9.193 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.193 * [taylor]: Taking taylor expansion of 1 in n
9.193 * [backup-simplify]: Simplify 1 into 1
9.193 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n
9.193 * [taylor]: Taking taylor expansion of (/ -1 n) in n
9.193 * [taylor]: Taking taylor expansion of -1 in n
9.193 * [backup-simplify]: Simplify -1 into -1
9.193 * [taylor]: Taking taylor expansion of n in n
9.193 * [backup-simplify]: Simplify 0 into 0
9.193 * [backup-simplify]: Simplify 1 into 1
9.194 * [backup-simplify]: Simplify (/ -1 1) into -1
9.194 * [backup-simplify]: Simplify (log -1) into (log -1)
9.194 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
9.194 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
9.195 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n))
9.195 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log -1) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))
9.196 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))
9.196 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) in k
9.196 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))) in k
9.196 * [taylor]: Taking taylor expansion of 1/2 in k
9.196 * [backup-simplify]: Simplify 1/2 into 1/2
9.196 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log -1) (log n))) in k
9.196 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
9.196 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.196 * [taylor]: Taking taylor expansion of k in k
9.196 * [backup-simplify]: Simplify 0 into 0
9.196 * [backup-simplify]: Simplify 1 into 1
9.197 * [backup-simplify]: Simplify (/ 1 1) into 1
9.197 * [taylor]: Taking taylor expansion of 1 in k
9.197 * [backup-simplify]: Simplify 1 into 1
9.197 * [taylor]: Taking taylor expansion of (- (log -1) (log n)) in k
9.197 * [taylor]: Taking taylor expansion of (log -1) in k
9.197 * [taylor]: Taking taylor expansion of -1 in k
9.197 * [backup-simplify]: Simplify -1 into -1
9.197 * [backup-simplify]: Simplify (log -1) into (log -1)
9.197 * [taylor]: Taking taylor expansion of (log n) in k
9.197 * [taylor]: Taking taylor expansion of n in k
9.197 * [backup-simplify]: Simplify n into n
9.197 * [backup-simplify]: Simplify (log n) into (log n)
9.198 * [backup-simplify]: Simplify (+ 1 0) into 1
9.198 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
9.198 * [backup-simplify]: Simplify (+ (log -1) (- (log n))) into (- (log -1) (log n))
9.199 * [backup-simplify]: Simplify (* 1 (- (log -1) (log n))) into (- (log -1) (log n))
9.199 * [backup-simplify]: Simplify (* 1/2 (- (log -1) (log n))) into (* 1/2 (- (log -1) (log n)))
9.200 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))
9.200 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))
9.201 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
9.203 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -1 1)))) 1) into 0
9.203 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
9.203 * [backup-simplify]: Simplify (+ 0 0) into 0
9.204 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (/ 1 k) 1))) into 0
9.204 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n))
9.205 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (- (log -1) (log n)))) into 0
9.206 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
9.206 * [taylor]: Taking taylor expansion of 0 in k
9.206 * [backup-simplify]: Simplify 0 into 0
9.206 * [backup-simplify]: Simplify 0 into 0
9.206 * [backup-simplify]: Simplify 0 into 0
9.207 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.210 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -1 1)))) 2) into 0
9.210 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
9.211 * [backup-simplify]: Simplify (+ 0 0) into 0
9.212 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0
9.212 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n))
9.213 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log -1) (log n))))) into 0
9.214 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
9.214 * [taylor]: Taking taylor expansion of 0 in k
9.214 * [backup-simplify]: Simplify 0 into 0
9.214 * [backup-simplify]: Simplify 0 into 0
9.214 * [backup-simplify]: Simplify 0 into 0
9.214 * [backup-simplify]: Simplify 0 into 0
9.215 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.218 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow -1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow -1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow -1 1)))) 6) into 0
9.218 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
9.218 * [backup-simplify]: Simplify (+ 0 0) into 0
9.219 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1))))) into 0
9.222 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n))
9.223 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log -1) (log n)))))) into 0
9.224 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
9.224 * [taylor]: Taking taylor expansion of 0 in k
9.224 * [backup-simplify]: Simplify 0 into 0
9.224 * [backup-simplify]: Simplify 0 into 0
9.224 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log -1) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n))))))
9.224 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1)
9.225 * [backup-simplify]: Simplify (pow (* 2 PI) (* (- 1 k) 1/2)) into (pow (* 2 PI) (* 1/2 (- 1 k)))
9.225 * [approximate]: Taking taylor expansion of (pow (* 2 PI) (* 1/2 (- 1 k))) in (k) around 0
9.225 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (* 1/2 (- 1 k))) in k
9.225 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 PI)))) in k
9.225 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 PI))) in k
9.225 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
9.225 * [taylor]: Taking taylor expansion of 1/2 in k
9.225 * [backup-simplify]: Simplify 1/2 into 1/2
9.225 * [taylor]: Taking taylor expansion of (- 1 k) in k
9.225 * [taylor]: Taking taylor expansion of 1 in k
9.225 * [backup-simplify]: Simplify 1 into 1
9.225 * [taylor]: Taking taylor expansion of k in k
9.225 * [backup-simplify]: Simplify 0 into 0
9.225 * [backup-simplify]: Simplify 1 into 1
9.225 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
9.225 * [taylor]: Taking taylor expansion of (* 2 PI) in k
9.225 * [taylor]: Taking taylor expansion of 2 in k
9.225 * [backup-simplify]: Simplify 2 into 2
9.225 * [taylor]: Taking taylor expansion of PI in k
9.225 * [backup-simplify]: Simplify PI into PI
9.225 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.226 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.226 * [backup-simplify]: Simplify (- 0) into 0
9.226 * [backup-simplify]: Simplify (+ 1 0) into 1
9.227 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
9.228 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI)))
9.229 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 PI)))) into (pow (* 2 PI) 1/2)
9.229 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (* 1/2 (- 1 k))) in k
9.229 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 PI)))) in k
9.229 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 PI))) in k
9.229 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
9.229 * [taylor]: Taking taylor expansion of 1/2 in k
9.229 * [backup-simplify]: Simplify 1/2 into 1/2
9.229 * [taylor]: Taking taylor expansion of (- 1 k) in k
9.229 * [taylor]: Taking taylor expansion of 1 in k
9.229 * [backup-simplify]: Simplify 1 into 1
9.229 * [taylor]: Taking taylor expansion of k in k
9.229 * [backup-simplify]: Simplify 0 into 0
9.229 * [backup-simplify]: Simplify 1 into 1
9.229 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
9.229 * [taylor]: Taking taylor expansion of (* 2 PI) in k
9.229 * [taylor]: Taking taylor expansion of 2 in k
9.229 * [backup-simplify]: Simplify 2 into 2
9.229 * [taylor]: Taking taylor expansion of PI in k
9.229 * [backup-simplify]: Simplify PI into PI
9.230 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.230 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.230 * [backup-simplify]: Simplify (- 0) into 0
9.231 * [backup-simplify]: Simplify (+ 1 0) into 1
9.231 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
9.232 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI)))
9.233 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 PI)))) into (pow (* 2 PI) 1/2)
9.234 * [backup-simplify]: Simplify (pow (* 2 PI) 1/2) into (pow (* 2 PI) 1/2)
9.234 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
9.235 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
9.236 * [backup-simplify]: Simplify (- 1) into -1
9.236 * [backup-simplify]: Simplify (+ 0 -1) into -1
9.236 * [backup-simplify]: Simplify (+ (* 1/2 -1) (* 0 1)) into -1/2
9.238 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 PI)))) into (- (* 1/2 (log (* 2 PI))))
9.245 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 1) 1)))) into (* -1/2 (* (sqrt (* PI 2)) (log (* 2 PI))))
9.250 * [backup-simplify]: Simplify (* -1/2 (* (sqrt (* PI 2)) (log (* 2 PI)))) into (* -1/2 (* (* (sqrt 2) (log (* 2 PI))) (sqrt PI)))
9.251 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
9.254 * [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
9.254 * [backup-simplify]: Simplify (- 0) into 0
9.255 * [backup-simplify]: Simplify (+ 0 0) into 0
9.256 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 -1) (* 0 1))) into 0
9.258 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 PI))))) into 0
9.277 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 2)))
9.282 * [backup-simplify]: Simplify (* 1/8 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 2))) into (* 1/8 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt PI)))
9.295 * [backup-simplify]: Simplify (+ (* (* 1/8 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt PI))) (pow k 2)) (+ (* (* -1/2 (* (* (sqrt 2) (log (* 2 PI))) (sqrt PI))) k) (pow (* 2 PI) 1/2))) into (- (+ (* 1/8 (* (* (sqrt 2) (* (pow k 2) (pow (log (* 2 PI)) 2))) (sqrt PI))) (pow (* 2 PI) 1/2)) (* 1/2 (* (* (sqrt 2) (* k (log (* 2 PI)))) (sqrt PI))))
9.296 * [backup-simplify]: Simplify (pow (* 2 PI) (* (- 1 (/ 1 k)) 1/2)) into (pow (* 2 PI) (* 1/2 (- 1 (/ 1 k))))
9.296 * [approximate]: Taking taylor expansion of (pow (* 2 PI) (* 1/2 (- 1 (/ 1 k)))) in (k) around 0
9.296 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (* 1/2 (- 1 (/ 1 k)))) in k
9.296 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 PI)))) in k
9.296 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 PI))) in k
9.296 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
9.296 * [taylor]: Taking taylor expansion of 1/2 in k
9.296 * [backup-simplify]: Simplify 1/2 into 1/2
9.296 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
9.296 * [taylor]: Taking taylor expansion of 1 in k
9.296 * [backup-simplify]: Simplify 1 into 1
9.296 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.296 * [taylor]: Taking taylor expansion of k in k
9.296 * [backup-simplify]: Simplify 0 into 0
9.296 * [backup-simplify]: Simplify 1 into 1
9.297 * [backup-simplify]: Simplify (/ 1 1) into 1
9.297 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
9.297 * [taylor]: Taking taylor expansion of (* 2 PI) in k
9.297 * [taylor]: Taking taylor expansion of 2 in k
9.297 * [backup-simplify]: Simplify 2 into 2
9.297 * [taylor]: Taking taylor expansion of PI in k
9.297 * [backup-simplify]: Simplify PI into PI
9.297 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.298 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.299 * [backup-simplify]: Simplify (- 1) into -1
9.299 * [backup-simplify]: Simplify (+ 0 -1) into -1
9.299 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
9.301 * [backup-simplify]: Simplify (* -1/2 (log (* 2 PI))) into (* -1/2 (log (* 2 PI)))
9.302 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 PI)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))
9.302 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (* 1/2 (- 1 (/ 1 k)))) in k
9.302 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 PI)))) in k
9.302 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 PI))) in k
9.302 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
9.302 * [taylor]: Taking taylor expansion of 1/2 in k
9.302 * [backup-simplify]: Simplify 1/2 into 1/2
9.303 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
9.303 * [taylor]: Taking taylor expansion of 1 in k
9.303 * [backup-simplify]: Simplify 1 into 1
9.303 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.303 * [taylor]: Taking taylor expansion of k in k
9.303 * [backup-simplify]: Simplify 0 into 0
9.303 * [backup-simplify]: Simplify 1 into 1
9.303 * [backup-simplify]: Simplify (/ 1 1) into 1
9.303 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
9.303 * [taylor]: Taking taylor expansion of (* 2 PI) in k
9.303 * [taylor]: Taking taylor expansion of 2 in k
9.303 * [backup-simplify]: Simplify 2 into 2
9.303 * [taylor]: Taking taylor expansion of PI in k
9.303 * [backup-simplify]: Simplify PI into PI
9.304 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.305 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.305 * [backup-simplify]: Simplify (- 1) into -1
9.306 * [backup-simplify]: Simplify (+ 0 -1) into -1
9.306 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
9.308 * [backup-simplify]: Simplify (* -1/2 (log (* 2 PI))) into (* -1/2 (log (* 2 PI)))
9.309 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 PI)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))
9.310 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))
9.310 * [backup-simplify]: Simplify 0 into 0
9.310 * [backup-simplify]: Simplify 0 into 0
9.310 * [backup-simplify]: Simplify 0 into 0
9.310 * [backup-simplify]: Simplify 0 into 0
9.310 * [backup-simplify]: Simplify 0 into 0
9.310 * [backup-simplify]: Simplify 0 into 0
9.311 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log (* 2 PI))))) into (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))
9.312 * [backup-simplify]: Simplify (pow (* 2 PI) (* (- 1 (/ 1 (- k))) 1/2)) into (pow (* 2 PI) (* 1/2 (+ (/ 1 k) 1)))
9.312 * [approximate]: Taking taylor expansion of (pow (* 2 PI) (* 1/2 (+ (/ 1 k) 1))) in (k) around 0
9.312 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (* 1/2 (+ (/ 1 k) 1))) in k
9.312 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* 2 PI)))) in k
9.312 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* 2 PI))) in k
9.312 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
9.312 * [taylor]: Taking taylor expansion of 1/2 in k
9.312 * [backup-simplify]: Simplify 1/2 into 1/2
9.312 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
9.312 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.312 * [taylor]: Taking taylor expansion of k in k
9.312 * [backup-simplify]: Simplify 0 into 0
9.312 * [backup-simplify]: Simplify 1 into 1
9.313 * [backup-simplify]: Simplify (/ 1 1) into 1
9.313 * [taylor]: Taking taylor expansion of 1 in k
9.313 * [backup-simplify]: Simplify 1 into 1
9.313 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
9.313 * [taylor]: Taking taylor expansion of (* 2 PI) in k
9.313 * [taylor]: Taking taylor expansion of 2 in k
9.313 * [backup-simplify]: Simplify 2 into 2
9.313 * [taylor]: Taking taylor expansion of PI in k
9.313 * [backup-simplify]: Simplify PI into PI
9.313 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.314 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.315 * [backup-simplify]: Simplify (+ 1 0) into 1
9.316 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
9.317 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI)))
9.318 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* 2 PI)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))
9.318 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (* 1/2 (+ (/ 1 k) 1))) in k
9.319 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* 2 PI)))) in k
9.319 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* 2 PI))) in k
9.319 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
9.319 * [taylor]: Taking taylor expansion of 1/2 in k
9.319 * [backup-simplify]: Simplify 1/2 into 1/2
9.319 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
9.319 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.319 * [taylor]: Taking taylor expansion of k in k
9.319 * [backup-simplify]: Simplify 0 into 0
9.319 * [backup-simplify]: Simplify 1 into 1
9.319 * [backup-simplify]: Simplify (/ 1 1) into 1
9.319 * [taylor]: Taking taylor expansion of 1 in k
9.319 * [backup-simplify]: Simplify 1 into 1
9.319 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
9.319 * [taylor]: Taking taylor expansion of (* 2 PI) in k
9.319 * [taylor]: Taking taylor expansion of 2 in k
9.319 * [backup-simplify]: Simplify 2 into 2
9.319 * [taylor]: Taking taylor expansion of PI in k
9.319 * [backup-simplify]: Simplify PI into PI
9.320 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.321 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.321 * [backup-simplify]: Simplify (+ 1 0) into 1
9.322 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
9.324 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI)))
9.325 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* 2 PI)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))
9.326 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))
9.326 * [backup-simplify]: Simplify 0 into 0
9.326 * [backup-simplify]: Simplify 0 into 0
9.326 * [backup-simplify]: Simplify 0 into 0
9.326 * [backup-simplify]: Simplify 0 into 0
9.326 * [backup-simplify]: Simplify 0 into 0
9.327 * [backup-simplify]: Simplify 0 into 0
9.328 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (log (* 2 PI))))) into (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))
9.328 * * * * [progress]: [ 3 / 4 ] generating series at (2 2)
9.329 * [backup-simplify]: Simplify (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k)) into (* (pow (* 2 PI) (* 1/2 (- 1 k))) (sqrt (/ 1 k)))
9.329 * [approximate]: Taking taylor expansion of (* (pow (* 2 PI) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in (k) around 0
9.329 * [taylor]: Taking taylor expansion of (* (pow (* 2 PI) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k
9.329 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (* 1/2 (- 1 k))) in k
9.329 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 PI)))) in k
9.329 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 PI))) in k
9.329 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
9.329 * [taylor]: Taking taylor expansion of 1/2 in k
9.329 * [backup-simplify]: Simplify 1/2 into 1/2
9.329 * [taylor]: Taking taylor expansion of (- 1 k) in k
9.329 * [taylor]: Taking taylor expansion of 1 in k
9.329 * [backup-simplify]: Simplify 1 into 1
9.329 * [taylor]: Taking taylor expansion of k in k
9.329 * [backup-simplify]: Simplify 0 into 0
9.329 * [backup-simplify]: Simplify 1 into 1
9.329 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
9.329 * [taylor]: Taking taylor expansion of (* 2 PI) in k
9.329 * [taylor]: Taking taylor expansion of 2 in k
9.329 * [backup-simplify]: Simplify 2 into 2
9.329 * [taylor]: Taking taylor expansion of PI in k
9.329 * [backup-simplify]: Simplify PI into PI
9.330 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.331 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.331 * [backup-simplify]: Simplify (- 0) into 0
9.332 * [backup-simplify]: Simplify (+ 1 0) into 1
9.332 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
9.334 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI)))
9.337 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 PI)))) into (pow (* 2 PI) 1/2)
9.337 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
9.337 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.337 * [taylor]: Taking taylor expansion of k in k
9.337 * [backup-simplify]: Simplify 0 into 0
9.337 * [backup-simplify]: Simplify 1 into 1
9.337 * [backup-simplify]: Simplify (/ 1 1) into 1
9.338 * [backup-simplify]: Simplify (sqrt 0) into 0
9.340 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
9.340 * [taylor]: Taking taylor expansion of (* (pow (* 2 PI) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k
9.340 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (* 1/2 (- 1 k))) in k
9.340 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 PI)))) in k
9.340 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 PI))) in k
9.340 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
9.340 * [taylor]: Taking taylor expansion of 1/2 in k
9.340 * [backup-simplify]: Simplify 1/2 into 1/2
9.340 * [taylor]: Taking taylor expansion of (- 1 k) in k
9.340 * [taylor]: Taking taylor expansion of 1 in k
9.340 * [backup-simplify]: Simplify 1 into 1
9.340 * [taylor]: Taking taylor expansion of k in k
9.340 * [backup-simplify]: Simplify 0 into 0
9.340 * [backup-simplify]: Simplify 1 into 1
9.340 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
9.340 * [taylor]: Taking taylor expansion of (* 2 PI) in k
9.340 * [taylor]: Taking taylor expansion of 2 in k
9.340 * [backup-simplify]: Simplify 2 into 2
9.340 * [taylor]: Taking taylor expansion of PI in k
9.340 * [backup-simplify]: Simplify PI into PI
9.341 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.342 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.342 * [backup-simplify]: Simplify (- 0) into 0
9.343 * [backup-simplify]: Simplify (+ 1 0) into 1
9.343 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
9.345 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI)))
9.347 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 PI)))) into (pow (* 2 PI) 1/2)
9.347 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
9.347 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.347 * [taylor]: Taking taylor expansion of k in k
9.347 * [backup-simplify]: Simplify 0 into 0
9.347 * [backup-simplify]: Simplify 1 into 1
9.348 * [backup-simplify]: Simplify (/ 1 1) into 1
9.348 * [backup-simplify]: Simplify (sqrt 0) into 0
9.350 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
9.350 * [backup-simplify]: Simplify (* (pow (* 2 PI) 1/2) 0) into 0
9.351 * [backup-simplify]: Simplify 0 into 0
9.351 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
9.353 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
9.354 * [backup-simplify]: Simplify (- 1) into -1
9.354 * [backup-simplify]: Simplify (+ 0 -1) into -1
9.355 * [backup-simplify]: Simplify (+ (* 1/2 -1) (* 0 1)) into -1/2
9.360 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 PI)))) into (- (* 1/2 (log (* 2 PI))))
9.373 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 1) 1)))) into (* -1/2 (* (sqrt (* PI 2)) (log (* 2 PI))))
9.380 * [backup-simplify]: Simplify (+ (* (pow (* 2 PI) 1/2) +nan.0) (* (* -1/2 (* (sqrt (* PI 2)) (log (* 2 PI)))) 0)) into (- (* +nan.0 (* (sqrt 2) (sqrt PI))))
9.383 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) (sqrt PI)))) into (- (* +nan.0 (* (sqrt 2) (sqrt PI))))
9.384 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
9.387 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
9.388 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
9.392 * [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
9.392 * [backup-simplify]: Simplify (- 0) into 0
9.393 * [backup-simplify]: Simplify (+ 0 0) into 0
9.394 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 -1) (* 0 1))) into 0
9.395 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 PI))))) into 0
9.409 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 2)))
9.428 * [backup-simplify]: Simplify (+ (* (pow (* 2 PI) 1/2) +nan.0) (+ (* (* -1/2 (* (sqrt (* PI 2)) (log (* 2 PI)))) +nan.0) (* (* 1/8 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 2))) 0))) into (- (+ (* +nan.0 (* (sqrt 2) (sqrt PI))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt PI))))))
9.435 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (sqrt 2) (sqrt PI))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt PI)))))) into (- (+ (* +nan.0 (* (sqrt 2) (sqrt PI))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt PI))))))
9.436 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.438 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
9.441 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
9.444 * [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
9.444 * [backup-simplify]: Simplify (- 0) into 0
9.444 * [backup-simplify]: Simplify (+ 0 0) into 0
9.445 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1)))) into 0
9.446 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log (* 2 PI)))))) into 0
9.456 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 3) 6)) (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 3)))
9.472 * [backup-simplify]: Simplify (+ (* (pow (* 2 PI) 1/2) +nan.0) (+ (* (* -1/2 (* (sqrt (* PI 2)) (log (* 2 PI)))) +nan.0) (+ (* (* 1/8 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 2))) +nan.0) (* (* -1/48 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 3))) 0)))) into (- (+ (* +nan.0 (* (sqrt 2) (sqrt PI))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt PI))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt PI))))))))
9.487 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (sqrt 2) (sqrt PI))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt PI))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt PI)))))))) into (- (+ (* +nan.0 (* (sqrt 2) (sqrt PI))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt PI))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt PI))))))))
9.517 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (sqrt 2) (sqrt PI))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt PI))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt PI)))))))) (pow k 2)) (+ (* (- (+ (* +nan.0 (* (sqrt 2) (sqrt PI))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt PI)))))) k) (- (* +nan.0 (* (sqrt 2) (sqrt PI)))))) into (- (+ (* +nan.0 (* (* (sqrt 2) (pow k 2)) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt PI))) (- (+ (* +nan.0 (* (* (log (* 2 PI)) (* (sqrt 2) (pow k 2))) (sqrt PI))) (- (+ (* +nan.0 (* (* (pow (log (* 2 PI)) 2) (* (sqrt 2) (pow k 2))) (sqrt PI))) (- (+ (* +nan.0 (* (* (sqrt 2) (* k (log (* 2 PI)))) (sqrt PI))) (- (* +nan.0 (* (* (sqrt 2) k) (sqrt PI))))))))))))))
9.517 * [backup-simplify]: Simplify (/ (pow (* 2 PI) (* (- 1 (/ 1 k)) 1/2)) (sqrt (/ 1 k))) into (* (pow (* 2 PI) (* 1/2 (- 1 (/ 1 k)))) (sqrt k))
9.517 * [approximate]: Taking taylor expansion of (* (pow (* 2 PI) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in (k) around 0
9.517 * [taylor]: Taking taylor expansion of (* (pow (* 2 PI) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k
9.517 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (* 1/2 (- 1 (/ 1 k)))) in k
9.517 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 PI)))) in k
9.517 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 PI))) in k
9.517 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
9.517 * [taylor]: Taking taylor expansion of 1/2 in k
9.517 * [backup-simplify]: Simplify 1/2 into 1/2
9.517 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
9.517 * [taylor]: Taking taylor expansion of 1 in k
9.517 * [backup-simplify]: Simplify 1 into 1
9.517 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.517 * [taylor]: Taking taylor expansion of k in k
9.517 * [backup-simplify]: Simplify 0 into 0
9.517 * [backup-simplify]: Simplify 1 into 1
9.518 * [backup-simplify]: Simplify (/ 1 1) into 1
9.518 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
9.518 * [taylor]: Taking taylor expansion of (* 2 PI) in k
9.518 * [taylor]: Taking taylor expansion of 2 in k
9.518 * [backup-simplify]: Simplify 2 into 2
9.518 * [taylor]: Taking taylor expansion of PI in k
9.518 * [backup-simplify]: Simplify PI into PI
9.518 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.519 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.519 * [backup-simplify]: Simplify (- 1) into -1
9.519 * [backup-simplify]: Simplify (+ 0 -1) into -1
9.519 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
9.520 * [backup-simplify]: Simplify (* -1/2 (log (* 2 PI))) into (* -1/2 (log (* 2 PI)))
9.521 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 PI)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))
9.521 * [taylor]: Taking taylor expansion of (sqrt k) in k
9.521 * [taylor]: Taking taylor expansion of k in k
9.521 * [backup-simplify]: Simplify 0 into 0
9.521 * [backup-simplify]: Simplify 1 into 1
9.521 * [backup-simplify]: Simplify (sqrt 0) into 0
9.522 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
9.522 * [taylor]: Taking taylor expansion of (* (pow (* 2 PI) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k
9.522 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (* 1/2 (- 1 (/ 1 k)))) in k
9.522 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 PI)))) in k
9.522 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 PI))) in k
9.522 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
9.522 * [taylor]: Taking taylor expansion of 1/2 in k
9.522 * [backup-simplify]: Simplify 1/2 into 1/2
9.522 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
9.522 * [taylor]: Taking taylor expansion of 1 in k
9.522 * [backup-simplify]: Simplify 1 into 1
9.522 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.522 * [taylor]: Taking taylor expansion of k in k
9.522 * [backup-simplify]: Simplify 0 into 0
9.523 * [backup-simplify]: Simplify 1 into 1
9.523 * [backup-simplify]: Simplify (/ 1 1) into 1
9.523 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
9.523 * [taylor]: Taking taylor expansion of (* 2 PI) in k
9.523 * [taylor]: Taking taylor expansion of 2 in k
9.523 * [backup-simplify]: Simplify 2 into 2
9.523 * [taylor]: Taking taylor expansion of PI in k
9.523 * [backup-simplify]: Simplify PI into PI
9.523 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.524 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.524 * [backup-simplify]: Simplify (- 1) into -1
9.524 * [backup-simplify]: Simplify (+ 0 -1) into -1
9.525 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
9.526 * [backup-simplify]: Simplify (* -1/2 (log (* 2 PI))) into (* -1/2 (log (* 2 PI)))
9.526 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 PI)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))
9.526 * [taylor]: Taking taylor expansion of (sqrt k) in k
9.526 * [taylor]: Taking taylor expansion of k in k
9.526 * [backup-simplify]: Simplify 0 into 0
9.526 * [backup-simplify]: Simplify 1 into 1
9.526 * [backup-simplify]: Simplify (sqrt 0) into 0
9.527 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
9.528 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) 0) into 0
9.528 * [backup-simplify]: Simplify 0 into 0
9.529 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))))
9.530 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))))
9.531 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
9.532 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))))
9.533 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))))
9.535 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
9.537 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))))
9.537 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))))
9.540 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log (* 2 PI))))))) (pow (/ 1 k) 3)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log (* 2 PI))))))) (pow (/ 1 k) 2)) (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log (* 2 PI))))))) (/ 1 k)))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) k)) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (pow k 2))))))))
9.540 * [backup-simplify]: Simplify (/ (pow (* 2 PI) (* (- 1 (/ 1 (- k))) 1/2)) (sqrt (/ 1 (- k)))) into (/ (pow (* 2 PI) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k)))
9.540 * [approximate]: Taking taylor expansion of (/ (pow (* 2 PI) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in (k) around 0
9.540 * [taylor]: Taking taylor expansion of (/ (pow (* 2 PI) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in k
9.540 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (* 1/2 (+ (/ 1 k) 1))) in k
9.540 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* 2 PI)))) in k
9.540 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* 2 PI))) in k
9.540 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
9.540 * [taylor]: Taking taylor expansion of 1/2 in k
9.540 * [backup-simplify]: Simplify 1/2 into 1/2
9.540 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
9.540 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.540 * [taylor]: Taking taylor expansion of k in k
9.540 * [backup-simplify]: Simplify 0 into 0
9.540 * [backup-simplify]: Simplify 1 into 1
9.540 * [backup-simplify]: Simplify (/ 1 1) into 1
9.540 * [taylor]: Taking taylor expansion of 1 in k
9.540 * [backup-simplify]: Simplify 1 into 1
9.541 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
9.541 * [taylor]: Taking taylor expansion of (* 2 PI) in k
9.541 * [taylor]: Taking taylor expansion of 2 in k
9.541 * [backup-simplify]: Simplify 2 into 2
9.541 * [taylor]: Taking taylor expansion of PI in k
9.541 * [backup-simplify]: Simplify PI into PI
9.541 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.541 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.542 * [backup-simplify]: Simplify (+ 1 0) into 1
9.542 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
9.543 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI)))
9.544 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* 2 PI)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))
9.544 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
9.544 * [taylor]: Taking taylor expansion of (/ -1 k) in k
9.544 * [taylor]: Taking taylor expansion of -1 in k
9.544 * [backup-simplify]: Simplify -1 into -1
9.544 * [taylor]: Taking taylor expansion of k in k
9.544 * [backup-simplify]: Simplify 0 into 0
9.544 * [backup-simplify]: Simplify 1 into 1
9.544 * [backup-simplify]: Simplify (/ -1 1) into -1
9.544 * [backup-simplify]: Simplify (sqrt 0) into 0
9.545 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
9.546 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))))
9.546 * [taylor]: Taking taylor expansion of (/ (pow (* 2 PI) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in k
9.546 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (* 1/2 (+ (/ 1 k) 1))) in k
9.546 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* 2 PI)))) in k
9.546 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* 2 PI))) in k
9.546 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
9.546 * [taylor]: Taking taylor expansion of 1/2 in k
9.546 * [backup-simplify]: Simplify 1/2 into 1/2
9.546 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
9.546 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.546 * [taylor]: Taking taylor expansion of k in k
9.546 * [backup-simplify]: Simplify 0 into 0
9.546 * [backup-simplify]: Simplify 1 into 1
9.546 * [backup-simplify]: Simplify (/ 1 1) into 1
9.546 * [taylor]: Taking taylor expansion of 1 in k
9.546 * [backup-simplify]: Simplify 1 into 1
9.546 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
9.546 * [taylor]: Taking taylor expansion of (* 2 PI) in k
9.546 * [taylor]: Taking taylor expansion of 2 in k
9.546 * [backup-simplify]: Simplify 2 into 2
9.546 * [taylor]: Taking taylor expansion of PI in k
9.546 * [backup-simplify]: Simplify PI into PI
9.547 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.547 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.547 * [backup-simplify]: Simplify (+ 1 0) into 1
9.548 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
9.549 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI)))
9.549 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* 2 PI)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))
9.549 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
9.549 * [taylor]: Taking taylor expansion of (/ -1 k) in k
9.549 * [taylor]: Taking taylor expansion of -1 in k
9.549 * [backup-simplify]: Simplify -1 into -1
9.549 * [taylor]: Taking taylor expansion of k in k
9.549 * [backup-simplify]: Simplify 0 into 0
9.549 * [backup-simplify]: Simplify 1 into 1
9.550 * [backup-simplify]: Simplify (/ -1 1) into -1
9.550 * [backup-simplify]: Simplify (sqrt 0) into 0
9.551 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
9.551 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))))
9.552 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))))
9.553 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
9.556 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
9.558 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))))
9.559 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))))
9.560 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.564 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
9.568 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))))
9.569 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))))
9.573 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (log (* 2 PI))))))) (pow (/ 1 (- k)) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (log (* 2 PI))))))) (/ 1 (- k))) (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (log (* 2 PI)))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))))))))
9.573 * * * * [progress]: [ 4 / 4 ] generating series at (2)
9.574 * [backup-simplify]: Simplify (* (pow n (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))) into (* (sqrt (/ 1 k)) (* (pow (* 2 PI) (* 1/2 (- 1 k))) (pow n (* 1/2 (- 1 k)))))
9.574 * [approximate]: Taking taylor expansion of (* (sqrt (/ 1 k)) (* (pow (* 2 PI) (* 1/2 (- 1 k))) (pow n (* 1/2 (- 1 k))))) in (n k) around 0
9.574 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (* (pow (* 2 PI) (* 1/2 (- 1 k))) (pow n (* 1/2 (- 1 k))))) in k
9.574 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
9.574 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.574 * [taylor]: Taking taylor expansion of k in k
9.574 * [backup-simplify]: Simplify 0 into 0
9.574 * [backup-simplify]: Simplify 1 into 1
9.574 * [backup-simplify]: Simplify (/ 1 1) into 1
9.575 * [backup-simplify]: Simplify (sqrt 0) into 0
9.576 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
9.576 * [taylor]: Taking taylor expansion of (* (pow (* 2 PI) (* 1/2 (- 1 k))) (pow n (* 1/2 (- 1 k)))) in k
9.576 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (* 1/2 (- 1 k))) in k
9.576 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 PI)))) in k
9.576 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 PI))) in k
9.576 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
9.576 * [taylor]: Taking taylor expansion of 1/2 in k
9.576 * [backup-simplify]: Simplify 1/2 into 1/2
9.576 * [taylor]: Taking taylor expansion of (- 1 k) in k
9.576 * [taylor]: Taking taylor expansion of 1 in k
9.576 * [backup-simplify]: Simplify 1 into 1
9.576 * [taylor]: Taking taylor expansion of k in k
9.576 * [backup-simplify]: Simplify 0 into 0
9.576 * [backup-simplify]: Simplify 1 into 1
9.576 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
9.576 * [taylor]: Taking taylor expansion of (* 2 PI) in k
9.576 * [taylor]: Taking taylor expansion of 2 in k
9.576 * [backup-simplify]: Simplify 2 into 2
9.576 * [taylor]: Taking taylor expansion of PI in k
9.576 * [backup-simplify]: Simplify PI into PI
9.577 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.578 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.578 * [backup-simplify]: Simplify (- 0) into 0
9.579 * [backup-simplify]: Simplify (+ 1 0) into 1
9.579 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
9.581 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI)))
9.583 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 PI)))) into (pow (* 2 PI) 1/2)
9.583 * [taylor]: Taking taylor expansion of (pow n (* 1/2 (- 1 k))) in k
9.583 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log n))) in k
9.583 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log n)) in k
9.583 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
9.583 * [taylor]: Taking taylor expansion of 1/2 in k
9.584 * [backup-simplify]: Simplify 1/2 into 1/2
9.584 * [taylor]: Taking taylor expansion of (- 1 k) in k
9.584 * [taylor]: Taking taylor expansion of 1 in k
9.584 * [backup-simplify]: Simplify 1 into 1
9.584 * [taylor]: Taking taylor expansion of k in k
9.584 * [backup-simplify]: Simplify 0 into 0
9.584 * [backup-simplify]: Simplify 1 into 1
9.584 * [taylor]: Taking taylor expansion of (log n) in k
9.584 * [taylor]: Taking taylor expansion of n in k
9.584 * [backup-simplify]: Simplify n into n
9.584 * [backup-simplify]: Simplify (log n) into (log n)
9.584 * [backup-simplify]: Simplify (- 0) into 0
9.585 * [backup-simplify]: Simplify (+ 1 0) into 1
9.585 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
9.585 * [backup-simplify]: Simplify (* 1/2 (log n)) into (* 1/2 (log n))
9.585 * [backup-simplify]: Simplify (exp (* 1/2 (log n))) into (pow n 1/2)
9.585 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (* (pow (* 2 PI) (* 1/2 (- 1 k))) (pow n (* 1/2 (- 1 k))))) in n
9.585 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
9.585 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.585 * [taylor]: Taking taylor expansion of k in n
9.585 * [backup-simplify]: Simplify k into k
9.585 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.585 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
9.586 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
9.586 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
9.586 * [taylor]: Taking taylor expansion of (* (pow (* 2 PI) (* 1/2 (- 1 k))) (pow n (* 1/2 (- 1 k)))) in n
9.586 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (* 1/2 (- 1 k))) in n
9.586 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 PI)))) in n
9.586 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 PI))) in n
9.586 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
9.586 * [taylor]: Taking taylor expansion of 1/2 in n
9.586 * [backup-simplify]: Simplify 1/2 into 1/2
9.586 * [taylor]: Taking taylor expansion of (- 1 k) in n
9.586 * [taylor]: Taking taylor expansion of 1 in n
9.586 * [backup-simplify]: Simplify 1 into 1
9.586 * [taylor]: Taking taylor expansion of k in n
9.586 * [backup-simplify]: Simplify k into k
9.586 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in n
9.586 * [taylor]: Taking taylor expansion of (* 2 PI) in n
9.586 * [taylor]: Taking taylor expansion of 2 in n
9.586 * [backup-simplify]: Simplify 2 into 2
9.586 * [taylor]: Taking taylor expansion of PI in n
9.586 * [backup-simplify]: Simplify PI into PI
9.587 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.588 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.588 * [backup-simplify]: Simplify (- k) into (- k)
9.588 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
9.588 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
9.589 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (log (* 2 PI))) into (* 1/2 (* (- 1 k) (log (* 2 PI))))
9.590 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) into (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))
9.590 * [taylor]: Taking taylor expansion of (pow n (* 1/2 (- 1 k))) in n
9.590 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log n))) in n
9.590 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log n)) in n
9.590 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
9.590 * [taylor]: Taking taylor expansion of 1/2 in n
9.590 * [backup-simplify]: Simplify 1/2 into 1/2
9.590 * [taylor]: Taking taylor expansion of (- 1 k) in n
9.590 * [taylor]: Taking taylor expansion of 1 in n
9.590 * [backup-simplify]: Simplify 1 into 1
9.590 * [taylor]: Taking taylor expansion of k in n
9.590 * [backup-simplify]: Simplify k into k
9.590 * [taylor]: Taking taylor expansion of (log n) in n
9.590 * [taylor]: Taking taylor expansion of n in n
9.590 * [backup-simplify]: Simplify 0 into 0
9.590 * [backup-simplify]: Simplify 1 into 1
9.591 * [backup-simplify]: Simplify (log 1) into 0
9.591 * [backup-simplify]: Simplify (- k) into (- k)
9.591 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
9.591 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
9.591 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
9.592 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (log n)) into (* 1/2 (* (- 1 k) (log n)))
9.592 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (log n)))) into (exp (* 1/2 (* (- 1 k) (log n))))
9.592 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (* (pow (* 2 PI) (* 1/2 (- 1 k))) (pow n (* 1/2 (- 1 k))))) in n
9.592 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
9.592 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.592 * [taylor]: Taking taylor expansion of k in n
9.592 * [backup-simplify]: Simplify k into k
9.592 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.592 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
9.592 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
9.592 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
9.592 * [taylor]: Taking taylor expansion of (* (pow (* 2 PI) (* 1/2 (- 1 k))) (pow n (* 1/2 (- 1 k)))) in n
9.592 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (* 1/2 (- 1 k))) in n
9.592 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 PI)))) in n
9.592 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 PI))) in n
9.592 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
9.592 * [taylor]: Taking taylor expansion of 1/2 in n
9.592 * [backup-simplify]: Simplify 1/2 into 1/2
9.592 * [taylor]: Taking taylor expansion of (- 1 k) in n
9.593 * [taylor]: Taking taylor expansion of 1 in n
9.593 * [backup-simplify]: Simplify 1 into 1
9.593 * [taylor]: Taking taylor expansion of k in n
9.593 * [backup-simplify]: Simplify k into k
9.593 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in n
9.593 * [taylor]: Taking taylor expansion of (* 2 PI) in n
9.593 * [taylor]: Taking taylor expansion of 2 in n
9.593 * [backup-simplify]: Simplify 2 into 2
9.593 * [taylor]: Taking taylor expansion of PI in n
9.593 * [backup-simplify]: Simplify PI into PI
9.593 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.594 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.594 * [backup-simplify]: Simplify (- k) into (- k)
9.594 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
9.594 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
9.595 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (log (* 2 PI))) into (* 1/2 (* (- 1 k) (log (* 2 PI))))
9.596 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) into (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))
9.596 * [taylor]: Taking taylor expansion of (pow n (* 1/2 (- 1 k))) in n
9.596 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log n))) in n
9.596 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log n)) in n
9.597 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
9.597 * [taylor]: Taking taylor expansion of 1/2 in n
9.597 * [backup-simplify]: Simplify 1/2 into 1/2
9.597 * [taylor]: Taking taylor expansion of (- 1 k) in n
9.597 * [taylor]: Taking taylor expansion of 1 in n
9.597 * [backup-simplify]: Simplify 1 into 1
9.597 * [taylor]: Taking taylor expansion of k in n
9.597 * [backup-simplify]: Simplify k into k
9.597 * [taylor]: Taking taylor expansion of (log n) in n
9.597 * [taylor]: Taking taylor expansion of n in n
9.597 * [backup-simplify]: Simplify 0 into 0
9.597 * [backup-simplify]: Simplify 1 into 1
9.597 * [backup-simplify]: Simplify (log 1) into 0
9.597 * [backup-simplify]: Simplify (- k) into (- k)
9.597 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
9.597 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
9.598 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
9.598 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (log n)) into (* 1/2 (* (- 1 k) (log n)))
9.598 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (log n)))) into (exp (* 1/2 (* (- 1 k) (log n))))
9.599 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (exp (* 1/2 (* (- 1 k) (log n))))) into (* (exp (* 1/2 (* (- 1 k) (log n)))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))))
9.600 * [backup-simplify]: Simplify (* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (- 1 k) (log n)))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))))) into (* (* (exp (* 1/2 (* (- 1 k) (log n)))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) (sqrt (/ 1 k)))
9.600 * [taylor]: Taking taylor expansion of (* (* (exp (* 1/2 (* (- 1 k) (log n)))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) (sqrt (/ 1 k))) in k
9.600 * [taylor]: Taking taylor expansion of (* (exp (* 1/2 (* (- 1 k) (log n)))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) in k
9.601 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (log n)))) in k
9.601 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 k) (log n))) in k
9.601 * [taylor]: Taking taylor expansion of 1/2 in k
9.601 * [backup-simplify]: Simplify 1/2 into 1/2
9.601 * [taylor]: Taking taylor expansion of (* (- 1 k) (log n)) in k
9.601 * [taylor]: Taking taylor expansion of (- 1 k) in k
9.601 * [taylor]: Taking taylor expansion of 1 in k
9.601 * [backup-simplify]: Simplify 1 into 1
9.601 * [taylor]: Taking taylor expansion of k in k
9.601 * [backup-simplify]: Simplify 0 into 0
9.601 * [backup-simplify]: Simplify 1 into 1
9.601 * [taylor]: Taking taylor expansion of (log n) in k
9.601 * [taylor]: Taking taylor expansion of n in k
9.601 * [backup-simplify]: Simplify n into n
9.601 * [backup-simplify]: Simplify (log n) into (log n)
9.601 * [backup-simplify]: Simplify (- 0) into 0
9.602 * [backup-simplify]: Simplify (+ 1 0) into 1
9.602 * [backup-simplify]: Simplify (* 1 (log n)) into (log n)
9.602 * [backup-simplify]: Simplify (* 1/2 (log n)) into (* 1/2 (log n))
9.602 * [backup-simplify]: Simplify (exp (* 1/2 (log n))) into (pow n 1/2)
9.602 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) in k
9.602 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 k) (log (* 2 PI)))) in k
9.602 * [taylor]: Taking taylor expansion of 1/2 in k
9.602 * [backup-simplify]: Simplify 1/2 into 1/2
9.602 * [taylor]: Taking taylor expansion of (* (- 1 k) (log (* 2 PI))) in k
9.602 * [taylor]: Taking taylor expansion of (- 1 k) in k
9.602 * [taylor]: Taking taylor expansion of 1 in k
9.602 * [backup-simplify]: Simplify 1 into 1
9.602 * [taylor]: Taking taylor expansion of k in k
9.602 * [backup-simplify]: Simplify 0 into 0
9.602 * [backup-simplify]: Simplify 1 into 1
9.602 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
9.602 * [taylor]: Taking taylor expansion of (* 2 PI) in k
9.602 * [taylor]: Taking taylor expansion of 2 in k
9.602 * [backup-simplify]: Simplify 2 into 2
9.602 * [taylor]: Taking taylor expansion of PI in k
9.602 * [backup-simplify]: Simplify PI into PI
9.603 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.604 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.604 * [backup-simplify]: Simplify (- 0) into 0
9.605 * [backup-simplify]: Simplify (+ 1 0) into 1
9.606 * [backup-simplify]: Simplify (* 1 (log (* 2 PI))) into (log (* 2 PI))
9.608 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI)))
9.610 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 PI)))) into (pow (* 2 PI) 1/2)
9.610 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
9.610 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.610 * [taylor]: Taking taylor expansion of k in k
9.610 * [backup-simplify]: Simplify 0 into 0
9.610 * [backup-simplify]: Simplify 1 into 1
9.611 * [backup-simplify]: Simplify (/ 1 1) into 1
9.611 * [backup-simplify]: Simplify (sqrt 0) into 0
9.613 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
9.614 * [backup-simplify]: Simplify (* (pow n 1/2) (pow (* 2 PI) 1/2)) into (sqrt (* PI (* n 2)))
9.614 * [backup-simplify]: Simplify (* (sqrt (* PI (* n 2))) 0) into 0
9.614 * [backup-simplify]: Simplify 0 into 0
9.615 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0
9.616 * [backup-simplify]: Simplify (- 0) into 0
9.616 * [backup-simplify]: Simplify (+ 0 0) into 0
9.617 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 k))) into 0
9.617 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
9.617 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (log n))) into 0
9.618 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
9.619 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
9.620 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
9.621 * [backup-simplify]: Simplify (- 0) into 0
9.621 * [backup-simplify]: Simplify (+ 0 0) into 0
9.622 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 k))) into 0
9.622 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (log (* 2 PI)))) into 0
9.624 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
9.631 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) 0) (* 0 (exp (* 1/2 (* (- 1 k) (log n)))))) into 0
9.632 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (* 0 (* (exp (* 1/2 (* (- 1 k) (log n)))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))))) into 0
9.632 * [taylor]: Taking taylor expansion of 0 in k
9.632 * [backup-simplify]: Simplify 0 into 0
9.633 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
9.635 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
9.635 * [backup-simplify]: Simplify (- 1) into -1
9.636 * [backup-simplify]: Simplify (+ 0 -1) into -1
9.641 * [backup-simplify]: Simplify (+ (* 1 0) (* -1 (log (* 2 PI)))) into (- (log (* 2 PI)))
9.645 * [backup-simplify]: Simplify (+ (* 1/2 (- (log (* 2 PI)))) (* 0 (log (* 2 PI)))) into (- (* 1/2 (log (* 2 PI))))
9.653 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 1) 1)))) into (* -1/2 (* (sqrt (* PI 2)) (log (* 2 PI))))
9.653 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
9.654 * [backup-simplify]: Simplify (- 1) into -1
9.654 * [backup-simplify]: Simplify (+ 0 -1) into -1
9.654 * [backup-simplify]: Simplify (+ (* 1 0) (* -1 (log n))) into (- (log n))
9.654 * [backup-simplify]: Simplify (+ (* 1/2 (- (log n))) (* 0 (log n))) into (- (* 1/2 (log n)))
9.654 * [backup-simplify]: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 1) 1)))) into (* -1/2 (* (sqrt n) (log n)))
9.658 * [backup-simplify]: Simplify (+ (* (pow n 1/2) (* -1/2 (* (sqrt (* PI 2)) (log (* 2 PI))))) (* (* -1/2 (* (sqrt n) (log n))) (pow (* 2 PI) 1/2))) into (- (+ (* 1/2 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (* 1/2 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))))
9.659 * [backup-simplify]: Simplify (+ (* (sqrt (* PI (* n 2))) +nan.0) (* (- (+ (* 1/2 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (* 1/2 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))))) 0)) into (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))
9.660 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) into (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))
9.661 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0
9.661 * [backup-simplify]: Simplify (- 0) into 0
9.662 * [backup-simplify]: Simplify (+ 0 0) into 0
9.662 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0
9.662 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
9.663 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (log n)))) into 0
9.664 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
9.664 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
9.666 * [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
9.666 * [backup-simplify]: Simplify (- 0) into 0
9.666 * [backup-simplify]: Simplify (+ 0 0) into 0
9.667 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0
9.667 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (log (* 2 PI))))) into 0
9.669 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
9.670 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (- 1 k) (log n))))))) into 0
9.670 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
9.670 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0
9.671 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (* 0 (* (exp (* 1/2 (* (- 1 k) (log n)))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))))))) into 0
9.671 * [taylor]: Taking taylor expansion of 0 in k
9.671 * [backup-simplify]: Simplify 0 into 0
9.671 * [backup-simplify]: Simplify 0 into 0
9.672 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
9.674 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
9.674 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
9.676 * [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
9.676 * [backup-simplify]: Simplify (- 0) into 0
9.677 * [backup-simplify]: Simplify (+ 0 0) into 0
9.678 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (log (* 2 PI))))) into 0
9.678 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (log (* 2 PI)))) (* 0 (log (* 2 PI))))) into 0
9.686 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 2)))
9.687 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
9.687 * [backup-simplify]: Simplify (- 0) into 0
9.688 * [backup-simplify]: Simplify (+ 0 0) into 0
9.688 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (log n)))) into 0
9.688 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (log n))) (* 0 (log n)))) into 0
9.689 * [backup-simplify]: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt n) (pow (log n) 2)))
9.695 * [backup-simplify]: Simplify (+ (* (pow n 1/2) (* 1/8 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 2)))) (+ (* (* -1/2 (* (sqrt n) (log n))) (* -1/2 (* (sqrt (* PI 2)) (log (* 2 PI))))) (* (* 1/8 (* (sqrt n) (pow (log n) 2))) (pow (* 2 PI) 1/2)))) into (+ (* 1/8 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (+ (* 1/8 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt (* n PI)))) (* 1/4 (* (* (sqrt 2) (* (log n) (log (* 2 PI)))) (sqrt (* n PI))))))
9.700 * [backup-simplify]: Simplify (+ (* (sqrt (* PI (* n 2))) +nan.0) (+ (* (- (+ (* 1/2 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (* 1/2 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))))) +nan.0) (* (+ (* 1/8 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (+ (* 1/8 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt (* n PI)))) (* 1/4 (* (* (sqrt 2) (* (log n) (log (* 2 PI)))) (sqrt (* n PI)))))) 0))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))))))))
9.702 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))))))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))))))))
9.705 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0
9.705 * [backup-simplify]: Simplify (- 0) into 0
9.706 * [backup-simplify]: Simplify (+ 0 0) into 0
9.706 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 k))))) into 0
9.707 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
9.707 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n))))) into 0
9.708 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
9.709 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
9.712 * [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
9.712 * [backup-simplify]: Simplify (- 0) into 0
9.712 * [backup-simplify]: Simplify (+ 0 0) into 0
9.713 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 k))))) into 0
9.714 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log (* 2 PI)))))) into 0
9.715 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
9.721 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (- 1 k) (log n)))))))) into 0
9.721 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
9.722 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0
9.723 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (exp (* 1/2 (* (- 1 k) (log n)))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))))))) into 0
9.723 * [taylor]: Taking taylor expansion of 0 in k
9.723 * [backup-simplify]: Simplify 0 into 0
9.723 * [backup-simplify]: Simplify 0 into 0
9.723 * [backup-simplify]: Simplify 0 into 0
9.724 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.726 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
9.727 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
9.730 * [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
9.730 * [backup-simplify]: Simplify (- 0) into 0
9.730 * [backup-simplify]: Simplify (+ 0 0) into 0
9.731 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (+ (* 0 0) (* 0 (log (* 2 PI)))))) into 0
9.733 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 (- (log (* 2 PI)))) (* 0 (log (* 2 PI)))))) into 0
9.743 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 3) 6)) (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 3)))
9.745 * [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
9.745 * [backup-simplify]: Simplify (- 0) into 0
9.745 * [backup-simplify]: Simplify (+ 0 0) into 0
9.746 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (+ (* 0 0) (* 0 (log n))))) into 0
9.746 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 (- (log n))) (* 0 (log n))))) into 0
9.747 * [backup-simplify]: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 3) 6)) (* (/ (pow (- (* 1/2 (log n))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (sqrt n) (pow (log n) 3)))
9.760 * [backup-simplify]: Simplify (+ (* (pow n 1/2) (* -1/48 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 3)))) (+ (* (* -1/2 (* (sqrt n) (log n))) (* 1/8 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 2)))) (+ (* (* 1/8 (* (sqrt n) (pow (log n) 2))) (* -1/2 (* (sqrt (* PI 2)) (log (* 2 PI))))) (* (* -1/48 (* (sqrt n) (pow (log n) 3))) (pow (* 2 PI) 1/2))))) into (- (+ (* 1/48 (* (* (sqrt 2) (pow (log n) 3)) (sqrt (* n PI)))) (+ (* 1/16 (* (* (sqrt 2) (* (log n) (pow (log (* 2 PI)) 2))) (sqrt (* n PI)))) (+ (* 1/16 (* (* (sqrt 2) (* (pow (log n) 2) (log (* 2 PI)))) (sqrt (* n PI)))) (* 1/48 (* (* (sqrt 2) (pow (log (* 2 PI)) 3)) (sqrt (* n PI))))))))
9.779 * [backup-simplify]: Simplify (+ (* (sqrt (* PI (* n 2))) +nan.0) (+ (* (- (+ (* 1/2 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (* 1/2 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))))) +nan.0) (+ (* (+ (* 1/8 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (+ (* 1/8 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt (* n PI)))) (* 1/4 (* (* (sqrt 2) (* (log n) (log (* 2 PI)))) (sqrt (* n PI)))))) +nan.0) (* (- (+ (* 1/48 (* (* (sqrt 2) (pow (log n) 3)) (sqrt (* n PI)))) (+ (* 1/16 (* (* (sqrt 2) (* (log n) (pow (log (* 2 PI)) 2))) (sqrt (* n PI)))) (+ (* 1/16 (* (* (sqrt 2) (* (pow (log n) 2) (log (* 2 PI)))) (sqrt (* n PI)))) (* 1/48 (* (* (sqrt 2) (pow (log (* 2 PI)) 3)) (sqrt (* n PI)))))))) 0)))) into (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (* (log n) (log (* 2 PI)))) (sqrt (* n PI)))))))))))))))
9.788 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (* (log n) (log (* 2 PI)))) (sqrt (* n PI))))))))))))))) into (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (* (log n) (log (* 2 PI)))) (sqrt (* n PI)))))))))))))))
9.797 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (* (log n) (log (* 2 PI)))) (sqrt (* n PI))))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))))))) (* k 1)) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) into (- (+ (* +nan.0 (* (* (sqrt 2) (pow k 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) k) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (pow (log (* 2 PI)) 2) (* (sqrt 2) (pow k 2))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (pow (log n) 2) (pow k 2))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log n) k)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log n) (pow k 2))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log (* 2 PI)) (* (sqrt 2) (* (log n) (pow k 2)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* k (log (* 2 PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (* (log (* 2 PI)) (* (sqrt 2) (pow k 2))) (sqrt (* n PI)))))))))))))))))))))))
9.798 * [backup-simplify]: Simplify (* (pow (/ 1 n) (* (- 1 (/ 1 k)) 1/2)) (/ (pow (* 2 PI) (* (- 1 (/ 1 k)) 1/2)) (sqrt (/ 1 k)))) into (* (* (pow (/ 1 n) (* 1/2 (- 1 (/ 1 k)))) (pow (* 2 PI) (* 1/2 (- 1 (/ 1 k))))) (sqrt k))
9.798 * [approximate]: Taking taylor expansion of (* (* (pow (/ 1 n) (* 1/2 (- 1 (/ 1 k)))) (pow (* 2 PI) (* 1/2 (- 1 (/ 1 k))))) (sqrt k)) in (n k) around 0
9.798 * [taylor]: Taking taylor expansion of (* (* (pow (/ 1 n) (* 1/2 (- 1 (/ 1 k)))) (pow (* 2 PI) (* 1/2 (- 1 (/ 1 k))))) (sqrt k)) in k
9.798 * [taylor]: Taking taylor expansion of (* (pow (/ 1 n) (* 1/2 (- 1 (/ 1 k)))) (pow (* 2 PI) (* 1/2 (- 1 (/ 1 k))))) in k
9.798 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (* 1/2 (- 1 (/ 1 k)))) in k
9.798 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (/ 1 n)))) in k
9.798 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (/ 1 n))) in k
9.798 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
9.798 * [taylor]: Taking taylor expansion of 1/2 in k
9.798 * [backup-simplify]: Simplify 1/2 into 1/2
9.798 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
9.798 * [taylor]: Taking taylor expansion of 1 in k
9.798 * [backup-simplify]: Simplify 1 into 1
9.798 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.798 * [taylor]: Taking taylor expansion of k in k
9.798 * [backup-simplify]: Simplify 0 into 0
9.798 * [backup-simplify]: Simplify 1 into 1
9.799 * [backup-simplify]: Simplify (/ 1 1) into 1
9.799 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in k
9.799 * [taylor]: Taking taylor expansion of (/ 1 n) in k
9.799 * [taylor]: Taking taylor expansion of n in k
9.799 * [backup-simplify]: Simplify n into n
9.799 * [backup-simplify]: Simplify (/ 1 n) into (/ 1 n)
9.799 * [backup-simplify]: Simplify (log (/ 1 n)) into (log (/ 1 n))
9.799 * [backup-simplify]: Simplify (- 1) into -1
9.799 * [backup-simplify]: Simplify (+ 0 -1) into -1
9.800 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
9.800 * [backup-simplify]: Simplify (* -1/2 (log (/ 1 n))) into (* -1/2 (log (/ 1 n)))
9.800 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (/ 1 n)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (/ 1 n)))))
9.800 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (* 1/2 (- 1 (/ 1 k)))) in k
9.800 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 PI)))) in k
9.800 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 PI))) in k
9.800 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
9.800 * [taylor]: Taking taylor expansion of 1/2 in k
9.800 * [backup-simplify]: Simplify 1/2 into 1/2
9.800 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
9.800 * [taylor]: Taking taylor expansion of 1 in k
9.800 * [backup-simplify]: Simplify 1 into 1
9.800 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.800 * [taylor]: Taking taylor expansion of k in k
9.800 * [backup-simplify]: Simplify 0 into 0
9.800 * [backup-simplify]: Simplify 1 into 1
9.800 * [backup-simplify]: Simplify (/ 1 1) into 1
9.800 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
9.800 * [taylor]: Taking taylor expansion of (* 2 PI) in k
9.800 * [taylor]: Taking taylor expansion of 2 in k
9.800 * [backup-simplify]: Simplify 2 into 2
9.800 * [taylor]: Taking taylor expansion of PI in k
9.800 * [backup-simplify]: Simplify PI into PI
9.801 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.801 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.802 * [backup-simplify]: Simplify (- 1) into -1
9.802 * [backup-simplify]: Simplify (+ 0 -1) into -1
9.802 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
9.803 * [backup-simplify]: Simplify (* -1/2 (log (* 2 PI))) into (* -1/2 (log (* 2 PI)))
9.804 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 PI)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))
9.804 * [taylor]: Taking taylor expansion of (sqrt k) in k
9.804 * [taylor]: Taking taylor expansion of k in k
9.804 * [backup-simplify]: Simplify 0 into 0
9.804 * [backup-simplify]: Simplify 1 into 1
9.804 * [backup-simplify]: Simplify (sqrt 0) into 0
9.806 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
9.806 * [taylor]: Taking taylor expansion of (* (* (pow (/ 1 n) (* 1/2 (- 1 (/ 1 k)))) (pow (* 2 PI) (* 1/2 (- 1 (/ 1 k))))) (sqrt k)) in n
9.806 * [taylor]: Taking taylor expansion of (* (pow (/ 1 n) (* 1/2 (- 1 (/ 1 k)))) (pow (* 2 PI) (* 1/2 (- 1 (/ 1 k))))) in n
9.806 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (* 1/2 (- 1 (/ 1 k)))) in n
9.806 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (/ 1 n)))) in n
9.806 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (/ 1 n))) in n
9.806 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
9.806 * [taylor]: Taking taylor expansion of 1/2 in n
9.806 * [backup-simplify]: Simplify 1/2 into 1/2
9.806 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
9.806 * [taylor]: Taking taylor expansion of 1 in n
9.806 * [backup-simplify]: Simplify 1 into 1
9.806 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.806 * [taylor]: Taking taylor expansion of k in n
9.806 * [backup-simplify]: Simplify k into k
9.806 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.806 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n
9.806 * [taylor]: Taking taylor expansion of (/ 1 n) in n
9.806 * [taylor]: Taking taylor expansion of n in n
9.806 * [backup-simplify]: Simplify 0 into 0
9.806 * [backup-simplify]: Simplify 1 into 1
9.806 * [backup-simplify]: Simplify (/ 1 1) into 1
9.806 * [backup-simplify]: Simplify (log 1) into 0
9.806 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
9.807 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
9.807 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
9.807 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n))
9.807 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log n))) into (* -1/2 (* (- 1 (/ 1 k)) (log n)))
9.807 * [backup-simplify]: Simplify (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) into (exp (* -1/2 (* (- 1 (/ 1 k)) (log n))))
9.807 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (* 1/2 (- 1 (/ 1 k)))) in n
9.807 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 PI)))) in n
9.807 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 PI))) in n
9.807 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
9.807 * [taylor]: Taking taylor expansion of 1/2 in n
9.807 * [backup-simplify]: Simplify 1/2 into 1/2
9.807 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
9.807 * [taylor]: Taking taylor expansion of 1 in n
9.807 * [backup-simplify]: Simplify 1 into 1
9.807 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.807 * [taylor]: Taking taylor expansion of k in n
9.807 * [backup-simplify]: Simplify k into k
9.807 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.807 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in n
9.807 * [taylor]: Taking taylor expansion of (* 2 PI) in n
9.807 * [taylor]: Taking taylor expansion of 2 in n
9.807 * [backup-simplify]: Simplify 2 into 2
9.807 * [taylor]: Taking taylor expansion of PI in n
9.807 * [backup-simplify]: Simplify PI into PI
9.808 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.808 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.808 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
9.808 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
9.808 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
9.809 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 PI))) into (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))
9.810 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))
9.810 * [taylor]: Taking taylor expansion of (sqrt k) in n
9.810 * [taylor]: Taking taylor expansion of k in n
9.810 * [backup-simplify]: Simplify k into k
9.810 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
9.810 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
9.810 * [taylor]: Taking taylor expansion of (* (* (pow (/ 1 n) (* 1/2 (- 1 (/ 1 k)))) (pow (* 2 PI) (* 1/2 (- 1 (/ 1 k))))) (sqrt k)) in n
9.810 * [taylor]: Taking taylor expansion of (* (pow (/ 1 n) (* 1/2 (- 1 (/ 1 k)))) (pow (* 2 PI) (* 1/2 (- 1 (/ 1 k))))) in n
9.810 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (* 1/2 (- 1 (/ 1 k)))) in n
9.810 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (/ 1 n)))) in n
9.810 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (/ 1 n))) in n
9.810 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
9.810 * [taylor]: Taking taylor expansion of 1/2 in n
9.810 * [backup-simplify]: Simplify 1/2 into 1/2
9.810 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
9.810 * [taylor]: Taking taylor expansion of 1 in n
9.810 * [backup-simplify]: Simplify 1 into 1
9.810 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.810 * [taylor]: Taking taylor expansion of k in n
9.810 * [backup-simplify]: Simplify k into k
9.810 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.810 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n
9.810 * [taylor]: Taking taylor expansion of (/ 1 n) in n
9.810 * [taylor]: Taking taylor expansion of n in n
9.810 * [backup-simplify]: Simplify 0 into 0
9.810 * [backup-simplify]: Simplify 1 into 1
9.811 * [backup-simplify]: Simplify (/ 1 1) into 1
9.811 * [backup-simplify]: Simplify (log 1) into 0
9.811 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
9.811 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
9.811 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
9.811 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n))
9.811 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log n))) into (* -1/2 (* (- 1 (/ 1 k)) (log n)))
9.811 * [backup-simplify]: Simplify (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) into (exp (* -1/2 (* (- 1 (/ 1 k)) (log n))))
9.811 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (* 1/2 (- 1 (/ 1 k)))) in n
9.811 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 PI)))) in n
9.811 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 PI))) in n
9.811 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
9.811 * [taylor]: Taking taylor expansion of 1/2 in n
9.812 * [backup-simplify]: Simplify 1/2 into 1/2
9.812 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
9.812 * [taylor]: Taking taylor expansion of 1 in n
9.812 * [backup-simplify]: Simplify 1 into 1
9.812 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.812 * [taylor]: Taking taylor expansion of k in n
9.812 * [backup-simplify]: Simplify k into k
9.812 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.812 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in n
9.812 * [taylor]: Taking taylor expansion of (* 2 PI) in n
9.812 * [taylor]: Taking taylor expansion of 2 in n
9.812 * [backup-simplify]: Simplify 2 into 2
9.812 * [taylor]: Taking taylor expansion of PI in n
9.812 * [backup-simplify]: Simplify PI into PI
9.812 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.818 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.818 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
9.819 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
9.819 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
9.820 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 PI))) into (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))
9.821 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))
9.821 * [taylor]: Taking taylor expansion of (sqrt k) in n
9.821 * [taylor]: Taking taylor expansion of k in n
9.821 * [backup-simplify]: Simplify k into k
9.821 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
9.822 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
9.823 * [backup-simplify]: Simplify (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) into (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))
9.824 * [backup-simplify]: Simplify (* (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) (sqrt k)) into (* (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) (sqrt k))
9.824 * [taylor]: Taking taylor expansion of (* (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) (sqrt k)) in k
9.824 * [taylor]: Taking taylor expansion of (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) in k
9.824 * [taylor]: Taking taylor expansion of (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) in k
9.824 * [taylor]: Taking taylor expansion of (* -1/2 (* (- 1 (/ 1 k)) (log n))) in k
9.824 * [taylor]: Taking taylor expansion of -1/2 in k
9.824 * [backup-simplify]: Simplify -1/2 into -1/2
9.824 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log n)) in k
9.824 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
9.824 * [taylor]: Taking taylor expansion of 1 in k
9.824 * [backup-simplify]: Simplify 1 into 1
9.824 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.824 * [taylor]: Taking taylor expansion of k in k
9.824 * [backup-simplify]: Simplify 0 into 0
9.824 * [backup-simplify]: Simplify 1 into 1
9.824 * [backup-simplify]: Simplify (/ 1 1) into 1
9.824 * [taylor]: Taking taylor expansion of (log n) in k
9.825 * [taylor]: Taking taylor expansion of n in k
9.825 * [backup-simplify]: Simplify n into n
9.825 * [backup-simplify]: Simplify (log n) into (log n)
9.825 * [backup-simplify]: Simplify (- 1) into -1
9.825 * [backup-simplify]: Simplify (+ 0 -1) into -1
9.825 * [backup-simplify]: Simplify (* -1 (log n)) into (* -1 (log n))
9.825 * [backup-simplify]: Simplify (* -1/2 (* -1 (log n))) into (* 1/2 (log n))
9.825 * [backup-simplify]: Simplify (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) into (exp (* -1/2 (* (- 1 (/ 1 k)) (log n))))
9.825 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) in k
9.825 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))) in k
9.825 * [taylor]: Taking taylor expansion of 1/2 in k
9.825 * [backup-simplify]: Simplify 1/2 into 1/2
9.825 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 PI))) in k
9.825 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
9.825 * [taylor]: Taking taylor expansion of 1 in k
9.825 * [backup-simplify]: Simplify 1 into 1
9.825 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.825 * [taylor]: Taking taylor expansion of k in k
9.825 * [backup-simplify]: Simplify 0 into 0
9.825 * [backup-simplify]: Simplify 1 into 1
9.826 * [backup-simplify]: Simplify (/ 1 1) into 1
9.826 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
9.826 * [taylor]: Taking taylor expansion of (* 2 PI) in k
9.826 * [taylor]: Taking taylor expansion of 2 in k
9.826 * [backup-simplify]: Simplify 2 into 2
9.826 * [taylor]: Taking taylor expansion of PI in k
9.826 * [backup-simplify]: Simplify PI into PI
9.826 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.827 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.827 * [backup-simplify]: Simplify (- 1) into -1
9.827 * [backup-simplify]: Simplify (+ 0 -1) into -1
9.828 * [backup-simplify]: Simplify (* -1 (log (* 2 PI))) into (* -1 (log (* 2 PI)))
9.830 * [backup-simplify]: Simplify (* 1/2 (* -1 (log (* 2 PI)))) into (* -1/2 (log (* 2 PI)))
9.830 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))
9.830 * [taylor]: Taking taylor expansion of (sqrt k) in k
9.830 * [taylor]: Taking taylor expansion of k in k
9.830 * [backup-simplify]: Simplify 0 into 0
9.830 * [backup-simplify]: Simplify 1 into 1
9.831 * [backup-simplify]: Simplify (sqrt 0) into 0
9.831 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
9.832 * [backup-simplify]: Simplify (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) into (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))
9.833 * [backup-simplify]: Simplify (* (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) 0) into 0
9.833 * [backup-simplify]: Simplify 0 into 0
9.833 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
9.834 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
9.835 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
9.835 * [backup-simplify]: Simplify (- 0) into 0
9.835 * [backup-simplify]: Simplify (+ 0 0) into 0
9.835 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 (/ 1 k)))) into 0
9.836 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (log (* 2 PI)))) into 0
9.837 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
9.837 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
9.838 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0
9.838 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
9.838 * [backup-simplify]: Simplify (- 0) into 0
9.839 * [backup-simplify]: Simplify (+ 0 0) into 0
9.839 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 (/ 1 k)))) into 0
9.839 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n))
9.839 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log n)))) into 0
9.840 * [backup-simplify]: Simplify (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
9.841 * [backup-simplify]: Simplify (+ (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) 0) (* 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))) into 0
9.841 * [backup-simplify]: Simplify (+ (* (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) 0) (* 0 (sqrt k))) into 0
9.841 * [taylor]: Taking taylor expansion of 0 in k
9.841 * [backup-simplify]: Simplify 0 into 0
9.841 * [backup-simplify]: Simplify 0 into 0
9.842 * [backup-simplify]: Simplify (+ (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) 0) (* 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))) into 0
9.843 * [backup-simplify]: Simplify (+ (* (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) +nan.0) (* 0 0)) into (- (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))))
9.844 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))))) into (- (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))))
9.844 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
9.845 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
9.847 * [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
9.847 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
9.847 * [backup-simplify]: Simplify (- 0) into 0
9.847 * [backup-simplify]: Simplify (+ 0 0) into 0
9.848 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0
9.849 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (log (* 2 PI))))) into 0
9.850 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
9.851 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.853 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0
9.853 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
9.853 * [backup-simplify]: Simplify (- 0) into 0
9.854 * [backup-simplify]: Simplify (+ 0 0) into 0
9.855 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0
9.855 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n))
9.855 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log n))))) into 0
9.857 * [backup-simplify]: Simplify (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
9.858 * [backup-simplify]: Simplify (+ (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))))) into 0
9.860 * [backup-simplify]: Simplify (+ (* (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) 0) (+ (* 0 0) (* 0 (sqrt k)))) into 0
9.860 * [taylor]: Taking taylor expansion of 0 in k
9.860 * [backup-simplify]: Simplify 0 into 0
9.860 * [backup-simplify]: Simplify 0 into 0
9.860 * [backup-simplify]: Simplify 0 into 0
9.863 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
9.865 * [backup-simplify]: Simplify (+ (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))))) into 0
9.866 * [backup-simplify]: Simplify (+ (* (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))))
9.868 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))))) into (- (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))))
9.869 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
9.870 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
9.875 * [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
9.876 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
9.876 * [backup-simplify]: Simplify (- 0) into 0
9.877 * [backup-simplify]: Simplify (+ 0 0) into 0
9.878 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0
9.879 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log (* 2 PI)))))) into 0
9.882 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
9.883 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.889 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0
9.889 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
9.889 * [backup-simplify]: Simplify (- 0) into 0
9.890 * [backup-simplify]: Simplify (+ 0 0) into 0
9.891 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0
9.892 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n))
9.892 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0
9.894 * [backup-simplify]: Simplify (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
9.896 * [backup-simplify]: Simplify (+ (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))))) into 0
9.898 * [backup-simplify]: Simplify (+ (* (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt k))))) into 0
9.898 * [taylor]: Taking taylor expansion of 0 in k
9.898 * [backup-simplify]: Simplify 0 into 0
9.898 * [backup-simplify]: Simplify 0 into 0
9.899 * [backup-simplify]: Simplify 0 into 0
9.899 * [backup-simplify]: Simplify 0 into 0
9.903 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
9.905 * [backup-simplify]: Simplify (+ (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))))) into 0
9.907 * [backup-simplify]: Simplify (+ (* (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))))
9.909 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))))) into (- (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))))
9.913 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 (/ 1 k))) (log (/ 1 n))))) (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log (* 2 PI)))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 (/ 1 k))) (log (/ 1 n))))) (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log (* 2 PI)))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 (/ 1 k))) (log (/ 1 n))))) (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log (* 2 PI)))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (* (exp (* -1/2 (* (- 1 k) (log (/ 1 n))))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) (pow k 2))) (- (+ (* +nan.0 (/ (* (exp (* -1/2 (* (- 1 k) (log (/ 1 n))))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) k)) (- (* +nan.0 (/ (* (exp (* -1/2 (* (- 1 k) (log (/ 1 n))))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) (pow k 3))))))))
9.914 * [backup-simplify]: Simplify (* (pow (/ 1 (- n)) (* (- 1 (/ 1 (- k))) 1/2)) (/ (pow (* 2 PI) (* (- 1 (/ 1 (- k))) 1/2)) (sqrt (/ 1 (- k))))) into (/ (* (pow (/ -1 n) (* 1/2 (+ (/ 1 k) 1))) (pow (* 2 PI) (* 1/2 (+ (/ 1 k) 1)))) (sqrt (/ -1 k)))
9.914 * [approximate]: Taking taylor expansion of (/ (* (pow (/ -1 n) (* 1/2 (+ (/ 1 k) 1))) (pow (* 2 PI) (* 1/2 (+ (/ 1 k) 1)))) (sqrt (/ -1 k))) in (n k) around 0
9.914 * [taylor]: Taking taylor expansion of (/ (* (pow (/ -1 n) (* 1/2 (+ (/ 1 k) 1))) (pow (* 2 PI) (* 1/2 (+ (/ 1 k) 1)))) (sqrt (/ -1 k))) in k
9.914 * [taylor]: Taking taylor expansion of (* (pow (/ -1 n) (* 1/2 (+ (/ 1 k) 1))) (pow (* 2 PI) (* 1/2 (+ (/ 1 k) 1)))) in k
9.914 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (* 1/2 (+ (/ 1 k) 1))) in k
9.914 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (/ -1 n)))) in k
9.914 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (/ -1 n))) in k
9.914 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
9.914 * [taylor]: Taking taylor expansion of 1/2 in k
9.914 * [backup-simplify]: Simplify 1/2 into 1/2
9.914 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
9.914 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.914 * [taylor]: Taking taylor expansion of k in k
9.915 * [backup-simplify]: Simplify 0 into 0
9.915 * [backup-simplify]: Simplify 1 into 1
9.915 * [backup-simplify]: Simplify (/ 1 1) into 1
9.915 * [taylor]: Taking taylor expansion of 1 in k
9.915 * [backup-simplify]: Simplify 1 into 1
9.915 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in k
9.915 * [taylor]: Taking taylor expansion of (/ -1 n) in k
9.915 * [taylor]: Taking taylor expansion of -1 in k
9.915 * [backup-simplify]: Simplify -1 into -1
9.915 * [taylor]: Taking taylor expansion of n in k
9.915 * [backup-simplify]: Simplify n into n
9.915 * [backup-simplify]: Simplify (/ -1 n) into (/ -1 n)
9.915 * [backup-simplify]: Simplify (log (/ -1 n)) into (log (/ -1 n))
9.916 * [backup-simplify]: Simplify (+ 1 0) into 1
9.916 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
9.916 * [backup-simplify]: Simplify (* 1/2 (log (/ -1 n))) into (* 1/2 (log (/ -1 n)))
9.916 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (/ -1 n)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (/ -1 n)))))
9.916 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (* 1/2 (+ (/ 1 k) 1))) in k
9.917 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* 2 PI)))) in k
9.917 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* 2 PI))) in k
9.917 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
9.917 * [taylor]: Taking taylor expansion of 1/2 in k
9.917 * [backup-simplify]: Simplify 1/2 into 1/2
9.917 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
9.917 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.917 * [taylor]: Taking taylor expansion of k in k
9.917 * [backup-simplify]: Simplify 0 into 0
9.917 * [backup-simplify]: Simplify 1 into 1
9.917 * [backup-simplify]: Simplify (/ 1 1) into 1
9.917 * [taylor]: Taking taylor expansion of 1 in k
9.917 * [backup-simplify]: Simplify 1 into 1
9.917 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
9.917 * [taylor]: Taking taylor expansion of (* 2 PI) in k
9.917 * [taylor]: Taking taylor expansion of 2 in k
9.917 * [backup-simplify]: Simplify 2 into 2
9.917 * [taylor]: Taking taylor expansion of PI in k
9.917 * [backup-simplify]: Simplify PI into PI
9.918 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.919 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.919 * [backup-simplify]: Simplify (+ 1 0) into 1
9.920 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
9.921 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI)))
9.922 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* 2 PI)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))
9.922 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
9.922 * [taylor]: Taking taylor expansion of (/ -1 k) in k
9.922 * [taylor]: Taking taylor expansion of -1 in k
9.922 * [backup-simplify]: Simplify -1 into -1
9.923 * [taylor]: Taking taylor expansion of k in k
9.923 * [backup-simplify]: Simplify 0 into 0
9.923 * [backup-simplify]: Simplify 1 into 1
9.923 * [backup-simplify]: Simplify (/ -1 1) into -1
9.923 * [backup-simplify]: Simplify (sqrt 0) into 0
9.925 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
9.926 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (/ -1 n))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))) into (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (/ -1 n))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))))
9.927 * [backup-simplify]: Simplify (/ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (/ -1 n))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))) +nan.0) into (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (/ -1 n))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))))
9.927 * [taylor]: Taking taylor expansion of (/ (* (pow (/ -1 n) (* 1/2 (+ (/ 1 k) 1))) (pow (* 2 PI) (* 1/2 (+ (/ 1 k) 1)))) (sqrt (/ -1 k))) in n
9.927 * [taylor]: Taking taylor expansion of (* (pow (/ -1 n) (* 1/2 (+ (/ 1 k) 1))) (pow (* 2 PI) (* 1/2 (+ (/ 1 k) 1)))) in n
9.927 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (* 1/2 (+ (/ 1 k) 1))) in n
9.927 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (/ -1 n)))) in n
9.927 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (/ -1 n))) in n
9.927 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
9.927 * [taylor]: Taking taylor expansion of 1/2 in n
9.927 * [backup-simplify]: Simplify 1/2 into 1/2
9.927 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
9.927 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.928 * [taylor]: Taking taylor expansion of k in n
9.928 * [backup-simplify]: Simplify k into k
9.928 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.928 * [taylor]: Taking taylor expansion of 1 in n
9.928 * [backup-simplify]: Simplify 1 into 1
9.928 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n
9.928 * [taylor]: Taking taylor expansion of (/ -1 n) in n
9.928 * [taylor]: Taking taylor expansion of -1 in n
9.928 * [backup-simplify]: Simplify -1 into -1
9.928 * [taylor]: Taking taylor expansion of n in n
9.928 * [backup-simplify]: Simplify 0 into 0
9.928 * [backup-simplify]: Simplify 1 into 1
9.928 * [backup-simplify]: Simplify (/ -1 1) into -1
9.929 * [backup-simplify]: Simplify (log -1) into (log -1)
9.929 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
9.929 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
9.930 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n))
9.930 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log -1) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))
9.931 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))
9.931 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (* 1/2 (+ (/ 1 k) 1))) in n
9.931 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* 2 PI)))) in n
9.931 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* 2 PI))) in n
9.931 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
9.931 * [taylor]: Taking taylor expansion of 1/2 in n
9.931 * [backup-simplify]: Simplify 1/2 into 1/2
9.931 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
9.931 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.931 * [taylor]: Taking taylor expansion of k in n
9.931 * [backup-simplify]: Simplify k into k
9.931 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.931 * [taylor]: Taking taylor expansion of 1 in n
9.931 * [backup-simplify]: Simplify 1 into 1
9.931 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in n
9.931 * [taylor]: Taking taylor expansion of (* 2 PI) in n
9.931 * [taylor]: Taking taylor expansion of 2 in n
9.931 * [backup-simplify]: Simplify 2 into 2
9.931 * [taylor]: Taking taylor expansion of PI in n
9.931 * [backup-simplify]: Simplify PI into PI
9.932 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.933 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.933 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
9.933 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
9.934 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (log (* 2 PI))) into (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))
9.935 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))
9.935 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
9.935 * [taylor]: Taking taylor expansion of (/ -1 k) in n
9.935 * [taylor]: Taking taylor expansion of -1 in n
9.935 * [backup-simplify]: Simplify -1 into -1
9.935 * [taylor]: Taking taylor expansion of k in n
9.935 * [backup-simplify]: Simplify k into k
9.935 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
9.935 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
9.936 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
9.936 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
9.942 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))) into (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))))
9.945 * [backup-simplify]: Simplify (/ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))) (sqrt (/ -1 k))) into (/ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))) (sqrt (/ -1 k)))
9.945 * [taylor]: Taking taylor expansion of (/ (* (pow (/ -1 n) (* 1/2 (+ (/ 1 k) 1))) (pow (* 2 PI) (* 1/2 (+ (/ 1 k) 1)))) (sqrt (/ -1 k))) in n
9.945 * [taylor]: Taking taylor expansion of (* (pow (/ -1 n) (* 1/2 (+ (/ 1 k) 1))) (pow (* 2 PI) (* 1/2 (+ (/ 1 k) 1)))) in n
9.945 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (* 1/2 (+ (/ 1 k) 1))) in n
9.945 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (/ -1 n)))) in n
9.945 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (/ -1 n))) in n
9.945 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
9.945 * [taylor]: Taking taylor expansion of 1/2 in n
9.945 * [backup-simplify]: Simplify 1/2 into 1/2
9.945 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
9.945 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.945 * [taylor]: Taking taylor expansion of k in n
9.945 * [backup-simplify]: Simplify k into k
9.945 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.945 * [taylor]: Taking taylor expansion of 1 in n
9.945 * [backup-simplify]: Simplify 1 into 1
9.945 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n
9.945 * [taylor]: Taking taylor expansion of (/ -1 n) in n
9.945 * [taylor]: Taking taylor expansion of -1 in n
9.945 * [backup-simplify]: Simplify -1 into -1
9.945 * [taylor]: Taking taylor expansion of n in n
9.945 * [backup-simplify]: Simplify 0 into 0
9.945 * [backup-simplify]: Simplify 1 into 1
9.946 * [backup-simplify]: Simplify (/ -1 1) into -1
9.946 * [backup-simplify]: Simplify (log -1) into (log -1)
9.946 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
9.946 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
9.947 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n))
9.948 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log -1) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))
9.948 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))
9.948 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (* 1/2 (+ (/ 1 k) 1))) in n
9.948 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* 2 PI)))) in n
9.948 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* 2 PI))) in n
9.948 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
9.948 * [taylor]: Taking taylor expansion of 1/2 in n
9.948 * [backup-simplify]: Simplify 1/2 into 1/2
9.949 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
9.949 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.949 * [taylor]: Taking taylor expansion of k in n
9.949 * [backup-simplify]: Simplify k into k
9.949 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.949 * [taylor]: Taking taylor expansion of 1 in n
9.949 * [backup-simplify]: Simplify 1 into 1
9.949 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in n
9.949 * [taylor]: Taking taylor expansion of (* 2 PI) in n
9.949 * [taylor]: Taking taylor expansion of 2 in n
9.949 * [backup-simplify]: Simplify 2 into 2
9.949 * [taylor]: Taking taylor expansion of PI in n
9.949 * [backup-simplify]: Simplify PI into PI
9.950 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.951 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.951 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
9.951 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
9.952 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (log (* 2 PI))) into (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))
9.953 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))
9.953 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
9.953 * [taylor]: Taking taylor expansion of (/ -1 k) in n
9.953 * [taylor]: Taking taylor expansion of -1 in n
9.953 * [backup-simplify]: Simplify -1 into -1
9.953 * [taylor]: Taking taylor expansion of k in n
9.954 * [backup-simplify]: Simplify k into k
9.954 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
9.954 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
9.954 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
9.954 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
9.955 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))) into (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))))
9.957 * [backup-simplify]: Simplify (/ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))) (sqrt (/ -1 k))) into (/ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))) (sqrt (/ -1 k)))
9.957 * [taylor]: Taking taylor expansion of (/ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))) (sqrt (/ -1 k))) in k
9.957 * [taylor]: Taking taylor expansion of (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))) in k
9.957 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) in k
9.957 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))) in k
9.957 * [taylor]: Taking taylor expansion of 1/2 in k
9.957 * [backup-simplify]: Simplify 1/2 into 1/2
9.957 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1) (log (* 2 PI))) in k
9.957 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
9.957 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.957 * [taylor]: Taking taylor expansion of k in k
9.957 * [backup-simplify]: Simplify 0 into 0
9.957 * [backup-simplify]: Simplify 1 into 1
9.957 * [backup-simplify]: Simplify (/ 1 1) into 1
9.957 * [taylor]: Taking taylor expansion of 1 in k
9.957 * [backup-simplify]: Simplify 1 into 1
9.957 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
9.957 * [taylor]: Taking taylor expansion of (* 2 PI) in k
9.957 * [taylor]: Taking taylor expansion of 2 in k
9.957 * [backup-simplify]: Simplify 2 into 2
9.957 * [taylor]: Taking taylor expansion of PI in k
9.957 * [backup-simplify]: Simplify PI into PI
9.958 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.958 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.958 * [backup-simplify]: Simplify (+ 1 0) into 1
9.959 * [backup-simplify]: Simplify (* 1 (log (* 2 PI))) into (log (* 2 PI))
9.960 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI)))
9.961 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))
9.961 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) in k
9.961 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))) in k
9.961 * [taylor]: Taking taylor expansion of 1/2 in k
9.961 * [backup-simplify]: Simplify 1/2 into 1/2
9.961 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log -1) (log n))) in k
9.961 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
9.961 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.961 * [taylor]: Taking taylor expansion of k in k
9.961 * [backup-simplify]: Simplify 0 into 0
9.961 * [backup-simplify]: Simplify 1 into 1
9.961 * [backup-simplify]: Simplify (/ 1 1) into 1
9.961 * [taylor]: Taking taylor expansion of 1 in k
9.961 * [backup-simplify]: Simplify 1 into 1
9.962 * [taylor]: Taking taylor expansion of (- (log -1) (log n)) in k
9.962 * [taylor]: Taking taylor expansion of (log -1) in k
9.962 * [taylor]: Taking taylor expansion of -1 in k
9.962 * [backup-simplify]: Simplify -1 into -1
9.962 * [backup-simplify]: Simplify (log -1) into (log -1)
9.962 * [taylor]: Taking taylor expansion of (log n) in k
9.962 * [taylor]: Taking taylor expansion of n in k
9.962 * [backup-simplify]: Simplify n into n
9.962 * [backup-simplify]: Simplify (log n) into (log n)
9.962 * [backup-simplify]: Simplify (+ 1 0) into 1
9.962 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
9.962 * [backup-simplify]: Simplify (+ (log -1) (- (log n))) into (- (log -1) (log n))
9.963 * [backup-simplify]: Simplify (* 1 (- (log -1) (log n))) into (- (log -1) (log n))
9.963 * [backup-simplify]: Simplify (* 1/2 (- (log -1) (log n))) into (* 1/2 (- (log -1) (log n)))
9.963 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))
9.963 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
9.963 * [taylor]: Taking taylor expansion of (/ -1 k) in k
9.963 * [taylor]: Taking taylor expansion of -1 in k
9.963 * [backup-simplify]: Simplify -1 into -1
9.963 * [taylor]: Taking taylor expansion of k in k
9.963 * [backup-simplify]: Simplify 0 into 0
9.963 * [backup-simplify]: Simplify 1 into 1
9.964 * [backup-simplify]: Simplify (/ -1 1) into -1
9.964 * [backup-simplify]: Simplify (sqrt 0) into 0
9.965 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
9.966 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))) into (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))))
9.967 * [backup-simplify]: Simplify (/ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))) +nan.0) into (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))))
9.968 * [backup-simplify]: Simplify (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))))) into (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))))
9.968 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
9.969 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
9.969 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
9.970 * [backup-simplify]: Simplify (+ 0 0) into 0
9.970 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (/ 1 k) 1))) into 0
9.970 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (log (* 2 PI)))) into 0
9.972 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
9.972 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
9.973 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -1 1)))) 1) into 0
9.973 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
9.973 * [backup-simplify]: Simplify (+ 0 0) into 0
9.974 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (/ 1 k) 1))) into 0
9.974 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n))
9.974 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (- (log -1) (log n)))) into 0
9.975 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
9.976 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) 0) (* 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))))) into 0
9.977 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0
9.977 * [taylor]: Taking taylor expansion of 0 in k
9.977 * [backup-simplify]: Simplify 0 into 0
9.977 * [backup-simplify]: Simplify 0 into 0
9.978 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) 0) (* 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))))) into 0
9.979 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
9.981 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
9.982 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))))))
9.983 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))))) into (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))))))
9.984 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
9.986 * [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
9.986 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
9.986 * [backup-simplify]: Simplify (+ 0 0) into 0
9.986 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0
9.987 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (log (* 2 PI))))) into 0
9.989 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
9.990 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.993 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -1 1)))) 2) into 0
9.993 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
9.994 * [backup-simplify]: Simplify (+ 0 0) into 0
9.994 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0
9.995 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n))
9.996 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log -1) (log n))))) into 0
9.998 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
10.000 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))))) into 0
10.000 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
10.001 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0
10.003 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0
10.003 * [taylor]: Taking taylor expansion of 0 in k
10.003 * [backup-simplify]: Simplify 0 into 0
10.003 * [backup-simplify]: Simplify 0 into 0
10.003 * [backup-simplify]: Simplify 0 into 0
10.005 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))))) into 0
10.006 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
10.011 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
10.016 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))))))
10.018 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))))) into (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))))))
10.024 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log -1) (log (/ 1 (- n)))))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log -1) (log (/ 1 (- n)))))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log -1) (log (/ 1 (- n))))))))))) into (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n)))))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n)))))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))))) (- (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n)))))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) k)))))))
10.024 * * * [progress]: simplifying candidates
10.024 * * * * [progress]: [ 1 / 184 ] simplifiying candidate #<alt (λ (k n) (* (exp (* (log n) (* (- 1 k) 1/2))) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))>
10.024 * * * * [progress]: [ 2 / 184 ] simplifiying candidate #<alt (λ (k n) (* (exp (* (log n) (* (- 1 k) 1/2))) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))>
10.024 * * * * [progress]: [ 3 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* 1 (* (- 1 k) 1/2))) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))>
10.024 * * * * [progress]: [ 4 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow (pow n (- 1 k)) 1/2) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))>
10.024 * * * * [progress]: [ 5 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* (cbrt n) (cbrt n)) (* (- 1 k) 1/2)) (pow (cbrt n) (* (- 1 k) 1/2))) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))>
10.024 * * * * [progress]: [ 6 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (sqrt n) (* (- 1 k) 1/2)) (pow (sqrt n) (* (- 1 k) 1/2))) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))>
10.025 * * * * [progress]: [ 7 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (pow 1 (* (- 1 k) 1/2)) (pow n (* (- 1 k) 1/2))) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))>
10.025 * * * * [progress]: [ 8 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow (pow n (* (- 1 k) 1/2)) 1) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))>
10.025 * * * * [progress]: [ 9 / 184 ] simplifiying candidate #<alt (λ (k n) (* (exp (log (pow n (* (- 1 k) 1/2)))) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))>
10.025 * * * * [progress]: [ 10 / 184 ] simplifiying candidate #<alt (λ (k n) (* (log (exp (pow n (* (- 1 k) 1/2)))) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))>
10.025 * * * * [progress]: [ 11 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (* (cbrt (pow n (* (- 1 k) 1/2))) (cbrt (pow n (* (- 1 k) 1/2)))) (cbrt (pow n (* (- 1 k) 1/2)))) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))>
10.025 * * * * [progress]: [ 12 / 184 ] simplifiying candidate #<alt (λ (k n) (* (cbrt (* (* (pow n (* (- 1 k) 1/2)) (pow n (* (- 1 k) 1/2))) (pow n (* (- 1 k) 1/2)))) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))>
10.025 * * * * [progress]: [ 13 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (pow n (* (- 1 k) 1/2))) (sqrt (pow n (* (- 1 k) 1/2)))) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))>
10.025 * * * * [progress]: [ 14 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* 1 (pow n (* (- 1 k) 1/2))) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))>
10.025 * * * * [progress]: [ 15 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (/ (* (- 1 k) 1/2) 2)) (pow n (/ (* (- 1 k) 1/2) 2))) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))>
10.025 * * * * [progress]: [ 16 / 184 ] simplifiying candidate #<alt (λ (k n) (* (posit16->real (real->posit16 (pow n (* (- 1 k) 1/2)))) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))>
10.025 * * * * [progress]: [ 17 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2))) (sqrt k))))>
10.025 * * * * [progress]: [ 18 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))) (sqrt k))))>
10.025 * * * * [progress]: [ 19 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))) (sqrt k))))>
10.025 * * * * [progress]: [ 20 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (* 1 (* (- 1 k) 1/2))) (sqrt k))))>
10.025 * * * * [progress]: [ 21 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (* 1 (* (- 1 k) 1/2))) (sqrt k))))>
10.026 * * * * [progress]: [ 22 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (pow (pow (* 2 PI) (- 1 k)) 1/2) (sqrt k))))>
10.026 * * * * [progress]: [ 23 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))>
10.026 * * * * [progress]: [ 24 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (pow (pow (* 2 PI) (* (- 1 k) 1/2)) 1) (sqrt k))))>
10.026 * * * * [progress]: [ 25 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (exp (log (pow (* 2 PI) (* (- 1 k) 1/2)))) (sqrt k))))>
10.026 * * * * [progress]: [ 26 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (log (exp (pow (* 2 PI) (* (- 1 k) 1/2)))) (sqrt k))))>
10.026 * * * * [progress]: [ 27 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (* (* (cbrt (pow (* 2 PI) (* (- 1 k) 1/2))) (cbrt (pow (* 2 PI) (* (- 1 k) 1/2)))) (cbrt (pow (* 2 PI) (* (- 1 k) 1/2)))) (sqrt k))))>
10.026 * * * * [progress]: [ 28 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (cbrt (* (* (pow (* 2 PI) (* (- 1 k) 1/2)) (pow (* 2 PI) (* (- 1 k) 1/2))) (pow (* 2 PI) (* (- 1 k) 1/2)))) (sqrt k))))>
10.026 * * * * [progress]: [ 29 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (* (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt (pow (* 2 PI) (* (- 1 k) 1/2)))) (sqrt k))))>
10.026 * * * * [progress]: [ 30 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (* 1 (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt k))))>
10.026 * * * * [progress]: [ 31 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (* (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2))) (sqrt k))))>
10.026 * * * * [progress]: [ 32 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (posit16->real (real->posit16 (pow (* 2 PI) (* (- 1 k) 1/2)))) (sqrt k))))>
10.026 * * * * [progress]: [ 33 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (pow (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k)) 1)))>
10.026 * * * * [progress]: [ 34 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (exp (- (* (+ (log 2) (log PI)) (* (- 1 k) 1/2)) (log (sqrt k))))))>
10.026 * * * * [progress]: [ 35 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (exp (- (* (log (* 2 PI)) (* (- 1 k) 1/2)) (log (sqrt k))))))>
10.026 * * * * [progress]: [ 36 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (exp (- (* (log (* 2 PI)) (* (- 1 k) 1/2)) (log (sqrt k))))))>
10.026 * * * * [progress]: [ 37 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (exp (- (log (pow (* 2 PI) (* (- 1 k) 1/2))) (log (sqrt k))))))>
10.027 * * * * [progress]: [ 38 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (exp (log (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))))>
10.027 * * * * [progress]: [ 39 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (log (exp (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))))>
10.027 * * * * [progress]: [ 40 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (cbrt (/ (* (* (pow (* 2 PI) (* (- 1 k) 1/2)) (pow (* 2 PI) (* (- 1 k) 1/2))) (pow (* 2 PI) (* (- 1 k) 1/2))) (* (* (sqrt k) (sqrt k)) (sqrt k))))))>
10.027 * * * * [progress]: [ 41 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (* (* (cbrt (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))) (cbrt (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k)))) (cbrt (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))))>
10.027 * * * * [progress]: [ 42 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (cbrt (* (* (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k)) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))))>
10.027 * * * * [progress]: [ 43 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (* (sqrt (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))))>
10.027 * * * * [progress]: [ 44 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (- (pow (* 2 PI) (* (- 1 k) 1/2))) (- (sqrt k)))))>
10.027 * * * * [progress]: [ 45 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (* (/ (pow 2 (* (- 1 k) 1/2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow PI (* (- 1 k) 1/2)) (cbrt (sqrt k))))))>
10.027 * * * * [progress]: [ 46 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (* (/ (pow 2 (* (- 1 k) 1/2)) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow PI (* (- 1 k) 1/2)) (sqrt (cbrt k))))))>
10.027 * * * * [progress]: [ 47 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (* (/ (pow 2 (* (- 1 k) 1/2)) (sqrt (sqrt k))) (/ (pow PI (* (- 1 k) 1/2)) (sqrt (sqrt k))))))>
10.027 * * * * [progress]: [ 48 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (* (/ (pow 2 (* (- 1 k) 1/2)) (sqrt 1)) (/ (pow PI (* (- 1 k) 1/2)) (sqrt k)))))>
10.027 * * * * [progress]: [ 49 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (* (/ (pow 2 (* (- 1 k) 1/2)) (sqrt (sqrt k))) (/ (pow PI (* (- 1 k) 1/2)) (sqrt (sqrt k))))))>
10.027 * * * * [progress]: [ 50 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (* (/ (pow 2 (* (- 1 k) 1/2)) 1) (/ (pow PI (* (- 1 k) 1/2)) (sqrt k)))))>
10.027 * * * * [progress]: [ 51 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (* (/ (* (cbrt (pow (* 2 PI) (* (- 1 k) 1/2))) (cbrt (pow (* 2 PI) (* (- 1 k) 1/2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* 2 PI) (* (- 1 k) 1/2))) (cbrt (sqrt k))))))>
10.028 * * * * [progress]: [ 52 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (* (/ (* (cbrt (pow (* 2 PI) (* (- 1 k) 1/2))) (cbrt (pow (* 2 PI) (* (- 1 k) 1/2)))) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt (cbrt k))))))>
10.028 * * * * [progress]: [ 53 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (* (/ (* (cbrt (pow (* 2 PI) (* (- 1 k) 1/2))) (cbrt (pow (* 2 PI) (* (- 1 k) 1/2)))) (sqrt (sqrt k))) (/ (cbrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt (sqrt k))))))>
10.028 * * * * [progress]: [ 54 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (* (/ (* (cbrt (pow (* 2 PI) (* (- 1 k) 1/2))) (cbrt (pow (* 2 PI) (* (- 1 k) 1/2)))) (sqrt 1)) (/ (cbrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt k)))))>
10.028 * * * * [progress]: [ 55 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (* (/ (* (cbrt (pow (* 2 PI) (* (- 1 k) 1/2))) (cbrt (pow (* 2 PI) (* (- 1 k) 1/2)))) (sqrt (sqrt k))) (/ (cbrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt (sqrt k))))))>
10.028 * * * * [progress]: [ 56 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (* (/ (* (cbrt (pow (* 2 PI) (* (- 1 k) 1/2))) (cbrt (pow (* 2 PI) (* (- 1 k) 1/2)))) 1) (/ (cbrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt k)))))>
10.028 * * * * [progress]: [ 57 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (* (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (cbrt (sqrt k))))))>
10.028 * * * * [progress]: [ 58 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (* (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt (cbrt k))))))>
10.028 * * * * [progress]: [ 59 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (* (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt (sqrt k))) (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt (sqrt k))))))>
10.028 * * * * [progress]: [ 60 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (* (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt 1)) (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt k)))))>
10.028 * * * * [progress]: [ 61 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (* (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt (sqrt k))) (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt (sqrt k))))))>
10.028 * * * * [progress]: [ 62 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (* (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) 1) (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt k)))))>
10.028 * * * * [progress]: [ 63 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (cbrt (sqrt k))))))>
10.028 * * * * [progress]: [ 64 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (* (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt (cbrt k))))))>
10.029 * * * * [progress]: [ 65 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt (sqrt k))))))>
10.029 * * * * [progress]: [ 66 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (* (/ 1 (sqrt 1)) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k)))))>
10.029 * * * * [progress]: [ 67 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt (sqrt k))))))>
10.029 * * * * [progress]: [ 68 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (* (/ 1 1) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k)))))>
10.029 * * * * [progress]: [ 69 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (* (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (cbrt (sqrt k))))))>
10.029 * * * * [progress]: [ 70 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (* (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt (cbrt k))))))>
10.029 * * * * [progress]: [ 71 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (* (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt (sqrt k))) (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt (sqrt k))))))>
10.029 * * * * [progress]: [ 72 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (* (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt 1)) (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt k)))))>
10.029 * * * * [progress]: [ 73 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (* (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt (sqrt k))) (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt (sqrt k))))))>
10.029 * * * * [progress]: [ 74 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (* (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) 1) (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt k)))))>
10.029 * * * * [progress]: [ 75 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (* 1 (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k)))))>
10.029 * * * * [progress]: [ 76 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (* (pow (* 2 PI) (* (- 1 k) 1/2)) (/ 1 (sqrt k)))))>
10.029 * * * * [progress]: [ 77 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ 1 (/ (sqrt k) (pow (* 2 PI) (* (- 1 k) 1/2))))))>
10.029 * * * * [progress]: [ 78 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k)))))>
10.030 * * * * [progress]: [ 79 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt (* (cbrt k) (cbrt k)))) (sqrt (cbrt k)))))>
10.030 * * * * [progress]: [ 80 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt (sqrt k))) (sqrt (sqrt k)))))>
10.030 * * * * [progress]: [ 81 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt 1)) (sqrt k))))>
10.030 * * * * [progress]: [ 82 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt (sqrt k))) (sqrt (sqrt k)))))>
10.030 * * * * [progress]: [ 83 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (/ (pow (* 2 PI) (* (- 1 k) 1/2)) 1) (sqrt k))))>
10.030 * * * * [progress]: [ 84 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (pow 2 (* (- 1 k) 1/2)) (/ (sqrt k) (pow PI (* (- 1 k) 1/2))))))>
10.030 * * * * [progress]: [ 85 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (* (cbrt (pow (* 2 PI) (* (- 1 k) 1/2))) (cbrt (pow (* 2 PI) (* (- 1 k) 1/2)))) (/ (sqrt k) (cbrt (pow (* 2 PI) (* (- 1 k) 1/2)))))))>
10.030 * * * * [progress]: [ 86 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (/ (sqrt k) (sqrt (pow (* 2 PI) (* (- 1 k) 1/2)))))))>
10.030 * * * * [progress]: [ 87 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ 1 (/ (sqrt k) (pow (* 2 PI) (* (- 1 k) 1/2))))))>
10.030 * * * * [progress]: [ 88 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (/ (sqrt k) (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2))))))>
10.030 * * * * [progress]: [ 89 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (posit16->real (real->posit16 (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))))>
10.030 * * * * [progress]: [ 90 / 184 ] simplifiying candidate #<alt (λ (k n) (pow (* (pow n (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))) 1))>
10.030 * * * * [progress]: [ 91 / 184 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log n) (* (- 1 k) 1/2)) (- (* (+ (log 2) (log PI)) (* (- 1 k) 1/2)) (log (sqrt k))))))>
10.030 * * * * [progress]: [ 92 / 184 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log n) (* (- 1 k) 1/2)) (- (* (log (* 2 PI)) (* (- 1 k) 1/2)) (log (sqrt k))))))>
10.031 * * * * [progress]: [ 93 / 184 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log n) (* (- 1 k) 1/2)) (- (* (log (* 2 PI)) (* (- 1 k) 1/2)) (log (sqrt k))))))>
10.031 * * * * [progress]: [ 94 / 184 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log n) (* (- 1 k) 1/2)) (- (log (pow (* 2 PI) (* (- 1 k) 1/2))) (log (sqrt k))))))>
10.031 * * * * [progress]: [ 95 / 184 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log n) (* (- 1 k) 1/2)) (log (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))))>
10.031 * * * * [progress]: [ 96 / 184 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log n) (* (- 1 k) 1/2)) (- (* (+ (log 2) (log PI)) (* (- 1 k) 1/2)) (log (sqrt k))))))>
10.031 * * * * [progress]: [ 97 / 184 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log n) (* (- 1 k) 1/2)) (- (* (log (* 2 PI)) (* (- 1 k) 1/2)) (log (sqrt k))))))>
10.031 * * * * [progress]: [ 98 / 184 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log n) (* (- 1 k) 1/2)) (- (* (log (* 2 PI)) (* (- 1 k) 1/2)) (log (sqrt k))))))>
10.031 * * * * [progress]: [ 99 / 184 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log n) (* (- 1 k) 1/2)) (- (log (pow (* 2 PI) (* (- 1 k) 1/2))) (log (sqrt k))))))>
10.031 * * * * [progress]: [ 100 / 184 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log n) (* (- 1 k) 1/2)) (log (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))))>
10.031 * * * * [progress]: [ 101 / 184 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (pow n (* (- 1 k) 1/2))) (- (* (+ (log 2) (log PI)) (* (- 1 k) 1/2)) (log (sqrt k))))))>
10.031 * * * * [progress]: [ 102 / 184 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (pow n (* (- 1 k) 1/2))) (- (* (log (* 2 PI)) (* (- 1 k) 1/2)) (log (sqrt k))))))>
10.031 * * * * [progress]: [ 103 / 184 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (pow n (* (- 1 k) 1/2))) (- (* (log (* 2 PI)) (* (- 1 k) 1/2)) (log (sqrt k))))))>
10.031 * * * * [progress]: [ 104 / 184 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (pow n (* (- 1 k) 1/2))) (- (log (pow (* 2 PI) (* (- 1 k) 1/2))) (log (sqrt k))))))>
10.031 * * * * [progress]: [ 105 / 184 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (pow n (* (- 1 k) 1/2))) (log (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))))>
10.031 * * * * [progress]: [ 106 / 184 ] simplifiying candidate #<alt (λ (k n) (exp (log (* (pow n (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))))>
10.031 * * * * [progress]: [ 107 / 184 ] simplifiying candidate #<alt (λ (k n) (log (exp (* (pow n (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))))>
10.032 * * * * [progress]: [ 108 / 184 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (* (pow n (* (- 1 k) 1/2)) (pow n (* (- 1 k) 1/2))) (pow n (* (- 1 k) 1/2))) (/ (* (* (pow (* 2 PI) (* (- 1 k) 1/2)) (pow (* 2 PI) (* (- 1 k) 1/2))) (pow (* 2 PI) (* (- 1 k) 1/2))) (* (* (sqrt k) (sqrt k)) (sqrt k))))))>
10.032 * * * * [progress]: [ 109 / 184 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (* (pow n (* (- 1 k) 1/2)) (pow n (* (- 1 k) 1/2))) (pow n (* (- 1 k) 1/2))) (* (* (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k)) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))))>
10.032 * * * * [progress]: [ 110 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (* (pow n (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k)))) (cbrt (* (pow n (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))) (cbrt (* (pow n (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))))>
10.032 * * * * [progress]: [ 111 / 184 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (* (pow n (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))) (* (pow n (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k)))) (* (pow n (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))))>
10.032 * * * * [progress]: [ 112 / 184 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (* (pow n (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k)))) (sqrt (* (pow n (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))))>
10.032 * * * * [progress]: [ 113 / 184 ] simplifiying candidate #<alt (λ (k n) (* 1 (* (pow n (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k)))))>
10.032 * * * * [progress]: [ 114 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (sqrt n) (* (- 1 k) 1/2)) (sqrt (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k)))) (* (pow (sqrt n) (* (- 1 k) 1/2)) (sqrt (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))))>
10.032 * * * * [progress]: [ 115 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (sqrt n) (* (- 1 k) 1/2)) (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt (sqrt k)))) (* (pow (sqrt n) (* (- 1 k) 1/2)) (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt (sqrt k))))))>
10.032 * * * * [progress]: [ 116 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (sqrt n) (* (- 1 k) 1/2)) (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt (sqrt k)))) (* (pow (sqrt n) (* (- 1 k) 1/2)) (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt (sqrt k))))))>
10.032 * * * * [progress]: [ 117 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (sqrt n) (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt (sqrt k)))) (* (pow (sqrt n) (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt (sqrt k))))))>
10.032 * * * * [progress]: [ 118 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (sqrt n) (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt (sqrt k)))) (* (pow (sqrt n) (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt (sqrt k))))))>
10.032 * * * * [progress]: [ 119 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (pow n (* (- 1 k) 1/2))) (sqrt (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k)))) (* (sqrt (pow n (* (- 1 k) 1/2))) (sqrt (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))))>
10.032 * * * * [progress]: [ 120 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (pow n (* (- 1 k) 1/2))) (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt (sqrt k)))) (* (sqrt (pow n (* (- 1 k) 1/2))) (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt (sqrt k))))))>
10.033 * * * * [progress]: [ 121 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (pow n (* (- 1 k) 1/2))) (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt (sqrt k)))) (* (sqrt (pow n (* (- 1 k) 1/2))) (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt (sqrt k))))))>
10.033 * * * * [progress]: [ 122 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (pow n (* (- 1 k) 1/2))) (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt (sqrt k)))) (* (sqrt (pow n (* (- 1 k) 1/2))) (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt (sqrt k))))))>
10.033 * * * * [progress]: [ 123 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (pow n (* (- 1 k) 1/2))) (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt (sqrt k)))) (* (sqrt (pow n (* (- 1 k) 1/2))) (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt (sqrt k))))))>
10.033 * * * * [progress]: [ 124 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (/ (* (- 1 k) 1/2) 2)) (sqrt (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k)))) (* (pow n (/ (* (- 1 k) 1/2) 2)) (sqrt (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))))>
10.033 * * * * [progress]: [ 125 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (/ (* (- 1 k) 1/2) 2)) (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt (sqrt k)))) (* (pow n (/ (* (- 1 k) 1/2) 2)) (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt (sqrt k))))))>
10.033 * * * * [progress]: [ 126 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (/ (* (- 1 k) 1/2) 2)) (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt (sqrt k)))) (* (pow n (/ (* (- 1 k) 1/2) 2)) (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt (sqrt k))))))>
10.033 * * * * [progress]: [ 127 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (/ (* (- 1 k) 1/2) 2)) (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt (sqrt k)))) (* (pow n (/ (* (- 1 k) 1/2) 2)) (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt (sqrt k))))))>
10.033 * * * * [progress]: [ 128 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (/ (* (- 1 k) 1/2) 2)) (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt (sqrt k)))) (* (pow n (/ (* (- 1 k) 1/2) 2)) (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt (sqrt k))))))>
10.033 * * * * [progress]: [ 129 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (* (- 1 k) 1/2)) (* (cbrt (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))) (cbrt (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))) (cbrt (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k)))))>
10.033 * * * * [progress]: [ 130 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (* (- 1 k) 1/2)) (sqrt (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k)))) (sqrt (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k)))))>
10.033 * * * * [progress]: [ 131 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (* (- 1 k) 1/2)) (/ (pow 2 (* (- 1 k) 1/2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow PI (* (- 1 k) 1/2)) (cbrt (sqrt k)))))>
10.033 * * * * [progress]: [ 132 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (* (- 1 k) 1/2)) (/ (pow 2 (* (- 1 k) 1/2)) (sqrt (* (cbrt k) (cbrt k))))) (/ (pow PI (* (- 1 k) 1/2)) (sqrt (cbrt k)))))>
10.033 * * * * [progress]: [ 133 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (* (- 1 k) 1/2)) (/ (pow 2 (* (- 1 k) 1/2)) (sqrt (sqrt k)))) (/ (pow PI (* (- 1 k) 1/2)) (sqrt (sqrt k)))))>
10.033 * * * * [progress]: [ 134 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (* (- 1 k) 1/2)) (/ (pow 2 (* (- 1 k) 1/2)) (sqrt 1))) (/ (pow PI (* (- 1 k) 1/2)) (sqrt k))))>
10.034 * * * * [progress]: [ 135 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (* (- 1 k) 1/2)) (/ (pow 2 (* (- 1 k) 1/2)) (sqrt (sqrt k)))) (/ (pow PI (* (- 1 k) 1/2)) (sqrt (sqrt k)))))>
10.034 * * * * [progress]: [ 136 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (* (- 1 k) 1/2)) (/ (pow 2 (* (- 1 k) 1/2)) 1)) (/ (pow PI (* (- 1 k) 1/2)) (sqrt k))))>
10.034 * * * * [progress]: [ 137 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (* (- 1 k) 1/2)) (/ (* (cbrt (pow (* 2 PI) (* (- 1 k) 1/2))) (cbrt (pow (* 2 PI) (* (- 1 k) 1/2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (cbrt (pow (* 2 PI) (* (- 1 k) 1/2))) (cbrt (sqrt k)))))>
10.034 * * * * [progress]: [ 138 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (* (- 1 k) 1/2)) (/ (* (cbrt (pow (* 2 PI) (* (- 1 k) 1/2))) (cbrt (pow (* 2 PI) (* (- 1 k) 1/2)))) (sqrt (* (cbrt k) (cbrt k))))) (/ (cbrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt (cbrt k)))))>
10.034 * * * * [progress]: [ 139 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (* (- 1 k) 1/2)) (/ (* (cbrt (pow (* 2 PI) (* (- 1 k) 1/2))) (cbrt (pow (* 2 PI) (* (- 1 k) 1/2)))) (sqrt (sqrt k)))) (/ (cbrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt (sqrt k)))))>
10.034 * * * * [progress]: [ 140 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (* (- 1 k) 1/2)) (/ (* (cbrt (pow (* 2 PI) (* (- 1 k) 1/2))) (cbrt (pow (* 2 PI) (* (- 1 k) 1/2)))) (sqrt 1))) (/ (cbrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt k))))>
10.034 * * * * [progress]: [ 141 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (* (- 1 k) 1/2)) (/ (* (cbrt (pow (* 2 PI) (* (- 1 k) 1/2))) (cbrt (pow (* 2 PI) (* (- 1 k) 1/2)))) (sqrt (sqrt k)))) (/ (cbrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt (sqrt k)))))>
10.034 * * * * [progress]: [ 142 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (* (- 1 k) 1/2)) (/ (* (cbrt (pow (* 2 PI) (* (- 1 k) 1/2))) (cbrt (pow (* 2 PI) (* (- 1 k) 1/2)))) 1)) (/ (cbrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt k))))>
10.034 * * * * [progress]: [ 143 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (* (- 1 k) 1/2)) (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (cbrt (sqrt k)))))>
10.034 * * * * [progress]: [ 144 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (* (- 1 k) 1/2)) (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt (* (cbrt k) (cbrt k))))) (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt (cbrt k)))))>
10.034 * * * * [progress]: [ 145 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (* (- 1 k) 1/2)) (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt (sqrt k)))) (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt (sqrt k)))))>
10.034 * * * * [progress]: [ 146 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (* (- 1 k) 1/2)) (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt 1))) (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt k))))>
10.034 * * * * [progress]: [ 147 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (* (- 1 k) 1/2)) (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt (sqrt k)))) (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt (sqrt k)))))>
10.034 * * * * [progress]: [ 148 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (* (- 1 k) 1/2)) (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) 1)) (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt k))))>
10.034 * * * * [progress]: [ 149 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (* (- 1 k) 1/2)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (cbrt (sqrt k)))))>
10.035 * * * * [progress]: [ 150 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (* (- 1 k) 1/2)) (/ 1 (sqrt (* (cbrt k) (cbrt k))))) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt (cbrt k)))))>
10.035 * * * * [progress]: [ 151 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (* (- 1 k) 1/2)) (/ 1 (sqrt (sqrt k)))) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt (sqrt k)))))>
10.035 * * * * [progress]: [ 152 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (* (- 1 k) 1/2)) (/ 1 (sqrt 1))) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))>
10.035 * * * * [progress]: [ 153 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (* (- 1 k) 1/2)) (/ 1 (sqrt (sqrt k)))) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt (sqrt k)))))>
10.035 * * * * [progress]: [ 154 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (* (- 1 k) 1/2)) (/ 1 1)) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))>
10.035 * * * * [progress]: [ 155 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (cbrt (sqrt k)))))>
10.035 * * * * [progress]: [ 156 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt (* (cbrt k) (cbrt k))))) (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt (cbrt k)))))>
10.035 * * * * [progress]: [ 157 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt (sqrt k)))) (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt (sqrt k)))))>
10.035 * * * * [progress]: [ 158 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt 1))) (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt k))))>
10.035 * * * * [progress]: [ 159 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt (sqrt k)))) (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt (sqrt k)))))>
10.035 * * * * [progress]: [ 160 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) 1)) (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt k))))>
10.036 * * * * [progress]: [ 161 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (* (- 1 k) 1/2)) 1) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))>
10.036 * * * * [progress]: [ 162 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (* (- 1 k) 1/2)) (pow (* 2 PI) (* (- 1 k) 1/2))) (/ 1 (sqrt k))))>
10.036 * * * * [progress]: [ 163 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow (* (cbrt n) (cbrt n)) (* (- 1 k) 1/2)) (* (pow (cbrt n) (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k)))))>
10.036 * * * * [progress]: [ 164 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow (sqrt n) (* (- 1 k) 1/2)) (* (pow (sqrt n) (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k)))))>
10.036 * * * * [progress]: [ 165 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow 1 (* (- 1 k) 1/2)) (* (pow n (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k)))))>
10.036 * * * * [progress]: [ 166 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (pow n (* (- 1 k) 1/2))) (cbrt (pow n (* (- 1 k) 1/2)))) (* (cbrt (pow n (* (- 1 k) 1/2))) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k)))))>
10.036 * * * * [progress]: [ 167 / 184 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (pow n (* (- 1 k) 1/2))) (* (sqrt (pow n (* (- 1 k) 1/2))) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k)))))>
10.036 * * * * [progress]: [ 168 / 184 ] simplifiying candidate #<alt (λ (k n) (* 1 (* (pow n (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k)))))>
10.036 * * * * [progress]: [ 169 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (* (- 1 k) 1/2) 2)) (* (pow n (/ (* (- 1 k) 1/2) 2)) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k)))))>
10.036 * * * * [progress]: [ 170 / 184 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow n (* (- 1 k) 1/2)) (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt k)))>
10.036 * * * * [progress]: [ 171 / 184 ] simplifiying candidate #<alt (λ (k n) (posit16->real (real->posit16 (* (pow n (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))))>
10.036 * * * * [progress]: [ 172 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k)) (pow n (* (- 1 k) 1/2))))>
10.036 * * * * [progress]: [ 173 / 184 ] simplifiying candidate #<alt (λ (k n) (* (- (+ (pow n 1/2) (* 1/8 (* (sqrt n) (* (pow (log n) 2) (pow k 2))))) (* 1/2 (* (sqrt n) (* (log n) k)))) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))>
10.037 * * * * [progress]: [ 174 / 184 ] simplifiying candidate #<alt (λ (k n) (* (exp (* -1/2 (* (- 1 k) (log (/ 1 n))))) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))>
10.037 * * * * [progress]: [ 175 / 184 ] simplifiying candidate #<alt (λ (k n) (* (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n)))))) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))>
10.037 * * * * [progress]: [ 176 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (- (+ (* 1/8 (* (* (sqrt 2) (* (pow k 2) (pow (log (* 2 PI)) 2))) (sqrt PI))) (pow (* 2 PI) 1/2)) (* 1/2 (* (* (sqrt 2) (* k (log (* 2 PI)))) (sqrt PI)))) (sqrt k))))>
10.037 * * * * [progress]: [ 177 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (sqrt k))))>
10.037 * * * * [progress]: [ 178 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (sqrt k))))>
10.037 * * * * [progress]: [ 179 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (- (+ (* +nan.0 (* (* (sqrt 2) (pow k 2)) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt PI))) (- (+ (* +nan.0 (* (* (log (* 2 PI)) (* (sqrt 2) (pow k 2))) (sqrt PI))) (- (+ (* +nan.0 (* (* (pow (log (* 2 PI)) 2) (* (sqrt 2) (pow k 2))) (sqrt PI))) (- (+ (* +nan.0 (* (* (sqrt 2) (* k (log (* 2 PI)))) (sqrt PI))) (- (* +nan.0 (* (* (sqrt 2) k) (sqrt PI))))))))))))))))>
10.037 * * * * [progress]: [ 180 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) k)) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (pow k 2))))))))))>
10.037 * * * * [progress]: [ 181 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))))))))))>
10.037 * * * * [progress]: [ 182 / 184 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (* (* (sqrt 2) (pow k 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) k) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (pow (log (* 2 PI)) 2) (* (sqrt 2) (pow k 2))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (pow (log n) 2) (pow k 2))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log n) k)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log n) (pow k 2))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log (* 2 PI)) (* (sqrt 2) (* (log n) (pow k 2)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* k (log (* 2 PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (* (log (* 2 PI)) (* (sqrt 2) (pow k 2))) (sqrt (* n PI))))))))))))))))))))))))>
10.037 * * * * [progress]: [ 183 / 184 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (* (exp (* -1/2 (* (- 1 k) (log (/ 1 n))))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) (pow k 2))) (- (+ (* +nan.0 (/ (* (exp (* -1/2 (* (- 1 k) (log (/ 1 n))))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) k)) (- (* +nan.0 (/ (* (exp (* -1/2 (* (- 1 k) (log (/ 1 n))))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) (pow k 3)))))))))>
10.037 * * * * [progress]: [ 184 / 184 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n)))))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n)))))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))))) (- (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n)))))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) k))))))))>
10.041 * [simplify]: Simplifying:
  (* (log n) (* (- 1 k) 1/2))
  (* (log n) (* (- 1 k) 1/2))
  (* 1 (* (- 1 k) 1/2))
  (pow n (- 1 k))
  (pow (* (cbrt n) (cbrt n)) (* (- 1 k) 1/2))
  (pow (cbrt n) (* (- 1 k) 1/2))
  (pow (sqrt n) (* (- 1 k) 1/2))
  (pow (sqrt n) (* (- 1 k) 1/2))
  (pow 1 (* (- 1 k) 1/2))
  (pow n (* (- 1 k) 1/2))
  (log (pow n (* (- 1 k) 1/2)))
  (exp (pow n (* (- 1 k) 1/2)))
  (* (cbrt (pow n (* (- 1 k) 1/2))) (cbrt (pow n (* (- 1 k) 1/2))))
  (cbrt (pow n (* (- 1 k) 1/2)))
  (* (* (pow n (* (- 1 k) 1/2)) (pow n (* (- 1 k) 1/2))) (pow n (* (- 1 k) 1/2)))
  (sqrt (pow n (* (- 1 k) 1/2)))
  (sqrt (pow n (* (- 1 k) 1/2)))
  (pow n (/ (* (- 1 k) 1/2) 2))
  (pow n (/ (* (- 1 k) 1/2) 2))
  (real->posit16 (pow n (* (- 1 k) 1/2)))
  (* (+ (log 2) (log PI)) (* (- 1 k) 1/2))
  (* (log (* 2 PI)) (* (- 1 k) 1/2))
  (* (log (* 2 PI)) (* (- 1 k) 1/2))
  (* 1 (* (- 1 k) 1/2))
  (* 1 (* (- 1 k) 1/2))
  (pow (* 2 PI) (- 1 k))
  (pow 2 (* (- 1 k) 1/2))
  (pow PI (* (- 1 k) 1/2))
  (log (pow (* 2 PI) (* (- 1 k) 1/2)))
  (exp (pow (* 2 PI) (* (- 1 k) 1/2)))
  (* (cbrt (pow (* 2 PI) (* (- 1 k) 1/2))) (cbrt (pow (* 2 PI) (* (- 1 k) 1/2))))
  (cbrt (pow (* 2 PI) (* (- 1 k) 1/2)))
  (* (* (pow (* 2 PI) (* (- 1 k) 1/2)) (pow (* 2 PI) (* (- 1 k) 1/2))) (pow (* 2 PI) (* (- 1 k) 1/2)))
  (sqrt (pow (* 2 PI) (* (- 1 k) 1/2)))
  (sqrt (pow (* 2 PI) (* (- 1 k) 1/2)))
  (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2))
  (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2))
  (real->posit16 (pow (* 2 PI) (* (- 1 k) 1/2)))
  (- (* (+ (log 2) (log PI)) (* (- 1 k) 1/2)) (log (sqrt k)))
  (- (* (log (* 2 PI)) (* (- 1 k) 1/2)) (log (sqrt k)))
  (- (* (log (* 2 PI)) (* (- 1 k) 1/2)) (log (sqrt k)))
  (- (log (pow (* 2 PI) (* (- 1 k) 1/2))) (log (sqrt k)))
  (log (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k)))
  (exp (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k)))
  (/ (* (* (pow (* 2 PI) (* (- 1 k) 1/2)) (pow (* 2 PI) (* (- 1 k) 1/2))) (pow (* 2 PI) (* (- 1 k) 1/2))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
  (* (cbrt (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))) (cbrt (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))
  (cbrt (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k)))
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  (sqrt (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k)))
  (sqrt (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k)))
  (- (pow (* 2 PI) (* (- 1 k) 1/2)))
  (- (sqrt k))
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  (/ (pow PI (* (- 1 k) 1/2)) (cbrt (sqrt k)))
  (/ (pow 2 (* (- 1 k) 1/2)) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow PI (* (- 1 k) 1/2)) (sqrt (cbrt k)))
  (/ (pow 2 (* (- 1 k) 1/2)) (sqrt (sqrt k)))
  (/ (pow PI (* (- 1 k) 1/2)) (sqrt (sqrt k)))
  (/ (pow 2 (* (- 1 k) 1/2)) (sqrt 1))
  (/ (pow PI (* (- 1 k) 1/2)) (sqrt k))
  (/ (pow 2 (* (- 1 k) 1/2)) (sqrt (sqrt k)))
  (/ (pow PI (* (- 1 k) 1/2)) (sqrt (sqrt k)))
  (/ (pow 2 (* (- 1 k) 1/2)) 1)
  (/ (pow PI (* (- 1 k) 1/2)) (sqrt k))
  (/ (* (cbrt (pow (* 2 PI) (* (- 1 k) 1/2))) (cbrt (pow (* 2 PI) (* (- 1 k) 1/2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (cbrt (pow (* 2 PI) (* (- 1 k) 1/2))) (cbrt (sqrt k)))
  (/ (* (cbrt (pow (* 2 PI) (* (- 1 k) 1/2))) (cbrt (pow (* 2 PI) (* (- 1 k) 1/2)))) (sqrt (* (cbrt k) (cbrt k))))
  (/ (cbrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt (cbrt k)))
  (/ (* (cbrt (pow (* 2 PI) (* (- 1 k) 1/2))) (cbrt (pow (* 2 PI) (* (- 1 k) 1/2)))) (sqrt (sqrt k)))
  (/ (cbrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt (sqrt k)))
  (/ (* (cbrt (pow (* 2 PI) (* (- 1 k) 1/2))) (cbrt (pow (* 2 PI) (* (- 1 k) 1/2)))) (sqrt 1))
  (/ (cbrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt k))
  (/ (* (cbrt (pow (* 2 PI) (* (- 1 k) 1/2))) (cbrt (pow (* 2 PI) (* (- 1 k) 1/2)))) (sqrt (sqrt k)))
  (/ (cbrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt (sqrt k)))
  (/ (* (cbrt (pow (* 2 PI) (* (- 1 k) 1/2))) (cbrt (pow (* 2 PI) (* (- 1 k) 1/2)))) 1)
  (/ (cbrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt k))
  (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (cbrt (sqrt k)))
  (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt (* (cbrt k) (cbrt k))))
  (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt (cbrt k)))
  (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt 1))
  (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt k))
  (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) 1)
  (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt k))
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (cbrt (sqrt k)))
  (/ 1 (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt (sqrt k)))
  (/ 1 (sqrt 1))
  (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt (sqrt k)))
  (/ 1 1)
  (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))
  (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (cbrt (sqrt k)))
  (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt (cbrt k)))
  (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt (sqrt k)))
  (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt (sqrt k)))
  (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt 1))
  (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt k))
  (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt (sqrt k)))
  (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt (sqrt k)))
  (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) 1)
  (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) (pow (* 2 PI) (* (- 1 k) 1/2)))
  (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt (sqrt k)))
  (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt 1))
  (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt (sqrt k)))
  (/ (pow (* 2 PI) (* (- 1 k) 1/2)) 1)
  (/ (sqrt k) (pow PI (* (- 1 k) 1/2)))
  (/ (sqrt k) (cbrt (pow (* 2 PI) (* (- 1 k) 1/2))))
  (/ (sqrt k) (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))))
  (/ (sqrt k) (pow (* 2 PI) (* (- 1 k) 1/2)))
  (/ (sqrt k) (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)))
  (real->posit16 (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k)))
  (+ (* (log n) (* (- 1 k) 1/2)) (- (* (+ (log 2) (log PI)) (* (- 1 k) 1/2)) (log (sqrt k))))
  (+ (* (log n) (* (- 1 k) 1/2)) (- (* (log (* 2 PI)) (* (- 1 k) 1/2)) (log (sqrt k))))
  (+ (* (log n) (* (- 1 k) 1/2)) (- (* (log (* 2 PI)) (* (- 1 k) 1/2)) (log (sqrt k))))
  (+ (* (log n) (* (- 1 k) 1/2)) (- (log (pow (* 2 PI) (* (- 1 k) 1/2))) (log (sqrt k))))
  (+ (* (log n) (* (- 1 k) 1/2)) (log (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))
  (+ (* (log n) (* (- 1 k) 1/2)) (- (* (+ (log 2) (log PI)) (* (- 1 k) 1/2)) (log (sqrt k))))
  (+ (* (log n) (* (- 1 k) 1/2)) (- (* (log (* 2 PI)) (* (- 1 k) 1/2)) (log (sqrt k))))
  (+ (* (log n) (* (- 1 k) 1/2)) (- (* (log (* 2 PI)) (* (- 1 k) 1/2)) (log (sqrt k))))
  (+ (* (log n) (* (- 1 k) 1/2)) (- (log (pow (* 2 PI) (* (- 1 k) 1/2))) (log (sqrt k))))
  (+ (* (log n) (* (- 1 k) 1/2)) (log (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))
  (+ (log (pow n (* (- 1 k) 1/2))) (- (* (+ (log 2) (log PI)) (* (- 1 k) 1/2)) (log (sqrt k))))
  (+ (log (pow n (* (- 1 k) 1/2))) (- (* (log (* 2 PI)) (* (- 1 k) 1/2)) (log (sqrt k))))
  (+ (log (pow n (* (- 1 k) 1/2))) (- (* (log (* 2 PI)) (* (- 1 k) 1/2)) (log (sqrt k))))
  (+ (log (pow n (* (- 1 k) 1/2))) (- (log (pow (* 2 PI) (* (- 1 k) 1/2))) (log (sqrt k))))
  (+ (log (pow n (* (- 1 k) 1/2))) (log (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))
  (log (* (pow n (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))
  (exp (* (pow n (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))
  (* (* (* (pow n (* (- 1 k) 1/2)) (pow n (* (- 1 k) 1/2))) (pow n (* (- 1 k) 1/2))) (/ (* (* (pow (* 2 PI) (* (- 1 k) 1/2)) (pow (* 2 PI) (* (- 1 k) 1/2))) (pow (* 2 PI) (* (- 1 k) 1/2))) (* (* (sqrt k) (sqrt k)) (sqrt k))))
  (* (* (* (pow n (* (- 1 k) 1/2)) (pow n (* (- 1 k) 1/2))) (pow n (* (- 1 k) 1/2))) (* (* (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k)) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))
  (* (cbrt (* (pow n (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k)))) (cbrt (* (pow n (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k)))))
  (cbrt (* (pow n (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))
  (* (* (* (pow n (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))) (* (pow n (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k)))) (* (pow n (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))
  (sqrt (* (pow n (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))
  (sqrt (* (pow n (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))
  (* (pow (sqrt n) (* (- 1 k) 1/2)) (sqrt (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))
  (* (pow (sqrt n) (* (- 1 k) 1/2)) (sqrt (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))
  (* (pow (sqrt n) (* (- 1 k) 1/2)) (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt (sqrt k))))
  (* (pow (sqrt n) (* (- 1 k) 1/2)) (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt (sqrt k))))
  (* (pow (sqrt n) (* (- 1 k) 1/2)) (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt (sqrt k))))
  (* (pow (sqrt n) (* (- 1 k) 1/2)) (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt (sqrt k))))
  (* (pow (sqrt n) (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt (sqrt k))))
  (* (pow (sqrt n) (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt (sqrt k))))
  (* (pow (sqrt n) (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt (sqrt k))))
  (* (pow (sqrt n) (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt (sqrt k))))
  (* (sqrt (pow n (* (- 1 k) 1/2))) (sqrt (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))
  (* (sqrt (pow n (* (- 1 k) 1/2))) (sqrt (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))
  (* (sqrt (pow n (* (- 1 k) 1/2))) (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt (sqrt k))))
  (* (sqrt (pow n (* (- 1 k) 1/2))) (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt (sqrt k))))
  (* (sqrt (pow n (* (- 1 k) 1/2))) (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt (sqrt k))))
  (* (sqrt (pow n (* (- 1 k) 1/2))) (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt (sqrt k))))
  (* (sqrt (pow n (* (- 1 k) 1/2))) (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt (sqrt k))))
  (* (sqrt (pow n (* (- 1 k) 1/2))) (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt (sqrt k))))
  (* (sqrt (pow n (* (- 1 k) 1/2))) (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt (sqrt k))))
  (* (sqrt (pow n (* (- 1 k) 1/2))) (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt (sqrt k))))
  (* (pow n (/ (* (- 1 k) 1/2) 2)) (sqrt (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))
  (* (pow n (/ (* (- 1 k) 1/2) 2)) (sqrt (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))
  (* (pow n (/ (* (- 1 k) 1/2) 2)) (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt (sqrt k))))
  (* (pow n (/ (* (- 1 k) 1/2) 2)) (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt (sqrt k))))
  (* (pow n (/ (* (- 1 k) 1/2) 2)) (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt (sqrt k))))
  (* (pow n (/ (* (- 1 k) 1/2) 2)) (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt (sqrt k))))
  (* (pow n (/ (* (- 1 k) 1/2) 2)) (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt (sqrt k))))
  (* (pow n (/ (* (- 1 k) 1/2) 2)) (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt (sqrt k))))
  (* (pow n (/ (* (- 1 k) 1/2) 2)) (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt (sqrt k))))
  (* (pow n (/ (* (- 1 k) 1/2) 2)) (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt (sqrt k))))
  (* (pow n (* (- 1 k) 1/2)) (* (cbrt (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))) (cbrt (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k)))))
  (* (pow n (* (- 1 k) 1/2)) (sqrt (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))
  (* (pow n (* (- 1 k) 1/2)) (/ (pow 2 (* (- 1 k) 1/2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (* (pow n (* (- 1 k) 1/2)) (/ (pow 2 (* (- 1 k) 1/2)) (sqrt (* (cbrt k) (cbrt k)))))
  (* (pow n (* (- 1 k) 1/2)) (/ (pow 2 (* (- 1 k) 1/2)) (sqrt (sqrt k))))
  (* (pow n (* (- 1 k) 1/2)) (/ (pow 2 (* (- 1 k) 1/2)) (sqrt 1)))
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  (* (pow n (* (- 1 k) 1/2)) (/ (pow 2 (* (- 1 k) 1/2)) 1))
  (* (pow n (* (- 1 k) 1/2)) (/ (* (cbrt (pow (* 2 PI) (* (- 1 k) 1/2))) (cbrt (pow (* 2 PI) (* (- 1 k) 1/2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (* (pow n (* (- 1 k) 1/2)) (/ (* (cbrt (pow (* 2 PI) (* (- 1 k) 1/2))) (cbrt (pow (* 2 PI) (* (- 1 k) 1/2)))) (sqrt (* (cbrt k) (cbrt k)))))
  (* (pow n (* (- 1 k) 1/2)) (/ (* (cbrt (pow (* 2 PI) (* (- 1 k) 1/2))) (cbrt (pow (* 2 PI) (* (- 1 k) 1/2)))) (sqrt (sqrt k))))
  (* (pow n (* (- 1 k) 1/2)) (/ (* (cbrt (pow (* 2 PI) (* (- 1 k) 1/2))) (cbrt (pow (* 2 PI) (* (- 1 k) 1/2)))) (sqrt 1)))
  (* (pow n (* (- 1 k) 1/2)) (/ (* (cbrt (pow (* 2 PI) (* (- 1 k) 1/2))) (cbrt (pow (* 2 PI) (* (- 1 k) 1/2)))) (sqrt (sqrt k))))
  (* (pow n (* (- 1 k) 1/2)) (/ (* (cbrt (pow (* 2 PI) (* (- 1 k) 1/2))) (cbrt (pow (* 2 PI) (* (- 1 k) 1/2)))) 1))
  (* (pow n (* (- 1 k) 1/2)) (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (* (pow n (* (- 1 k) 1/2)) (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt (* (cbrt k) (cbrt k)))))
  (* (pow n (* (- 1 k) 1/2)) (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt (sqrt k))))
  (* (pow n (* (- 1 k) 1/2)) (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt 1)))
  (* (pow n (* (- 1 k) 1/2)) (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt (sqrt k))))
  (* (pow n (* (- 1 k) 1/2)) (/ (sqrt (pow (* 2 PI) (* (- 1 k) 1/2))) 1))
  (* (pow n (* (- 1 k) 1/2)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (* (pow n (* (- 1 k) 1/2)) (/ 1 (sqrt (* (cbrt k) (cbrt k)))))
  (* (pow n (* (- 1 k) 1/2)) (/ 1 (sqrt (sqrt k))))
  (* (pow n (* (- 1 k) 1/2)) (/ 1 (sqrt 1)))
  (* (pow n (* (- 1 k) 1/2)) (/ 1 (sqrt (sqrt k))))
  (* (pow n (* (- 1 k) 1/2)) (/ 1 1))
  (* (pow n (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (* (pow n (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt (* (cbrt k) (cbrt k)))))
  (* (pow n (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt (sqrt k))))
  (* (pow n (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt 1)))
  (* (pow n (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt (sqrt k))))
  (* (pow n (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) 1))
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  (* (pow (sqrt n) (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k)))
  (* (pow n (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k)))
  (* (cbrt (pow n (* (- 1 k) 1/2))) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k)))
  (* (sqrt (pow n (* (- 1 k) 1/2))) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k)))
  (* (pow n (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k)))
  (* (pow n (/ (* (- 1 k) 1/2) 2)) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k)))
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  (- (+ (pow n 1/2) (* 1/8 (* (sqrt n) (* (pow (log n) 2) (pow k 2))))) (* 1/2 (* (sqrt n) (* (log n) k))))
  (exp (* -1/2 (* (- 1 k) (log (/ 1 n)))))
  (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n))))))
  (- (+ (* 1/8 (* (* (sqrt 2) (* (pow k 2) (pow (log (* 2 PI)) 2))) (sqrt PI))) (pow (* 2 PI) 1/2)) (* 1/2 (* (* (sqrt 2) (* k (log (* 2 PI)))) (sqrt PI))))
  (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))
  (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))
  (- (+ (* +nan.0 (* (* (sqrt 2) (pow k 2)) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt PI))) (- (+ (* +nan.0 (* (* (log (* 2 PI)) (* (sqrt 2) (pow k 2))) (sqrt PI))) (- (+ (* +nan.0 (* (* (pow (log (* 2 PI)) 2) (* (sqrt 2) (pow k 2))) (sqrt PI))) (- (+ (* +nan.0 (* (* (sqrt 2) (* k (log (* 2 PI)))) (sqrt PI))) (- (* +nan.0 (* (* (sqrt 2) k) (sqrt PI))))))))))))))
  (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) k)) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (pow k 2))))))))
  (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))))))))
  (- (+ (* +nan.0 (* (* (sqrt 2) (pow k 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) k) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (pow (log (* 2 PI)) 2) (* (sqrt 2) (pow k 2))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (pow (log n) 2) (pow k 2))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log n) k)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log n) (pow k 2))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log (* 2 PI)) (* (sqrt 2) (* (log n) (pow k 2)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* k (log (* 2 PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (* (log (* 2 PI)) (* (sqrt 2) (pow k 2))) (sqrt (* n PI)))))))))))))))))))))))
  (- (+ (* +nan.0 (/ (* (exp (* -1/2 (* (- 1 k) (log (/ 1 n))))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) (pow k 2))) (- (+ (* +nan.0 (/ (* (exp (* -1/2 (* (- 1 k) (log (/ 1 n))))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) k)) (- (* +nan.0 (/ (* (exp (* -1/2 (* (- 1 k) (log (/ 1 n))))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) (pow k 3))))))))
  (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n)))))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n)))))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))))) (- (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n)))))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) k)))))))
10.045 * * [simplify]: iteration 1: (349 enodes)
10.251 * * [simplify]: iteration 2: (1606 enodes)
10.737 * * [simplify]: Extracting #0: cost 133 inf + 0
10.739 * * [simplify]: Extracting #1: cost 682 inf + 1
10.755 * * [simplify]: Extracting #2: cost 1016 inf + 8187
10.783 * * [simplify]: Extracting #3: cost 980 inf + 126954
10.848 * * [simplify]: Extracting #4: cost 559 inf + 383098
10.960 * * [simplify]: Extracting #5: cost 257 inf + 545495
11.126 * * [simplify]: Extracting #6: cost 138 inf + 626971
11.306 * * [simplify]: Extracting #7: cost 26 inf + 705863
11.490 * * [simplify]: Extracting #8: cost 0 inf + 730968
11.668 * * [simplify]: Extracting #9: cost 0 inf + 728208
11.872 * * [simplify]: Extracting #10: cost 0 inf + 727688
12.071 * * [simplify]: Extracting #11: cost 0 inf + 727648
12.250 * [simplify]: Simplified to:
  (* (* (- 1 k) 1/2) (log n))
  (* (* (- 1 k) 1/2) (log n))
  (* (- 1 k) 1/2)
  (pow n (- 1 k))
  (pow (* (cbrt n) (cbrt n)) (* (- 1 k) 1/2))
  (pow (cbrt n) (* (- 1 k) 1/2))
  (pow (sqrt n) (* (- 1 k) 1/2))
  (pow (sqrt n) (* (- 1 k) 1/2))
  1
  (pow n (* (- 1 k) 1/2))
  (* (* (- 1 k) 1/2) (log n))
  (exp (pow n (* (- 1 k) 1/2)))
  (* (cbrt (pow n (* (- 1 k) 1/2))) (cbrt (pow n (* (- 1 k) 1/2))))
  (cbrt (pow n (* (- 1 k) 1/2)))
  (pow (pow n (* (- 1 k) 1/2)) 3)
  (sqrt (pow n (* (- 1 k) 1/2)))
  (sqrt (pow n (* (- 1 k) 1/2)))
  (pow n (- 1/4 (/ k 4)))
  (pow n (- 1/4 (/ k 4)))
  (real->posit16 (pow n (* (- 1 k) 1/2)))
  (* (log (* 2 PI)) (* (- 1 k) 1/2))
  (* (log (* 2 PI)) (* (- 1 k) 1/2))
  (* (log (* 2 PI)) (* (- 1 k) 1/2))
  (* (- 1 k) 1/2)
  (* (- 1 k) 1/2)
  (pow (* 2 PI) (- 1 k))
  (pow 2 (* (- 1 k) 1/2))
  (pow PI (* (- 1 k) 1/2))
  (* (log (* 2 PI)) (* (- 1 k) 1/2))
  (exp (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))))
  (* (cbrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))) (cbrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))))
  (cbrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))))
  (pow (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))) 3)
  (sqrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))))
  (sqrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))))
  (pow (* 2 PI) (- 1/4 (/ k 4)))
  (pow (* 2 PI) (- 1/4 (/ k 4)))
  (real->posit16 (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))))
  (- (* (log (* 2 PI)) (* (- 1 k) 1/2)) (log (sqrt k)))
  (- (* (log (* 2 PI)) (* (- 1 k) 1/2)) (log (sqrt k)))
  (- (* (log (* 2 PI)) (* (- 1 k) 1/2)) (log (sqrt k)))
  (- (* (log (* 2 PI)) (* (- 1 k) 1/2)) (log (sqrt k)))
  (- (* (log (* 2 PI)) (* (- 1 k) 1/2)) (log (sqrt k)))
  (exp (/ (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))) (sqrt k)))
  (/ (/ (pow (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))) 3) (sqrt k)) k)
  (* (cbrt (/ (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))) (sqrt k))) (cbrt (/ (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))) (sqrt k))))
  (cbrt (/ (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))) (sqrt k)))
  (/ (* (* (/ (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))) (sqrt k)) (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))) (/ (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))) (sqrt k))) (sqrt k))
  (sqrt (/ (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))) (sqrt k)))
  (sqrt (/ (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))) (sqrt k)))
  (- (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))))
  (- (sqrt k))
  (/ (/ (pow 2 (* (- 1 k) 1/2)) (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ (pow PI (* (- 1 k) 1/2)) (cbrt (sqrt k)))
  (/ (pow 2 (* (- 1 k) 1/2)) (fabs (cbrt k)))
  (/ (pow PI (* (- 1 k) 1/2)) (sqrt (cbrt k)))
  (/ (pow 2 (* (- 1 k) 1/2)) (sqrt (sqrt k)))
  (/ (pow PI (* (- 1 k) 1/2)) (sqrt (sqrt k)))
  (pow 2 (* (- 1 k) 1/2))
  (/ (pow PI (* (- 1 k) 1/2)) (sqrt k))
  (/ (pow 2 (* (- 1 k) 1/2)) (sqrt (sqrt k)))
  (/ (pow PI (* (- 1 k) 1/2)) (sqrt (sqrt k)))
  (pow 2 (* (- 1 k) 1/2))
  (/ (pow PI (* (- 1 k) 1/2)) (sqrt k))
  (* (/ (cbrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))) (cbrt (sqrt k))) (/ (cbrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))) (cbrt (sqrt k))))
  (/ (cbrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))) (cbrt (sqrt k)))
  (* (/ (cbrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))) (fabs (cbrt k))) (cbrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))))
  (/ (cbrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt (cbrt k)))
  (/ (cbrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))) (/ (sqrt (sqrt k)) (cbrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))))))
  (/ (cbrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt (sqrt k)))
  (* (cbrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))) (cbrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))))
  (/ (cbrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt k))
  (/ (cbrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))) (/ (sqrt (sqrt k)) (cbrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))))))
  (/ (cbrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt (sqrt k)))
  (* (cbrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))) (cbrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))))
  (/ (cbrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt k))
  (/ (/ (sqrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))) (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ (sqrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))) (cbrt (sqrt k)))
  (/ (sqrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))) (fabs (cbrt k)))
  (/ (sqrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt (cbrt k)))
  (/ (sqrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt (sqrt k)))
  (/ (sqrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt (sqrt k)))
  (sqrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))))
  (/ (sqrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt k))
  (/ (sqrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt (sqrt k)))
  (/ (sqrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt (sqrt k)))
  (sqrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))))
  (/ (sqrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt k))
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))) (cbrt (sqrt k)))
  (/ 1 (fabs (cbrt k)))
  (/ (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))) (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))) (sqrt (sqrt k)))
  1
  (/ (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))) (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))) (sqrt (sqrt k)))
  1
  (/ (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))) (sqrt k))
  (/ (pow (* 2 PI) (- 1/4 (/ k 4))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* 2 PI) (- 1/4 (/ k 4))) (cbrt (sqrt k)))
  (/ (pow (* 2 PI) (- 1/4 (/ k 4))) (fabs (cbrt k)))
  (/ (pow (* 2 PI) (- 1/4 (/ k 4))) (sqrt (cbrt k)))
  (/ (pow (* 2 PI) (- 1/4 (/ k 4))) (sqrt (sqrt k)))
  (/ (pow (* 2 PI) (- 1/4 (/ k 4))) (sqrt (sqrt k)))
  (pow (* 2 PI) (- 1/4 (/ k 4)))
  (/ (pow (* 2 PI) (- 1/4 (/ k 4))) (sqrt k))
  (/ (pow (* 2 PI) (- 1/4 (/ k 4))) (sqrt (sqrt k)))
  (/ (pow (* 2 PI) (- 1/4 (/ k 4))) (sqrt (sqrt k)))
  (pow (* 2 PI) (- 1/4 (/ k 4)))
  (/ (pow (* 2 PI) (- 1/4 (/ k 4))) (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))))
  (/ (/ (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))) (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))) (fabs (cbrt k)))
  (/ (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))) (sqrt (sqrt k)))
  (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))
  (/ (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))) (sqrt (sqrt k)))
  (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))
  (/ (sqrt k) (pow PI (* (- 1 k) 1/2)))
  (/ (sqrt k) (cbrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))))
  (/ (sqrt k) (sqrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))))
  (/ (sqrt k) (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))))
  (/ (sqrt k) (pow (* 2 PI) (- 1/4 (/ k 4))))
  (real->posit16 (/ (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))) (sqrt k)))
  (- (* (* (- 1 k) 1/2) (+ (log n) (log (* 2 PI)))) (log (sqrt k)))
  (- (* (* (- 1 k) 1/2) (+ (log n) (log (* 2 PI)))) (log (sqrt k)))
  (- (* (* (- 1 k) 1/2) (+ (log n) (log (* 2 PI)))) (log (sqrt k)))
  (- (* (* (- 1 k) 1/2) (+ (log n) (log (* 2 PI)))) (log (sqrt k)))
  (- (* (* (- 1 k) 1/2) (+ (log n) (log (* 2 PI)))) (log (sqrt k)))
  (- (* (* (- 1 k) 1/2) (+ (log n) (log (* 2 PI)))) (log (sqrt k)))
  (- (* (* (- 1 k) 1/2) (+ (log n) (log (* 2 PI)))) (log (sqrt k)))
  (- (* (* (- 1 k) 1/2) (+ (log n) (log (* 2 PI)))) (log (sqrt k)))
  (- (* (* (- 1 k) 1/2) (+ (log n) (log (* 2 PI)))) (log (sqrt k)))
  (- (* (* (- 1 k) 1/2) (+ (log n) (log (* 2 PI)))) (log (sqrt k)))
  (- (* (* (- 1 k) 1/2) (+ (log n) (log (* 2 PI)))) (log (sqrt k)))
  (- (* (* (- 1 k) 1/2) (+ (log n) (log (* 2 PI)))) (log (sqrt k)))
  (- (* (* (- 1 k) 1/2) (+ (log n) (log (* 2 PI)))) (log (sqrt k)))
  (- (* (* (- 1 k) 1/2) (+ (log n) (log (* 2 PI)))) (log (sqrt k)))
  (- (* (* (- 1 k) 1/2) (+ (log n) (log (* 2 PI)))) (log (sqrt k)))
  (- (* (* (- 1 k) 1/2) (+ (log n) (log (* 2 PI)))) (log (sqrt k)))
  (exp (/ (* (pow n (* (- 1 k) 1/2)) (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt k)))
  (* (pow n (* (- 1 k) 1/2)) (* (pow n (* (- 1 k) 1/2)) (* (/ (/ (pow (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))) 3) (sqrt k)) k) (pow n (* (- 1 k) 1/2)))))
  (* (* (/ (* (pow n (* (- 1 k) 1/2)) (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt k)) (* (/ (* (pow n (* (- 1 k) 1/2)) (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt k)) (pow n (* (- 1 k) 1/2)))) (/ (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))) (sqrt k)))
  (* (cbrt (/ (* (pow n (* (- 1 k) 1/2)) (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt k))) (cbrt (/ (* (pow n (* (- 1 k) 1/2)) (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt k))))
  (cbrt (/ (* (pow n (* (- 1 k) 1/2)) (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt k)))
  (* (* (/ (* (pow n (* (- 1 k) 1/2)) (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt k)) (* (/ (* (pow n (* (- 1 k) 1/2)) (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt k)) (pow n (* (- 1 k) 1/2)))) (/ (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))) (sqrt k)))
  (sqrt (/ (* (pow n (* (- 1 k) 1/2)) (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt k)))
  (sqrt (/ (* (pow n (* (- 1 k) 1/2)) (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt k)))
  (* (pow (sqrt n) (* (- 1 k) 1/2)) (sqrt (/ (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))) (sqrt k))))
  (* (pow (sqrt n) (* (- 1 k) 1/2)) (sqrt (/ (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))) (sqrt k))))
  (* (/ (sqrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt (sqrt k))) (pow (sqrt n) (* (- 1 k) 1/2)))
  (* (/ (sqrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt (sqrt k))) (pow (sqrt n) (* (- 1 k) 1/2)))
  (* (/ (sqrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt (sqrt k))) (pow (sqrt n) (* (- 1 k) 1/2)))
  (* (/ (sqrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt (sqrt k))) (pow (sqrt n) (* (- 1 k) 1/2)))
  (* (pow (sqrt n) (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt (sqrt k))))
  (* (pow (sqrt n) (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt (sqrt k))))
  (* (pow (sqrt n) (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt (sqrt k))))
  (* (pow (sqrt n) (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt (sqrt k))))
  (* (sqrt (/ (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))) (sqrt k))) (sqrt (pow n (* (- 1 k) 1/2))))
  (* (sqrt (/ (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))) (sqrt k))) (sqrt (pow n (* (- 1 k) 1/2))))
  (* (sqrt (pow n (* (- 1 k) 1/2))) (/ (sqrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt (sqrt k))))
  (* (sqrt (pow n (* (- 1 k) 1/2))) (/ (sqrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt (sqrt k))))
  (* (sqrt (pow n (* (- 1 k) 1/2))) (/ (sqrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt (sqrt k))))
  (* (sqrt (pow n (* (- 1 k) 1/2))) (/ (sqrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt (sqrt k))))
  (/ (* (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt (pow n (* (- 1 k) 1/2)))) (sqrt (sqrt k)))
  (/ (* (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt (pow n (* (- 1 k) 1/2)))) (sqrt (sqrt k)))
  (/ (* (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt (pow n (* (- 1 k) 1/2)))) (sqrt (sqrt k)))
  (/ (* (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (sqrt (pow n (* (- 1 k) 1/2)))) (sqrt (sqrt k)))
  (* (pow n (/ (- 1 k) 8)) (* (pow n (/ (- 1 k) 8)) (sqrt (/ (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))) (sqrt k)))))
  (* (pow n (/ (- 1 k) 8)) (* (pow n (/ (- 1 k) 8)) (sqrt (/ (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))) (sqrt k)))))
  (/ (* (sqrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))) (pow n (/ (* (- 1 k) 1/2) 2))) (sqrt (sqrt k)))
  (/ (* (sqrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))) (pow n (/ (* (- 1 k) 1/2) 2))) (sqrt (sqrt k)))
  (/ (* (sqrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))) (pow n (/ (* (- 1 k) 1/2) 2))) (sqrt (sqrt k)))
  (/ (* (sqrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))) (pow n (/ (* (- 1 k) 1/2) 2))) (sqrt (sqrt k)))
  (* (pow n (- 1/4 (/ k 4))) (/ (pow (* 2 PI) (- 1/4 (/ k 4))) (sqrt (sqrt k))))
  (* (pow n (- 1/4 (/ k 4))) (/ (pow (* 2 PI) (- 1/4 (/ k 4))) (sqrt (sqrt k))))
  (* (pow n (- 1/4 (/ k 4))) (/ (pow (* 2 PI) (- 1/4 (/ k 4))) (sqrt (sqrt k))))
  (* (pow n (- 1/4 (/ k 4))) (/ (pow (* 2 PI) (- 1/4 (/ k 4))) (sqrt (sqrt k))))
  (* (cbrt (/ (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))) (sqrt k))) (* (cbrt (/ (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))) (sqrt k))) (pow n (* (- 1 k) 1/2))))
  (* (pow n (* (- 1 k) 1/2)) (sqrt (/ (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))) (sqrt k))))
  (/ (* (pow 2 (* (- 1 k) 1/2)) (pow n (* (- 1 k) 1/2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (* (pow 2 (* (- 1 k) 1/2)) (pow n (* (- 1 k) 1/2))) (fabs (cbrt k)))
  (/ (* (pow n (* (- 1 k) 1/2)) (pow 2 (* (- 1 k) 1/2))) (sqrt (sqrt k)))
  (* (pow 2 (* (- 1 k) 1/2)) (pow n (* (- 1 k) 1/2)))
  (/ (* (pow n (* (- 1 k) 1/2)) (pow 2 (* (- 1 k) 1/2))) (sqrt (sqrt k)))
  (* (pow 2 (* (- 1 k) 1/2)) (pow n (* (- 1 k) 1/2)))
  (* (pow n (* (- 1 k) 1/2)) (* (/ (cbrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))) (cbrt (sqrt k))) (/ (cbrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))) (cbrt (sqrt k)))))
  (* (* (/ (cbrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))) (fabs (cbrt k))) (cbrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))))) (pow n (* (- 1 k) 1/2)))
  (* (pow n (* (- 1 k) 1/2)) (/ (cbrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))) (/ (sqrt (sqrt k)) (cbrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))))))
  (* (pow n (* (- 1 k) 1/2)) (* (cbrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))) (cbrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))))))
  (* (pow n (* (- 1 k) 1/2)) (/ (cbrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))) (/ (sqrt (sqrt k)) (cbrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))))))
  (* (pow n (* (- 1 k) 1/2)) (* (cbrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))) (cbrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))))))
  (/ (* (pow n (* (- 1 k) 1/2)) (sqrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (* (pow n (* (- 1 k) 1/2)) (sqrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))))) (fabs (cbrt k)))
  (* (pow n (* (- 1 k) 1/2)) (/ (sqrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt (sqrt k))))
  (* (pow n (* (- 1 k) 1/2)) (sqrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))))
  (* (pow n (* (- 1 k) 1/2)) (/ (sqrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt (sqrt k))))
  (* (pow n (* (- 1 k) 1/2)) (sqrt (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))))
  (/ (pow n (* (- 1 k) 1/2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow n (* (- 1 k) 1/2)) (fabs (cbrt k)))
  (/ (pow n (* (- 1 k) 1/2)) (sqrt (sqrt k)))
  (pow n (* (- 1 k) 1/2))
  (/ (pow n (* (- 1 k) 1/2)) (sqrt (sqrt k)))
  (pow n (* (- 1 k) 1/2))
  (* (/ (pow n (* (- 1 k) 1/2)) (cbrt (sqrt k))) (/ (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (cbrt (sqrt k))))
  (/ (* (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)) (pow n (* (- 1 k) 1/2))) (fabs (cbrt k)))
  (/ (* (pow n (* (- 1 k) 1/2)) (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2))) (sqrt (sqrt k)))
  (* (pow n (* (- 1 k) 1/2)) (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)))
  (/ (* (pow n (* (- 1 k) 1/2)) (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2))) (sqrt (sqrt k)))
  (* (pow n (* (- 1 k) 1/2)) (pow (* 2 PI) (/ (* (- 1 k) 1/2) 2)))
  (pow n (* (- 1 k) 1/2))
  (* (pow n (* (- 1 k) 1/2)) (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))))
  (/ (* (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))) (pow (cbrt n) (* (- 1 k) 1/2))) (sqrt k))
  (/ (pow (sqrt n) (* (- 1 k) 1/2)) (/ (sqrt k) (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))))
  (/ (* (pow n (* (- 1 k) 1/2)) (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt k))
  (/ (* (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))) (cbrt (pow n (* (- 1 k) 1/2)))) (sqrt k))
  (/ (* (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))) (sqrt (pow n (* (- 1 k) 1/2)))) (sqrt k))
  (/ (* (pow n (* (- 1 k) 1/2)) (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt k))
  (/ (pow n (/ (* (- 1 k) 1/2) 2)) (/ (sqrt k) (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))))
  (* (pow n (* (- 1 k) 1/2)) (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))))
  (real->posit16 (/ (* (pow n (* (- 1 k) 1/2)) (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt k)))
  (+ (* (* 1/8 (sqrt n)) (* (* k (log n)) (* k (log n)))) (- (sqrt n) (* (* k (log n)) (* 1/2 (sqrt n)))))
  (exp (* (* -1/2 (- (log n))) (- 1 k)))
  (exp (* (* (- 1 k) 1/2) (- (log -1) (- (log -1) (log n)))))
  (+ (* 1/8 (* (* (sqrt PI) (sqrt 2)) (* (* k (log (* 2 PI))) (* k (log (* 2 PI)))))) (- (sqrt (* 2 PI)) (* (sqrt 2) (* (* (* k (log (* 2 PI))) (sqrt PI)) 1/2))))
  (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))
  (exp (* (log (* 2 PI)) (* (- 1 k) 1/2)))
  (- (- (- (* (* (* +nan.0 (* k k)) (sqrt 2)) (sqrt PI)) (* (* (sqrt PI) (sqrt 2)) +nan.0)) (+ (- (* (* (log (* 2 PI)) (log (* 2 PI))) (* (* (* +nan.0 (* k k)) (sqrt 2)) (sqrt PI))) (* +nan.0 (- (* (sqrt 2) (* (* k (log (* 2 PI))) (sqrt PI))) (* k (* (sqrt PI) (sqrt 2)))))) (* (- (* (* (log (* 2 PI)) (sqrt PI)) (* (sqrt 2) (* k k)))) +nan.0))))
  (- (- (* (/ +nan.0 k) (/ (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))) (* k k))) (- (/ (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))) (/ k +nan.0)) (/ (/ (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))) (/ k +nan.0)) k))))
  (- (+ (- (/ (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))) (/ k +nan.0)) (/ (/ (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))) (/ k +nan.0)) k)) (* +nan.0 (exp (* (log (* 2 PI)) (* (- 1 k) 1/2))))))
  (+ (* (- (* (* +nan.0 (* k k)) (sqrt 2))) (sqrt (* n PI))) (+ (- (* (* k (sqrt 2)) (* (sqrt (* n PI)) +nan.0)) (* (* +nan.0 (sqrt (* n PI))) (* (* (* k (log (* 2 PI))) (* k (log (* 2 PI)))) (sqrt 2)))) (- (* (* +nan.0 (* (sqrt 2) (* (* k (log n)) (* k (log n))))) (sqrt (* n PI))) (+ (- (* (* +nan.0 (sqrt 2)) (* (* k (log n)) (sqrt (* n PI)))) (* (* (* (log n) (* k (sqrt 2))) k) (* (sqrt (* n PI)) +nan.0))) (+ (- (* (* (* (* k (* k (log n))) (* (sqrt (* n PI)) (sqrt 2))) (log (* 2 PI))) +nan.0) (* (sqrt 2) (* (sqrt (* n PI)) +nan.0))) (* (sqrt (* n PI)) (- (* (* (* k (sqrt 2)) (log (* 2 PI))) +nan.0) (* (* +nan.0 (log (* 2 PI))) (* (sqrt 2) (* k k))))))))))
  (- (- (/ +nan.0 (/ (* k k) (exp (+ (* (* -1/2 (- (log n))) (- 1 k)) (* (log (* 2 PI)) (* (- 1 k) 1/2)))))) (* +nan.0 (- (/ (exp (+ (* (* -1/2 (- (log n))) (- 1 k)) (* (log (* 2 PI)) (* (- 1 k) 1/2)))) k) (/ (/ (exp (+ (* (* -1/2 (- (log n))) (- 1 k)) (* (log (* 2 PI)) (* (- 1 k) 1/2)))) k) (* k k))))))
  (+ (* +nan.0 (- (exp (* 1/2 (+ (* (- 1 k) (- (log -1) (- (log -1) (log n)))) (* (log (* 2 PI)) (- 1 k))))) (/ (exp (* 1/2 (+ (* (- 1 k) (- (log -1) (- (log -1) (log n)))) (* (log (* 2 PI)) (- 1 k))))) k))) (- (/ +nan.0 (/ (* k k) (exp (* 1/2 (+ (* (- 1 k) (- (log -1) (- (log -1) (log n)))) (* (log (* 2 PI)) (- 1 k)))))))))
12.274 * * * [progress]: adding candidates to table
14.739 * * [progress]: iteration 4 / 4
14.739 * * * [progress]: picking best candidate
14.764 * * * * [pick]: Picked  #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))>
14.764 * * * [progress]: localizing error
14.821 * * * [progress]: generating rewritten candidates
14.821 * * * * [progress]: [ 1 / 4 ] rewriting at (2 1)
14.824 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1 2)
14.827 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2)
14.843 * * * * [progress]: [ 4 / 4 ] rewriting at (2)
14.873 * * * [progress]: generating series expansions
14.873 * * * * [progress]: [ 1 / 4 ] generating series at (2 1)
14.874 * [backup-simplify]: Simplify (pow n (* (- 1 k) 1/2)) into (pow n (* 1/2 (- 1 k)))
14.874 * [approximate]: Taking taylor expansion of (pow n (* 1/2 (- 1 k))) in (n k) around 0
14.874 * [taylor]: Taking taylor expansion of (pow n (* 1/2 (- 1 k))) in k
14.874 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log n))) in k
14.874 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log n)) in k
14.874 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
14.874 * [taylor]: Taking taylor expansion of 1/2 in k
14.874 * [backup-simplify]: Simplify 1/2 into 1/2
14.874 * [taylor]: Taking taylor expansion of (- 1 k) in k
14.874 * [taylor]: Taking taylor expansion of 1 in k
14.874 * [backup-simplify]: Simplify 1 into 1
14.874 * [taylor]: Taking taylor expansion of k in k
14.874 * [backup-simplify]: Simplify 0 into 0
14.874 * [backup-simplify]: Simplify 1 into 1
14.874 * [taylor]: Taking taylor expansion of (log n) in k
14.874 * [taylor]: Taking taylor expansion of n in k
14.874 * [backup-simplify]: Simplify n into n
14.874 * [backup-simplify]: Simplify (log n) into (log n)
14.875 * [backup-simplify]: Simplify (- 0) into 0
14.875 * [backup-simplify]: Simplify (+ 1 0) into 1
14.876 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
14.876 * [backup-simplify]: Simplify (* 1/2 (log n)) into (* 1/2 (log n))
14.876 * [backup-simplify]: Simplify (exp (* 1/2 (log n))) into (pow n 1/2)
14.876 * [taylor]: Taking taylor expansion of (pow n (* 1/2 (- 1 k))) in n
14.876 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log n))) in n
14.876 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log n)) in n
14.876 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
14.876 * [taylor]: Taking taylor expansion of 1/2 in n
14.876 * [backup-simplify]: Simplify 1/2 into 1/2
14.876 * [taylor]: Taking taylor expansion of (- 1 k) in n
14.876 * [taylor]: Taking taylor expansion of 1 in n
14.876 * [backup-simplify]: Simplify 1 into 1
14.876 * [taylor]: Taking taylor expansion of k in n
14.876 * [backup-simplify]: Simplify k into k
14.876 * [taylor]: Taking taylor expansion of (log n) in n
14.876 * [taylor]: Taking taylor expansion of n in n
14.876 * [backup-simplify]: Simplify 0 into 0
14.876 * [backup-simplify]: Simplify 1 into 1
14.876 * [backup-simplify]: Simplify (log 1) into 0
14.876 * [backup-simplify]: Simplify (- k) into (- k)
14.877 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
14.877 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
14.877 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
14.877 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (log n)) into (* 1/2 (* (- 1 k) (log n)))
14.877 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (log n)))) into (exp (* 1/2 (* (- 1 k) (log n))))
14.877 * [taylor]: Taking taylor expansion of (pow n (* 1/2 (- 1 k))) in n
14.877 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log n))) in n
14.877 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log n)) in n
14.877 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
14.877 * [taylor]: Taking taylor expansion of 1/2 in n
14.877 * [backup-simplify]: Simplify 1/2 into 1/2
14.877 * [taylor]: Taking taylor expansion of (- 1 k) in n
14.878 * [taylor]: Taking taylor expansion of 1 in n
14.878 * [backup-simplify]: Simplify 1 into 1
14.878 * [taylor]: Taking taylor expansion of k in n
14.878 * [backup-simplify]: Simplify k into k
14.878 * [taylor]: Taking taylor expansion of (log n) in n
14.878 * [taylor]: Taking taylor expansion of n in n
14.878 * [backup-simplify]: Simplify 0 into 0
14.878 * [backup-simplify]: Simplify 1 into 1
14.878 * [backup-simplify]: Simplify (log 1) into 0
14.878 * [backup-simplify]: Simplify (- k) into (- k)
14.878 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
14.878 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
14.879 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
14.879 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (log n)) into (* 1/2 (* (- 1 k) (log n)))
14.879 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (log n)))) into (exp (* 1/2 (* (- 1 k) (log n))))
14.879 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (log n)))) in k
14.879 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 k) (log n))) in k
14.879 * [taylor]: Taking taylor expansion of 1/2 in k
14.879 * [backup-simplify]: Simplify 1/2 into 1/2
14.879 * [taylor]: Taking taylor expansion of (* (- 1 k) (log n)) in k
14.879 * [taylor]: Taking taylor expansion of (- 1 k) in k
14.879 * [taylor]: Taking taylor expansion of 1 in k
14.879 * [backup-simplify]: Simplify 1 into 1
14.879 * [taylor]: Taking taylor expansion of k in k
14.879 * [backup-simplify]: Simplify 0 into 0
14.879 * [backup-simplify]: Simplify 1 into 1
14.879 * [taylor]: Taking taylor expansion of (log n) in k
14.879 * [taylor]: Taking taylor expansion of n in k
14.879 * [backup-simplify]: Simplify n into n
14.879 * [backup-simplify]: Simplify (log n) into (log n)
14.880 * [backup-simplify]: Simplify (- 0) into 0
14.880 * [backup-simplify]: Simplify (+ 1 0) into 1
14.880 * [backup-simplify]: Simplify (* 1 (log n)) into (log n)
14.880 * [backup-simplify]: Simplify (* 1/2 (log n)) into (* 1/2 (log n))
14.880 * [backup-simplify]: Simplify (exp (* 1/2 (log n))) into (pow n 1/2)
14.880 * [backup-simplify]: Simplify (pow n 1/2) into (pow n 1/2)
14.881 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0
14.882 * [backup-simplify]: Simplify (- 0) into 0
14.882 * [backup-simplify]: Simplify (+ 0 0) into 0
14.883 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 k))) into 0
14.883 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
14.883 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (log n))) into 0
14.884 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
14.884 * [taylor]: Taking taylor expansion of 0 in k
14.884 * [backup-simplify]: Simplify 0 into 0
14.884 * [backup-simplify]: Simplify 0 into 0
14.885 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
14.885 * [backup-simplify]: Simplify (- 1) into -1
14.885 * [backup-simplify]: Simplify (+ 0 -1) into -1
14.886 * [backup-simplify]: Simplify (+ (* 1 0) (* -1 (log n))) into (- (log n))
14.886 * [backup-simplify]: Simplify (+ (* 1/2 (- (log n))) (* 0 (log n))) into (- (* 1/2 (log n)))
14.886 * [backup-simplify]: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 1) 1)))) into (* -1/2 (* (sqrt n) (log n)))
14.886 * [backup-simplify]: Simplify (* -1/2 (* (sqrt n) (log n))) into (* -1/2 (* (sqrt n) (log n)))
14.893 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0
14.893 * [backup-simplify]: Simplify (- 0) into 0
14.894 * [backup-simplify]: Simplify (+ 0 0) into 0
14.894 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0
14.895 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
14.895 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (log n)))) into 0
14.897 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
14.897 * [taylor]: Taking taylor expansion of 0 in k
14.897 * [backup-simplify]: Simplify 0 into 0
14.897 * [backup-simplify]: Simplify 0 into 0
14.897 * [backup-simplify]: Simplify 0 into 0
14.899 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
14.900 * [backup-simplify]: Simplify (- 0) into 0
14.900 * [backup-simplify]: Simplify (+ 0 0) into 0
14.901 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (log n)))) into 0
14.902 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (log n))) (* 0 (log n)))) into 0
14.902 * [backup-simplify]: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt n) (pow (log n) 2)))
14.903 * [backup-simplify]: Simplify (* 1/8 (* (sqrt n) (pow (log n) 2))) into (* 1/8 (* (sqrt n) (pow (log n) 2)))
14.903 * [backup-simplify]: Simplify (+ (* (* 1/8 (* (sqrt n) (pow (log n) 2))) (pow (* k 1) 2)) (+ (* (* -1/2 (* (sqrt n) (log n))) (* k 1)) (pow n 1/2))) into (- (+ (pow n 1/2) (* 1/8 (* (sqrt n) (* (pow (log n) 2) (pow k 2))))) (* 1/2 (* (sqrt n) (* (log n) k))))
14.903 * [backup-simplify]: Simplify (pow (/ 1 n) (* (- 1 (/ 1 k)) 1/2)) into (pow (/ 1 n) (* 1/2 (- 1 (/ 1 k))))
14.903 * [approximate]: Taking taylor expansion of (pow (/ 1 n) (* 1/2 (- 1 (/ 1 k)))) in (n k) around 0
14.904 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (* 1/2 (- 1 (/ 1 k)))) in k
14.904 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (/ 1 n)))) in k
14.904 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (/ 1 n))) in k
14.904 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
14.904 * [taylor]: Taking taylor expansion of 1/2 in k
14.904 * [backup-simplify]: Simplify 1/2 into 1/2
14.904 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
14.904 * [taylor]: Taking taylor expansion of 1 in k
14.904 * [backup-simplify]: Simplify 1 into 1
14.904 * [taylor]: Taking taylor expansion of (/ 1 k) in k
14.904 * [taylor]: Taking taylor expansion of k in k
14.904 * [backup-simplify]: Simplify 0 into 0
14.904 * [backup-simplify]: Simplify 1 into 1
14.904 * [backup-simplify]: Simplify (/ 1 1) into 1
14.904 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in k
14.904 * [taylor]: Taking taylor expansion of (/ 1 n) in k
14.904 * [taylor]: Taking taylor expansion of n in k
14.904 * [backup-simplify]: Simplify n into n
14.904 * [backup-simplify]: Simplify (/ 1 n) into (/ 1 n)
14.905 * [backup-simplify]: Simplify (log (/ 1 n)) into (log (/ 1 n))
14.905 * [backup-simplify]: Simplify (- 1) into -1
14.905 * [backup-simplify]: Simplify (+ 0 -1) into -1
14.906 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
14.906 * [backup-simplify]: Simplify (* -1/2 (log (/ 1 n))) into (* -1/2 (log (/ 1 n)))
14.906 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (/ 1 n)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (/ 1 n)))))
14.906 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (* 1/2 (- 1 (/ 1 k)))) in n
14.906 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (/ 1 n)))) in n
14.906 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (/ 1 n))) in n
14.906 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
14.906 * [taylor]: Taking taylor expansion of 1/2 in n
14.906 * [backup-simplify]: Simplify 1/2 into 1/2
14.906 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
14.906 * [taylor]: Taking taylor expansion of 1 in n
14.906 * [backup-simplify]: Simplify 1 into 1
14.906 * [taylor]: Taking taylor expansion of (/ 1 k) in n
14.906 * [taylor]: Taking taylor expansion of k in n
14.907 * [backup-simplify]: Simplify k into k
14.907 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
14.907 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n
14.907 * [taylor]: Taking taylor expansion of (/ 1 n) in n
14.907 * [taylor]: Taking taylor expansion of n in n
14.907 * [backup-simplify]: Simplify 0 into 0
14.907 * [backup-simplify]: Simplify 1 into 1
14.907 * [backup-simplify]: Simplify (/ 1 1) into 1
14.908 * [backup-simplify]: Simplify (log 1) into 0
14.908 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
14.908 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
14.908 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
14.908 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n))
14.908 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log n))) into (* -1/2 (* (- 1 (/ 1 k)) (log n)))
14.909 * [backup-simplify]: Simplify (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) into (exp (* -1/2 (* (- 1 (/ 1 k)) (log n))))
14.909 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (* 1/2 (- 1 (/ 1 k)))) in n
14.909 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (/ 1 n)))) in n
14.909 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (/ 1 n))) in n
14.909 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
14.909 * [taylor]: Taking taylor expansion of 1/2 in n
14.909 * [backup-simplify]: Simplify 1/2 into 1/2
14.909 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
14.909 * [taylor]: Taking taylor expansion of 1 in n
14.909 * [backup-simplify]: Simplify 1 into 1
14.909 * [taylor]: Taking taylor expansion of (/ 1 k) in n
14.909 * [taylor]: Taking taylor expansion of k in n
14.909 * [backup-simplify]: Simplify k into k
14.909 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
14.909 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n
14.909 * [taylor]: Taking taylor expansion of (/ 1 n) in n
14.909 * [taylor]: Taking taylor expansion of n in n
14.909 * [backup-simplify]: Simplify 0 into 0
14.909 * [backup-simplify]: Simplify 1 into 1
14.910 * [backup-simplify]: Simplify (/ 1 1) into 1
14.910 * [backup-simplify]: Simplify (log 1) into 0
14.910 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
14.910 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
14.910 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
14.911 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n))
14.911 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log n))) into (* -1/2 (* (- 1 (/ 1 k)) (log n)))
14.911 * [backup-simplify]: Simplify (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) into (exp (* -1/2 (* (- 1 (/ 1 k)) (log n))))
14.911 * [taylor]: Taking taylor expansion of (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) in k
14.911 * [taylor]: Taking taylor expansion of (* -1/2 (* (- 1 (/ 1 k)) (log n))) in k
14.911 * [taylor]: Taking taylor expansion of -1/2 in k
14.911 * [backup-simplify]: Simplify -1/2 into -1/2
14.911 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log n)) in k
14.911 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
14.911 * [taylor]: Taking taylor expansion of 1 in k
14.911 * [backup-simplify]: Simplify 1 into 1
14.911 * [taylor]: Taking taylor expansion of (/ 1 k) in k
14.911 * [taylor]: Taking taylor expansion of k in k
14.911 * [backup-simplify]: Simplify 0 into 0
14.911 * [backup-simplify]: Simplify 1 into 1
14.912 * [backup-simplify]: Simplify (/ 1 1) into 1
14.912 * [taylor]: Taking taylor expansion of (log n) in k
14.912 * [taylor]: Taking taylor expansion of n in k
14.912 * [backup-simplify]: Simplify n into n
14.912 * [backup-simplify]: Simplify (log n) into (log n)
14.912 * [backup-simplify]: Simplify (- 1) into -1
14.913 * [backup-simplify]: Simplify (+ 0 -1) into -1
14.913 * [backup-simplify]: Simplify (* -1 (log n)) into (* -1 (log n))
14.913 * [backup-simplify]: Simplify (* -1/2 (* -1 (log n))) into (* 1/2 (log n))
14.913 * [backup-simplify]: Simplify (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) into (exp (* -1/2 (* (- 1 (/ 1 k)) (log n))))
14.913 * [backup-simplify]: Simplify (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) into (exp (* -1/2 (* (- 1 (/ 1 k)) (log n))))
14.914 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
14.915 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0
14.915 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
14.916 * [backup-simplify]: Simplify (- 0) into 0
14.916 * [backup-simplify]: Simplify (+ 0 0) into 0
14.917 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 (/ 1 k)))) into 0
14.917 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n))
14.917 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log n)))) into 0
14.918 * [backup-simplify]: Simplify (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
14.918 * [taylor]: Taking taylor expansion of 0 in k
14.918 * [backup-simplify]: Simplify 0 into 0
14.918 * [backup-simplify]: Simplify 0 into 0
14.918 * [backup-simplify]: Simplify 0 into 0
14.919 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
14.922 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0
14.922 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
14.923 * [backup-simplify]: Simplify (- 0) into 0
14.923 * [backup-simplify]: Simplify (+ 0 0) into 0
14.924 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0
14.925 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n))
14.925 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log n))))) into 0
14.927 * [backup-simplify]: Simplify (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
14.927 * [taylor]: Taking taylor expansion of 0 in k
14.927 * [backup-simplify]: Simplify 0 into 0
14.927 * [backup-simplify]: Simplify 0 into 0
14.927 * [backup-simplify]: Simplify 0 into 0
14.927 * [backup-simplify]: Simplify 0 into 0
14.928 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
14.930 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0
14.931 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
14.931 * [backup-simplify]: Simplify (- 0) into 0
14.931 * [backup-simplify]: Simplify (+ 0 0) into 0
14.932 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0
14.932 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n))
14.933 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0
14.934 * [backup-simplify]: Simplify (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
14.934 * [taylor]: Taking taylor expansion of 0 in k
14.934 * [backup-simplify]: Simplify 0 into 0
14.934 * [backup-simplify]: Simplify 0 into 0
14.934 * [backup-simplify]: Simplify (exp (* -1/2 (* (- 1 (/ 1 (/ 1 k))) (log (/ 1 n))))) into (exp (* -1/2 (* (- 1 k) (log (/ 1 n)))))
14.934 * [backup-simplify]: Simplify (pow (/ 1 (- n)) (* (- 1 (/ 1 (- k))) 1/2)) into (pow (/ -1 n) (* 1/2 (+ (/ 1 k) 1)))
14.934 * [approximate]: Taking taylor expansion of (pow (/ -1 n) (* 1/2 (+ (/ 1 k) 1))) in (n k) around 0
14.934 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (* 1/2 (+ (/ 1 k) 1))) in k
14.934 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (/ -1 n)))) in k
14.934 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (/ -1 n))) in k
14.934 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
14.934 * [taylor]: Taking taylor expansion of 1/2 in k
14.934 * [backup-simplify]: Simplify 1/2 into 1/2
14.934 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
14.934 * [taylor]: Taking taylor expansion of (/ 1 k) in k
14.934 * [taylor]: Taking taylor expansion of k in k
14.934 * [backup-simplify]: Simplify 0 into 0
14.934 * [backup-simplify]: Simplify 1 into 1
14.934 * [backup-simplify]: Simplify (/ 1 1) into 1
14.934 * [taylor]: Taking taylor expansion of 1 in k
14.934 * [backup-simplify]: Simplify 1 into 1
14.934 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in k
14.934 * [taylor]: Taking taylor expansion of (/ -1 n) in k
14.934 * [taylor]: Taking taylor expansion of -1 in k
14.934 * [backup-simplify]: Simplify -1 into -1
14.934 * [taylor]: Taking taylor expansion of n in k
14.934 * [backup-simplify]: Simplify n into n
14.935 * [backup-simplify]: Simplify (/ -1 n) into (/ -1 n)
14.935 * [backup-simplify]: Simplify (log (/ -1 n)) into (log (/ -1 n))
14.935 * [backup-simplify]: Simplify (+ 1 0) into 1
14.935 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
14.935 * [backup-simplify]: Simplify (* 1/2 (log (/ -1 n))) into (* 1/2 (log (/ -1 n)))
14.935 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (/ -1 n)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (/ -1 n)))))
14.935 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (* 1/2 (+ (/ 1 k) 1))) in n
14.935 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (/ -1 n)))) in n
14.935 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (/ -1 n))) in n
14.935 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
14.935 * [taylor]: Taking taylor expansion of 1/2 in n
14.935 * [backup-simplify]: Simplify 1/2 into 1/2
14.935 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
14.935 * [taylor]: Taking taylor expansion of (/ 1 k) in n
14.935 * [taylor]: Taking taylor expansion of k in n
14.935 * [backup-simplify]: Simplify k into k
14.935 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
14.935 * [taylor]: Taking taylor expansion of 1 in n
14.935 * [backup-simplify]: Simplify 1 into 1
14.935 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n
14.935 * [taylor]: Taking taylor expansion of (/ -1 n) in n
14.936 * [taylor]: Taking taylor expansion of -1 in n
14.936 * [backup-simplify]: Simplify -1 into -1
14.936 * [taylor]: Taking taylor expansion of n in n
14.936 * [backup-simplify]: Simplify 0 into 0
14.936 * [backup-simplify]: Simplify 1 into 1
14.936 * [backup-simplify]: Simplify (/ -1 1) into -1
14.936 * [backup-simplify]: Simplify (log -1) into (log -1)
14.936 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
14.936 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
14.937 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n))
14.937 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log -1) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))
14.937 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))
14.937 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (* 1/2 (+ (/ 1 k) 1))) in n
14.937 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (/ -1 n)))) in n
14.937 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (/ -1 n))) in n
14.937 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
14.937 * [taylor]: Taking taylor expansion of 1/2 in n
14.937 * [backup-simplify]: Simplify 1/2 into 1/2
14.937 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
14.938 * [taylor]: Taking taylor expansion of (/ 1 k) in n
14.938 * [taylor]: Taking taylor expansion of k in n
14.938 * [backup-simplify]: Simplify k into k
14.938 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
14.938 * [taylor]: Taking taylor expansion of 1 in n
14.938 * [backup-simplify]: Simplify 1 into 1
14.938 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n
14.938 * [taylor]: Taking taylor expansion of (/ -1 n) in n
14.938 * [taylor]: Taking taylor expansion of -1 in n
14.938 * [backup-simplify]: Simplify -1 into -1
14.938 * [taylor]: Taking taylor expansion of n in n
14.938 * [backup-simplify]: Simplify 0 into 0
14.938 * [backup-simplify]: Simplify 1 into 1
14.938 * [backup-simplify]: Simplify (/ -1 1) into -1
14.938 * [backup-simplify]: Simplify (log -1) into (log -1)
14.938 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
14.938 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
14.939 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n))
14.939 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log -1) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))
14.939 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))
14.940 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) in k
14.940 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))) in k
14.940 * [taylor]: Taking taylor expansion of 1/2 in k
14.940 * [backup-simplify]: Simplify 1/2 into 1/2
14.940 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log -1) (log n))) in k
14.940 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
14.940 * [taylor]: Taking taylor expansion of (/ 1 k) in k
14.940 * [taylor]: Taking taylor expansion of k in k
14.940 * [backup-simplify]: Simplify 0 into 0
14.940 * [backup-simplify]: Simplify 1 into 1
14.940 * [backup-simplify]: Simplify (/ 1 1) into 1
14.940 * [taylor]: Taking taylor expansion of 1 in k
14.940 * [backup-simplify]: Simplify 1 into 1
14.940 * [taylor]: Taking taylor expansion of (- (log -1) (log n)) in k
14.940 * [taylor]: Taking taylor expansion of (log -1) in k
14.940 * [taylor]: Taking taylor expansion of -1 in k
14.940 * [backup-simplify]: Simplify -1 into -1
14.940 * [backup-simplify]: Simplify (log -1) into (log -1)
14.940 * [taylor]: Taking taylor expansion of (log n) in k
14.940 * [taylor]: Taking taylor expansion of n in k
14.940 * [backup-simplify]: Simplify n into n
14.940 * [backup-simplify]: Simplify (log n) into (log n)
14.941 * [backup-simplify]: Simplify (+ 1 0) into 1
14.941 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
14.941 * [backup-simplify]: Simplify (+ (log -1) (- (log n))) into (- (log -1) (log n))
14.941 * [backup-simplify]: Simplify (* 1 (- (log -1) (log n))) into (- (log -1) (log n))
14.941 * [backup-simplify]: Simplify (* 1/2 (- (log -1) (log n))) into (* 1/2 (- (log -1) (log n)))
14.942 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))
14.942 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))
14.943 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
14.943 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -1 1)))) 1) into 0
14.944 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
14.944 * [backup-simplify]: Simplify (+ 0 0) into 0
14.944 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (/ 1 k) 1))) into 0
14.945 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n))
14.945 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (- (log -1) (log n)))) into 0
14.946 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
14.946 * [taylor]: Taking taylor expansion of 0 in k
14.946 * [backup-simplify]: Simplify 0 into 0
14.946 * [backup-simplify]: Simplify 0 into 0
14.946 * [backup-simplify]: Simplify 0 into 0
14.946 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
14.948 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -1 1)))) 2) into 0
14.948 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
14.948 * [backup-simplify]: Simplify (+ 0 0) into 0
14.949 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0
14.949 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n))
14.950 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log -1) (log n))))) into 0
14.951 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
14.951 * [taylor]: Taking taylor expansion of 0 in k
14.951 * [backup-simplify]: Simplify 0 into 0
14.951 * [backup-simplify]: Simplify 0 into 0
14.951 * [backup-simplify]: Simplify 0 into 0
14.951 * [backup-simplify]: Simplify 0 into 0
14.952 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
14.955 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow -1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow -1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow -1 1)))) 6) into 0
14.955 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
14.955 * [backup-simplify]: Simplify (+ 0 0) into 0
14.956 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1))))) into 0
14.956 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n))
14.957 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log -1) (log n)))))) into 0
14.958 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
14.958 * [taylor]: Taking taylor expansion of 0 in k
14.958 * [backup-simplify]: Simplify 0 into 0
14.958 * [backup-simplify]: Simplify 0 into 0
14.959 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log -1) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n))))))
14.959 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1 2)
14.959 * [backup-simplify]: Simplify (pow PI (* (- 1 k) 1/2)) into (pow PI (* 1/2 (- 1 k)))
14.959 * [approximate]: Taking taylor expansion of (pow PI (* 1/2 (- 1 k))) in (k) around 0
14.959 * [taylor]: Taking taylor expansion of (pow PI (* 1/2 (- 1 k))) in k
14.959 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log PI))) in k
14.959 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log PI)) in k
14.959 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
14.959 * [taylor]: Taking taylor expansion of 1/2 in k
14.959 * [backup-simplify]: Simplify 1/2 into 1/2
14.959 * [taylor]: Taking taylor expansion of (- 1 k) in k
14.959 * [taylor]: Taking taylor expansion of 1 in k
14.959 * [backup-simplify]: Simplify 1 into 1
14.959 * [taylor]: Taking taylor expansion of k in k
14.959 * [backup-simplify]: Simplify 0 into 0
14.959 * [backup-simplify]: Simplify 1 into 1
14.959 * [taylor]: Taking taylor expansion of (log PI) in k
14.959 * [taylor]: Taking taylor expansion of PI in k
14.959 * [backup-simplify]: Simplify PI into PI
14.959 * [backup-simplify]: Simplify (log PI) into (log PI)
14.960 * [backup-simplify]: Simplify (- 0) into 0
14.960 * [backup-simplify]: Simplify (+ 1 0) into 1
14.961 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
14.962 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI))
14.964 * [backup-simplify]: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2)
14.964 * [taylor]: Taking taylor expansion of (pow PI (* 1/2 (- 1 k))) in k
14.964 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log PI))) in k
14.964 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log PI)) in k
14.964 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
14.964 * [taylor]: Taking taylor expansion of 1/2 in k
14.964 * [backup-simplify]: Simplify 1/2 into 1/2
14.964 * [taylor]: Taking taylor expansion of (- 1 k) in k
14.964 * [taylor]: Taking taylor expansion of 1 in k
14.964 * [backup-simplify]: Simplify 1 into 1
14.964 * [taylor]: Taking taylor expansion of k in k
14.964 * [backup-simplify]: Simplify 0 into 0
14.964 * [backup-simplify]: Simplify 1 into 1
14.964 * [taylor]: Taking taylor expansion of (log PI) in k
14.964 * [taylor]: Taking taylor expansion of PI in k
14.964 * [backup-simplify]: Simplify PI into PI
14.964 * [backup-simplify]: Simplify (log PI) into (log PI)
14.965 * [backup-simplify]: Simplify (- 0) into 0
14.965 * [backup-simplify]: Simplify (+ 1 0) into 1
14.966 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
14.967 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI))
14.968 * [backup-simplify]: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2)
14.969 * [backup-simplify]: Simplify (pow PI 1/2) into (pow PI 1/2)
14.970 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0
14.971 * [backup-simplify]: Simplify (- 1) into -1
14.971 * [backup-simplify]: Simplify (+ 0 -1) into -1
14.973 * [backup-simplify]: Simplify (+ (* 1/2 -1) (* 0 1)) into -1/2
14.975 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log PI))) into (- (* 1/2 (log PI)))
14.984 * [backup-simplify]: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 1) 1)))) into (* -1/2 (* (log PI) (sqrt PI)))
14.986 * [backup-simplify]: Simplify (* -1/2 (* (log PI) (sqrt PI))) into (* -1/2 (* (log PI) (sqrt PI)))
14.988 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0
14.989 * [backup-simplify]: Simplify (- 0) into 0
14.989 * [backup-simplify]: Simplify (+ 0 0) into 0
14.990 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 -1) (* 0 1))) into 0
14.992 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log PI)))) into 0
15.004 * [backup-simplify]: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI)))
15.007 * [backup-simplify]: Simplify (* 1/8 (* (pow (log PI) 2) (sqrt PI))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI)))
15.013 * [backup-simplify]: Simplify (+ (* (* 1/8 (* (pow (log PI) 2) (sqrt PI))) (pow k 2)) (+ (* (* -1/2 (* (log PI) (sqrt PI))) k) (pow PI 1/2))) into (- (+ (pow PI 1/2) (* 1/8 (* (* (pow (log PI) 2) (pow k 2)) (sqrt PI)))) (* 1/2 (* (* (log PI) k) (sqrt PI))))
15.013 * [backup-simplify]: Simplify (pow PI (* (- 1 (/ 1 k)) 1/2)) into (pow PI (* 1/2 (- 1 (/ 1 k))))
15.013 * [approximate]: Taking taylor expansion of (pow PI (* 1/2 (- 1 (/ 1 k)))) in (k) around 0
15.013 * [taylor]: Taking taylor expansion of (pow PI (* 1/2 (- 1 (/ 1 k)))) in k
15.013 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log PI))) in k
15.013 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log PI)) in k
15.013 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
15.013 * [taylor]: Taking taylor expansion of 1/2 in k
15.013 * [backup-simplify]: Simplify 1/2 into 1/2
15.013 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
15.013 * [taylor]: Taking taylor expansion of 1 in k
15.013 * [backup-simplify]: Simplify 1 into 1
15.013 * [taylor]: Taking taylor expansion of (/ 1 k) in k
15.013 * [taylor]: Taking taylor expansion of k in k
15.013 * [backup-simplify]: Simplify 0 into 0
15.013 * [backup-simplify]: Simplify 1 into 1
15.013 * [backup-simplify]: Simplify (/ 1 1) into 1
15.013 * [taylor]: Taking taylor expansion of (log PI) in k
15.013 * [taylor]: Taking taylor expansion of PI in k
15.013 * [backup-simplify]: Simplify PI into PI
15.018 * [backup-simplify]: Simplify (log PI) into (log PI)
15.018 * [backup-simplify]: Simplify (- 1) into -1
15.018 * [backup-simplify]: Simplify (+ 0 -1) into -1
15.019 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
15.019 * [backup-simplify]: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI))
15.020 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log PI))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI))))
15.020 * [taylor]: Taking taylor expansion of (pow PI (* 1/2 (- 1 (/ 1 k)))) in k
15.020 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log PI))) in k
15.020 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log PI)) in k
15.020 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
15.020 * [taylor]: Taking taylor expansion of 1/2 in k
15.020 * [backup-simplify]: Simplify 1/2 into 1/2
15.020 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
15.020 * [taylor]: Taking taylor expansion of 1 in k
15.020 * [backup-simplify]: Simplify 1 into 1
15.020 * [taylor]: Taking taylor expansion of (/ 1 k) in k
15.020 * [taylor]: Taking taylor expansion of k in k
15.020 * [backup-simplify]: Simplify 0 into 0
15.020 * [backup-simplify]: Simplify 1 into 1
15.020 * [backup-simplify]: Simplify (/ 1 1) into 1
15.020 * [taylor]: Taking taylor expansion of (log PI) in k
15.020 * [taylor]: Taking taylor expansion of PI in k
15.020 * [backup-simplify]: Simplify PI into PI
15.021 * [backup-simplify]: Simplify (log PI) into (log PI)
15.021 * [backup-simplify]: Simplify (- 1) into -1
15.021 * [backup-simplify]: Simplify (+ 0 -1) into -1
15.021 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
15.022 * [backup-simplify]: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI))
15.022 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log PI))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI))))
15.023 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI))))
15.023 * [backup-simplify]: Simplify 0 into 0
15.023 * [backup-simplify]: Simplify 0 into 0
15.023 * [backup-simplify]: Simplify 0 into 0
15.023 * [backup-simplify]: Simplify 0 into 0
15.023 * [backup-simplify]: Simplify 0 into 0
15.023 * [backup-simplify]: Simplify 0 into 0
15.023 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log PI)))) into (exp (* 1/2 (* (- 1 k) (log PI))))
15.023 * [backup-simplify]: Simplify (pow PI (* (- 1 (/ 1 (- k))) 1/2)) into (pow PI (* 1/2 (+ (/ 1 k) 1)))
15.023 * [approximate]: Taking taylor expansion of (pow PI (* 1/2 (+ (/ 1 k) 1))) in (k) around 0
15.023 * [taylor]: Taking taylor expansion of (pow PI (* 1/2 (+ (/ 1 k) 1))) in k
15.023 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log PI))) in k
15.023 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log PI)) in k
15.023 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
15.023 * [taylor]: Taking taylor expansion of 1/2 in k
15.023 * [backup-simplify]: Simplify 1/2 into 1/2
15.023 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
15.023 * [taylor]: Taking taylor expansion of (/ 1 k) in k
15.023 * [taylor]: Taking taylor expansion of k in k
15.023 * [backup-simplify]: Simplify 0 into 0
15.023 * [backup-simplify]: Simplify 1 into 1
15.024 * [backup-simplify]: Simplify (/ 1 1) into 1
15.024 * [taylor]: Taking taylor expansion of 1 in k
15.024 * [backup-simplify]: Simplify 1 into 1
15.024 * [taylor]: Taking taylor expansion of (log PI) in k
15.024 * [taylor]: Taking taylor expansion of PI in k
15.024 * [backup-simplify]: Simplify PI into PI
15.024 * [backup-simplify]: Simplify (log PI) into (log PI)
15.024 * [backup-simplify]: Simplify (+ 1 0) into 1
15.025 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
15.025 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI))
15.025 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log PI))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI))))
15.025 * [taylor]: Taking taylor expansion of (pow PI (* 1/2 (+ (/ 1 k) 1))) in k
15.025 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log PI))) in k
15.025 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log PI)) in k
15.025 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
15.026 * [taylor]: Taking taylor expansion of 1/2 in k
15.026 * [backup-simplify]: Simplify 1/2 into 1/2
15.026 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
15.026 * [taylor]: Taking taylor expansion of (/ 1 k) in k
15.026 * [taylor]: Taking taylor expansion of k in k
15.026 * [backup-simplify]: Simplify 0 into 0
15.026 * [backup-simplify]: Simplify 1 into 1
15.026 * [backup-simplify]: Simplify (/ 1 1) into 1
15.026 * [taylor]: Taking taylor expansion of 1 in k
15.026 * [backup-simplify]: Simplify 1 into 1
15.026 * [taylor]: Taking taylor expansion of (log PI) in k
15.026 * [taylor]: Taking taylor expansion of PI in k
15.026 * [backup-simplify]: Simplify PI into PI
15.026 * [backup-simplify]: Simplify (log PI) into (log PI)
15.026 * [backup-simplify]: Simplify (+ 1 0) into 1
15.027 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
15.027 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI))
15.028 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log PI))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI))))
15.028 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI))))
15.028 * [backup-simplify]: Simplify 0 into 0
15.028 * [backup-simplify]: Simplify 0 into 0
15.028 * [backup-simplify]: Simplify 0 into 0
15.028 * [backup-simplify]: Simplify 0 into 0
15.028 * [backup-simplify]: Simplify 0 into 0
15.028 * [backup-simplify]: Simplify 0 into 0
15.028 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (log PI)))) into (exp (* 1/2 (* (- 1 k) (log PI))))
15.029 * * * * [progress]: [ 3 / 4 ] generating series at (2 2)
15.029 * [backup-simplify]: Simplify (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k)) into (* (* (pow PI (* 1/2 (- 1 k))) (pow 2 (* 1/2 (- 1 k)))) (sqrt (/ 1 k)))
15.029 * [approximate]: Taking taylor expansion of (* (* (pow PI (* 1/2 (- 1 k))) (pow 2 (* 1/2 (- 1 k)))) (sqrt (/ 1 k))) in (k) around 0
15.029 * [taylor]: Taking taylor expansion of (* (* (pow PI (* 1/2 (- 1 k))) (pow 2 (* 1/2 (- 1 k)))) (sqrt (/ 1 k))) in k
15.029 * [taylor]: Taking taylor expansion of (* (pow PI (* 1/2 (- 1 k))) (pow 2 (* 1/2 (- 1 k)))) in k
15.029 * [taylor]: Taking taylor expansion of (pow PI (* 1/2 (- 1 k))) in k
15.029 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log PI))) in k
15.029 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log PI)) in k
15.029 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
15.029 * [taylor]: Taking taylor expansion of 1/2 in k
15.029 * [backup-simplify]: Simplify 1/2 into 1/2
15.029 * [taylor]: Taking taylor expansion of (- 1 k) in k
15.029 * [taylor]: Taking taylor expansion of 1 in k
15.029 * [backup-simplify]: Simplify 1 into 1
15.029 * [taylor]: Taking taylor expansion of k in k
15.029 * [backup-simplify]: Simplify 0 into 0
15.029 * [backup-simplify]: Simplify 1 into 1
15.029 * [taylor]: Taking taylor expansion of (log PI) in k
15.029 * [taylor]: Taking taylor expansion of PI in k
15.029 * [backup-simplify]: Simplify PI into PI
15.029 * [backup-simplify]: Simplify (log PI) into (log PI)
15.029 * [backup-simplify]: Simplify (- 0) into 0
15.030 * [backup-simplify]: Simplify (+ 1 0) into 1
15.030 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
15.031 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI))
15.031 * [backup-simplify]: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2)
15.031 * [taylor]: Taking taylor expansion of (pow 2 (* 1/2 (- 1 k))) in k
15.031 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log 2))) in k
15.032 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log 2)) in k
15.032 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
15.032 * [taylor]: Taking taylor expansion of 1/2 in k
15.032 * [backup-simplify]: Simplify 1/2 into 1/2
15.032 * [taylor]: Taking taylor expansion of (- 1 k) in k
15.032 * [taylor]: Taking taylor expansion of 1 in k
15.032 * [backup-simplify]: Simplify 1 into 1
15.032 * [taylor]: Taking taylor expansion of k in k
15.032 * [backup-simplify]: Simplify 0 into 0
15.032 * [backup-simplify]: Simplify 1 into 1
15.032 * [taylor]: Taking taylor expansion of (log 2) in k
15.032 * [taylor]: Taking taylor expansion of 2 in k
15.032 * [backup-simplify]: Simplify 2 into 2
15.032 * [backup-simplify]: Simplify (log 2) into (log 2)
15.032 * [backup-simplify]: Simplify (- 0) into 0
15.032 * [backup-simplify]: Simplify (+ 1 0) into 1
15.033 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
15.033 * [backup-simplify]: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2))
15.034 * [backup-simplify]: Simplify (exp (* 1/2 (log 2))) into (pow 2 1/2)
15.034 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
15.034 * [taylor]: Taking taylor expansion of (/ 1 k) in k
15.034 * [taylor]: Taking taylor expansion of k in k
15.034 * [backup-simplify]: Simplify 0 into 0
15.034 * [backup-simplify]: Simplify 1 into 1
15.034 * [backup-simplify]: Simplify (/ 1 1) into 1
15.035 * [backup-simplify]: Simplify (sqrt 0) into 0
15.036 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
15.036 * [taylor]: Taking taylor expansion of (* (* (pow PI (* 1/2 (- 1 k))) (pow 2 (* 1/2 (- 1 k)))) (sqrt (/ 1 k))) in k
15.036 * [taylor]: Taking taylor expansion of (* (pow PI (* 1/2 (- 1 k))) (pow 2 (* 1/2 (- 1 k)))) in k
15.036 * [taylor]: Taking taylor expansion of (pow PI (* 1/2 (- 1 k))) in k
15.036 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log PI))) in k
15.036 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log PI)) in k
15.036 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
15.036 * [taylor]: Taking taylor expansion of 1/2 in k
15.036 * [backup-simplify]: Simplify 1/2 into 1/2
15.036 * [taylor]: Taking taylor expansion of (- 1 k) in k
15.036 * [taylor]: Taking taylor expansion of 1 in k
15.036 * [backup-simplify]: Simplify 1 into 1
15.036 * [taylor]: Taking taylor expansion of k in k
15.036 * [backup-simplify]: Simplify 0 into 0
15.036 * [backup-simplify]: Simplify 1 into 1
15.036 * [taylor]: Taking taylor expansion of (log PI) in k
15.036 * [taylor]: Taking taylor expansion of PI in k
15.036 * [backup-simplify]: Simplify PI into PI
15.036 * [backup-simplify]: Simplify (log PI) into (log PI)
15.036 * [backup-simplify]: Simplify (- 0) into 0
15.037 * [backup-simplify]: Simplify (+ 1 0) into 1
15.037 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
15.038 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI))
15.038 * [backup-simplify]: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2)
15.038 * [taylor]: Taking taylor expansion of (pow 2 (* 1/2 (- 1 k))) in k
15.038 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log 2))) in k
15.038 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log 2)) in k
15.038 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
15.039 * [taylor]: Taking taylor expansion of 1/2 in k
15.039 * [backup-simplify]: Simplify 1/2 into 1/2
15.039 * [taylor]: Taking taylor expansion of (- 1 k) in k
15.039 * [taylor]: Taking taylor expansion of 1 in k
15.039 * [backup-simplify]: Simplify 1 into 1
15.039 * [taylor]: Taking taylor expansion of k in k
15.039 * [backup-simplify]: Simplify 0 into 0
15.039 * [backup-simplify]: Simplify 1 into 1
15.039 * [taylor]: Taking taylor expansion of (log 2) in k
15.039 * [taylor]: Taking taylor expansion of 2 in k
15.039 * [backup-simplify]: Simplify 2 into 2
15.039 * [backup-simplify]: Simplify (log 2) into (log 2)
15.039 * [backup-simplify]: Simplify (- 0) into 0
15.039 * [backup-simplify]: Simplify (+ 1 0) into 1
15.040 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
15.040 * [backup-simplify]: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2))
15.041 * [backup-simplify]: Simplify (exp (* 1/2 (log 2))) into (pow 2 1/2)
15.041 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
15.041 * [taylor]: Taking taylor expansion of (/ 1 k) in k
15.041 * [taylor]: Taking taylor expansion of k in k
15.041 * [backup-simplify]: Simplify 0 into 0
15.041 * [backup-simplify]: Simplify 1 into 1
15.041 * [backup-simplify]: Simplify (/ 1 1) into 1
15.042 * [backup-simplify]: Simplify (sqrt 0) into 0
15.043 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
15.044 * [backup-simplify]: Simplify (* (pow PI 1/2) (pow 2 1/2)) into (sqrt (* PI 2))
15.044 * [backup-simplify]: Simplify (* (sqrt (* PI 2)) 0) into 0
15.044 * [backup-simplify]: Simplify 0 into 0
15.046 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0
15.046 * [backup-simplify]: Simplify (- 1) into -1
15.047 * [backup-simplify]: Simplify (+ 0 -1) into -1
15.048 * [backup-simplify]: Simplify (+ (* 1/2 -1) (* 0 1)) into -1/2
15.050 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log 2))) into (- (* 1/2 (log 2)))
15.059 * [backup-simplify]: Simplify (* (exp (* 1/2 (log 2))) (+ (* (/ (pow (- (* 1/2 (log 2))) 1) 1)))) into (* -1/2 (* (log 2) (sqrt 2)))
15.060 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0
15.061 * [backup-simplify]: Simplify (- 1) into -1
15.061 * [backup-simplify]: Simplify (+ 0 -1) into -1
15.062 * [backup-simplify]: Simplify (+ (* 1/2 -1) (* 0 1)) into -1/2
15.064 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log PI))) into (- (* 1/2 (log PI)))
15.073 * [backup-simplify]: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 1) 1)))) into (* -1/2 (* (log PI) (sqrt PI)))
15.084 * [backup-simplify]: Simplify (+ (* (pow PI 1/2) (* -1/2 (* (log 2) (sqrt 2)))) (* (* -1/2 (* (log PI) (sqrt PI))) (pow 2 1/2))) into (- (+ (* 1/2 (* (* (sqrt 2) (log PI)) (sqrt PI))) (* 1/2 (* (* (log 2) (sqrt 2)) (sqrt PI)))))
15.092 * [backup-simplify]: Simplify (+ (* (sqrt (* PI 2)) +nan.0) (* (- (+ (* 1/2 (* (* (sqrt 2) (log PI)) (sqrt PI))) (* 1/2 (* (* (log 2) (sqrt 2)) (sqrt PI))))) 0)) into (- (* +nan.0 (* (sqrt 2) (sqrt PI))))
15.095 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) (sqrt PI)))) into (- (* +nan.0 (* (sqrt 2) (sqrt PI))))
15.096 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
15.099 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
15.102 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0
15.102 * [backup-simplify]: Simplify (- 0) into 0
15.103 * [backup-simplify]: Simplify (+ 0 0) into 0
15.104 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 -1) (* 0 1))) into 0
15.105 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log 2)))) into 0
15.116 * [backup-simplify]: Simplify (* (exp (* 1/2 (log 2))) (+ (* (/ (pow (- (* 1/2 (log 2))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log 2) 2) (sqrt 2)))
15.119 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0
15.119 * [backup-simplify]: Simplify (- 0) into 0
15.120 * [backup-simplify]: Simplify (+ 0 0) into 0
15.121 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 -1) (* 0 1))) into 0
15.122 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log PI)))) into 0
15.130 * [backup-simplify]: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI)))
15.151 * [backup-simplify]: Simplify (+ (* (pow PI 1/2) (* 1/8 (* (pow (log 2) 2) (sqrt 2)))) (+ (* (* -1/2 (* (log PI) (sqrt PI))) (* -1/2 (* (log 2) (sqrt 2)))) (* (* 1/8 (* (pow (log PI) 2) (sqrt PI))) (pow 2 1/2)))) into (+ (* 1/8 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt PI))) (+ (* 1/4 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt PI))) (* 1/8 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt PI)))))
15.180 * [backup-simplify]: Simplify (+ (* (sqrt (* PI 2)) +nan.0) (+ (* (- (+ (* 1/2 (* (* (sqrt 2) (log PI)) (sqrt PI))) (* 1/2 (* (* (log 2) (sqrt 2)) (sqrt PI))))) +nan.0) (* (+ (* 1/8 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt PI))) (+ (* 1/4 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt PI))) (* 1/8 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt PI))))) 0))) into (- (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt PI))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt PI))) (- (* +nan.0 (* (sqrt 2) (sqrt PI))))))))
15.203 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt PI))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt PI))) (- (* +nan.0 (* (sqrt 2) (sqrt PI)))))))) into (- (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt PI))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt PI))) (- (* +nan.0 (* (sqrt 2) (sqrt PI))))))))
15.205 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
15.209 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
15.215 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0
15.216 * [backup-simplify]: Simplify (- 0) into 0
15.216 * [backup-simplify]: Simplify (+ 0 0) into 0
15.218 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1)))) into 0
15.219 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log 2))))) into 0
15.235 * [backup-simplify]: Simplify (* (exp (* 1/2 (log 2))) (+ (* (/ (pow (- (* 1/2 (log 2))) 3) 6)) (* (/ (pow (- (* 1/2 (log 2))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (pow (log 2) 3) (sqrt 2)))
15.241 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0
15.242 * [backup-simplify]: Simplify (- 0) into 0
15.242 * [backup-simplify]: Simplify (+ 0 0) into 0
15.244 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1)))) into 0
15.245 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log PI))))) into 0
15.260 * [backup-simplify]: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 3) 6)) (* (/ (pow (- (* 1/2 (log PI))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (pow (log PI) 3) (sqrt PI)))
15.306 * [backup-simplify]: Simplify (+ (* (pow PI 1/2) (* -1/48 (* (pow (log 2) 3) (sqrt 2)))) (+ (* (* -1/2 (* (log PI) (sqrt PI))) (* 1/8 (* (pow (log 2) 2) (sqrt 2)))) (+ (* (* 1/8 (* (pow (log PI) 2) (sqrt PI))) (* -1/2 (* (log 2) (sqrt 2)))) (* (* -1/48 (* (pow (log PI) 3) (sqrt PI))) (pow 2 1/2))))) into (- (+ (* 1/48 (* (* (sqrt 2) (pow (log PI) 3)) (sqrt PI))) (+ (* 1/48 (* (* (pow (log 2) 3) (sqrt 2)) (sqrt PI))) (+ (* 1/16 (* (* (pow (log 2) 2) (* (sqrt 2) (log PI))) (sqrt PI))) (* 1/16 (* (* (log 2) (* (sqrt 2) (pow (log PI) 2))) (sqrt PI)))))))
15.389 * [backup-simplify]: Simplify (+ (* (sqrt (* PI 2)) +nan.0) (+ (* (- (+ (* 1/2 (* (* (sqrt 2) (log PI)) (sqrt PI))) (* 1/2 (* (* (log 2) (sqrt 2)) (sqrt PI))))) +nan.0) (+ (* (+ (* 1/8 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt PI))) (+ (* 1/4 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt PI))) (* 1/8 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt PI))))) +nan.0) (* (- (+ (* 1/48 (* (* (sqrt 2) (pow (log PI) 3)) (sqrt PI))) (+ (* 1/48 (* (* (pow (log 2) 3) (sqrt 2)) (sqrt PI))) (+ (* 1/16 (* (* (pow (log 2) 2) (* (sqrt 2) (log PI))) (sqrt PI))) (* 1/16 (* (* (log 2) (* (sqrt 2) (pow (log PI) 2))) (sqrt PI))))))) 0)))) into (- (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt PI))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt PI))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt PI))) (- (* +nan.0 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt PI))))))))))))))
15.471 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt PI))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt PI))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt PI))) (- (* +nan.0 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt PI)))))))))))))) into (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt PI))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt PI))) (- (* +nan.0 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt PI))))))))))))))
15.592 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt PI))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt PI))) (- (* +nan.0 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt PI)))))))))))))) (pow k 2)) (+ (* (- (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt PI))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt PI))) (- (* +nan.0 (* (sqrt 2) (sqrt PI)))))))) k) (- (* +nan.0 (* (sqrt 2) (sqrt PI)))))) into (- (+ (* +nan.0 (* (* (sqrt 2) (* (pow (log PI) 2) (pow k 2))) (sqrt PI))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow k 2)) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (* (log PI) (pow k 2)))) (sqrt PI))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) k)) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (pow k 2))) (sqrt PI))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (* (sqrt 2) (pow k 2))) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt PI))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (pow k 2))) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) k)) (sqrt PI))) (- (* +nan.0 (* (* (sqrt 2) k) (sqrt PI))))))))))))))))))))))
15.593 * [backup-simplify]: Simplify (/ (* (pow 2 (* (- 1 (/ 1 k)) 1/2)) (pow PI (* (- 1 (/ 1 k)) 1/2))) (sqrt (/ 1 k))) into (* (* (pow PI (* 1/2 (- 1 (/ 1 k)))) (pow 2 (* 1/2 (- 1 (/ 1 k))))) (sqrt k))
15.593 * [approximate]: Taking taylor expansion of (* (* (pow PI (* 1/2 (- 1 (/ 1 k)))) (pow 2 (* 1/2 (- 1 (/ 1 k))))) (sqrt k)) in (k) around 0
15.593 * [taylor]: Taking taylor expansion of (* (* (pow PI (* 1/2 (- 1 (/ 1 k)))) (pow 2 (* 1/2 (- 1 (/ 1 k))))) (sqrt k)) in k
15.593 * [taylor]: Taking taylor expansion of (* (pow PI (* 1/2 (- 1 (/ 1 k)))) (pow 2 (* 1/2 (- 1 (/ 1 k))))) in k
15.593 * [taylor]: Taking taylor expansion of (pow PI (* 1/2 (- 1 (/ 1 k)))) in k
15.593 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log PI))) in k
15.593 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log PI)) in k
15.593 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
15.593 * [taylor]: Taking taylor expansion of 1/2 in k
15.593 * [backup-simplify]: Simplify 1/2 into 1/2
15.593 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
15.593 * [taylor]: Taking taylor expansion of 1 in k
15.593 * [backup-simplify]: Simplify 1 into 1
15.593 * [taylor]: Taking taylor expansion of (/ 1 k) in k
15.593 * [taylor]: Taking taylor expansion of k in k
15.593 * [backup-simplify]: Simplify 0 into 0
15.593 * [backup-simplify]: Simplify 1 into 1
15.594 * [backup-simplify]: Simplify (/ 1 1) into 1
15.594 * [taylor]: Taking taylor expansion of (log PI) in k
15.594 * [taylor]: Taking taylor expansion of PI in k
15.594 * [backup-simplify]: Simplify PI into PI
15.594 * [backup-simplify]: Simplify (log PI) into (log PI)
15.595 * [backup-simplify]: Simplify (- 1) into -1
15.595 * [backup-simplify]: Simplify (+ 0 -1) into -1
15.596 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
15.597 * [backup-simplify]: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI))
15.597 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log PI))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI))))
15.597 * [taylor]: Taking taylor expansion of (pow 2 (* 1/2 (- 1 (/ 1 k)))) in k
15.597 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log 2))) in k
15.597 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log 2)) in k
15.597 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
15.597 * [taylor]: Taking taylor expansion of 1/2 in k
15.597 * [backup-simplify]: Simplify 1/2 into 1/2
15.597 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
15.597 * [taylor]: Taking taylor expansion of 1 in k
15.597 * [backup-simplify]: Simplify 1 into 1
15.597 * [taylor]: Taking taylor expansion of (/ 1 k) in k
15.597 * [taylor]: Taking taylor expansion of k in k
15.598 * [backup-simplify]: Simplify 0 into 0
15.598 * [backup-simplify]: Simplify 1 into 1
15.598 * [backup-simplify]: Simplify (/ 1 1) into 1
15.598 * [taylor]: Taking taylor expansion of (log 2) in k
15.598 * [taylor]: Taking taylor expansion of 2 in k
15.598 * [backup-simplify]: Simplify 2 into 2
15.598 * [backup-simplify]: Simplify (log 2) into (log 2)
15.599 * [backup-simplify]: Simplify (- 1) into -1
15.599 * [backup-simplify]: Simplify (+ 0 -1) into -1
15.600 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
15.601 * [backup-simplify]: Simplify (* -1/2 (log 2)) into (* -1/2 (log 2))
15.601 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log 2))) into (exp (* 1/2 (* (log 2) (- 1 (/ 1 k)))))
15.601 * [taylor]: Taking taylor expansion of (sqrt k) in k
15.601 * [taylor]: Taking taylor expansion of k in k
15.601 * [backup-simplify]: Simplify 0 into 0
15.601 * [backup-simplify]: Simplify 1 into 1
15.602 * [backup-simplify]: Simplify (sqrt 0) into 0
15.603 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
15.604 * [taylor]: Taking taylor expansion of (* (* (pow PI (* 1/2 (- 1 (/ 1 k)))) (pow 2 (* 1/2 (- 1 (/ 1 k))))) (sqrt k)) in k
15.604 * [taylor]: Taking taylor expansion of (* (pow PI (* 1/2 (- 1 (/ 1 k)))) (pow 2 (* 1/2 (- 1 (/ 1 k))))) in k
15.604 * [taylor]: Taking taylor expansion of (pow PI (* 1/2 (- 1 (/ 1 k)))) in k
15.604 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log PI))) in k
15.604 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log PI)) in k
15.604 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
15.604 * [taylor]: Taking taylor expansion of 1/2 in k
15.604 * [backup-simplify]: Simplify 1/2 into 1/2
15.604 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
15.604 * [taylor]: Taking taylor expansion of 1 in k
15.604 * [backup-simplify]: Simplify 1 into 1
15.604 * [taylor]: Taking taylor expansion of (/ 1 k) in k
15.604 * [taylor]: Taking taylor expansion of k in k
15.604 * [backup-simplify]: Simplify 0 into 0
15.604 * [backup-simplify]: Simplify 1 into 1
15.604 * [backup-simplify]: Simplify (/ 1 1) into 1
15.604 * [taylor]: Taking taylor expansion of (log PI) in k
15.604 * [taylor]: Taking taylor expansion of PI in k
15.604 * [backup-simplify]: Simplify PI into PI
15.605 * [backup-simplify]: Simplify (log PI) into (log PI)
15.605 * [backup-simplify]: Simplify (- 1) into -1
15.606 * [backup-simplify]: Simplify (+ 0 -1) into -1
15.606 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
15.607 * [backup-simplify]: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI))
15.608 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log PI))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI))))
15.608 * [taylor]: Taking taylor expansion of (pow 2 (* 1/2 (- 1 (/ 1 k)))) in k
15.608 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log 2))) in k
15.608 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log 2)) in k
15.608 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
15.608 * [taylor]: Taking taylor expansion of 1/2 in k
15.608 * [backup-simplify]: Simplify 1/2 into 1/2
15.608 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
15.608 * [taylor]: Taking taylor expansion of 1 in k
15.608 * [backup-simplify]: Simplify 1 into 1
15.608 * [taylor]: Taking taylor expansion of (/ 1 k) in k
15.608 * [taylor]: Taking taylor expansion of k in k
15.608 * [backup-simplify]: Simplify 0 into 0
15.608 * [backup-simplify]: Simplify 1 into 1
15.609 * [backup-simplify]: Simplify (/ 1 1) into 1
15.609 * [taylor]: Taking taylor expansion of (log 2) in k
15.609 * [taylor]: Taking taylor expansion of 2 in k
15.609 * [backup-simplify]: Simplify 2 into 2
15.609 * [backup-simplify]: Simplify (log 2) into (log 2)
15.610 * [backup-simplify]: Simplify (- 1) into -1
15.610 * [backup-simplify]: Simplify (+ 0 -1) into -1
15.610 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
15.612 * [backup-simplify]: Simplify (* -1/2 (log 2)) into (* -1/2 (log 2))
15.612 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log 2))) into (exp (* 1/2 (* (log 2) (- 1 (/ 1 k)))))
15.612 * [taylor]: Taking taylor expansion of (sqrt k) in k
15.612 * [taylor]: Taking taylor expansion of k in k
15.612 * [backup-simplify]: Simplify 0 into 0
15.612 * [backup-simplify]: Simplify 1 into 1
15.613 * [backup-simplify]: Simplify (sqrt 0) into 0
15.615 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
15.616 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (exp (* 1/2 (* (log 2) (- 1 (/ 1 k)))))) into (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))))
15.617 * [backup-simplify]: Simplify (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (exp (* 1/2 (* (log 2) (- 1 (/ 1 k)))))) 0) into 0
15.617 * [backup-simplify]: Simplify 0 into 0
15.618 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) 0) (* 0 (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))))) into 0
15.620 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (exp (* 1/2 (* (log 2) (- 1 (/ 1 k)))))) +nan.0) (* 0 0)) into (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))))))
15.621 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (exp (* 1/2 (* (log 2) (- 1 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))))))
15.625 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
15.627 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (log 2) (- 1 (/ 1 k)))))))) into 0
15.628 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (exp (* 1/2 (* (log 2) (- 1 (/ 1 k)))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))))))
15.630 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (exp (* 1/2 (* (log 2) (- 1 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))))))
15.635 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
15.637 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))))))) into 0
15.639 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (exp (* 1/2 (* (log 2) (- 1 (/ 1 k)))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))))))
15.640 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (exp (* 1/2 (* (log 2) (- 1 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))))))
15.644 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log PI)))) (exp (* 1/2 (* (log 2) (- 1 (/ 1 (/ 1 k))))))))) (pow (/ 1 k) 3)) (+ (* (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log PI)))) (exp (* 1/2 (* (log 2) (- 1 (/ 1 (/ 1 k))))))))) (pow (/ 1 k) 2)) (* (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log PI)))) (exp (* 1/2 (* (log 2) (- 1 (/ 1 (/ 1 k))))))))) (/ 1 k)))) into (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (- 1 k) (log PI))))) k)) (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (- 1 k) (log PI))))) (pow k 3))) (- (* +nan.0 (/ (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (- 1 k) (log PI))))) (pow k 2))))))))
15.645 * [backup-simplify]: Simplify (/ (* (pow 2 (* (- 1 (/ 1 (- k))) 1/2)) (pow PI (* (- 1 (/ 1 (- k))) 1/2))) (sqrt (/ 1 (- k)))) into (/ (* (pow 2 (* 1/2 (+ (/ 1 k) 1))) (pow PI (* 1/2 (+ (/ 1 k) 1)))) (sqrt (/ -1 k)))
15.645 * [approximate]: Taking taylor expansion of (/ (* (pow 2 (* 1/2 (+ (/ 1 k) 1))) (pow PI (* 1/2 (+ (/ 1 k) 1)))) (sqrt (/ -1 k))) in (k) around 0
15.645 * [taylor]: Taking taylor expansion of (/ (* (pow 2 (* 1/2 (+ (/ 1 k) 1))) (pow PI (* 1/2 (+ (/ 1 k) 1)))) (sqrt (/ -1 k))) in k
15.645 * [taylor]: Taking taylor expansion of (* (pow 2 (* 1/2 (+ (/ 1 k) 1))) (pow PI (* 1/2 (+ (/ 1 k) 1)))) in k
15.645 * [taylor]: Taking taylor expansion of (pow 2 (* 1/2 (+ (/ 1 k) 1))) in k
15.645 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log 2))) in k
15.645 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log 2)) in k
15.645 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
15.645 * [taylor]: Taking taylor expansion of 1/2 in k
15.645 * [backup-simplify]: Simplify 1/2 into 1/2
15.645 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
15.645 * [taylor]: Taking taylor expansion of (/ 1 k) in k
15.645 * [taylor]: Taking taylor expansion of k in k
15.645 * [backup-simplify]: Simplify 0 into 0
15.645 * [backup-simplify]: Simplify 1 into 1
15.646 * [backup-simplify]: Simplify (/ 1 1) into 1
15.646 * [taylor]: Taking taylor expansion of 1 in k
15.646 * [backup-simplify]: Simplify 1 into 1
15.646 * [taylor]: Taking taylor expansion of (log 2) in k
15.646 * [taylor]: Taking taylor expansion of 2 in k
15.646 * [backup-simplify]: Simplify 2 into 2
15.647 * [backup-simplify]: Simplify (log 2) into (log 2)
15.647 * [backup-simplify]: Simplify (+ 1 0) into 1
15.648 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
15.649 * [backup-simplify]: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2))
15.649 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log 2))) into (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1))))
15.649 * [taylor]: Taking taylor expansion of (pow PI (* 1/2 (+ (/ 1 k) 1))) in k
15.649 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log PI))) in k
15.649 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log PI)) in k
15.649 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
15.649 * [taylor]: Taking taylor expansion of 1/2 in k
15.649 * [backup-simplify]: Simplify 1/2 into 1/2
15.649 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
15.649 * [taylor]: Taking taylor expansion of (/ 1 k) in k
15.649 * [taylor]: Taking taylor expansion of k in k
15.649 * [backup-simplify]: Simplify 0 into 0
15.650 * [backup-simplify]: Simplify 1 into 1
15.650 * [backup-simplify]: Simplify (/ 1 1) into 1
15.650 * [taylor]: Taking taylor expansion of 1 in k
15.650 * [backup-simplify]: Simplify 1 into 1
15.650 * [taylor]: Taking taylor expansion of (log PI) in k
15.650 * [taylor]: Taking taylor expansion of PI in k
15.650 * [backup-simplify]: Simplify PI into PI
15.650 * [backup-simplify]: Simplify (log PI) into (log PI)
15.651 * [backup-simplify]: Simplify (+ 1 0) into 1
15.651 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
15.652 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI))
15.653 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log PI))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI))))
15.653 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
15.653 * [taylor]: Taking taylor expansion of (/ -1 k) in k
15.653 * [taylor]: Taking taylor expansion of -1 in k
15.653 * [backup-simplify]: Simplify -1 into -1
15.653 * [taylor]: Taking taylor expansion of k in k
15.653 * [backup-simplify]: Simplify 0 into 0
15.653 * [backup-simplify]: Simplify 1 into 1
15.654 * [backup-simplify]: Simplify (/ -1 1) into -1
15.654 * [backup-simplify]: Simplify (sqrt 0) into 0
15.656 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
15.657 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI))))) into (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))))
15.658 * [backup-simplify]: Simplify (/ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1))))) +nan.0) into (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1))))))
15.658 * [taylor]: Taking taylor expansion of (/ (* (pow 2 (* 1/2 (+ (/ 1 k) 1))) (pow PI (* 1/2 (+ (/ 1 k) 1)))) (sqrt (/ -1 k))) in k
15.658 * [taylor]: Taking taylor expansion of (* (pow 2 (* 1/2 (+ (/ 1 k) 1))) (pow PI (* 1/2 (+ (/ 1 k) 1)))) in k
15.658 * [taylor]: Taking taylor expansion of (pow 2 (* 1/2 (+ (/ 1 k) 1))) in k
15.658 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log 2))) in k
15.658 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log 2)) in k
15.658 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
15.658 * [taylor]: Taking taylor expansion of 1/2 in k
15.658 * [backup-simplify]: Simplify 1/2 into 1/2
15.658 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
15.658 * [taylor]: Taking taylor expansion of (/ 1 k) in k
15.658 * [taylor]: Taking taylor expansion of k in k
15.658 * [backup-simplify]: Simplify 0 into 0
15.658 * [backup-simplify]: Simplify 1 into 1
15.659 * [backup-simplify]: Simplify (/ 1 1) into 1
15.659 * [taylor]: Taking taylor expansion of 1 in k
15.659 * [backup-simplify]: Simplify 1 into 1
15.659 * [taylor]: Taking taylor expansion of (log 2) in k
15.659 * [taylor]: Taking taylor expansion of 2 in k
15.659 * [backup-simplify]: Simplify 2 into 2
15.659 * [backup-simplify]: Simplify (log 2) into (log 2)
15.660 * [backup-simplify]: Simplify (+ 1 0) into 1
15.660 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
15.661 * [backup-simplify]: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2))
15.661 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log 2))) into (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1))))
15.662 * [taylor]: Taking taylor expansion of (pow PI (* 1/2 (+ (/ 1 k) 1))) in k
15.662 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log PI))) in k
15.662 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log PI)) in k
15.662 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
15.662 * [taylor]: Taking taylor expansion of 1/2 in k
15.662 * [backup-simplify]: Simplify 1/2 into 1/2
15.662 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
15.662 * [taylor]: Taking taylor expansion of (/ 1 k) in k
15.662 * [taylor]: Taking taylor expansion of k in k
15.662 * [backup-simplify]: Simplify 0 into 0
15.662 * [backup-simplify]: Simplify 1 into 1
15.662 * [backup-simplify]: Simplify (/ 1 1) into 1
15.662 * [taylor]: Taking taylor expansion of 1 in k
15.662 * [backup-simplify]: Simplify 1 into 1
15.662 * [taylor]: Taking taylor expansion of (log PI) in k
15.662 * [taylor]: Taking taylor expansion of PI in k
15.662 * [backup-simplify]: Simplify PI into PI
15.663 * [backup-simplify]: Simplify (log PI) into (log PI)
15.663 * [backup-simplify]: Simplify (+ 1 0) into 1
15.664 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
15.665 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI))
15.665 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log PI))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI))))
15.665 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
15.665 * [taylor]: Taking taylor expansion of (/ -1 k) in k
15.665 * [taylor]: Taking taylor expansion of -1 in k
15.665 * [backup-simplify]: Simplify -1 into -1
15.665 * [taylor]: Taking taylor expansion of k in k
15.665 * [backup-simplify]: Simplify 0 into 0
15.665 * [backup-simplify]: Simplify 1 into 1
15.666 * [backup-simplify]: Simplify (/ -1 1) into -1
15.666 * [backup-simplify]: Simplify (sqrt 0) into 0
15.668 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
15.669 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI))))) into (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))))
15.670 * [backup-simplify]: Simplify (/ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1))))) +nan.0) into (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1))))))
15.671 * [backup-simplify]: Simplify (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))))) into (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1))))))
15.673 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))) 0) (* 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))))) into 0
15.674 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
15.677 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
15.679 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))))))
15.680 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1))))))) into (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))))))
15.682 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI))))))) into 0
15.683 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
15.687 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
15.691 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))))))
15.692 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1))))))) into (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))))))
15.696 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (log PI)))) (exp (* 1/2 (* (log 2) (+ (/ 1 (/ 1 (- k))) 1))))))) (pow (/ 1 (- k)) 2)) (+ (* (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (log PI)))) (exp (* 1/2 (* (log 2) (+ (/ 1 (/ 1 (- k))) 1))))))) (/ 1 (- k))) (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (log PI)))) (exp (* 1/2 (* (log 2) (+ (/ 1 (/ 1 (- k))) 1)))))))) into (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (- 1 k) (log PI))))) k)) (- (+ (* +nan.0 (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (- 1 k) (log PI)))))) (- (* +nan.0 (/ (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (- 1 k) (log PI))))) (pow k 2))))))))
15.696 * * * * [progress]: [ 4 / 4 ] generating series at (2)
15.696 * [backup-simplify]: Simplify (* (pow n (* (- 1 k) 1/2)) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))) into (* (* (pow 2 (* 1/2 (- 1 k))) (* (pow PI (* 1/2 (- 1 k))) (pow n (* 1/2 (- 1 k))))) (sqrt (/ 1 k)))
15.696 * [approximate]: Taking taylor expansion of (* (* (pow 2 (* 1/2 (- 1 k))) (* (pow PI (* 1/2 (- 1 k))) (pow n (* 1/2 (- 1 k))))) (sqrt (/ 1 k))) in (n k) around 0
15.697 * [taylor]: Taking taylor expansion of (* (* (pow 2 (* 1/2 (- 1 k))) (* (pow PI (* 1/2 (- 1 k))) (pow n (* 1/2 (- 1 k))))) (sqrt (/ 1 k))) in k
15.697 * [taylor]: Taking taylor expansion of (* (pow 2 (* 1/2 (- 1 k))) (* (pow PI (* 1/2 (- 1 k))) (pow n (* 1/2 (- 1 k))))) in k
15.697 * [taylor]: Taking taylor expansion of (pow 2 (* 1/2 (- 1 k))) in k
15.697 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log 2))) in k
15.697 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log 2)) in k
15.697 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
15.697 * [taylor]: Taking taylor expansion of 1/2 in k
15.697 * [backup-simplify]: Simplify 1/2 into 1/2
15.697 * [taylor]: Taking taylor expansion of (- 1 k) in k
15.697 * [taylor]: Taking taylor expansion of 1 in k
15.697 * [backup-simplify]: Simplify 1 into 1
15.697 * [taylor]: Taking taylor expansion of k in k
15.697 * [backup-simplify]: Simplify 0 into 0
15.697 * [backup-simplify]: Simplify 1 into 1
15.697 * [taylor]: Taking taylor expansion of (log 2) in k
15.697 * [taylor]: Taking taylor expansion of 2 in k
15.697 * [backup-simplify]: Simplify 2 into 2
15.697 * [backup-simplify]: Simplify (log 2) into (log 2)
15.698 * [backup-simplify]: Simplify (- 0) into 0
15.698 * [backup-simplify]: Simplify (+ 1 0) into 1
15.699 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
15.700 * [backup-simplify]: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2))
15.702 * [backup-simplify]: Simplify (exp (* 1/2 (log 2))) into (pow 2 1/2)
15.702 * [taylor]: Taking taylor expansion of (* (pow PI (* 1/2 (- 1 k))) (pow n (* 1/2 (- 1 k)))) in k
15.702 * [taylor]: Taking taylor expansion of (pow PI (* 1/2 (- 1 k))) in k
15.702 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log PI))) in k
15.702 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log PI)) in k
15.702 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
15.702 * [taylor]: Taking taylor expansion of 1/2 in k
15.702 * [backup-simplify]: Simplify 1/2 into 1/2
15.702 * [taylor]: Taking taylor expansion of (- 1 k) in k
15.702 * [taylor]: Taking taylor expansion of 1 in k
15.702 * [backup-simplify]: Simplify 1 into 1
15.702 * [taylor]: Taking taylor expansion of k in k
15.702 * [backup-simplify]: Simplify 0 into 0
15.702 * [backup-simplify]: Simplify 1 into 1
15.702 * [taylor]: Taking taylor expansion of (log PI) in k
15.702 * [taylor]: Taking taylor expansion of PI in k
15.702 * [backup-simplify]: Simplify PI into PI
15.703 * [backup-simplify]: Simplify (log PI) into (log PI)
15.703 * [backup-simplify]: Simplify (- 0) into 0
15.704 * [backup-simplify]: Simplify (+ 1 0) into 1
15.704 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
15.705 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI))
15.707 * [backup-simplify]: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2)
15.707 * [taylor]: Taking taylor expansion of (pow n (* 1/2 (- 1 k))) in k
15.707 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log n))) in k
15.707 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log n)) in k
15.707 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
15.707 * [taylor]: Taking taylor expansion of 1/2 in k
15.707 * [backup-simplify]: Simplify 1/2 into 1/2
15.707 * [taylor]: Taking taylor expansion of (- 1 k) in k
15.707 * [taylor]: Taking taylor expansion of 1 in k
15.707 * [backup-simplify]: Simplify 1 into 1
15.707 * [taylor]: Taking taylor expansion of k in k
15.707 * [backup-simplify]: Simplify 0 into 0
15.707 * [backup-simplify]: Simplify 1 into 1
15.707 * [taylor]: Taking taylor expansion of (log n) in k
15.707 * [taylor]: Taking taylor expansion of n in k
15.707 * [backup-simplify]: Simplify n into n
15.708 * [backup-simplify]: Simplify (log n) into (log n)
15.714 * [backup-simplify]: Simplify (- 0) into 0
15.715 * [backup-simplify]: Simplify (+ 1 0) into 1
15.716 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
15.716 * [backup-simplify]: Simplify (* 1/2 (log n)) into (* 1/2 (log n))
15.716 * [backup-simplify]: Simplify (exp (* 1/2 (log n))) into (pow n 1/2)
15.716 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
15.716 * [taylor]: Taking taylor expansion of (/ 1 k) in k
15.716 * [taylor]: Taking taylor expansion of k in k
15.716 * [backup-simplify]: Simplify 0 into 0
15.716 * [backup-simplify]: Simplify 1 into 1
15.717 * [backup-simplify]: Simplify (/ 1 1) into 1
15.718 * [backup-simplify]: Simplify (sqrt 0) into 0
15.720 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
15.720 * [taylor]: Taking taylor expansion of (* (* (pow 2 (* 1/2 (- 1 k))) (* (pow PI (* 1/2 (- 1 k))) (pow n (* 1/2 (- 1 k))))) (sqrt (/ 1 k))) in n
15.720 * [taylor]: Taking taylor expansion of (* (pow 2 (* 1/2 (- 1 k))) (* (pow PI (* 1/2 (- 1 k))) (pow n (* 1/2 (- 1 k))))) in n
15.720 * [taylor]: Taking taylor expansion of (pow 2 (* 1/2 (- 1 k))) in n
15.720 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log 2))) in n
15.720 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log 2)) in n
15.720 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
15.720 * [taylor]: Taking taylor expansion of 1/2 in n
15.720 * [backup-simplify]: Simplify 1/2 into 1/2
15.720 * [taylor]: Taking taylor expansion of (- 1 k) in n
15.720 * [taylor]: Taking taylor expansion of 1 in n
15.720 * [backup-simplify]: Simplify 1 into 1
15.720 * [taylor]: Taking taylor expansion of k in n
15.720 * [backup-simplify]: Simplify k into k
15.720 * [taylor]: Taking taylor expansion of (log 2) in n
15.721 * [taylor]: Taking taylor expansion of 2 in n
15.721 * [backup-simplify]: Simplify 2 into 2
15.721 * [backup-simplify]: Simplify (log 2) into (log 2)
15.721 * [backup-simplify]: Simplify (- k) into (- k)
15.721 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
15.721 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
15.722 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (log 2)) into (* 1/2 (* (- 1 k) (log 2)))
15.723 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (log 2)))) into (exp (* 1/2 (* (- 1 k) (log 2))))
15.723 * [taylor]: Taking taylor expansion of (* (pow PI (* 1/2 (- 1 k))) (pow n (* 1/2 (- 1 k)))) in n
15.723 * [taylor]: Taking taylor expansion of (pow PI (* 1/2 (- 1 k))) in n
15.723 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log PI))) in n
15.723 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log PI)) in n
15.723 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
15.723 * [taylor]: Taking taylor expansion of 1/2 in n
15.723 * [backup-simplify]: Simplify 1/2 into 1/2
15.723 * [taylor]: Taking taylor expansion of (- 1 k) in n
15.723 * [taylor]: Taking taylor expansion of 1 in n
15.723 * [backup-simplify]: Simplify 1 into 1
15.723 * [taylor]: Taking taylor expansion of k in n
15.723 * [backup-simplify]: Simplify k into k
15.723 * [taylor]: Taking taylor expansion of (log PI) in n
15.723 * [taylor]: Taking taylor expansion of PI in n
15.723 * [backup-simplify]: Simplify PI into PI
15.724 * [backup-simplify]: Simplify (log PI) into (log PI)
15.724 * [backup-simplify]: Simplify (- k) into (- k)
15.724 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
15.724 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
15.724 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (log PI)) into (* 1/2 (* (- 1 k) (log PI)))
15.725 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (log PI)))) into (exp (* 1/2 (* (- 1 k) (log PI))))
15.725 * [taylor]: Taking taylor expansion of (pow n (* 1/2 (- 1 k))) in n
15.725 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log n))) in n
15.725 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log n)) in n
15.725 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
15.725 * [taylor]: Taking taylor expansion of 1/2 in n
15.725 * [backup-simplify]: Simplify 1/2 into 1/2
15.725 * [taylor]: Taking taylor expansion of (- 1 k) in n
15.725 * [taylor]: Taking taylor expansion of 1 in n
15.725 * [backup-simplify]: Simplify 1 into 1
15.725 * [taylor]: Taking taylor expansion of k in n
15.725 * [backup-simplify]: Simplify k into k
15.725 * [taylor]: Taking taylor expansion of (log n) in n
15.725 * [taylor]: Taking taylor expansion of n in n
15.725 * [backup-simplify]: Simplify 0 into 0
15.725 * [backup-simplify]: Simplify 1 into 1
15.726 * [backup-simplify]: Simplify (log 1) into 0
15.726 * [backup-simplify]: Simplify (- k) into (- k)
15.726 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
15.726 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
15.726 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
15.726 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (log n)) into (* 1/2 (* (- 1 k) (log n)))
15.727 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (log n)))) into (exp (* 1/2 (* (- 1 k) (log n))))
15.727 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
15.727 * [taylor]: Taking taylor expansion of (/ 1 k) in n
15.727 * [taylor]: Taking taylor expansion of k in n
15.727 * [backup-simplify]: Simplify k into k
15.727 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
15.727 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
15.727 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
15.727 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
15.727 * [taylor]: Taking taylor expansion of (* (* (pow 2 (* 1/2 (- 1 k))) (* (pow PI (* 1/2 (- 1 k))) (pow n (* 1/2 (- 1 k))))) (sqrt (/ 1 k))) in n
15.727 * [taylor]: Taking taylor expansion of (* (pow 2 (* 1/2 (- 1 k))) (* (pow PI (* 1/2 (- 1 k))) (pow n (* 1/2 (- 1 k))))) in n
15.727 * [taylor]: Taking taylor expansion of (pow 2 (* 1/2 (- 1 k))) in n
15.727 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log 2))) in n
15.727 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log 2)) in n
15.727 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
15.727 * [taylor]: Taking taylor expansion of 1/2 in n
15.727 * [backup-simplify]: Simplify 1/2 into 1/2
15.727 * [taylor]: Taking taylor expansion of (- 1 k) in n
15.727 * [taylor]: Taking taylor expansion of 1 in n
15.727 * [backup-simplify]: Simplify 1 into 1
15.728 * [taylor]: Taking taylor expansion of k in n
15.728 * [backup-simplify]: Simplify k into k
15.728 * [taylor]: Taking taylor expansion of (log 2) in n
15.728 * [taylor]: Taking taylor expansion of 2 in n
15.728 * [backup-simplify]: Simplify 2 into 2
15.728 * [backup-simplify]: Simplify (log 2) into (log 2)
15.728 * [backup-simplify]: Simplify (- k) into (- k)
15.728 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
15.728 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
15.729 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (log 2)) into (* 1/2 (* (- 1 k) (log 2)))
15.729 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (log 2)))) into (exp (* 1/2 (* (- 1 k) (log 2))))
15.729 * [taylor]: Taking taylor expansion of (* (pow PI (* 1/2 (- 1 k))) (pow n (* 1/2 (- 1 k)))) in n
15.729 * [taylor]: Taking taylor expansion of (pow PI (* 1/2 (- 1 k))) in n
15.729 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log PI))) in n
15.729 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log PI)) in n
15.729 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
15.729 * [taylor]: Taking taylor expansion of 1/2 in n
15.730 * [backup-simplify]: Simplify 1/2 into 1/2
15.730 * [taylor]: Taking taylor expansion of (- 1 k) in n
15.730 * [taylor]: Taking taylor expansion of 1 in n
15.730 * [backup-simplify]: Simplify 1 into 1
15.730 * [taylor]: Taking taylor expansion of k in n
15.730 * [backup-simplify]: Simplify k into k
15.730 * [taylor]: Taking taylor expansion of (log PI) in n
15.730 * [taylor]: Taking taylor expansion of PI in n
15.730 * [backup-simplify]: Simplify PI into PI
15.730 * [backup-simplify]: Simplify (log PI) into (log PI)
15.730 * [backup-simplify]: Simplify (- k) into (- k)
15.730 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
15.730 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
15.731 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (log PI)) into (* 1/2 (* (- 1 k) (log PI)))
15.731 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (log PI)))) into (exp (* 1/2 (* (- 1 k) (log PI))))
15.731 * [taylor]: Taking taylor expansion of (pow n (* 1/2 (- 1 k))) in n
15.731 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log n))) in n
15.731 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log n)) in n
15.732 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
15.732 * [taylor]: Taking taylor expansion of 1/2 in n
15.732 * [backup-simplify]: Simplify 1/2 into 1/2
15.732 * [taylor]: Taking taylor expansion of (- 1 k) in n
15.732 * [taylor]: Taking taylor expansion of 1 in n
15.732 * [backup-simplify]: Simplify 1 into 1
15.732 * [taylor]: Taking taylor expansion of k in n
15.732 * [backup-simplify]: Simplify k into k
15.732 * [taylor]: Taking taylor expansion of (log n) in n
15.732 * [taylor]: Taking taylor expansion of n in n
15.732 * [backup-simplify]: Simplify 0 into 0
15.732 * [backup-simplify]: Simplify 1 into 1
15.732 * [backup-simplify]: Simplify (log 1) into 0
15.732 * [backup-simplify]: Simplify (- k) into (- k)
15.732 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
15.732 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
15.733 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
15.733 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (log n)) into (* 1/2 (* (- 1 k) (log n)))
15.733 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (log n)))) into (exp (* 1/2 (* (- 1 k) (log n))))
15.733 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
15.733 * [taylor]: Taking taylor expansion of (/ 1 k) in n
15.733 * [taylor]: Taking taylor expansion of k in n
15.733 * [backup-simplify]: Simplify k into k
15.733 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
15.733 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
15.734 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
15.734 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
15.734 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (log PI)))) (exp (* 1/2 (* (- 1 k) (log n))))) into (* (exp (* 1/2 (* (- 1 k) (log PI)))) (exp (* 1/2 (* (- 1 k) (log n)))))
15.735 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (log 2)))) (* (exp (* 1/2 (* (- 1 k) (log PI)))) (exp (* 1/2 (* (- 1 k) (log n)))))) into (* (exp (* 1/2 (* (- 1 k) (log 2)))) (* (exp (* 1/2 (* (- 1 k) (log PI)))) (exp (* 1/2 (* (- 1 k) (log n))))))
15.737 * [backup-simplify]: Simplify (* (* (exp (* 1/2 (* (- 1 k) (log 2)))) (* (exp (* 1/2 (* (- 1 k) (log PI)))) (exp (* 1/2 (* (- 1 k) (log n)))))) (sqrt (/ 1 k))) into (* (* (exp (* 1/2 (* (- 1 k) (log 2)))) (* (exp (* 1/2 (* (- 1 k) (log PI)))) (exp (* 1/2 (* (- 1 k) (log n)))))) (sqrt (/ 1 k)))
15.737 * [taylor]: Taking taylor expansion of (* (* (exp (* 1/2 (* (- 1 k) (log 2)))) (* (exp (* 1/2 (* (- 1 k) (log PI)))) (exp (* 1/2 (* (- 1 k) (log n)))))) (sqrt (/ 1 k))) in k
15.737 * [taylor]: Taking taylor expansion of (* (exp (* 1/2 (* (- 1 k) (log 2)))) (* (exp (* 1/2 (* (- 1 k) (log PI)))) (exp (* 1/2 (* (- 1 k) (log n)))))) in k
15.737 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (log 2)))) in k
15.737 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 k) (log 2))) in k
15.737 * [taylor]: Taking taylor expansion of 1/2 in k
15.737 * [backup-simplify]: Simplify 1/2 into 1/2
15.737 * [taylor]: Taking taylor expansion of (* (- 1 k) (log 2)) in k
15.737 * [taylor]: Taking taylor expansion of (- 1 k) in k
15.737 * [taylor]: Taking taylor expansion of 1 in k
15.737 * [backup-simplify]: Simplify 1 into 1
15.737 * [taylor]: Taking taylor expansion of k in k
15.737 * [backup-simplify]: Simplify 0 into 0
15.737 * [backup-simplify]: Simplify 1 into 1
15.737 * [taylor]: Taking taylor expansion of (log 2) in k
15.737 * [taylor]: Taking taylor expansion of 2 in k
15.737 * [backup-simplify]: Simplify 2 into 2
15.738 * [backup-simplify]: Simplify (log 2) into (log 2)
15.738 * [backup-simplify]: Simplify (- 0) into 0
15.738 * [backup-simplify]: Simplify (+ 1 0) into 1
15.739 * [backup-simplify]: Simplify (* 1 (log 2)) into (log 2)
15.740 * [backup-simplify]: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2))
15.742 * [backup-simplify]: Simplify (exp (* 1/2 (log 2))) into (pow 2 1/2)
15.742 * [taylor]: Taking taylor expansion of (* (exp (* 1/2 (* (- 1 k) (log PI)))) (exp (* 1/2 (* (- 1 k) (log n))))) in k
15.742 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (log PI)))) in k
15.742 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 k) (log PI))) in k
15.742 * [taylor]: Taking taylor expansion of 1/2 in k
15.742 * [backup-simplify]: Simplify 1/2 into 1/2
15.742 * [taylor]: Taking taylor expansion of (* (- 1 k) (log PI)) in k
15.742 * [taylor]: Taking taylor expansion of (- 1 k) in k
15.742 * [taylor]: Taking taylor expansion of 1 in k
15.742 * [backup-simplify]: Simplify 1 into 1
15.742 * [taylor]: Taking taylor expansion of k in k
15.742 * [backup-simplify]: Simplify 0 into 0
15.742 * [backup-simplify]: Simplify 1 into 1
15.742 * [taylor]: Taking taylor expansion of (log PI) in k
15.742 * [taylor]: Taking taylor expansion of PI in k
15.743 * [backup-simplify]: Simplify PI into PI
15.743 * [backup-simplify]: Simplify (log PI) into (log PI)
15.743 * [backup-simplify]: Simplify (- 0) into 0
15.744 * [backup-simplify]: Simplify (+ 1 0) into 1
15.745 * [backup-simplify]: Simplify (* 1 (log PI)) into (log PI)
15.746 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI))
15.747 * [backup-simplify]: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2)
15.747 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (log n)))) in k
15.747 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 k) (log n))) in k
15.747 * [taylor]: Taking taylor expansion of 1/2 in k
15.748 * [backup-simplify]: Simplify 1/2 into 1/2
15.748 * [taylor]: Taking taylor expansion of (* (- 1 k) (log n)) in k
15.748 * [taylor]: Taking taylor expansion of (- 1 k) in k
15.748 * [taylor]: Taking taylor expansion of 1 in k
15.748 * [backup-simplify]: Simplify 1 into 1
15.748 * [taylor]: Taking taylor expansion of k in k
15.748 * [backup-simplify]: Simplify 0 into 0
15.748 * [backup-simplify]: Simplify 1 into 1
15.748 * [taylor]: Taking taylor expansion of (log n) in k
15.748 * [taylor]: Taking taylor expansion of n in k
15.748 * [backup-simplify]: Simplify n into n
15.748 * [backup-simplify]: Simplify (log n) into (log n)
15.748 * [backup-simplify]: Simplify (- 0) into 0
15.749 * [backup-simplify]: Simplify (+ 1 0) into 1
15.749 * [backup-simplify]: Simplify (* 1 (log n)) into (log n)
15.749 * [backup-simplify]: Simplify (* 1/2 (log n)) into (* 1/2 (log n))
15.749 * [backup-simplify]: Simplify (exp (* 1/2 (log n))) into (pow n 1/2)
15.749 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
15.749 * [taylor]: Taking taylor expansion of (/ 1 k) in k
15.749 * [taylor]: Taking taylor expansion of k in k
15.749 * [backup-simplify]: Simplify 0 into 0
15.749 * [backup-simplify]: Simplify 1 into 1
15.750 * [backup-simplify]: Simplify (/ 1 1) into 1
15.750 * [backup-simplify]: Simplify (sqrt 0) into 0
15.751 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
15.752 * [backup-simplify]: Simplify (* (pow PI 1/2) (pow n 1/2)) into (sqrt (* n PI))
15.753 * [backup-simplify]: Simplify (* (pow 2 1/2) (sqrt (* n PI))) into (sqrt (* PI (* n 2)))
15.753 * [backup-simplify]: Simplify (* (sqrt (* PI (* n 2))) 0) into 0
15.753 * [backup-simplify]: Simplify 0 into 0
15.754 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0
15.755 * [backup-simplify]: Simplify (- 0) into 0
15.755 * [backup-simplify]: Simplify (+ 0 0) into 0
15.756 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 k))) into 0
15.756 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
15.756 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (log n))) into 0
15.757 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
15.759 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0
15.759 * [backup-simplify]: Simplify (- 0) into 0
15.759 * [backup-simplify]: Simplify (+ 0 0) into 0
15.760 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 k))) into 0
15.761 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (log PI))) into 0
15.762 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (log PI)))) (+ (* (/ (pow 0 1) 1)))) into 0
15.762 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 k) (log PI)))) 0) (* 0 (exp (* 1/2 (* (- 1 k) (log n)))))) into 0
15.764 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0
15.764 * [backup-simplify]: Simplify (- 0) into 0
15.765 * [backup-simplify]: Simplify (+ 0 0) into 0
15.765 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 k))) into 0
15.766 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (log 2))) into 0
15.767 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (log 2)))) (+ (* (/ (pow 0 1) 1)))) into 0
15.768 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 k) (log 2)))) 0) (* 0 (* (exp (* 1/2 (* (- 1 k) (log PI)))) (exp (* 1/2 (* (- 1 k) (log n))))))) into 0
15.769 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (* (- 1 k) (log 2)))) (* (exp (* 1/2 (* (- 1 k) (log PI)))) (exp (* 1/2 (* (- 1 k) (log n)))))) 0) (* 0 (sqrt (/ 1 k)))) into 0
15.769 * [taylor]: Taking taylor expansion of 0 in k
15.770 * [backup-simplify]: Simplify 0 into 0
15.770 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
15.771 * [backup-simplify]: Simplify (- 1) into -1
15.771 * [backup-simplify]: Simplify (+ 0 -1) into -1
15.772 * [backup-simplify]: Simplify (+ (* 1 0) (* -1 (log n))) into (- (log n))
15.772 * [backup-simplify]: Simplify (+ (* 1/2 (- (log n))) (* 0 (log n))) into (- (* 1/2 (log n)))
15.772 * [backup-simplify]: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 1) 1)))) into (* -1/2 (* (sqrt n) (log n)))
15.774 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0
15.774 * [backup-simplify]: Simplify (- 1) into -1
15.775 * [backup-simplify]: Simplify (+ 0 -1) into -1
15.777 * [backup-simplify]: Simplify (+ (* 1 0) (* -1 (log PI))) into (- (log PI))
15.780 * [backup-simplify]: Simplify (+ (* 1/2 (- (log PI))) (* 0 (log PI))) into (- (* 1/2 (log PI)))
15.790 * [backup-simplify]: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 1) 1)))) into (* -1/2 (* (log PI) (sqrt PI)))
15.793 * [backup-simplify]: Simplify (+ (* (pow PI 1/2) (* -1/2 (* (sqrt n) (log n)))) (* (* -1/2 (* (log PI) (sqrt PI))) (pow n 1/2))) into (- (+ (* 1/2 (* (sqrt (* n PI)) (log n))) (* 1/2 (* (log PI) (sqrt (* PI n))))))
15.795 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0
15.795 * [backup-simplify]: Simplify (- 1) into -1
15.795 * [backup-simplify]: Simplify (+ 0 -1) into -1
15.797 * [backup-simplify]: Simplify (+ (* 1 0) (* -1 (log 2))) into (- (log 2))
15.801 * [backup-simplify]: Simplify (+ (* 1/2 (- (log 2))) (* 0 (log 2))) into (- (* 1/2 (log 2)))
15.809 * [backup-simplify]: Simplify (* (exp (* 1/2 (log 2))) (+ (* (/ (pow (- (* 1/2 (log 2))) 1) 1)))) into (* -1/2 (* (log 2) (sqrt 2)))
15.811 * [backup-simplify]: Simplify (+ (* (pow 2 1/2) (- (+ (* 1/2 (* (sqrt (* n PI)) (log n))) (* 1/2 (* (log PI) (sqrt (* PI n))))))) (* (* -1/2 (* (log 2) (sqrt 2))) (sqrt (* n PI)))) into (- (+ (* 1/2 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (+ (* 1/2 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (* 1/2 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))))))
15.813 * [backup-simplify]: Simplify (+ (* (sqrt (* PI (* n 2))) +nan.0) (* (- (+ (* 1/2 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (+ (* 1/2 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (* 1/2 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))))) 0)) into (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))
15.814 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) into (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))
15.814 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
15.814 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0
15.816 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0
15.816 * [backup-simplify]: Simplify (- 0) into 0
15.816 * [backup-simplify]: Simplify (+ 0 0) into 0
15.817 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0
15.817 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
15.817 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (log n)))) into 0
15.818 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
15.820 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0
15.820 * [backup-simplify]: Simplify (- 0) into 0
15.820 * [backup-simplify]: Simplify (+ 0 0) into 0
15.821 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0
15.821 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (log PI)))) into 0
15.822 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (log PI)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
15.823 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 k) (log PI)))) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (- 1 k) (log n))))))) into 0
15.824 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0
15.825 * [backup-simplify]: Simplify (- 0) into 0
15.825 * [backup-simplify]: Simplify (+ 0 0) into 0
15.825 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0
15.826 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (log 2)))) into 0
15.827 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (log 2)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
15.828 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 k) (log 2)))) 0) (+ (* 0 0) (* 0 (* (exp (* 1/2 (* (- 1 k) (log PI)))) (exp (* 1/2 (* (- 1 k) (log n)))))))) into 0
15.829 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (* (- 1 k) (log 2)))) (* (exp (* 1/2 (* (- 1 k) (log PI)))) (exp (* 1/2 (* (- 1 k) (log n)))))) 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k))))) into 0
15.829 * [taylor]: Taking taylor expansion of 0 in k
15.829 * [backup-simplify]: Simplify 0 into 0
15.829 * [backup-simplify]: Simplify 0 into 0
15.829 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
15.831 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
15.832 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
15.832 * [backup-simplify]: Simplify (- 0) into 0
15.832 * [backup-simplify]: Simplify (+ 0 0) into 0
15.833 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (log n)))) into 0
15.833 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (log n))) (* 0 (log n)))) into 0
15.834 * [backup-simplify]: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt n) (pow (log n) 2)))
15.835 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0
15.836 * [backup-simplify]: Simplify (- 0) into 0
15.836 * [backup-simplify]: Simplify (+ 0 0) into 0
15.837 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (log PI)))) into 0
15.839 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (log PI))) (* 0 (log PI)))) into 0
15.858 * [backup-simplify]: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI)))
15.865 * [backup-simplify]: Simplify (+ (* (pow PI 1/2) (* 1/8 (* (sqrt n) (pow (log n) 2)))) (+ (* (* -1/2 (* (log PI) (sqrt PI))) (* -1/2 (* (sqrt n) (log n)))) (* (* 1/8 (* (pow (log PI) 2) (sqrt PI))) (pow n 1/2)))) into (+ (* 1/8 (* (sqrt (* n PI)) (pow (log n) 2))) (+ (* 1/8 (* (pow (log PI) 2) (sqrt (* PI n)))) (* 1/4 (* (* (log PI) (log n)) (sqrt (* PI n))))))
15.868 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0
15.869 * [backup-simplify]: Simplify (- 0) into 0
15.870 * [backup-simplify]: Simplify (+ 0 0) into 0
15.871 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (log 2)))) into 0
15.872 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (log 2))) (* 0 (log 2)))) into 0
15.878 * [backup-simplify]: Simplify (* (exp (* 1/2 (log 2))) (+ (* (/ (pow (- (* 1/2 (log 2))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log 2) 2) (sqrt 2)))
15.883 * [backup-simplify]: Simplify (+ (* (pow 2 1/2) (+ (* 1/8 (* (sqrt (* n PI)) (pow (log n) 2))) (+ (* 1/8 (* (pow (log PI) 2) (sqrt (* PI n)))) (* 1/4 (* (* (log PI) (log n)) (sqrt (* PI n))))))) (+ (* (* -1/2 (* (log 2) (sqrt 2))) (- (+ (* 1/2 (* (sqrt (* n PI)) (log n))) (* 1/2 (* (log PI) (sqrt (* PI n))))))) (* (* 1/8 (* (pow (log 2) 2) (sqrt 2))) (sqrt (* n PI))))) into (+ (* 1/8 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (+ (* 1/8 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (+ (* 1/4 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (+ (* 1/4 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (+ (* 1/8 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (* 1/4 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))))))))
15.892 * [backup-simplify]: Simplify (+ (* (sqrt (* PI (* n 2))) +nan.0) (+ (* (- (+ (* 1/2 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (+ (* 1/2 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (* 1/2 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))))) +nan.0) (* (+ (* 1/8 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (+ (* 1/8 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (+ (* 1/4 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (+ (* 1/4 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (+ (* 1/8 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (* 1/4 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n))))))))) 0))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))))))))))
15.895 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))))))))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))))))))))
15.895 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
15.895 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0
15.898 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0
15.898 * [backup-simplify]: Simplify (- 0) into 0
15.899 * [backup-simplify]: Simplify (+ 0 0) into 0
15.899 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 k))))) into 0
15.900 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
15.900 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n))))) into 0
15.901 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
15.904 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0
15.905 * [backup-simplify]: Simplify (- 0) into 0
15.905 * [backup-simplify]: Simplify (+ 0 0) into 0
15.905 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 k))))) into 0
15.906 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log PI))))) into 0
15.907 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (log PI)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
15.908 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 k) (log PI)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (- 1 k) (log n)))))))) into 0
15.911 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0
15.911 * [backup-simplify]: Simplify (- 0) into 0
15.911 * [backup-simplify]: Simplify (+ 0 0) into 0
15.912 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 k))))) into 0
15.913 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log 2))))) into 0
15.915 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (log 2)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
15.917 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 k) (log 2)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (exp (* 1/2 (* (- 1 k) (log PI)))) (exp (* 1/2 (* (- 1 k) (log n))))))))) into 0
15.919 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (* (- 1 k) (log 2)))) (* (exp (* 1/2 (* (- 1 k) (log PI)))) (exp (* 1/2 (* (- 1 k) (log n)))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k)))))) into 0
15.920 * [taylor]: Taking taylor expansion of 0 in k
15.920 * [backup-simplify]: Simplify 0 into 0
15.920 * [backup-simplify]: Simplify 0 into 0
15.920 * [backup-simplify]: Simplify 0 into 0
15.921 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
15.925 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
15.927 * [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
15.928 * [backup-simplify]: Simplify (- 0) into 0
15.928 * [backup-simplify]: Simplify (+ 0 0) into 0
15.929 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (+ (* 0 0) (* 0 (log n))))) into 0
15.930 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 (- (log n))) (* 0 (log n))))) into 0
15.932 * [backup-simplify]: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 3) 6)) (* (/ (pow (- (* 1/2 (log n))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (sqrt n) (pow (log n) 3)))
15.937 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0
15.937 * [backup-simplify]: Simplify (- 0) into 0
15.938 * [backup-simplify]: Simplify (+ 0 0) into 0
15.939 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (+ (* 0 0) (* 0 (log PI))))) into 0
15.941 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 (- (log PI))) (* 0 (log PI))))) into 0
15.956 * [backup-simplify]: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 3) 6)) (* (/ (pow (- (* 1/2 (log PI))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (pow (log PI) 3) (sqrt PI)))
15.967 * [backup-simplify]: Simplify (+ (* (pow PI 1/2) (* -1/48 (* (sqrt n) (pow (log n) 3)))) (+ (* (* -1/2 (* (log PI) (sqrt PI))) (* 1/8 (* (sqrt n) (pow (log n) 2)))) (+ (* (* 1/8 (* (pow (log PI) 2) (sqrt PI))) (* -1/2 (* (sqrt n) (log n)))) (* (* -1/48 (* (pow (log PI) 3) (sqrt PI))) (pow n 1/2))))) into (- (+ (* 1/48 (* (pow (log PI) 3) (sqrt (* PI n)))) (+ (* 1/16 (* (* (pow (log PI) 2) (log n)) (sqrt (* PI n)))) (+ (* 1/48 (* (sqrt (* n PI)) (pow (log n) 3))) (* 1/16 (* (* (log PI) (pow (log n) 2)) (sqrt (* PI n))))))))
15.970 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0
15.971 * [backup-simplify]: Simplify (- 0) into 0
15.971 * [backup-simplify]: Simplify (+ 0 0) into 0
15.972 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (+ (* 0 0) (* 0 (log 2))))) into 0
15.973 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 (- (log 2))) (* 0 (log 2))))) into 0
15.981 * [backup-simplify]: Simplify (* (exp (* 1/2 (log 2))) (+ (* (/ (pow (- (* 1/2 (log 2))) 3) 6)) (* (/ (pow (- (* 1/2 (log 2))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (pow (log 2) 3) (sqrt 2)))
15.997 * [backup-simplify]: Simplify (+ (* (pow 2 1/2) (- (+ (* 1/48 (* (pow (log PI) 3) (sqrt (* PI n)))) (+ (* 1/16 (* (* (pow (log PI) 2) (log n)) (sqrt (* PI n)))) (+ (* 1/48 (* (sqrt (* n PI)) (pow (log n) 3))) (* 1/16 (* (* (log PI) (pow (log n) 2)) (sqrt (* PI n))))))))) (+ (* (* -1/2 (* (log 2) (sqrt 2))) (+ (* 1/8 (* (sqrt (* n PI)) (pow (log n) 2))) (+ (* 1/8 (* (pow (log PI) 2) (sqrt (* PI n)))) (* 1/4 (* (* (log PI) (log n)) (sqrt (* PI n))))))) (+ (* (* 1/8 (* (pow (log 2) 2) (sqrt 2))) (- (+ (* 1/2 (* (sqrt (* n PI)) (log n))) (* 1/2 (* (log PI) (sqrt (* PI n))))))) (* (* -1/48 (* (pow (log 2) 3) (sqrt 2))) (sqrt (* n PI)))))) into (- (+ (* 1/48 (* (* (pow (log 2) 3) (sqrt 2)) (sqrt (* n PI)))) (+ (* 1/16 (* (* (pow (log 2) 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (+ (* 1/16 (* (* (sqrt 2) (* (pow (log PI) 2) (log n))) (sqrt (* PI n)))) (+ (* 1/16 (* (* (log 2) (* (sqrt 2) (pow (log PI) 2))) (sqrt (* PI n)))) (+ (* 1/48 (* (* (sqrt 2) (pow (log n) 3)) (sqrt (* n PI)))) (+ (* 1/16 (* (* (pow (log 2) 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (+ (* 1/16 (* (* (sqrt 2) (* (log PI) (pow (log n) 2))) (sqrt (* PI n)))) (+ (* 1/8 (* (* (log 2) (* (sqrt 2) (* (log PI) (log n)))) (sqrt (* PI n)))) (+ (* 1/48 (* (* (sqrt 2) (pow (log PI) 3)) (sqrt (* PI n)))) (* 1/16 (* (* (log 2) (* (sqrt 2) (pow (log n) 2))) (sqrt (* n PI))))))))))))))
16.039 * [backup-simplify]: Simplify (+ (* (sqrt (* PI (* n 2))) +nan.0) (+ (* (- (+ (* 1/2 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (+ (* 1/2 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (* 1/2 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))))) +nan.0) (+ (* (+ (* 1/8 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (+ (* 1/8 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (+ (* 1/4 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (+ (* 1/4 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (+ (* 1/8 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (* 1/4 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n))))))))) +nan.0) (* (- (+ (* 1/48 (* (* (pow (log 2) 3) (sqrt 2)) (sqrt (* n PI)))) (+ (* 1/16 (* (* (pow (log 2) 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (+ (* 1/16 (* (* (sqrt 2) (* (pow (log PI) 2) (log n))) (sqrt (* PI n)))) (+ (* 1/16 (* (* (log 2) (* (sqrt 2) (pow (log PI) 2))) (sqrt (* PI n)))) (+ (* 1/48 (* (* (sqrt 2) (pow (log n) 3)) (sqrt (* n PI)))) (+ (* 1/16 (* (* (pow (log 2) 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (+ (* 1/16 (* (* (sqrt 2) (* (log PI) (pow (log n) 2))) (sqrt (* PI n)))) (+ (* 1/8 (* (* (log 2) (* (sqrt 2) (* (log PI) (log n)))) (sqrt (* PI n)))) (+ (* 1/48 (* (* (sqrt 2) (pow (log PI) 3)) (sqrt (* PI n)))) (* 1/16 (* (* (log 2) (* (sqrt 2) (pow (log n) 2))) (sqrt (* n PI)))))))))))))) 0)))) into (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))))))))))))))))))))))
16.059 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI))))))))))))))))))))))) into (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))))))))))))))))))))))
16.080 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI))))))))))))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))))))))) (* k 1)) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) into (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (* (log n) (pow k 2)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) k) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (pow k 2))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log n) (pow k 2))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (* (log PI) (pow k 2)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (pow k 2))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (* (sqrt 2) (pow k 2))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow k 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (pow (log n) 2) (pow k 2))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log n) k)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) k)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) k)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (* (log n) (pow k 2)))) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (* (pow (log PI) 2) (pow k 2))) (sqrt (* n PI)))))))))))))))))))))))))))))))))
16.080 * [backup-simplify]: Simplify (* (pow (/ 1 n) (* (- 1 (/ 1 k)) 1/2)) (/ (* (pow 2 (* (- 1 (/ 1 k)) 1/2)) (pow PI (* (- 1 (/ 1 k)) 1/2))) (sqrt (/ 1 k)))) into (* (* (pow PI (* 1/2 (- 1 (/ 1 k)))) (* (pow (/ 1 n) (* 1/2 (- 1 (/ 1 k)))) (pow 2 (* 1/2 (- 1 (/ 1 k)))))) (sqrt k))
16.080 * [approximate]: Taking taylor expansion of (* (* (pow PI (* 1/2 (- 1 (/ 1 k)))) (* (pow (/ 1 n) (* 1/2 (- 1 (/ 1 k)))) (pow 2 (* 1/2 (- 1 (/ 1 k)))))) (sqrt k)) in (n k) around 0
16.080 * [taylor]: Taking taylor expansion of (* (* (pow PI (* 1/2 (- 1 (/ 1 k)))) (* (pow (/ 1 n) (* 1/2 (- 1 (/ 1 k)))) (pow 2 (* 1/2 (- 1 (/ 1 k)))))) (sqrt k)) in k
16.080 * [taylor]: Taking taylor expansion of (* (pow PI (* 1/2 (- 1 (/ 1 k)))) (* (pow (/ 1 n) (* 1/2 (- 1 (/ 1 k)))) (pow 2 (* 1/2 (- 1 (/ 1 k)))))) in k
16.080 * [taylor]: Taking taylor expansion of (pow PI (* 1/2 (- 1 (/ 1 k)))) in k
16.080 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log PI))) in k
16.080 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log PI)) in k
16.080 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
16.080 * [taylor]: Taking taylor expansion of 1/2 in k
16.080 * [backup-simplify]: Simplify 1/2 into 1/2
16.080 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
16.080 * [taylor]: Taking taylor expansion of 1 in k
16.080 * [backup-simplify]: Simplify 1 into 1
16.080 * [taylor]: Taking taylor expansion of (/ 1 k) in k
16.080 * [taylor]: Taking taylor expansion of k in k
16.080 * [backup-simplify]: Simplify 0 into 0
16.080 * [backup-simplify]: Simplify 1 into 1
16.081 * [backup-simplify]: Simplify (/ 1 1) into 1
16.081 * [taylor]: Taking taylor expansion of (log PI) in k
16.081 * [taylor]: Taking taylor expansion of PI in k
16.081 * [backup-simplify]: Simplify PI into PI
16.081 * [backup-simplify]: Simplify (log PI) into (log PI)
16.081 * [backup-simplify]: Simplify (- 1) into -1
16.082 * [backup-simplify]: Simplify (+ 0 -1) into -1
16.082 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
16.083 * [backup-simplify]: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI))
16.083 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log PI))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI))))
16.083 * [taylor]: Taking taylor expansion of (* (pow (/ 1 n) (* 1/2 (- 1 (/ 1 k)))) (pow 2 (* 1/2 (- 1 (/ 1 k))))) in k
16.083 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (* 1/2 (- 1 (/ 1 k)))) in k
16.083 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (/ 1 n)))) in k
16.083 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (/ 1 n))) in k
16.083 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
16.083 * [taylor]: Taking taylor expansion of 1/2 in k
16.083 * [backup-simplify]: Simplify 1/2 into 1/2
16.083 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
16.083 * [taylor]: Taking taylor expansion of 1 in k
16.083 * [backup-simplify]: Simplify 1 into 1
16.083 * [taylor]: Taking taylor expansion of (/ 1 k) in k
16.083 * [taylor]: Taking taylor expansion of k in k
16.083 * [backup-simplify]: Simplify 0 into 0
16.083 * [backup-simplify]: Simplify 1 into 1
16.084 * [backup-simplify]: Simplify (/ 1 1) into 1
16.084 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in k
16.084 * [taylor]: Taking taylor expansion of (/ 1 n) in k
16.084 * [taylor]: Taking taylor expansion of n in k
16.084 * [backup-simplify]: Simplify n into n
16.084 * [backup-simplify]: Simplify (/ 1 n) into (/ 1 n)
16.084 * [backup-simplify]: Simplify (log (/ 1 n)) into (log (/ 1 n))
16.084 * [backup-simplify]: Simplify (- 1) into -1
16.084 * [backup-simplify]: Simplify (+ 0 -1) into -1
16.085 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
16.085 * [backup-simplify]: Simplify (* -1/2 (log (/ 1 n))) into (* -1/2 (log (/ 1 n)))
16.085 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (/ 1 n)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (/ 1 n)))))
16.085 * [taylor]: Taking taylor expansion of (pow 2 (* 1/2 (- 1 (/ 1 k)))) in k
16.085 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log 2))) in k
16.085 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log 2)) in k
16.085 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
16.085 * [taylor]: Taking taylor expansion of 1/2 in k
16.085 * [backup-simplify]: Simplify 1/2 into 1/2
16.085 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
16.085 * [taylor]: Taking taylor expansion of 1 in k
16.085 * [backup-simplify]: Simplify 1 into 1
16.085 * [taylor]: Taking taylor expansion of (/ 1 k) in k
16.085 * [taylor]: Taking taylor expansion of k in k
16.085 * [backup-simplify]: Simplify 0 into 0
16.085 * [backup-simplify]: Simplify 1 into 1
16.085 * [backup-simplify]: Simplify (/ 1 1) into 1
16.085 * [taylor]: Taking taylor expansion of (log 2) in k
16.085 * [taylor]: Taking taylor expansion of 2 in k
16.085 * [backup-simplify]: Simplify 2 into 2
16.085 * [backup-simplify]: Simplify (log 2) into (log 2)
16.086 * [backup-simplify]: Simplify (- 1) into -1
16.086 * [backup-simplify]: Simplify (+ 0 -1) into -1
16.086 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
16.087 * [backup-simplify]: Simplify (* -1/2 (log 2)) into (* -1/2 (log 2))
16.087 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log 2))) into (exp (* 1/2 (* (log 2) (- 1 (/ 1 k)))))
16.087 * [taylor]: Taking taylor expansion of (sqrt k) in k
16.087 * [taylor]: Taking taylor expansion of k in k
16.087 * [backup-simplify]: Simplify 0 into 0
16.087 * [backup-simplify]: Simplify 1 into 1
16.087 * [backup-simplify]: Simplify (sqrt 0) into 0
16.088 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
16.088 * [taylor]: Taking taylor expansion of (* (* (pow PI (* 1/2 (- 1 (/ 1 k)))) (* (pow (/ 1 n) (* 1/2 (- 1 (/ 1 k)))) (pow 2 (* 1/2 (- 1 (/ 1 k)))))) (sqrt k)) in n
16.088 * [taylor]: Taking taylor expansion of (* (pow PI (* 1/2 (- 1 (/ 1 k)))) (* (pow (/ 1 n) (* 1/2 (- 1 (/ 1 k)))) (pow 2 (* 1/2 (- 1 (/ 1 k)))))) in n
16.088 * [taylor]: Taking taylor expansion of (pow PI (* 1/2 (- 1 (/ 1 k)))) in n
16.088 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log PI))) in n
16.088 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log PI)) in n
16.088 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
16.088 * [taylor]: Taking taylor expansion of 1/2 in n
16.089 * [backup-simplify]: Simplify 1/2 into 1/2
16.089 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
16.089 * [taylor]: Taking taylor expansion of 1 in n
16.089 * [backup-simplify]: Simplify 1 into 1
16.089 * [taylor]: Taking taylor expansion of (/ 1 k) in n
16.089 * [taylor]: Taking taylor expansion of k in n
16.089 * [backup-simplify]: Simplify k into k
16.089 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
16.089 * [taylor]: Taking taylor expansion of (log PI) in n
16.089 * [taylor]: Taking taylor expansion of PI in n
16.089 * [backup-simplify]: Simplify PI into PI
16.089 * [backup-simplify]: Simplify (log PI) into (log PI)
16.089 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
16.089 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
16.089 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
16.089 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (log PI)) into (* 1/2 (* (- 1 (/ 1 k)) (log PI)))
16.090 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI))))
16.090 * [taylor]: Taking taylor expansion of (* (pow (/ 1 n) (* 1/2 (- 1 (/ 1 k)))) (pow 2 (* 1/2 (- 1 (/ 1 k))))) in n
16.090 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (* 1/2 (- 1 (/ 1 k)))) in n
16.090 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (/ 1 n)))) in n
16.090 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (/ 1 n))) in n
16.090 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
16.090 * [taylor]: Taking taylor expansion of 1/2 in n
16.090 * [backup-simplify]: Simplify 1/2 into 1/2
16.090 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
16.090 * [taylor]: Taking taylor expansion of 1 in n
16.090 * [backup-simplify]: Simplify 1 into 1
16.090 * [taylor]: Taking taylor expansion of (/ 1 k) in n
16.090 * [taylor]: Taking taylor expansion of k in n
16.090 * [backup-simplify]: Simplify k into k
16.090 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
16.090 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n
16.090 * [taylor]: Taking taylor expansion of (/ 1 n) in n
16.090 * [taylor]: Taking taylor expansion of n in n
16.090 * [backup-simplify]: Simplify 0 into 0
16.090 * [backup-simplify]: Simplify 1 into 1
16.090 * [backup-simplify]: Simplify (/ 1 1) into 1
16.091 * [backup-simplify]: Simplify (log 1) into 0
16.091 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
16.091 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
16.091 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
16.091 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n))
16.091 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log n))) into (* -1/2 (* (- 1 (/ 1 k)) (log n)))
16.091 * [backup-simplify]: Simplify (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) into (exp (* -1/2 (* (- 1 (/ 1 k)) (log n))))
16.091 * [taylor]: Taking taylor expansion of (pow 2 (* 1/2 (- 1 (/ 1 k)))) in n
16.091 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log 2))) in n
16.091 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log 2)) in n
16.091 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
16.091 * [taylor]: Taking taylor expansion of 1/2 in n
16.091 * [backup-simplify]: Simplify 1/2 into 1/2
16.091 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
16.091 * [taylor]: Taking taylor expansion of 1 in n
16.091 * [backup-simplify]: Simplify 1 into 1
16.091 * [taylor]: Taking taylor expansion of (/ 1 k) in n
16.091 * [taylor]: Taking taylor expansion of k in n
16.091 * [backup-simplify]: Simplify k into k
16.091 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
16.091 * [taylor]: Taking taylor expansion of (log 2) in n
16.091 * [taylor]: Taking taylor expansion of 2 in n
16.091 * [backup-simplify]: Simplify 2 into 2
16.092 * [backup-simplify]: Simplify (log 2) into (log 2)
16.092 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
16.092 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
16.092 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
16.092 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (log 2)) into (* 1/2 (* (log 2) (- 1 (/ 1 k))))
16.093 * [backup-simplify]: Simplify (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) into (exp (* 1/2 (* (log 2) (- 1 (/ 1 k)))))
16.093 * [taylor]: Taking taylor expansion of (sqrt k) in n
16.093 * [taylor]: Taking taylor expansion of k in n
16.093 * [backup-simplify]: Simplify k into k
16.093 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
16.093 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
16.093 * [taylor]: Taking taylor expansion of (* (* (pow PI (* 1/2 (- 1 (/ 1 k)))) (* (pow (/ 1 n) (* 1/2 (- 1 (/ 1 k)))) (pow 2 (* 1/2 (- 1 (/ 1 k)))))) (sqrt k)) in n
16.093 * [taylor]: Taking taylor expansion of (* (pow PI (* 1/2 (- 1 (/ 1 k)))) (* (pow (/ 1 n) (* 1/2 (- 1 (/ 1 k)))) (pow 2 (* 1/2 (- 1 (/ 1 k)))))) in n
16.093 * [taylor]: Taking taylor expansion of (pow PI (* 1/2 (- 1 (/ 1 k)))) in n
16.093 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log PI))) in n
16.093 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log PI)) in n
16.093 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
16.093 * [taylor]: Taking taylor expansion of 1/2 in n
16.093 * [backup-simplify]: Simplify 1/2 into 1/2
16.093 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
16.093 * [taylor]: Taking taylor expansion of 1 in n
16.093 * [backup-simplify]: Simplify 1 into 1
16.094 * [taylor]: Taking taylor expansion of (/ 1 k) in n
16.094 * [taylor]: Taking taylor expansion of k in n
16.094 * [backup-simplify]: Simplify k into k
16.094 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
16.094 * [taylor]: Taking taylor expansion of (log PI) in n
16.094 * [taylor]: Taking taylor expansion of PI in n
16.094 * [backup-simplify]: Simplify PI into PI
16.094 * [backup-simplify]: Simplify (log PI) into (log PI)
16.094 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
16.094 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
16.094 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
16.095 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (log PI)) into (* 1/2 (* (- 1 (/ 1 k)) (log PI)))
16.095 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI))))
16.095 * [taylor]: Taking taylor expansion of (* (pow (/ 1 n) (* 1/2 (- 1 (/ 1 k)))) (pow 2 (* 1/2 (- 1 (/ 1 k))))) in n
16.095 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (* 1/2 (- 1 (/ 1 k)))) in n
16.095 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (/ 1 n)))) in n
16.095 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (/ 1 n))) in n
16.095 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
16.095 * [taylor]: Taking taylor expansion of 1/2 in n
16.096 * [backup-simplify]: Simplify 1/2 into 1/2
16.096 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
16.096 * [taylor]: Taking taylor expansion of 1 in n
16.096 * [backup-simplify]: Simplify 1 into 1
16.096 * [taylor]: Taking taylor expansion of (/ 1 k) in n
16.096 * [taylor]: Taking taylor expansion of k in n
16.096 * [backup-simplify]: Simplify k into k
16.096 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
16.096 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n
16.096 * [taylor]: Taking taylor expansion of (/ 1 n) in n
16.096 * [taylor]: Taking taylor expansion of n in n
16.096 * [backup-simplify]: Simplify 0 into 0
16.096 * [backup-simplify]: Simplify 1 into 1
16.096 * [backup-simplify]: Simplify (/ 1 1) into 1
16.097 * [backup-simplify]: Simplify (log 1) into 0
16.097 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
16.097 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
16.097 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
16.097 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n))
16.097 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log n))) into (* -1/2 (* (- 1 (/ 1 k)) (log n)))
16.098 * [backup-simplify]: Simplify (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) into (exp (* -1/2 (* (- 1 (/ 1 k)) (log n))))
16.098 * [taylor]: Taking taylor expansion of (pow 2 (* 1/2 (- 1 (/ 1 k)))) in n
16.098 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log 2))) in n
16.098 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log 2)) in n
16.098 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
16.098 * [taylor]: Taking taylor expansion of 1/2 in n
16.098 * [backup-simplify]: Simplify 1/2 into 1/2
16.098 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
16.098 * [taylor]: Taking taylor expansion of 1 in n
16.098 * [backup-simplify]: Simplify 1 into 1
16.098 * [taylor]: Taking taylor expansion of (/ 1 k) in n
16.098 * [taylor]: Taking taylor expansion of k in n
16.098 * [backup-simplify]: Simplify k into k
16.098 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
16.098 * [taylor]: Taking taylor expansion of (log 2) in n
16.098 * [taylor]: Taking taylor expansion of 2 in n
16.098 * [backup-simplify]: Simplify 2 into 2
16.098 * [backup-simplify]: Simplify (log 2) into (log 2)
16.098 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
16.099 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
16.099 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
16.099 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (log 2)) into (* 1/2 (* (log 2) (- 1 (/ 1 k))))
16.100 * [backup-simplify]: Simplify (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) into (exp (* 1/2 (* (log 2) (- 1 (/ 1 k)))))
16.100 * [taylor]: Taking taylor expansion of (sqrt k) in n
16.100 * [taylor]: Taking taylor expansion of k in n
16.100 * [backup-simplify]: Simplify k into k
16.100 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
16.100 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
16.100 * [backup-simplify]: Simplify (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (log 2) (- 1 (/ 1 k)))))) into (* (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))))
16.102 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (* (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))))) into (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (log 2) (- 1 (/ 1 k)))))))
16.103 * [backup-simplify]: Simplify (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))))) (sqrt k)) into (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))))) (sqrt k))
16.103 * [taylor]: Taking taylor expansion of (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))))) (sqrt k)) in k
16.103 * [taylor]: Taking taylor expansion of (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))))) in k
16.103 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) in k
16.103 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log PI))) in k
16.103 * [taylor]: Taking taylor expansion of 1/2 in k
16.103 * [backup-simplify]: Simplify 1/2 into 1/2
16.103 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log PI)) in k
16.103 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
16.103 * [taylor]: Taking taylor expansion of 1 in k
16.103 * [backup-simplify]: Simplify 1 into 1
16.103 * [taylor]: Taking taylor expansion of (/ 1 k) in k
16.103 * [taylor]: Taking taylor expansion of k in k
16.103 * [backup-simplify]: Simplify 0 into 0
16.103 * [backup-simplify]: Simplify 1 into 1
16.103 * [backup-simplify]: Simplify (/ 1 1) into 1
16.104 * [taylor]: Taking taylor expansion of (log PI) in k
16.104 * [taylor]: Taking taylor expansion of PI in k
16.104 * [backup-simplify]: Simplify PI into PI
16.104 * [backup-simplify]: Simplify (log PI) into (log PI)
16.104 * [backup-simplify]: Simplify (- 1) into -1
16.105 * [backup-simplify]: Simplify (+ 0 -1) into -1
16.106 * [backup-simplify]: Simplify (* -1 (log PI)) into (* -1 (log PI))
16.107 * [backup-simplify]: Simplify (* 1/2 (* -1 (log PI))) into (* -1/2 (log PI))
16.108 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI))))
16.108 * [taylor]: Taking taylor expansion of (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (log 2) (- 1 (/ 1 k)))))) in k
16.108 * [taylor]: Taking taylor expansion of (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) in k
16.108 * [taylor]: Taking taylor expansion of (* -1/2 (* (- 1 (/ 1 k)) (log n))) in k
16.108 * [taylor]: Taking taylor expansion of -1/2 in k
16.108 * [backup-simplify]: Simplify -1/2 into -1/2
16.108 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log n)) in k
16.108 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
16.108 * [taylor]: Taking taylor expansion of 1 in k
16.108 * [backup-simplify]: Simplify 1 into 1
16.108 * [taylor]: Taking taylor expansion of (/ 1 k) in k
16.108 * [taylor]: Taking taylor expansion of k in k
16.108 * [backup-simplify]: Simplify 0 into 0
16.108 * [backup-simplify]: Simplify 1 into 1
16.108 * [backup-simplify]: Simplify (/ 1 1) into 1
16.108 * [taylor]: Taking taylor expansion of (log n) in k
16.108 * [taylor]: Taking taylor expansion of n in k
16.108 * [backup-simplify]: Simplify n into n
16.108 * [backup-simplify]: Simplify (log n) into (log n)
16.109 * [backup-simplify]: Simplify (- 1) into -1
16.109 * [backup-simplify]: Simplify (+ 0 -1) into -1
16.109 * [backup-simplify]: Simplify (* -1 (log n)) into (* -1 (log n))
16.109 * [backup-simplify]: Simplify (* -1/2 (* -1 (log n))) into (* 1/2 (log n))
16.110 * [backup-simplify]: Simplify (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) into (exp (* -1/2 (* (- 1 (/ 1 k)) (log n))))
16.110 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) in k
16.110 * [taylor]: Taking taylor expansion of (* 1/2 (* (log 2) (- 1 (/ 1 k)))) in k
16.110 * [taylor]: Taking taylor expansion of 1/2 in k
16.110 * [backup-simplify]: Simplify 1/2 into 1/2
16.110 * [taylor]: Taking taylor expansion of (* (log 2) (- 1 (/ 1 k))) in k
16.110 * [taylor]: Taking taylor expansion of (log 2) in k
16.110 * [taylor]: Taking taylor expansion of 2 in k
16.110 * [backup-simplify]: Simplify 2 into 2
16.110 * [backup-simplify]: Simplify (log 2) into (log 2)
16.110 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
16.110 * [taylor]: Taking taylor expansion of 1 in k
16.110 * [backup-simplify]: Simplify 1 into 1
16.110 * [taylor]: Taking taylor expansion of (/ 1 k) in k
16.110 * [taylor]: Taking taylor expansion of k in k
16.110 * [backup-simplify]: Simplify 0 into 0
16.110 * [backup-simplify]: Simplify 1 into 1
16.111 * [backup-simplify]: Simplify (/ 1 1) into 1
16.111 * [backup-simplify]: Simplify (- 1) into -1
16.111 * [backup-simplify]: Simplify (+ 0 -1) into -1
16.112 * [backup-simplify]: Simplify (* (log 2) -1) into (* -1 (log 2))
16.114 * [backup-simplify]: Simplify (* 1/2 (* -1 (log 2))) into (* -1/2 (log 2))
16.114 * [backup-simplify]: Simplify (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) into (exp (* 1/2 (* (log 2) (- 1 (/ 1 k)))))
16.114 * [taylor]: Taking taylor expansion of (sqrt k) in k
16.114 * [taylor]: Taking taylor expansion of k in k
16.114 * [backup-simplify]: Simplify 0 into 0
16.114 * [backup-simplify]: Simplify 1 into 1
16.115 * [backup-simplify]: Simplify (sqrt 0) into 0
16.116 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
16.117 * [backup-simplify]: Simplify (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (log 2) (- 1 (/ 1 k)))))) into (* (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))))
16.118 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (* (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))))) into (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (log 2) (- 1 (/ 1 k)))))))
16.119 * [backup-simplify]: Simplify (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))))) 0) into 0
16.119 * [backup-simplify]: Simplify 0 into 0
16.121 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0
16.121 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
16.121 * [backup-simplify]: Simplify (- 0) into 0
16.122 * [backup-simplify]: Simplify (+ 0 0) into 0
16.122 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 (/ 1 k)))) into 0
16.123 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (log 2))) into 0
16.124 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0
16.125 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
16.127 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0
16.127 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
16.127 * [backup-simplify]: Simplify (- 0) into 0
16.127 * [backup-simplify]: Simplify (+ 0 0) into 0
16.128 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 (/ 1 k)))) into 0
16.128 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n))
16.129 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log n)))) into 0
16.129 * [backup-simplify]: Simplify (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
16.130 * [backup-simplify]: Simplify (+ (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) 0) (* 0 (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))))) into 0
16.132 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0
16.132 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
16.132 * [backup-simplify]: Simplify (- 0) into 0
16.132 * [backup-simplify]: Simplify (+ 0 0) into 0
16.133 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 (/ 1 k)))) into 0
16.134 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (log PI))) into 0
16.135 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (+ (* (/ (pow 0 1) 1)))) into 0
16.136 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) 0) (* 0 (* (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) (exp (* -1/2 (* (- 1 (/ 1 k)) (log n))))))) into 0
16.137 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))))) 0) (* 0 (sqrt k))) into 0
16.137 * [taylor]: Taking taylor expansion of 0 in k
16.137 * [backup-simplify]: Simplify 0 into 0
16.137 * [backup-simplify]: Simplify 0 into 0
16.138 * [backup-simplify]: Simplify (+ (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) 0) (* 0 (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))))) into 0
16.139 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) 0) (* 0 (* (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) (exp (* -1/2 (* (- 1 (/ 1 k)) (log n))))))) into 0
16.141 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))))) +nan.0) (* 0 0)) into (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (log 2) (- 1 (/ 1 k)))))))))
16.142 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))))))) into (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (log 2) (- 1 (/ 1 k)))))))))
16.143 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
16.146 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0
16.146 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
16.147 * [backup-simplify]: Simplify (- 0) into 0
16.147 * [backup-simplify]: Simplify (+ 0 0) into 0
16.148 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0
16.149 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (log 2)))) into 0
16.151 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
16.152 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.155 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0
16.156 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
16.156 * [backup-simplify]: Simplify (- 0) into 0
16.157 * [backup-simplify]: Simplify (+ 0 0) into 0
16.158 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0
16.159 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n))
16.159 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log n))))) into 0
16.161 * [backup-simplify]: Simplify (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
16.162 * [backup-simplify]: Simplify (+ (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (log 2) (- 1 (/ 1 k)))))))) into 0
16.166 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0
16.166 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
16.167 * [backup-simplify]: Simplify (- 0) into 0
16.167 * [backup-simplify]: Simplify (+ 0 0) into 0
16.168 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0
16.169 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (log PI)))) into 0
16.170 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
16.171 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) 0) (+ (* 0 0) (* 0 (* (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))))))) into 0
16.172 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))))) 0) (+ (* 0 0) (* 0 (sqrt k)))) into 0
16.172 * [taylor]: Taking taylor expansion of 0 in k
16.172 * [backup-simplify]: Simplify 0 into 0
16.172 * [backup-simplify]: Simplify 0 into 0
16.172 * [backup-simplify]: Simplify 0 into 0
16.175 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
16.175 * [backup-simplify]: Simplify (+ (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (log 2) (- 1 (/ 1 k)))))))) into 0
16.177 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) 0) (+ (* 0 0) (* 0 (* (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))))))) into 0
16.178 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (log 2) (- 1 (/ 1 k)))))))))
16.179 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))))))) into (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (log 2) (- 1 (/ 1 k)))))))))
16.179 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
16.182 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0
16.182 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
16.182 * [backup-simplify]: Simplify (- 0) into 0
16.183 * [backup-simplify]: Simplify (+ 0 0) into 0
16.184 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0
16.184 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log 2))))) into 0
16.186 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
16.190 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.193 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0
16.193 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
16.194 * [backup-simplify]: Simplify (- 0) into 0
16.194 * [backup-simplify]: Simplify (+ 0 0) into 0
16.195 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0
16.195 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n))
16.196 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0
16.197 * [backup-simplify]: Simplify (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
16.198 * [backup-simplify]: Simplify (+ (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))))))) into 0
16.200 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0
16.201 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
16.201 * [backup-simplify]: Simplify (- 0) into 0
16.201 * [backup-simplify]: Simplify (+ 0 0) into 0
16.204 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0
16.205 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log PI))))) into 0
16.206 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
16.207 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) (exp (* -1/2 (* (- 1 (/ 1 k)) (log n))))))))) into 0
16.208 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt k))))) into 0
16.208 * [taylor]: Taking taylor expansion of 0 in k
16.208 * [backup-simplify]: Simplify 0 into 0
16.208 * [backup-simplify]: Simplify 0 into 0
16.208 * [backup-simplify]: Simplify 0 into 0
16.208 * [backup-simplify]: Simplify 0 into 0
16.211 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
16.212 * [backup-simplify]: Simplify (+ (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))))))) into 0
16.214 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) (exp (* -1/2 (* (- 1 (/ 1 k)) (log n))))))))) into 0
16.216 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (log 2) (- 1 (/ 1 k)))))))))
16.217 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))))))) into (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (log 2) (- 1 (/ 1 k)))))))))
16.222 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log PI)))) (* (exp (* -1/2 (* (- 1 (/ 1 (/ 1 k))) (log (/ 1 n))))) (exp (* 1/2 (* (log 2) (- 1 (/ 1 (/ 1 k)))))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log PI)))) (* (exp (* -1/2 (* (- 1 (/ 1 (/ 1 k))) (log (/ 1 n))))) (exp (* 1/2 (* (log 2) (- 1 (/ 1 (/ 1 k)))))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log PI)))) (* (exp (* -1/2 (* (- 1 (/ 1 (/ 1 k))) (log (/ 1 n))))) (exp (* 1/2 (* (log 2) (- 1 (/ 1 (/ 1 k)))))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (log PI)))) (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* -1/2 (* (- 1 k) (log (/ 1 n))))))) (pow k 3))) (- (+ (* +nan.0 (/ (* (exp (* -1/2 (* (- 1 k) (log (/ 1 n))))) (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (- 1 k) (log PI)))))) (pow k 2))) (- (* +nan.0 (/ (* (exp (* -1/2 (* (- 1 k) (log (/ 1 n))))) (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (- 1 k) (log PI)))))) k)))))))
16.223 * [backup-simplify]: Simplify (* (pow (/ 1 (- n)) (* (- 1 (/ 1 (- k))) 1/2)) (/ (* (pow 2 (* (- 1 (/ 1 (- k))) 1/2)) (pow PI (* (- 1 (/ 1 (- k))) 1/2))) (sqrt (/ 1 (- k))))) into (/ (* (pow (/ -1 n) (* 1/2 (+ (/ 1 k) 1))) (* (pow 2 (* 1/2 (+ (/ 1 k) 1))) (pow PI (* 1/2 (+ (/ 1 k) 1))))) (sqrt (/ -1 k)))
16.223 * [approximate]: Taking taylor expansion of (/ (* (pow (/ -1 n) (* 1/2 (+ (/ 1 k) 1))) (* (pow 2 (* 1/2 (+ (/ 1 k) 1))) (pow PI (* 1/2 (+ (/ 1 k) 1))))) (sqrt (/ -1 k))) in (n k) around 0
16.223 * [taylor]: Taking taylor expansion of (/ (* (pow (/ -1 n) (* 1/2 (+ (/ 1 k) 1))) (* (pow 2 (* 1/2 (+ (/ 1 k) 1))) (pow PI (* 1/2 (+ (/ 1 k) 1))))) (sqrt (/ -1 k))) in k
16.223 * [taylor]: Taking taylor expansion of (* (pow (/ -1 n) (* 1/2 (+ (/ 1 k) 1))) (* (pow 2 (* 1/2 (+ (/ 1 k) 1))) (pow PI (* 1/2 (+ (/ 1 k) 1))))) in k
16.223 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (* 1/2 (+ (/ 1 k) 1))) in k
16.223 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (/ -1 n)))) in k
16.223 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (/ -1 n))) in k
16.223 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
16.223 * [taylor]: Taking taylor expansion of 1/2 in k
16.223 * [backup-simplify]: Simplify 1/2 into 1/2
16.223 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
16.223 * [taylor]: Taking taylor expansion of (/ 1 k) in k
16.223 * [taylor]: Taking taylor expansion of k in k
16.223 * [backup-simplify]: Simplify 0 into 0
16.223 * [backup-simplify]: Simplify 1 into 1
16.224 * [backup-simplify]: Simplify (/ 1 1) into 1
16.224 * [taylor]: Taking taylor expansion of 1 in k
16.224 * [backup-simplify]: Simplify 1 into 1
16.224 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in k
16.224 * [taylor]: Taking taylor expansion of (/ -1 n) in k
16.224 * [taylor]: Taking taylor expansion of -1 in k
16.224 * [backup-simplify]: Simplify -1 into -1
16.224 * [taylor]: Taking taylor expansion of n in k
16.224 * [backup-simplify]: Simplify n into n
16.224 * [backup-simplify]: Simplify (/ -1 n) into (/ -1 n)
16.224 * [backup-simplify]: Simplify (log (/ -1 n)) into (log (/ -1 n))
16.225 * [backup-simplify]: Simplify (+ 1 0) into 1
16.225 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
16.225 * [backup-simplify]: Simplify (* 1/2 (log (/ -1 n))) into (* 1/2 (log (/ -1 n)))
16.226 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (/ -1 n)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (/ -1 n)))))
16.226 * [taylor]: Taking taylor expansion of (* (pow 2 (* 1/2 (+ (/ 1 k) 1))) (pow PI (* 1/2 (+ (/ 1 k) 1)))) in k
16.226 * [taylor]: Taking taylor expansion of (pow 2 (* 1/2 (+ (/ 1 k) 1))) in k
16.226 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log 2))) in k
16.226 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log 2)) in k
16.226 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
16.226 * [taylor]: Taking taylor expansion of 1/2 in k
16.226 * [backup-simplify]: Simplify 1/2 into 1/2
16.226 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
16.226 * [taylor]: Taking taylor expansion of (/ 1 k) in k
16.226 * [taylor]: Taking taylor expansion of k in k
16.226 * [backup-simplify]: Simplify 0 into 0
16.226 * [backup-simplify]: Simplify 1 into 1
16.226 * [backup-simplify]: Simplify (/ 1 1) into 1
16.226 * [taylor]: Taking taylor expansion of 1 in k
16.227 * [backup-simplify]: Simplify 1 into 1
16.227 * [taylor]: Taking taylor expansion of (log 2) in k
16.227 * [taylor]: Taking taylor expansion of 2 in k
16.227 * [backup-simplify]: Simplify 2 into 2
16.227 * [backup-simplify]: Simplify (log 2) into (log 2)
16.228 * [backup-simplify]: Simplify (+ 1 0) into 1
16.228 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
16.229 * [backup-simplify]: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2))
16.230 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log 2))) into (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1))))
16.230 * [taylor]: Taking taylor expansion of (pow PI (* 1/2 (+ (/ 1 k) 1))) in k
16.230 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log PI))) in k
16.230 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log PI)) in k
16.230 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
16.230 * [taylor]: Taking taylor expansion of 1/2 in k
16.230 * [backup-simplify]: Simplify 1/2 into 1/2
16.230 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
16.230 * [taylor]: Taking taylor expansion of (/ 1 k) in k
16.230 * [taylor]: Taking taylor expansion of k in k
16.230 * [backup-simplify]: Simplify 0 into 0
16.230 * [backup-simplify]: Simplify 1 into 1
16.231 * [backup-simplify]: Simplify (/ 1 1) into 1
16.231 * [taylor]: Taking taylor expansion of 1 in k
16.231 * [backup-simplify]: Simplify 1 into 1
16.231 * [taylor]: Taking taylor expansion of (log PI) in k
16.231 * [taylor]: Taking taylor expansion of PI in k
16.231 * [backup-simplify]: Simplify PI into PI
16.231 * [backup-simplify]: Simplify (log PI) into (log PI)
16.232 * [backup-simplify]: Simplify (+ 1 0) into 1
16.233 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
16.234 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI))
16.234 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log PI))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI))))
16.234 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
16.234 * [taylor]: Taking taylor expansion of (/ -1 k) in k
16.234 * [taylor]: Taking taylor expansion of -1 in k
16.234 * [backup-simplify]: Simplify -1 into -1
16.234 * [taylor]: Taking taylor expansion of k in k
16.234 * [backup-simplify]: Simplify 0 into 0
16.234 * [backup-simplify]: Simplify 1 into 1
16.235 * [backup-simplify]: Simplify (/ -1 1) into -1
16.236 * [backup-simplify]: Simplify (sqrt 0) into 0
16.237 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
16.238 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI))))) into (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))))
16.239 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (/ -1 n))))) (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))))) into (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (/ -1 n))))) (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1))))))
16.240 * [backup-simplify]: Simplify (/ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (/ -1 n))))) (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))))) +nan.0) into (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (/ -1 n))))) (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))))))
16.240 * [taylor]: Taking taylor expansion of (/ (* (pow (/ -1 n) (* 1/2 (+ (/ 1 k) 1))) (* (pow 2 (* 1/2 (+ (/ 1 k) 1))) (pow PI (* 1/2 (+ (/ 1 k) 1))))) (sqrt (/ -1 k))) in n
16.240 * [taylor]: Taking taylor expansion of (* (pow (/ -1 n) (* 1/2 (+ (/ 1 k) 1))) (* (pow 2 (* 1/2 (+ (/ 1 k) 1))) (pow PI (* 1/2 (+ (/ 1 k) 1))))) in n
16.240 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (* 1/2 (+ (/ 1 k) 1))) in n
16.240 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (/ -1 n)))) in n
16.240 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (/ -1 n))) in n
16.240 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
16.240 * [taylor]: Taking taylor expansion of 1/2 in n
16.240 * [backup-simplify]: Simplify 1/2 into 1/2
16.240 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
16.240 * [taylor]: Taking taylor expansion of (/ 1 k) in n
16.240 * [taylor]: Taking taylor expansion of k in n
16.240 * [backup-simplify]: Simplify k into k
16.241 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
16.241 * [taylor]: Taking taylor expansion of 1 in n
16.241 * [backup-simplify]: Simplify 1 into 1
16.241 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n
16.241 * [taylor]: Taking taylor expansion of (/ -1 n) in n
16.241 * [taylor]: Taking taylor expansion of -1 in n
16.241 * [backup-simplify]: Simplify -1 into -1
16.241 * [taylor]: Taking taylor expansion of n in n
16.241 * [backup-simplify]: Simplify 0 into 0
16.241 * [backup-simplify]: Simplify 1 into 1
16.241 * [backup-simplify]: Simplify (/ -1 1) into -1
16.241 * [backup-simplify]: Simplify (log -1) into (log -1)
16.241 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
16.241 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
16.242 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n))
16.242 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log -1) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))
16.242 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))
16.243 * [taylor]: Taking taylor expansion of (* (pow 2 (* 1/2 (+ (/ 1 k) 1))) (pow PI (* 1/2 (+ (/ 1 k) 1)))) in n
16.243 * [taylor]: Taking taylor expansion of (pow 2 (* 1/2 (+ (/ 1 k) 1))) in n
16.243 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log 2))) in n
16.243 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log 2)) in n
16.243 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
16.243 * [taylor]: Taking taylor expansion of 1/2 in n
16.243 * [backup-simplify]: Simplify 1/2 into 1/2
16.243 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
16.243 * [taylor]: Taking taylor expansion of (/ 1 k) in n
16.243 * [taylor]: Taking taylor expansion of k in n
16.243 * [backup-simplify]: Simplify k into k
16.243 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
16.243 * [taylor]: Taking taylor expansion of 1 in n
16.243 * [backup-simplify]: Simplify 1 into 1
16.243 * [taylor]: Taking taylor expansion of (log 2) in n
16.243 * [taylor]: Taking taylor expansion of 2 in n
16.243 * [backup-simplify]: Simplify 2 into 2
16.243 * [backup-simplify]: Simplify (log 2) into (log 2)
16.243 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
16.243 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
16.243 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (log 2)) into (* 1/2 (* (log 2) (+ (/ 1 k) 1)))
16.244 * [backup-simplify]: Simplify (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))) into (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1))))
16.244 * [taylor]: Taking taylor expansion of (pow PI (* 1/2 (+ (/ 1 k) 1))) in n
16.244 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log PI))) in n
16.244 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log PI)) in n
16.244 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
16.244 * [taylor]: Taking taylor expansion of 1/2 in n
16.244 * [backup-simplify]: Simplify 1/2 into 1/2
16.244 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
16.244 * [taylor]: Taking taylor expansion of (/ 1 k) in n
16.244 * [taylor]: Taking taylor expansion of k in n
16.244 * [backup-simplify]: Simplify k into k
16.244 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
16.244 * [taylor]: Taking taylor expansion of 1 in n
16.244 * [backup-simplify]: Simplify 1 into 1
16.244 * [taylor]: Taking taylor expansion of (log PI) in n
16.244 * [taylor]: Taking taylor expansion of PI in n
16.244 * [backup-simplify]: Simplify PI into PI
16.244 * [backup-simplify]: Simplify (log PI) into (log PI)
16.244 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
16.244 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
16.245 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (log PI)) into (* 1/2 (* (+ (/ 1 k) 1) (log PI)))
16.245 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI))))
16.245 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
16.245 * [taylor]: Taking taylor expansion of (/ -1 k) in n
16.245 * [taylor]: Taking taylor expansion of -1 in n
16.245 * [backup-simplify]: Simplify -1 into -1
16.245 * [taylor]: Taking taylor expansion of k in n
16.245 * [backup-simplify]: Simplify k into k
16.245 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
16.245 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
16.245 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
16.245 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
16.246 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI))))) into (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))))
16.247 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))))) into (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (* (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))))
16.248 * [backup-simplify]: Simplify (/ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (* (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))))) (sqrt (/ -1 k))) into (/ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (* (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))))) (sqrt (/ -1 k)))
16.248 * [taylor]: Taking taylor expansion of (/ (* (pow (/ -1 n) (* 1/2 (+ (/ 1 k) 1))) (* (pow 2 (* 1/2 (+ (/ 1 k) 1))) (pow PI (* 1/2 (+ (/ 1 k) 1))))) (sqrt (/ -1 k))) in n
16.248 * [taylor]: Taking taylor expansion of (* (pow (/ -1 n) (* 1/2 (+ (/ 1 k) 1))) (* (pow 2 (* 1/2 (+ (/ 1 k) 1))) (pow PI (* 1/2 (+ (/ 1 k) 1))))) in n
16.248 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (* 1/2 (+ (/ 1 k) 1))) in n
16.248 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (/ -1 n)))) in n
16.248 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (/ -1 n))) in n
16.248 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
16.248 * [taylor]: Taking taylor expansion of 1/2 in n
16.248 * [backup-simplify]: Simplify 1/2 into 1/2
16.248 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
16.248 * [taylor]: Taking taylor expansion of (/ 1 k) in n
16.248 * [taylor]: Taking taylor expansion of k in n
16.248 * [backup-simplify]: Simplify k into k
16.248 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
16.248 * [taylor]: Taking taylor expansion of 1 in n
16.248 * [backup-simplify]: Simplify 1 into 1
16.248 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n
16.248 * [taylor]: Taking taylor expansion of (/ -1 n) in n
16.248 * [taylor]: Taking taylor expansion of -1 in n
16.248 * [backup-simplify]: Simplify -1 into -1
16.248 * [taylor]: Taking taylor expansion of n in n
16.248 * [backup-simplify]: Simplify 0 into 0
16.248 * [backup-simplify]: Simplify 1 into 1
16.249 * [backup-simplify]: Simplify (/ -1 1) into -1
16.249 * [backup-simplify]: Simplify (log -1) into (log -1)
16.249 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
16.249 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
16.249 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n))
16.250 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log -1) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))
16.250 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))
16.250 * [taylor]: Taking taylor expansion of (* (pow 2 (* 1/2 (+ (/ 1 k) 1))) (pow PI (* 1/2 (+ (/ 1 k) 1)))) in n
16.250 * [taylor]: Taking taylor expansion of (pow 2 (* 1/2 (+ (/ 1 k) 1))) in n
16.250 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log 2))) in n
16.250 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log 2)) in n
16.250 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
16.250 * [taylor]: Taking taylor expansion of 1/2 in n
16.250 * [backup-simplify]: Simplify 1/2 into 1/2
16.250 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
16.250 * [taylor]: Taking taylor expansion of (/ 1 k) in n
16.250 * [taylor]: Taking taylor expansion of k in n
16.250 * [backup-simplify]: Simplify k into k
16.250 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
16.250 * [taylor]: Taking taylor expansion of 1 in n
16.250 * [backup-simplify]: Simplify 1 into 1
16.250 * [taylor]: Taking taylor expansion of (log 2) in n
16.250 * [taylor]: Taking taylor expansion of 2 in n
16.250 * [backup-simplify]: Simplify 2 into 2
16.251 * [backup-simplify]: Simplify (log 2) into (log 2)
16.251 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
16.251 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
16.251 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (log 2)) into (* 1/2 (* (log 2) (+ (/ 1 k) 1)))
16.251 * [backup-simplify]: Simplify (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))) into (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1))))
16.251 * [taylor]: Taking taylor expansion of (pow PI (* 1/2 (+ (/ 1 k) 1))) in n
16.251 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log PI))) in n
16.251 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log PI)) in n
16.251 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
16.251 * [taylor]: Taking taylor expansion of 1/2 in n
16.251 * [backup-simplify]: Simplify 1/2 into 1/2
16.252 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
16.252 * [taylor]: Taking taylor expansion of (/ 1 k) in n
16.252 * [taylor]: Taking taylor expansion of k in n
16.252 * [backup-simplify]: Simplify k into k
16.252 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
16.252 * [taylor]: Taking taylor expansion of 1 in n
16.252 * [backup-simplify]: Simplify 1 into 1
16.252 * [taylor]: Taking taylor expansion of (log PI) in n
16.252 * [taylor]: Taking taylor expansion of PI in n
16.252 * [backup-simplify]: Simplify PI into PI
16.252 * [backup-simplify]: Simplify (log PI) into (log PI)
16.252 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
16.252 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
16.252 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (log PI)) into (* 1/2 (* (+ (/ 1 k) 1) (log PI)))
16.253 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI))))
16.253 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
16.253 * [taylor]: Taking taylor expansion of (/ -1 k) in n
16.253 * [taylor]: Taking taylor expansion of -1 in n
16.253 * [backup-simplify]: Simplify -1 into -1
16.253 * [taylor]: Taking taylor expansion of k in n
16.253 * [backup-simplify]: Simplify k into k
16.253 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
16.253 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
16.253 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
16.253 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
16.254 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI))))) into (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))))
16.255 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))))) into (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (* (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))))
16.256 * [backup-simplify]: Simplify (/ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (* (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))))) (sqrt (/ -1 k))) into (/ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (* (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))))) (sqrt (/ -1 k)))
16.256 * [taylor]: Taking taylor expansion of (/ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (* (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))))) (sqrt (/ -1 k))) in k
16.256 * [taylor]: Taking taylor expansion of (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (* (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))))) in k
16.256 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) in k
16.256 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (log PI))) in k
16.256 * [taylor]: Taking taylor expansion of 1/2 in k
16.256 * [backup-simplify]: Simplify 1/2 into 1/2
16.256 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1) (log PI)) in k
16.256 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
16.256 * [taylor]: Taking taylor expansion of (/ 1 k) in k
16.256 * [taylor]: Taking taylor expansion of k in k
16.256 * [backup-simplify]: Simplify 0 into 0
16.256 * [backup-simplify]: Simplify 1 into 1
16.256 * [backup-simplify]: Simplify (/ 1 1) into 1
16.256 * [taylor]: Taking taylor expansion of 1 in k
16.256 * [backup-simplify]: Simplify 1 into 1
16.256 * [taylor]: Taking taylor expansion of (log PI) in k
16.256 * [taylor]: Taking taylor expansion of PI in k
16.256 * [backup-simplify]: Simplify PI into PI
16.257 * [backup-simplify]: Simplify (log PI) into (log PI)
16.257 * [backup-simplify]: Simplify (+ 1 0) into 1
16.257 * [backup-simplify]: Simplify (* 1 (log PI)) into (log PI)
16.258 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI))
16.258 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI))))
16.258 * [taylor]: Taking taylor expansion of (* (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))) in k
16.258 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))) in k
16.258 * [taylor]: Taking taylor expansion of (* 1/2 (* (log 2) (+ (/ 1 k) 1))) in k
16.258 * [taylor]: Taking taylor expansion of 1/2 in k
16.258 * [backup-simplify]: Simplify 1/2 into 1/2
16.258 * [taylor]: Taking taylor expansion of (* (log 2) (+ (/ 1 k) 1)) in k
16.258 * [taylor]: Taking taylor expansion of (log 2) in k
16.258 * [taylor]: Taking taylor expansion of 2 in k
16.258 * [backup-simplify]: Simplify 2 into 2
16.259 * [backup-simplify]: Simplify (log 2) into (log 2)
16.259 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
16.259 * [taylor]: Taking taylor expansion of (/ 1 k) in k
16.259 * [taylor]: Taking taylor expansion of k in k
16.259 * [backup-simplify]: Simplify 0 into 0
16.259 * [backup-simplify]: Simplify 1 into 1
16.259 * [backup-simplify]: Simplify (/ 1 1) into 1
16.259 * [taylor]: Taking taylor expansion of 1 in k
16.259 * [backup-simplify]: Simplify 1 into 1
16.259 * [backup-simplify]: Simplify (+ 1 0) into 1
16.260 * [backup-simplify]: Simplify (* (log 2) 1) into (log 2)
16.260 * [backup-simplify]: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2))
16.261 * [backup-simplify]: Simplify (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))) into (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1))))
16.261 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) in k
16.261 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))) in k
16.261 * [taylor]: Taking taylor expansion of 1/2 in k
16.261 * [backup-simplify]: Simplify 1/2 into 1/2
16.261 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log -1) (log n))) in k
16.261 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
16.261 * [taylor]: Taking taylor expansion of (/ 1 k) in k
16.261 * [taylor]: Taking taylor expansion of k in k
16.261 * [backup-simplify]: Simplify 0 into 0
16.261 * [backup-simplify]: Simplify 1 into 1
16.261 * [backup-simplify]: Simplify (/ 1 1) into 1
16.261 * [taylor]: Taking taylor expansion of 1 in k
16.261 * [backup-simplify]: Simplify 1 into 1
16.261 * [taylor]: Taking taylor expansion of (- (log -1) (log n)) in k
16.261 * [taylor]: Taking taylor expansion of (log -1) in k
16.261 * [taylor]: Taking taylor expansion of -1 in k
16.261 * [backup-simplify]: Simplify -1 into -1
16.262 * [backup-simplify]: Simplify (log -1) into (log -1)
16.262 * [taylor]: Taking taylor expansion of (log n) in k
16.262 * [taylor]: Taking taylor expansion of n in k
16.262 * [backup-simplify]: Simplify n into n
16.262 * [backup-simplify]: Simplify (log n) into (log n)
16.262 * [backup-simplify]: Simplify (+ 1 0) into 1
16.262 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
16.262 * [backup-simplify]: Simplify (+ (log -1) (- (log n))) into (- (log -1) (log n))
16.263 * [backup-simplify]: Simplify (* 1 (- (log -1) (log n))) into (- (log -1) (log n))
16.263 * [backup-simplify]: Simplify (* 1/2 (- (log -1) (log n))) into (* 1/2 (- (log -1) (log n)))
16.263 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))
16.263 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
16.263 * [taylor]: Taking taylor expansion of (/ -1 k) in k
16.263 * [taylor]: Taking taylor expansion of -1 in k
16.263 * [backup-simplify]: Simplify -1 into -1
16.263 * [taylor]: Taking taylor expansion of k in k
16.263 * [backup-simplify]: Simplify 0 into 0
16.263 * [backup-simplify]: Simplify 1 into 1
16.264 * [backup-simplify]: Simplify (/ -1 1) into -1
16.264 * [backup-simplify]: Simplify (sqrt 0) into 0
16.265 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
16.265 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))) into (* (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))))
16.266 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (* (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))))) into (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (* (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))))
16.267 * [backup-simplify]: Simplify (/ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (* (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))))) +nan.0) into (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (* (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))))))
16.268 * [backup-simplify]: Simplify (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (* (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))))) into (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (* (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))))))
16.269 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0
16.269 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
16.269 * [backup-simplify]: Simplify (+ 0 0) into 0
16.270 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (/ 1 k) 1))) into 0
16.270 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (log PI))) into 0
16.271 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (+ (* (/ (pow 0 1) 1)))) into 0
16.272 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0
16.272 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
16.272 * [backup-simplify]: Simplify (+ 0 0) into 0
16.273 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (/ 1 k) 1))) into 0
16.273 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (log 2))) into 0
16.275 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))) (+ (* (/ (pow 0 1) 1)))) into 0
16.276 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))) 0) (* 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))))) into 0
16.277 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
16.278 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -1 1)))) 1) into 0
16.278 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
16.279 * [backup-simplify]: Simplify (+ 0 0) into 0
16.279 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (/ 1 k) 1))) into 0
16.280 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n))
16.281 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (- (log -1) (log n)))) into 0
16.282 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
16.284 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) 0) (* 0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1))))))) into 0
16.286 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (* (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0
16.286 * [taylor]: Taking taylor expansion of 0 in k
16.286 * [backup-simplify]: Simplify 0 into 0
16.286 * [backup-simplify]: Simplify 0 into 0
16.287 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))) 0) (* 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))))) into 0
16.289 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) 0) (* 0 (* (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))))) into 0
16.290 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
16.293 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
16.296 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (* (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (* (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))))))
16.297 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (* (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))))))) into (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (* (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))))))
16.305 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0
16.305 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
16.307 * [backup-simplify]: Simplify (+ 0 0) into 0
16.308 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0
16.309 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (log PI)))) into 0
16.311 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
16.314 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0
16.314 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
16.315 * [backup-simplify]: Simplify (+ 0 0) into 0
16.316 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0
16.316 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (log 2)))) into 0
16.318 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
16.320 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI))))))) into 0
16.321 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.324 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -1 1)))) 2) into 0
16.324 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
16.324 * [backup-simplify]: Simplify (+ 0 0) into 0
16.325 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0
16.326 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n))
16.327 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log -1) (log n))))) into 0
16.329 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
16.331 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) 0) (+ (* 0 0) (* 0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))))))) into 0
16.331 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
16.332 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0
16.334 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (* (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0
16.334 * [taylor]: Taking taylor expansion of 0 in k
16.334 * [backup-simplify]: Simplify 0 into 0
16.334 * [backup-simplify]: Simplify 0 into 0
16.334 * [backup-simplify]: Simplify 0 into 0
16.336 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))))) into 0
16.338 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) 0) (+ (* 0 0) (* 0 (* (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))))))) into 0
16.339 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.343 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
16.349 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (* (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (* (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (* (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))))))
16.350 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (* (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))))))) into (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (* (exp (* 1/2 (* (log 2) (+ (/ 1 k) 1)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))))))
16.358 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (log PI)))) (* (exp (* 1/2 (* (log 2) (+ (/ 1 (/ 1 (- k))) 1)))) (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log -1) (log (/ 1 (- n))))))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (log PI)))) (* (exp (* 1/2 (* (log 2) (+ (/ 1 (/ 1 (- k))) 1)))) (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log -1) (log (/ 1 (- n))))))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (log PI)))) (* (exp (* 1/2 (* (log 2) (+ (/ 1 (/ 1 (- k))) 1)))) (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log -1) (log (/ 1 (- n)))))))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n)))))) (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (- 1 k) (log PI))))))) (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n)))))) (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (- 1 k) (log PI)))))) k)) (- (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n)))))) (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (- 1 k) (log PI)))))) (pow k 2))))))))
16.359 * * * [progress]: simplifying candidates
16.359 * * * * [progress]: [ 1 / 146 ] simplifiying candidate #<alt (λ (k n) (* (exp (* (log n) (* (- 1 k) 1/2))) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))>
16.359 * * * * [progress]: [ 2 / 146 ] simplifiying candidate #<alt (λ (k n) (* (exp (* (log n) (* (- 1 k) 1/2))) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))>
16.359 * * * * [progress]: [ 3 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* 1 (* (- 1 k) 1/2))) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))>
16.359 * * * * [progress]: [ 4 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow (pow n (- 1 k)) 1/2) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))>
16.359 * * * * [progress]: [ 5 / 146 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* (cbrt n) (cbrt n)) (* (- 1 k) 1/2)) (pow (cbrt n) (* (- 1 k) 1/2))) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))>
16.359 * * * * [progress]: [ 6 / 146 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (sqrt n) (* (- 1 k) 1/2)) (pow (sqrt n) (* (- 1 k) 1/2))) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))>
16.359 * * * * [progress]: [ 7 / 146 ] simplifiying candidate #<alt (λ (k n) (* (* (pow 1 (* (- 1 k) 1/2)) (pow n (* (- 1 k) 1/2))) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))>
16.360 * * * * [progress]: [ 8 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow (pow n (* (- 1 k) 1/2)) 1) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))>
16.360 * * * * [progress]: [ 9 / 146 ] simplifiying candidate #<alt (λ (k n) (* (exp (log (pow n (* (- 1 k) 1/2)))) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))>
16.360 * * * * [progress]: [ 10 / 146 ] simplifiying candidate #<alt (λ (k n) (* (log (exp (pow n (* (- 1 k) 1/2)))) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))>
16.360 * * * * [progress]: [ 11 / 146 ] simplifiying candidate #<alt (λ (k n) (* (* (* (cbrt (pow n (* (- 1 k) 1/2))) (cbrt (pow n (* (- 1 k) 1/2)))) (cbrt (pow n (* (- 1 k) 1/2)))) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))>
16.360 * * * * [progress]: [ 12 / 146 ] simplifiying candidate #<alt (λ (k n) (* (cbrt (* (* (pow n (* (- 1 k) 1/2)) (pow n (* (- 1 k) 1/2))) (pow n (* (- 1 k) 1/2)))) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))>
16.360 * * * * [progress]: [ 13 / 146 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (pow n (* (- 1 k) 1/2))) (sqrt (pow n (* (- 1 k) 1/2)))) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))>
16.360 * * * * [progress]: [ 14 / 146 ] simplifiying candidate #<alt (λ (k n) (* (* 1 (pow n (* (- 1 k) 1/2))) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))>
16.360 * * * * [progress]: [ 15 / 146 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (/ (* (- 1 k) 1/2) 2)) (pow n (/ (* (- 1 k) 1/2) 2))) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))>
16.360 * * * * [progress]: [ 16 / 146 ] simplifiying candidate #<alt (λ (k n) (* (posit16->real (real->posit16 (pow n (* (- 1 k) 1/2)))) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))>
16.360 * * * * [progress]: [ 17 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (* (pow 2 (* (- 1 k) 1/2)) (exp (* (log PI) (* (- 1 k) 1/2)))) (sqrt k))))>
16.360 * * * * [progress]: [ 18 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (* (pow 2 (* (- 1 k) 1/2)) (exp (* (log PI) (* (- 1 k) 1/2)))) (sqrt k))))>
16.360 * * * * [progress]: [ 19 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* 1 (* (- 1 k) 1/2)))) (sqrt k))))>
16.361 * * * * [progress]: [ 20 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow (pow PI (- 1 k)) 1/2)) (sqrt k))))>
16.361 * * * * [progress]: [ 21 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (* (pow 2 (* (- 1 k) 1/2)) (* (pow (* (cbrt PI) (cbrt PI)) (* (- 1 k) 1/2)) (pow (cbrt PI) (* (- 1 k) 1/2)))) (sqrt k))))>
16.361 * * * * [progress]: [ 22 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (* (pow 2 (* (- 1 k) 1/2)) (* (pow (sqrt PI) (* (- 1 k) 1/2)) (pow (sqrt PI) (* (- 1 k) 1/2)))) (sqrt k))))>
16.361 * * * * [progress]: [ 23 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (* (pow 2 (* (- 1 k) 1/2)) (* (pow 1 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2)))) (sqrt k))))>
16.361 * * * * [progress]: [ 24 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow (pow PI (* (- 1 k) 1/2)) 1)) (sqrt k))))>
16.361 * * * * [progress]: [ 25 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (* (pow 2 (* (- 1 k) 1/2)) (exp (log (pow PI (* (- 1 k) 1/2))))) (sqrt k))))>
16.361 * * * * [progress]: [ 26 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (* (pow 2 (* (- 1 k) 1/2)) (log (exp (pow PI (* (- 1 k) 1/2))))) (sqrt k))))>
16.361 * * * * [progress]: [ 27 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (* (pow 2 (* (- 1 k) 1/2)) (* (* (cbrt (pow PI (* (- 1 k) 1/2))) (cbrt (pow PI (* (- 1 k) 1/2)))) (cbrt (pow PI (* (- 1 k) 1/2))))) (sqrt k))))>
16.361 * * * * [progress]: [ 28 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (* (pow 2 (* (- 1 k) 1/2)) (cbrt (* (* (pow PI (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (pow PI (* (- 1 k) 1/2))))) (sqrt k))))>
16.361 * * * * [progress]: [ 29 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (* (pow 2 (* (- 1 k) 1/2)) (* (sqrt (pow PI (* (- 1 k) 1/2))) (sqrt (pow PI (* (- 1 k) 1/2))))) (sqrt k))))>
16.361 * * * * [progress]: [ 30 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (* (pow 2 (* (- 1 k) 1/2)) (* 1 (pow PI (* (- 1 k) 1/2)))) (sqrt k))))>
16.361 * * * * [progress]: [ 31 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (* (pow 2 (* (- 1 k) 1/2)) (* (pow PI (/ (* (- 1 k) 1/2) 2)) (pow PI (/ (* (- 1 k) 1/2) 2)))) (sqrt k))))>
16.362 * * * * [progress]: [ 32 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (* (pow 2 (* (- 1 k) 1/2)) (posit16->real (real->posit16 (pow PI (* (- 1 k) 1/2))))) (sqrt k))))>
16.362 * * * * [progress]: [ 33 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (pow (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k)) 1)))>
16.362 * * * * [progress]: [ 34 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (exp (- (+ (* (log 2) (* (- 1 k) 1/2)) (* (log PI) (* (- 1 k) 1/2))) (log (sqrt k))))))>
16.362 * * * * [progress]: [ 35 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (exp (- (+ (* (log 2) (* (- 1 k) 1/2)) (* (log PI) (* (- 1 k) 1/2))) (log (sqrt k))))))>
16.362 * * * * [progress]: [ 36 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (exp (- (+ (* (log 2) (* (- 1 k) 1/2)) (log (pow PI (* (- 1 k) 1/2)))) (log (sqrt k))))))>
16.362 * * * * [progress]: [ 37 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (exp (- (+ (* (log 2) (* (- 1 k) 1/2)) (* (log PI) (* (- 1 k) 1/2))) (log (sqrt k))))))>
16.362 * * * * [progress]: [ 38 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (exp (- (+ (* (log 2) (* (- 1 k) 1/2)) (* (log PI) (* (- 1 k) 1/2))) (log (sqrt k))))))>
16.362 * * * * [progress]: [ 39 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (exp (- (+ (* (log 2) (* (- 1 k) 1/2)) (log (pow PI (* (- 1 k) 1/2)))) (log (sqrt k))))))>
16.362 * * * * [progress]: [ 40 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (exp (- (+ (log (pow 2 (* (- 1 k) 1/2))) (* (log PI) (* (- 1 k) 1/2))) (log (sqrt k))))))>
16.362 * * * * [progress]: [ 41 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (exp (- (+ (log (pow 2 (* (- 1 k) 1/2))) (* (log PI) (* (- 1 k) 1/2))) (log (sqrt k))))))>
16.362 * * * * [progress]: [ 42 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (exp (- (+ (log (pow 2 (* (- 1 k) 1/2))) (log (pow PI (* (- 1 k) 1/2)))) (log (sqrt k))))))>
16.362 * * * * [progress]: [ 43 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (exp (- (log (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2)))) (log (sqrt k))))))>
16.363 * * * * [progress]: [ 44 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (exp (log (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))))>
16.363 * * * * [progress]: [ 45 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (log (exp (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))))>
16.363 * * * * [progress]: [ 46 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (cbrt (/ (* (* (* (pow 2 (* (- 1 k) 1/2)) (pow 2 (* (- 1 k) 1/2))) (pow 2 (* (- 1 k) 1/2))) (* (* (pow PI (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (pow PI (* (- 1 k) 1/2)))) (* (* (sqrt k) (sqrt k)) (sqrt k))))))>
16.363 * * * * [progress]: [ 47 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (cbrt (/ (* (* (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2)))) (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2)))) (* (* (sqrt k) (sqrt k)) (sqrt k))))))>
16.363 * * * * [progress]: [ 48 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (* (* (cbrt (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))) (cbrt (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k)))) (cbrt (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))))>
16.363 * * * * [progress]: [ 49 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (cbrt (* (* (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k)) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))))>
16.363 * * * * [progress]: [ 50 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (* (sqrt (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))) (sqrt (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))))>
16.363 * * * * [progress]: [ 51 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (- (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2)))) (- (sqrt k)))))>
16.363 * * * * [progress]: [ 52 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (* (/ (pow 2 (* (- 1 k) 1/2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow PI (* (- 1 k) 1/2)) (cbrt (sqrt k))))))>
16.363 * * * * [progress]: [ 53 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (* (/ (pow 2 (* (- 1 k) 1/2)) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow PI (* (- 1 k) 1/2)) (sqrt (cbrt k))))))>
16.363 * * * * [progress]: [ 54 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (* (/ (pow 2 (* (- 1 k) 1/2)) (sqrt (sqrt k))) (/ (pow PI (* (- 1 k) 1/2)) (sqrt (sqrt k))))))>
16.363 * * * * [progress]: [ 55 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (* (/ (pow 2 (* (- 1 k) 1/2)) (sqrt 1)) (/ (pow PI (* (- 1 k) 1/2)) (sqrt k)))))>
16.363 * * * * [progress]: [ 56 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (* (/ (pow 2 (* (- 1 k) 1/2)) (sqrt (sqrt k))) (/ (pow PI (* (- 1 k) 1/2)) (sqrt (sqrt k))))))>
16.364 * * * * [progress]: [ 57 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (* (/ (pow 2 (* (- 1 k) 1/2)) 1) (/ (pow PI (* (- 1 k) 1/2)) (sqrt k)))))>
16.364 * * * * [progress]: [ 58 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (* 1 (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k)))))>
16.364 * * * * [progress]: [ 59 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (* (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (/ 1 (sqrt k)))))>
16.364 * * * * [progress]: [ 60 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ 1 (/ (sqrt k) (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2)))))))>
16.364 * * * * [progress]: [ 61 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k)))))>
16.364 * * * * [progress]: [ 62 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt (* (cbrt k) (cbrt k)))) (sqrt (cbrt k)))))>
16.364 * * * * [progress]: [ 63 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt (sqrt k))) (sqrt (sqrt k)))))>
16.364 * * * * [progress]: [ 64 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt 1)) (sqrt k))))>
16.364 * * * * [progress]: [ 65 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt (sqrt k))) (sqrt (sqrt k)))))>
16.364 * * * * [progress]: [ 66 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) 1) (sqrt k))))>
16.364 * * * * [progress]: [ 67 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (pow 2 (* (- 1 k) 1/2)) (/ (sqrt k) (pow PI (* (- 1 k) 1/2))))))>
16.364 * * * * [progress]: [ 68 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (posit16->real (real->posit16 (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))))>
16.364 * * * * [progress]: [ 69 / 146 ] simplifiying candidate #<alt (λ (k n) (pow (* (pow n (* (- 1 k) 1/2)) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))) 1))>
16.364 * * * * [progress]: [ 70 / 146 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log n) (* (- 1 k) 1/2)) (- (+ (* (log 2) (* (- 1 k) 1/2)) (* (log PI) (* (- 1 k) 1/2))) (log (sqrt k))))))>
16.365 * * * * [progress]: [ 71 / 146 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log n) (* (- 1 k) 1/2)) (- (+ (* (log 2) (* (- 1 k) 1/2)) (* (log PI) (* (- 1 k) 1/2))) (log (sqrt k))))))>
16.365 * * * * [progress]: [ 72 / 146 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log n) (* (- 1 k) 1/2)) (- (+ (* (log 2) (* (- 1 k) 1/2)) (log (pow PI (* (- 1 k) 1/2)))) (log (sqrt k))))))>
16.365 * * * * [progress]: [ 73 / 146 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log n) (* (- 1 k) 1/2)) (- (+ (* (log 2) (* (- 1 k) 1/2)) (* (log PI) (* (- 1 k) 1/2))) (log (sqrt k))))))>
16.365 * * * * [progress]: [ 74 / 146 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log n) (* (- 1 k) 1/2)) (- (+ (* (log 2) (* (- 1 k) 1/2)) (* (log PI) (* (- 1 k) 1/2))) (log (sqrt k))))))>
16.365 * * * * [progress]: [ 75 / 146 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log n) (* (- 1 k) 1/2)) (- (+ (* (log 2) (* (- 1 k) 1/2)) (log (pow PI (* (- 1 k) 1/2)))) (log (sqrt k))))))>
16.365 * * * * [progress]: [ 76 / 146 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log n) (* (- 1 k) 1/2)) (- (+ (log (pow 2 (* (- 1 k) 1/2))) (* (log PI) (* (- 1 k) 1/2))) (log (sqrt k))))))>
16.365 * * * * [progress]: [ 77 / 146 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log n) (* (- 1 k) 1/2)) (- (+ (log (pow 2 (* (- 1 k) 1/2))) (* (log PI) (* (- 1 k) 1/2))) (log (sqrt k))))))>
16.365 * * * * [progress]: [ 78 / 146 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log n) (* (- 1 k) 1/2)) (- (+ (log (pow 2 (* (- 1 k) 1/2))) (log (pow PI (* (- 1 k) 1/2)))) (log (sqrt k))))))>
16.365 * * * * [progress]: [ 79 / 146 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log n) (* (- 1 k) 1/2)) (- (log (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2)))) (log (sqrt k))))))>
16.365 * * * * [progress]: [ 80 / 146 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log n) (* (- 1 k) 1/2)) (log (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))))>
16.365 * * * * [progress]: [ 81 / 146 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log n) (* (- 1 k) 1/2)) (- (+ (* (log 2) (* (- 1 k) 1/2)) (* (log PI) (* (- 1 k) 1/2))) (log (sqrt k))))))>
16.365 * * * * [progress]: [ 82 / 146 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log n) (* (- 1 k) 1/2)) (- (+ (* (log 2) (* (- 1 k) 1/2)) (* (log PI) (* (- 1 k) 1/2))) (log (sqrt k))))))>
16.366 * * * * [progress]: [ 83 / 146 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log n) (* (- 1 k) 1/2)) (- (+ (* (log 2) (* (- 1 k) 1/2)) (log (pow PI (* (- 1 k) 1/2)))) (log (sqrt k))))))>
16.366 * * * * [progress]: [ 84 / 146 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log n) (* (- 1 k) 1/2)) (- (+ (* (log 2) (* (- 1 k) 1/2)) (* (log PI) (* (- 1 k) 1/2))) (log (sqrt k))))))>
16.366 * * * * [progress]: [ 85 / 146 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log n) (* (- 1 k) 1/2)) (- (+ (* (log 2) (* (- 1 k) 1/2)) (* (log PI) (* (- 1 k) 1/2))) (log (sqrt k))))))>
16.366 * * * * [progress]: [ 86 / 146 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log n) (* (- 1 k) 1/2)) (- (+ (* (log 2) (* (- 1 k) 1/2)) (log (pow PI (* (- 1 k) 1/2)))) (log (sqrt k))))))>
16.366 * * * * [progress]: [ 87 / 146 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log n) (* (- 1 k) 1/2)) (- (+ (log (pow 2 (* (- 1 k) 1/2))) (* (log PI) (* (- 1 k) 1/2))) (log (sqrt k))))))>
16.366 * * * * [progress]: [ 88 / 146 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log n) (* (- 1 k) 1/2)) (- (+ (log (pow 2 (* (- 1 k) 1/2))) (* (log PI) (* (- 1 k) 1/2))) (log (sqrt k))))))>
16.366 * * * * [progress]: [ 89 / 146 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log n) (* (- 1 k) 1/2)) (- (+ (log (pow 2 (* (- 1 k) 1/2))) (log (pow PI (* (- 1 k) 1/2)))) (log (sqrt k))))))>
16.366 * * * * [progress]: [ 90 / 146 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log n) (* (- 1 k) 1/2)) (- (log (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2)))) (log (sqrt k))))))>
16.366 * * * * [progress]: [ 91 / 146 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log n) (* (- 1 k) 1/2)) (log (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))))>
16.366 * * * * [progress]: [ 92 / 146 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (pow n (* (- 1 k) 1/2))) (- (+ (* (log 2) (* (- 1 k) 1/2)) (* (log PI) (* (- 1 k) 1/2))) (log (sqrt k))))))>
16.366 * * * * [progress]: [ 93 / 146 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (pow n (* (- 1 k) 1/2))) (- (+ (* (log 2) (* (- 1 k) 1/2)) (* (log PI) (* (- 1 k) 1/2))) (log (sqrt k))))))>
16.366 * * * * [progress]: [ 94 / 146 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (pow n (* (- 1 k) 1/2))) (- (+ (* (log 2) (* (- 1 k) 1/2)) (log (pow PI (* (- 1 k) 1/2)))) (log (sqrt k))))))>
16.366 * * * * [progress]: [ 95 / 146 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (pow n (* (- 1 k) 1/2))) (- (+ (* (log 2) (* (- 1 k) 1/2)) (* (log PI) (* (- 1 k) 1/2))) (log (sqrt k))))))>
16.367 * * * * [progress]: [ 96 / 146 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (pow n (* (- 1 k) 1/2))) (- (+ (* (log 2) (* (- 1 k) 1/2)) (* (log PI) (* (- 1 k) 1/2))) (log (sqrt k))))))>
16.367 * * * * [progress]: [ 97 / 146 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (pow n (* (- 1 k) 1/2))) (- (+ (* (log 2) (* (- 1 k) 1/2)) (log (pow PI (* (- 1 k) 1/2)))) (log (sqrt k))))))>
16.367 * * * * [progress]: [ 98 / 146 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (pow n (* (- 1 k) 1/2))) (- (+ (log (pow 2 (* (- 1 k) 1/2))) (* (log PI) (* (- 1 k) 1/2))) (log (sqrt k))))))>
16.367 * * * * [progress]: [ 99 / 146 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (pow n (* (- 1 k) 1/2))) (- (+ (log (pow 2 (* (- 1 k) 1/2))) (* (log PI) (* (- 1 k) 1/2))) (log (sqrt k))))))>
16.367 * * * * [progress]: [ 100 / 146 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (pow n (* (- 1 k) 1/2))) (- (+ (log (pow 2 (* (- 1 k) 1/2))) (log (pow PI (* (- 1 k) 1/2)))) (log (sqrt k))))))>
16.367 * * * * [progress]: [ 101 / 146 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (pow n (* (- 1 k) 1/2))) (- (log (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2)))) (log (sqrt k))))))>
16.367 * * * * [progress]: [ 102 / 146 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (pow n (* (- 1 k) 1/2))) (log (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))))>
16.367 * * * * [progress]: [ 103 / 146 ] simplifiying candidate #<alt (λ (k n) (exp (log (* (pow n (* (- 1 k) 1/2)) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))))>
16.367 * * * * [progress]: [ 104 / 146 ] simplifiying candidate #<alt (λ (k n) (log (exp (* (pow n (* (- 1 k) 1/2)) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))))>
16.367 * * * * [progress]: [ 105 / 146 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (* (pow n (* (- 1 k) 1/2)) (pow n (* (- 1 k) 1/2))) (pow n (* (- 1 k) 1/2))) (/ (* (* (* (pow 2 (* (- 1 k) 1/2)) (pow 2 (* (- 1 k) 1/2))) (pow 2 (* (- 1 k) 1/2))) (* (* (pow PI (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (pow PI (* (- 1 k) 1/2)))) (* (* (sqrt k) (sqrt k)) (sqrt k))))))>
16.367 * * * * [progress]: [ 106 / 146 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (* (pow n (* (- 1 k) 1/2)) (pow n (* (- 1 k) 1/2))) (pow n (* (- 1 k) 1/2))) (/ (* (* (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2)))) (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2)))) (* (* (sqrt k) (sqrt k)) (sqrt k))))))>
16.367 * * * * [progress]: [ 107 / 146 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (* (pow n (* (- 1 k) 1/2)) (pow n (* (- 1 k) 1/2))) (pow n (* (- 1 k) 1/2))) (* (* (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k)) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))))>
16.367 * * * * [progress]: [ 108 / 146 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (* (pow n (* (- 1 k) 1/2)) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k)))) (cbrt (* (pow n (* (- 1 k) 1/2)) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))) (cbrt (* (pow n (* (- 1 k) 1/2)) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))))>
16.368 * * * * [progress]: [ 109 / 146 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (* (pow n (* (- 1 k) 1/2)) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))) (* (pow n (* (- 1 k) 1/2)) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k)))) (* (pow n (* (- 1 k) 1/2)) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))))>
16.368 * * * * [progress]: [ 110 / 146 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (* (pow n (* (- 1 k) 1/2)) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k)))) (sqrt (* (pow n (* (- 1 k) 1/2)) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))))>
16.368 * * * * [progress]: [ 111 / 146 ] simplifiying candidate #<alt (λ (k n) (* 1 (* (pow n (* (- 1 k) 1/2)) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k)))))>
16.368 * * * * [progress]: [ 112 / 146 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (sqrt n) (* (- 1 k) 1/2)) (sqrt (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k)))) (* (pow (sqrt n) (* (- 1 k) 1/2)) (sqrt (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))))>
16.368 * * * * [progress]: [ 113 / 146 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (pow n (* (- 1 k) 1/2))) (sqrt (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k)))) (* (sqrt (pow n (* (- 1 k) 1/2))) (sqrt (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))))>
16.368 * * * * [progress]: [ 114 / 146 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (/ (* (- 1 k) 1/2) 2)) (sqrt (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k)))) (* (pow n (/ (* (- 1 k) 1/2) 2)) (sqrt (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))))>
16.368 * * * * [progress]: [ 115 / 146 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (* (- 1 k) 1/2)) (* (cbrt (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))) (cbrt (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))) (cbrt (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k)))))>
16.368 * * * * [progress]: [ 116 / 146 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (* (- 1 k) 1/2)) (sqrt (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k)))) (sqrt (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k)))))>
16.368 * * * * [progress]: [ 117 / 146 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (* (- 1 k) 1/2)) (/ (pow 2 (* (- 1 k) 1/2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow PI (* (- 1 k) 1/2)) (cbrt (sqrt k)))))>
16.368 * * * * [progress]: [ 118 / 146 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (* (- 1 k) 1/2)) (/ (pow 2 (* (- 1 k) 1/2)) (sqrt (* (cbrt k) (cbrt k))))) (/ (pow PI (* (- 1 k) 1/2)) (sqrt (cbrt k)))))>
16.368 * * * * [progress]: [ 119 / 146 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (* (- 1 k) 1/2)) (/ (pow 2 (* (- 1 k) 1/2)) (sqrt (sqrt k)))) (/ (pow PI (* (- 1 k) 1/2)) (sqrt (sqrt k)))))>
16.368 * * * * [progress]: [ 120 / 146 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (* (- 1 k) 1/2)) (/ (pow 2 (* (- 1 k) 1/2)) (sqrt 1))) (/ (pow PI (* (- 1 k) 1/2)) (sqrt k))))>
16.369 * * * * [progress]: [ 121 / 146 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (* (- 1 k) 1/2)) (/ (pow 2 (* (- 1 k) 1/2)) (sqrt (sqrt k)))) (/ (pow PI (* (- 1 k) 1/2)) (sqrt (sqrt k)))))>
16.369 * * * * [progress]: [ 122 / 146 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (* (- 1 k) 1/2)) (/ (pow 2 (* (- 1 k) 1/2)) 1)) (/ (pow PI (* (- 1 k) 1/2)) (sqrt k))))>
16.369 * * * * [progress]: [ 123 / 146 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (* (- 1 k) 1/2)) 1) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))>
16.369 * * * * [progress]: [ 124 / 146 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (* (- 1 k) 1/2)) (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2)))) (/ 1 (sqrt k))))>
16.369 * * * * [progress]: [ 125 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow (* (cbrt n) (cbrt n)) (* (- 1 k) 1/2)) (* (pow (cbrt n) (* (- 1 k) 1/2)) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k)))))>
16.369 * * * * [progress]: [ 126 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow (sqrt n) (* (- 1 k) 1/2)) (* (pow (sqrt n) (* (- 1 k) 1/2)) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k)))))>
16.369 * * * * [progress]: [ 127 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow 1 (* (- 1 k) 1/2)) (* (pow n (* (- 1 k) 1/2)) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k)))))>
16.369 * * * * [progress]: [ 128 / 146 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (pow n (* (- 1 k) 1/2))) (cbrt (pow n (* (- 1 k) 1/2)))) (* (cbrt (pow n (* (- 1 k) 1/2))) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k)))))>
16.369 * * * * [progress]: [ 129 / 146 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (pow n (* (- 1 k) 1/2))) (* (sqrt (pow n (* (- 1 k) 1/2))) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k)))))>
16.369 * * * * [progress]: [ 130 / 146 ] simplifiying candidate #<alt (λ (k n) (* 1 (* (pow n (* (- 1 k) 1/2)) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k)))))>
16.369 * * * * [progress]: [ 131 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (* (- 1 k) 1/2) 2)) (* (pow n (/ (* (- 1 k) 1/2) 2)) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k)))))>
16.369 * * * * [progress]: [ 132 / 146 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow n (* (- 1 k) 1/2)) (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2)))) (sqrt k)))>
16.369 * * * * [progress]: [ 133 / 146 ] simplifiying candidate #<alt (λ (k n) (posit16->real (real->posit16 (* (pow n (* (- 1 k) 1/2)) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))))>
16.369 * * * * [progress]: [ 134 / 146 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k)) (pow n (* (- 1 k) 1/2))))>
16.370 * * * * [progress]: [ 135 / 146 ] simplifiying candidate #<alt (λ (k n) (* (- (+ (pow n 1/2) (* 1/8 (* (sqrt n) (* (pow (log n) 2) (pow k 2))))) (* 1/2 (* (sqrt n) (* (log n) k)))) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))>
16.370 * * * * [progress]: [ 136 / 146 ] simplifiying candidate #<alt (λ (k n) (* (exp (* -1/2 (* (- 1 k) (log (/ 1 n))))) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))>
16.370 * * * * [progress]: [ 137 / 146 ] simplifiying candidate #<alt (λ (k n) (* (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n)))))) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))>
16.370 * * * * [progress]: [ 138 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (* (pow 2 (* (- 1 k) 1/2)) (- (+ (pow PI 1/2) (* 1/8 (* (* (pow (log PI) 2) (pow k 2)) (sqrt PI)))) (* 1/2 (* (* (log PI) k) (sqrt PI))))) (sqrt k))))>
16.370 * * * * [progress]: [ 139 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (* (pow 2 (* (- 1 k) 1/2)) (exp (* 1/2 (* (- 1 k) (log PI))))) (sqrt k))))>
16.370 * * * * [progress]: [ 140 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (* (pow 2 (* (- 1 k) 1/2)) (exp (* 1/2 (* (- 1 k) (log PI))))) (sqrt k))))>
16.370 * * * * [progress]: [ 141 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (- (+ (* +nan.0 (* (* (sqrt 2) (* (pow (log PI) 2) (pow k 2))) (sqrt PI))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow k 2)) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (* (log PI) (pow k 2)))) (sqrt PI))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) k)) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (pow k 2))) (sqrt PI))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (* (sqrt 2) (pow k 2))) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt PI))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (pow k 2))) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) k)) (sqrt PI))) (- (* +nan.0 (* (* (sqrt 2) k) (sqrt PI))))))))))))))))))))))))>
16.370 * * * * [progress]: [ 142 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (- 1 k) (log PI))))) k)) (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (- 1 k) (log PI))))) (pow k 3))) (- (* +nan.0 (/ (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (- 1 k) (log PI))))) (pow k 2))))))))))>
16.370 * * * * [progress]: [ 143 / 146 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (- 1 k) (log PI))))) k)) (- (+ (* +nan.0 (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (- 1 k) (log PI)))))) (- (* +nan.0 (/ (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (- 1 k) (log PI))))) (pow k 2))))))))))>
16.370 * * * * [progress]: [ 144 / 146 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (* (log n) (pow k 2)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) k) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (pow k 2))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log n) (pow k 2))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (* (log PI) (pow k 2)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (pow k 2))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (* (sqrt 2) (pow k 2))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow k 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (pow (log n) 2) (pow k 2))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log n) k)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) k)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) k)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (* (log n) (pow k 2)))) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (* (pow (log PI) 2) (pow k 2))) (sqrt (* n PI))))))))))))))))))))))))))))))))))>
16.370 * * * * [progress]: [ 145 / 146 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (log PI)))) (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* -1/2 (* (- 1 k) (log (/ 1 n))))))) (pow k 3))) (- (+ (* +nan.0 (/ (* (exp (* -1/2 (* (- 1 k) (log (/ 1 n))))) (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (- 1 k) (log PI)))))) (pow k 2))) (- (* +nan.0 (/ (* (exp (* -1/2 (* (- 1 k) (log (/ 1 n))))) (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (- 1 k) (log PI)))))) k))))))))>
16.371 * * * * [progress]: [ 146 / 146 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (* (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n)))))) (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (- 1 k) (log PI))))))) (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n)))))) (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (- 1 k) (log PI)))))) k)) (- (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n)))))) (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (- 1 k) (log PI)))))) (pow k 2)))))))))>
16.374 * [simplify]: Simplifying:
  (* (log n) (* (- 1 k) 1/2))
  (* (log n) (* (- 1 k) 1/2))
  (* 1 (* (- 1 k) 1/2))
  (pow n (- 1 k))
  (pow (* (cbrt n) (cbrt n)) (* (- 1 k) 1/2))
  (pow (cbrt n) (* (- 1 k) 1/2))
  (pow (sqrt n) (* (- 1 k) 1/2))
  (pow (sqrt n) (* (- 1 k) 1/2))
  (pow 1 (* (- 1 k) 1/2))
  (pow n (* (- 1 k) 1/2))
  (log (pow n (* (- 1 k) 1/2)))
  (exp (pow n (* (- 1 k) 1/2)))
  (* (cbrt (pow n (* (- 1 k) 1/2))) (cbrt (pow n (* (- 1 k) 1/2))))
  (cbrt (pow n (* (- 1 k) 1/2)))
  (* (* (pow n (* (- 1 k) 1/2)) (pow n (* (- 1 k) 1/2))) (pow n (* (- 1 k) 1/2)))
  (sqrt (pow n (* (- 1 k) 1/2)))
  (sqrt (pow n (* (- 1 k) 1/2)))
  (pow n (/ (* (- 1 k) 1/2) 2))
  (pow n (/ (* (- 1 k) 1/2) 2))
  (real->posit16 (pow n (* (- 1 k) 1/2)))
  (* (log PI) (* (- 1 k) 1/2))
  (* (log PI) (* (- 1 k) 1/2))
  (* 1 (* (- 1 k) 1/2))
  (pow PI (- 1 k))
  (pow (* (cbrt PI) (cbrt PI)) (* (- 1 k) 1/2))
  (pow (cbrt PI) (* (- 1 k) 1/2))
  (pow (sqrt PI) (* (- 1 k) 1/2))
  (pow (sqrt PI) (* (- 1 k) 1/2))
  (pow 1 (* (- 1 k) 1/2))
  (pow PI (* (- 1 k) 1/2))
  (log (pow PI (* (- 1 k) 1/2)))
  (exp (pow PI (* (- 1 k) 1/2)))
  (* (cbrt (pow PI (* (- 1 k) 1/2))) (cbrt (pow PI (* (- 1 k) 1/2))))
  (cbrt (pow PI (* (- 1 k) 1/2)))
  (* (* (pow PI (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (pow PI (* (- 1 k) 1/2)))
  (sqrt (pow PI (* (- 1 k) 1/2)))
  (sqrt (pow PI (* (- 1 k) 1/2)))
  (pow PI (/ (* (- 1 k) 1/2) 2))
  (pow PI (/ (* (- 1 k) 1/2) 2))
  (real->posit16 (pow PI (* (- 1 k) 1/2)))
  (- (+ (* (log 2) (* (- 1 k) 1/2)) (* (log PI) (* (- 1 k) 1/2))) (log (sqrt k)))
  (- (+ (* (log 2) (* (- 1 k) 1/2)) (* (log PI) (* (- 1 k) 1/2))) (log (sqrt k)))
  (- (+ (* (log 2) (* (- 1 k) 1/2)) (log (pow PI (* (- 1 k) 1/2)))) (log (sqrt k)))
  (- (+ (* (log 2) (* (- 1 k) 1/2)) (* (log PI) (* (- 1 k) 1/2))) (log (sqrt k)))
  (- (+ (* (log 2) (* (- 1 k) 1/2)) (* (log PI) (* (- 1 k) 1/2))) (log (sqrt k)))
  (- (+ (* (log 2) (* (- 1 k) 1/2)) (log (pow PI (* (- 1 k) 1/2)))) (log (sqrt k)))
  (- (+ (log (pow 2 (* (- 1 k) 1/2))) (* (log PI) (* (- 1 k) 1/2))) (log (sqrt k)))
  (- (+ (log (pow 2 (* (- 1 k) 1/2))) (* (log PI) (* (- 1 k) 1/2))) (log (sqrt k)))
  (- (+ (log (pow 2 (* (- 1 k) 1/2))) (log (pow PI (* (- 1 k) 1/2)))) (log (sqrt k)))
  (- (log (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2)))) (log (sqrt k)))
  (log (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k)))
  (exp (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k)))
  (/ (* (* (* (pow 2 (* (- 1 k) 1/2)) (pow 2 (* (- 1 k) 1/2))) (pow 2 (* (- 1 k) 1/2))) (* (* (pow PI (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (pow PI (* (- 1 k) 1/2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
  (/ (* (* (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2)))) (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
  (* (cbrt (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))) (cbrt (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))
  (cbrt (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k)))
  (* (* (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k)) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k)))
  (sqrt (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k)))
  (sqrt (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k)))
  (- (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))))
  (- (sqrt k))
  (/ (pow 2 (* (- 1 k) 1/2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow PI (* (- 1 k) 1/2)) (cbrt (sqrt k)))
  (/ (pow 2 (* (- 1 k) 1/2)) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow PI (* (- 1 k) 1/2)) (sqrt (cbrt k)))
  (/ (pow 2 (* (- 1 k) 1/2)) (sqrt (sqrt k)))
  (/ (pow PI (* (- 1 k) 1/2)) (sqrt (sqrt k)))
  (/ (pow 2 (* (- 1 k) 1/2)) (sqrt 1))
  (/ (pow PI (* (- 1 k) 1/2)) (sqrt k))
  (/ (pow 2 (* (- 1 k) 1/2)) (sqrt (sqrt k)))
  (/ (pow PI (* (- 1 k) 1/2)) (sqrt (sqrt k)))
  (/ (pow 2 (* (- 1 k) 1/2)) 1)
  (/ (pow PI (* (- 1 k) 1/2)) (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))))
  (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt (* (cbrt k) (cbrt k))))
  (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt (sqrt k)))
  (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt 1))
  (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt (sqrt k)))
  (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) 1)
  (/ (sqrt k) (pow PI (* (- 1 k) 1/2)))
  (real->posit16 (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k)))
  (+ (* (log n) (* (- 1 k) 1/2)) (- (+ (* (log 2) (* (- 1 k) 1/2)) (* (log PI) (* (- 1 k) 1/2))) (log (sqrt k))))
  (+ (* (log n) (* (- 1 k) 1/2)) (- (+ (* (log 2) (* (- 1 k) 1/2)) (* (log PI) (* (- 1 k) 1/2))) (log (sqrt k))))
  (+ (* (log n) (* (- 1 k) 1/2)) (- (+ (* (log 2) (* (- 1 k) 1/2)) (log (pow PI (* (- 1 k) 1/2)))) (log (sqrt k))))
  (+ (* (log n) (* (- 1 k) 1/2)) (- (+ (* (log 2) (* (- 1 k) 1/2)) (* (log PI) (* (- 1 k) 1/2))) (log (sqrt k))))
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  (+ (log (pow n (* (- 1 k) 1/2))) (- (+ (* (log 2) (* (- 1 k) 1/2)) (* (log PI) (* (- 1 k) 1/2))) (log (sqrt k))))
  (+ (log (pow n (* (- 1 k) 1/2))) (- (+ (* (log 2) (* (- 1 k) 1/2)) (log (pow PI (* (- 1 k) 1/2)))) (log (sqrt k))))
  (+ (log (pow n (* (- 1 k) 1/2))) (- (+ (log (pow 2 (* (- 1 k) 1/2))) (* (log PI) (* (- 1 k) 1/2))) (log (sqrt k))))
  (+ (log (pow n (* (- 1 k) 1/2))) (- (+ (log (pow 2 (* (- 1 k) 1/2))) (* (log PI) (* (- 1 k) 1/2))) (log (sqrt k))))
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  (+ (log (pow n (* (- 1 k) 1/2))) (- (log (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2)))) (log (sqrt k))))
  (+ (log (pow n (* (- 1 k) 1/2))) (log (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))
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  (exp (* (pow n (* (- 1 k) 1/2)) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))
  (* (* (* (pow n (* (- 1 k) 1/2)) (pow n (* (- 1 k) 1/2))) (pow n (* (- 1 k) 1/2))) (/ (* (* (* (pow 2 (* (- 1 k) 1/2)) (pow 2 (* (- 1 k) 1/2))) (pow 2 (* (- 1 k) 1/2))) (* (* (pow PI (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (pow PI (* (- 1 k) 1/2)))) (* (* (sqrt k) (sqrt k)) (sqrt k))))
  (* (* (* (pow n (* (- 1 k) 1/2)) (pow n (* (- 1 k) 1/2))) (pow n (* (- 1 k) 1/2))) (/ (* (* (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2)))) (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2)))) (* (* (sqrt k) (sqrt k)) (sqrt k))))
  (* (* (* (pow n (* (- 1 k) 1/2)) (pow n (* (- 1 k) 1/2))) (pow n (* (- 1 k) 1/2))) (* (* (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k)) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))
  (* (cbrt (* (pow n (* (- 1 k) 1/2)) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k)))) (cbrt (* (pow n (* (- 1 k) 1/2)) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k)))))
  (cbrt (* (pow n (* (- 1 k) 1/2)) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))
  (* (* (* (pow n (* (- 1 k) 1/2)) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))) (* (pow n (* (- 1 k) 1/2)) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k)))) (* (pow n (* (- 1 k) 1/2)) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))
  (sqrt (* (pow n (* (- 1 k) 1/2)) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))
  (sqrt (* (pow n (* (- 1 k) 1/2)) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))
  (* (pow (sqrt n) (* (- 1 k) 1/2)) (sqrt (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))
  (* (pow (sqrt n) (* (- 1 k) 1/2)) (sqrt (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))
  (* (sqrt (pow n (* (- 1 k) 1/2))) (sqrt (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))
  (* (sqrt (pow n (* (- 1 k) 1/2))) (sqrt (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))
  (* (pow n (/ (* (- 1 k) 1/2) 2)) (sqrt (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))
  (* (pow n (/ (* (- 1 k) 1/2) 2)) (sqrt (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))
  (* (pow n (* (- 1 k) 1/2)) (* (cbrt (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))) (cbrt (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k)))))
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  (* (pow n (* (- 1 k) 1/2)) (/ (pow 2 (* (- 1 k) 1/2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (* (pow n (* (- 1 k) 1/2)) (/ (pow 2 (* (- 1 k) 1/2)) (sqrt (* (cbrt k) (cbrt k)))))
  (* (pow n (* (- 1 k) 1/2)) (/ (pow 2 (* (- 1 k) 1/2)) (sqrt (sqrt k))))
  (* (pow n (* (- 1 k) 1/2)) (/ (pow 2 (* (- 1 k) 1/2)) (sqrt 1)))
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  (* (pow n (* (- 1 k) 1/2)) (/ (pow 2 (* (- 1 k) 1/2)) 1))
  (* (pow n (* (- 1 k) 1/2)) 1)
  (* (pow n (* (- 1 k) 1/2)) (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))))
  (* (pow (cbrt n) (* (- 1 k) 1/2)) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k)))
  (* (pow (sqrt n) (* (- 1 k) 1/2)) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k)))
  (* (pow n (* (- 1 k) 1/2)) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k)))
  (* (cbrt (pow n (* (- 1 k) 1/2))) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k)))
  (* (sqrt (pow n (* (- 1 k) 1/2))) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k)))
  (* (pow n (* (- 1 k) 1/2)) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k)))
  (* (pow n (/ (* (- 1 k) 1/2) 2)) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k)))
  (* (pow n (* (- 1 k) 1/2)) (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))))
  (real->posit16 (* (pow n (* (- 1 k) 1/2)) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))
  (- (+ (pow n 1/2) (* 1/8 (* (sqrt n) (* (pow (log n) 2) (pow k 2))))) (* 1/2 (* (sqrt n) (* (log n) k))))
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  (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n))))))
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  (exp (* 1/2 (* (- 1 k) (log PI))))
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  (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (- 1 k) (log PI))))) k)) (- (+ (* +nan.0 (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (- 1 k) (log PI)))))) (- (* +nan.0 (/ (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (- 1 k) (log PI))))) (pow k 2))))))))
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  (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (log PI)))) (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* -1/2 (* (- 1 k) (log (/ 1 n))))))) (pow k 3))) (- (+ (* +nan.0 (/ (* (exp (* -1/2 (* (- 1 k) (log (/ 1 n))))) (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (- 1 k) (log PI)))))) (pow k 2))) (- (* +nan.0 (/ (* (exp (* -1/2 (* (- 1 k) (log (/ 1 n))))) (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (- 1 k) (log PI)))))) k)))))))
  (- (+ (* +nan.0 (* (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n)))))) (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (- 1 k) (log PI))))))) (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n)))))) (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (- 1 k) (log PI)))))) k)) (- (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n)))))) (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (- 1 k) (log PI)))))) (pow k 2))))))))
16.382 * * [simplify]: iteration 1: (358 enodes)
16.564 * * [simplify]: iteration 2: (1773 enodes)
17.216 * * [simplify]: Extracting #0: cost 89 inf + 0
17.217 * * [simplify]: Extracting #1: cost 574 inf + 1
17.220 * * [simplify]: Extracting #2: cost 1017 inf + 9741
17.237 * * [simplify]: Extracting #3: cost 960 inf + 178686
17.294 * * [simplify]: Extracting #4: cost 599 inf + 484544
17.386 * * [simplify]: Extracting #5: cost 331 inf + 641106
17.505 * * [simplify]: Extracting #6: cost 215 inf + 687755
17.696 * * [simplify]: Extracting #7: cost 154 inf + 726703
17.868 * * [simplify]: Extracting #8: cost 110 inf + 776457
18.058 * * [simplify]: Extracting #9: cost 101 inf + 791789
18.260 * * [simplify]: Extracting #10: cost 95 inf + 798909
18.491 * * [simplify]: Extracting #11: cost 64 inf + 818110
18.752 * * [simplify]: Extracting #12: cost 22 inf + 885210
19.042 * * [simplify]: Extracting #13: cost 4 inf + 922280
19.321 * * [simplify]: Extracting #14: cost 0 inf + 932820
19.603 * [simplify]: Simplified to:
  (* (* (- 1 k) 1/2) (log n))
  (* (* (- 1 k) 1/2) (log n))
  (* (- 1 k) 1/2)
  (pow n (- 1 k))
  (pow (* (cbrt n) (cbrt n)) (* (- 1 k) 1/2))
  (pow (cbrt n) (* (- 1 k) 1/2))
  (pow (sqrt n) (* (- 1 k) 1/2))
  (pow (sqrt n) (* (- 1 k) 1/2))
  1
  (pow n (* (- 1 k) 1/2))
  (* (* (- 1 k) 1/2) (log n))
  (exp (pow n (* (- 1 k) 1/2)))
  (* (cbrt (pow n (* (- 1 k) 1/2))) (cbrt (pow n (* (- 1 k) 1/2))))
  (cbrt (pow n (* (- 1 k) 1/2)))
  (pow (pow n (* (- 1 k) 1/2)) 3)
  (sqrt (pow n (* (- 1 k) 1/2)))
  (sqrt (pow n (* (- 1 k) 1/2)))
  (pow n (/ (- 1 k) 4))
  (pow n (/ (- 1 k) 4))
  (real->posit16 (pow n (* (- 1 k) 1/2)))
  (* (* (log PI) 1/2) (- 1 k))
  (* (* (log PI) 1/2) (- 1 k))
  (* (- 1 k) 1/2)
  (pow PI (- 1 k))
  (pow (* (cbrt PI) (cbrt PI)) (* (- 1 k) 1/2))
  (pow (cbrt PI) (* (- 1 k) 1/2))
  (pow (sqrt PI) (* (- 1 k) 1/2))
  (pow (sqrt PI) (* (- 1 k) 1/2))
  1
  (exp (* (* (log PI) 1/2) (- 1 k)))
  (* (* (log PI) 1/2) (- 1 k))
  (exp (exp (* (* (log PI) 1/2) (- 1 k))))
  (* (cbrt (exp (* (* (log PI) 1/2) (- 1 k)))) (cbrt (exp (* (* (log PI) 1/2) (- 1 k)))))
  (cbrt (exp (* (* (log PI) 1/2) (- 1 k))))
  (* (* (exp (* (* (log PI) 1/2) (- 1 k))) (exp (* (* (log PI) 1/2) (- 1 k)))) (exp (* (* (log PI) 1/2) (- 1 k))))
  (sqrt (exp (* (* (log PI) 1/2) (- 1 k))))
  (sqrt (exp (* (* (log PI) 1/2) (- 1 k))))
  (pow PI (/ (- 1 k) 4))
  (pow PI (/ (- 1 k) 4))
  (real->posit16 (exp (* (* (log PI) 1/2) (- 1 k))))
  (- (* (+ (log 2) (log PI)) (* (- 1 k) 1/2)) (log (sqrt k)))
  (- (* (+ (log 2) (log PI)) (* (- 1 k) 1/2)) (log (sqrt k)))
  (- (* (+ (log 2) (log PI)) (* (- 1 k) 1/2)) (log (sqrt k)))
  (- (* (+ (log 2) (log PI)) (* (- 1 k) 1/2)) (log (sqrt k)))
  (- (* (+ (log 2) (log PI)) (* (- 1 k) 1/2)) (log (sqrt k)))
  (- (* (+ (log 2) (log PI)) (* (- 1 k) 1/2)) (log (sqrt k)))
  (- (* (+ (log 2) (log PI)) (* (- 1 k) 1/2)) (log (sqrt k)))
  (- (* (+ (log 2) (log PI)) (* (- 1 k) 1/2)) (log (sqrt k)))
  (- (* (+ (log 2) (log PI)) (* (- 1 k) 1/2)) (log (sqrt k)))
  (- (* (+ (log 2) (log PI)) (* (- 1 k) 1/2)) (log (sqrt k)))
  (- (* (+ (log 2) (log PI)) (* (- 1 k) 1/2)) (log (sqrt k)))
  (exp (/ (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2))) (sqrt k)))
  (/ (* (pow (exp (* (log 2) (* (- 1 k) 1/2))) 3) (/ (* (* (pow PI (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (pow PI (* (- 1 k) 1/2))) (sqrt k))) k)
  (* (/ (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2))) k) (/ (* (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2))) (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2)))) (sqrt k)))
  (* (cbrt (/ (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2))) (sqrt k))) (cbrt (/ (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2))) (sqrt k))))
  (cbrt (/ (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2))) (sqrt k)))
  (* (* (/ (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2))) (sqrt k)) (/ (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2))) (sqrt k))) (/ (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2))) (sqrt k)))
  (sqrt (/ (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2))) (sqrt k)))
  (sqrt (/ (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2))) (sqrt k)))
  (- (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2))))
  (- (sqrt k))
  (/ (/ (exp (* (log 2) (* (- 1 k) 1/2))) (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ (exp (* (* (log PI) 1/2) (- 1 k))) (cbrt (sqrt k)))
  (/ (exp (* (log 2) (* (- 1 k) 1/2))) (fabs (cbrt k)))
  (/ (exp (* (* (log PI) 1/2) (- 1 k))) (sqrt (cbrt k)))
  (/ (exp (* (log 2) (* (- 1 k) 1/2))) (sqrt (sqrt k)))
  (/ (exp (* (* (log PI) 1/2) (- 1 k))) (sqrt (sqrt k)))
  (exp (* (log 2) (* (- 1 k) 1/2)))
  (/ (exp (* (* (log PI) 1/2) (- 1 k))) (sqrt k))
  (/ (exp (* (log 2) (* (- 1 k) 1/2))) (sqrt (sqrt k)))
  (/ (exp (* (* (log PI) 1/2) (- 1 k))) (sqrt (sqrt k)))
  (exp (* (log 2) (* (- 1 k) 1/2)))
  (/ (exp (* (* (log PI) 1/2) (- 1 k))) (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2))))
  (/ (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2))) (fabs (cbrt k)))
  (/ (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2))) (sqrt (sqrt k)))
  (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2)))
  (/ (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2))) (sqrt (sqrt k)))
  (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2)))
  (/ (sqrt k) (exp (* (* (log PI) 1/2) (- 1 k))))
  (real->posit16 (/ (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2))) (sqrt k)))
  (- (* (* (- 1 k) 1/2) (+ (log n) (+ (log 2) (log PI)))) (log (sqrt k)))
  (- (* (* (- 1 k) 1/2) (+ (log n) (+ (log 2) (log PI)))) (log (sqrt k)))
  (- (* (* (- 1 k) 1/2) (+ (log n) (+ (log 2) (log PI)))) (log (sqrt k)))
  (- (* (* (- 1 k) 1/2) (+ (log n) (+ (log 2) (log PI)))) (log (sqrt k)))
  (- (* (* (- 1 k) 1/2) (+ (log n) (+ (log 2) (log PI)))) (log (sqrt k)))
  (- (* (* (- 1 k) 1/2) (+ (log n) (+ (log 2) (log PI)))) (log (sqrt k)))
  (- (* (* (- 1 k) 1/2) (+ (log n) (+ (log 2) (log PI)))) (log (sqrt k)))
  (- (* (* (- 1 k) 1/2) (+ (log n) (+ (log 2) (log PI)))) (log (sqrt k)))
  (- (* (* (- 1 k) 1/2) (+ (log n) (+ (log 2) (log PI)))) (log (sqrt k)))
  (- (* (* (- 1 k) 1/2) (+ (log n) (+ (log 2) (log PI)))) (log (sqrt k)))
  (- (* (* (- 1 k) 1/2) (+ (log n) (+ (log 2) (log PI)))) (log (sqrt k)))
  (- (* (* (- 1 k) 1/2) (+ (log n) (+ (log 2) (log PI)))) (log (sqrt k)))
  (- (* (* (- 1 k) 1/2) (+ (log n) (+ (log 2) (log PI)))) (log (sqrt k)))
  (- (* (* (- 1 k) 1/2) (+ (log n) (+ (log 2) (log PI)))) (log (sqrt k)))
  (- (* (* (- 1 k) 1/2) (+ (log n) (+ (log 2) (log PI)))) (log (sqrt k)))
  (- (* (* (- 1 k) 1/2) (+ (log n) (+ (log 2) (log PI)))) (log (sqrt k)))
  (- (* (* (- 1 k) 1/2) (+ (log n) (+ (log 2) (log PI)))) (log (sqrt k)))
  (- (* (* (- 1 k) 1/2) (+ (log n) (+ (log 2) (log PI)))) (log (sqrt k)))
  (- (* (* (- 1 k) 1/2) (+ (log n) (+ (log 2) (log PI)))) (log (sqrt k)))
  (- (* (* (- 1 k) 1/2) (+ (log n) (+ (log 2) (log PI)))) (log (sqrt k)))
  (- (* (* (- 1 k) 1/2) (+ (log n) (+ (log 2) (log PI)))) (log (sqrt k)))
  (- (* (* (- 1 k) 1/2) (+ (log n) (+ (log 2) (log PI)))) (log (sqrt k)))
  (- (* (* (- 1 k) 1/2) (+ (log n) (+ (log 2) (log PI)))) (log (sqrt k)))
  (- (* (* (- 1 k) 1/2) (+ (log n) (+ (log 2) (log PI)))) (log (sqrt k)))
  (- (* (* (- 1 k) 1/2) (+ (log n) (+ (log 2) (log PI)))) (log (sqrt k)))
  (- (* (* (- 1 k) 1/2) (+ (log n) (+ (log 2) (log PI)))) (log (sqrt k)))
  (- (* (* (- 1 k) 1/2) (+ (log n) (+ (log 2) (log PI)))) (log (sqrt k)))
  (- (* (* (- 1 k) 1/2) (+ (log n) (+ (log 2) (log PI)))) (log (sqrt k)))
  (- (* (* (- 1 k) 1/2) (+ (log n) (+ (log 2) (log PI)))) (log (sqrt k)))
  (- (* (* (- 1 k) 1/2) (+ (log n) (+ (log 2) (log PI)))) (log (sqrt k)))
  (- (* (* (- 1 k) 1/2) (+ (log n) (+ (log 2) (log PI)))) (log (sqrt k)))
  (- (* (* (- 1 k) 1/2) (+ (log n) (+ (log 2) (log PI)))) (log (sqrt k)))
  (- (* (* (- 1 k) 1/2) (+ (log n) (+ (log 2) (log PI)))) (log (sqrt k)))
  (- (* (* (- 1 k) 1/2) (+ (log n) (+ (log 2) (log PI)))) (log (sqrt k)))
  (exp (/ (* (pow n (* (- 1 k) 1/2)) (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2)))) (sqrt k)))
  (* (pow n (* (- 1 k) 1/2)) (* (pow n (* (- 1 k) 1/2)) (* (/ (* (pow (exp (* (log 2) (* (- 1 k) 1/2))) 3) (/ (* (* (pow PI (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (pow PI (* (- 1 k) 1/2))) (sqrt k))) k) (pow n (* (- 1 k) 1/2)))))
  (* (pow n (* (- 1 k) 1/2)) (* (pow n (* (- 1 k) 1/2)) (* (* (/ (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2))) k) (/ (* (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2))) (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2)))) (sqrt k))) (pow n (* (- 1 k) 1/2)))))
  (* (pow n (* (- 1 k) 1/2)) (* (pow n (* (- 1 k) 1/2)) (* (* (pow n (* (- 1 k) 1/2)) (* (/ (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2))) (sqrt k)) (/ (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2))) (sqrt k)))) (/ (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2))) (sqrt k)))))
  (* (cbrt (/ (* (pow n (* (- 1 k) 1/2)) (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2)))) (sqrt k))) (cbrt (/ (* (pow n (* (- 1 k) 1/2)) (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2)))) (sqrt k))))
  (cbrt (/ (* (pow n (* (- 1 k) 1/2)) (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2)))) (sqrt k)))
  (* (pow n (* (- 1 k) 1/2)) (* (pow n (* (- 1 k) 1/2)) (* (* (pow n (* (- 1 k) 1/2)) (* (/ (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2))) (sqrt k)) (/ (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2))) (sqrt k)))) (/ (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2))) (sqrt k)))))
  (sqrt (/ (* (pow n (* (- 1 k) 1/2)) (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2)))) (sqrt k)))
  (sqrt (/ (* (pow n (* (- 1 k) 1/2)) (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2)))) (sqrt k)))
  (* (sqrt (/ (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2))) (sqrt k))) (pow (sqrt n) (* (- 1 k) 1/2)))
  (* (sqrt (/ (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2))) (sqrt k))) (pow (sqrt n) (* (- 1 k) 1/2)))
  (* (sqrt (/ (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2))) (sqrt k))) (sqrt (pow n (* (- 1 k) 1/2))))
  (* (sqrt (/ (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2))) (sqrt k))) (sqrt (pow n (* (- 1 k) 1/2))))
  (* (pow n (/ (- 1 k) 4)) (sqrt (/ (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2))) (sqrt k))))
  (* (pow n (/ (- 1 k) 4)) (sqrt (/ (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2))) (sqrt k))))
  (* (* (pow n (* (- 1 k) 1/2)) (cbrt (/ (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2))) (sqrt k)))) (cbrt (/ (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2))) (sqrt k))))
  (* (sqrt (/ (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2))) (sqrt k))) (pow n (* (- 1 k) 1/2)))
  (/ (* (exp (* (log 2) (* (- 1 k) 1/2))) (pow n (* (- 1 k) 1/2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (* (/ (exp (* (log 2) (* (- 1 k) 1/2))) (fabs (cbrt k))) (pow n (* (- 1 k) 1/2)))
  (* (/ (exp (* (log 2) (* (- 1 k) 1/2))) (sqrt (sqrt k))) (pow n (* (- 1 k) 1/2)))
  (* (pow n (* (- 1 k) 1/2)) (exp (* (log 2) (* (- 1 k) 1/2))))
  (* (/ (exp (* (log 2) (* (- 1 k) 1/2))) (sqrt (sqrt k))) (pow n (* (- 1 k) 1/2)))
  (* (pow n (* (- 1 k) 1/2)) (exp (* (log 2) (* (- 1 k) 1/2))))
  (pow n (* (- 1 k) 1/2))
  (* (pow n (* (- 1 k) 1/2)) (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2))))
  (/ (* (pow (cbrt n) (* (- 1 k) 1/2)) (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2)))) (sqrt k))
  (* (pow (sqrt n) (* (- 1 k) 1/2)) (/ (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2))) (sqrt k)))
  (/ (* (pow n (* (- 1 k) 1/2)) (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2)))) (sqrt k))
  (/ (* (cbrt (pow n (* (- 1 k) 1/2))) (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2)))) (sqrt k))
  (* (/ (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2))) (sqrt k)) (sqrt (pow n (* (- 1 k) 1/2))))
  (/ (* (pow n (* (- 1 k) 1/2)) (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2)))) (sqrt k))
  (* (pow n (/ (- 1 k) 4)) (/ (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2))) (sqrt k)))
  (* (pow n (* (- 1 k) 1/2)) (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2))))
  (real->posit16 (/ (* (pow n (* (- 1 k) 1/2)) (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2)))) (sqrt k)))
  (+ (+ (* (* (* k (log n)) (* k (log n))) (* (sqrt n) 1/8)) (* (* (* k (log n)) (sqrt n)) -1/2)) (sqrt n))
  (exp (* (* -1/2 (- (log n))) (- 1 k)))
  (exp (* (- (log -1) (- (log -1) (log n))) (* (- 1 k) 1/2)))
  (+ (sqrt PI) (* (sqrt PI) (- (* (* (* (log PI) k) (* (log PI) k)) 1/8) (* (* (log PI) k) 1/2))))
  (exp (* (* (log PI) 1/2) (- 1 k)))
  (exp (* (* (log PI) 1/2) (- 1 k)))
  (+ (+ (- (* +nan.0 (* (sqrt 2) (* (* k k) (sqrt PI)))) (* (* +nan.0 (log 2)) (* (* (* k (* (log PI) k)) (sqrt 2)) (sqrt PI)))) (+ (- (* (* (* (sqrt PI) (sqrt 2)) (* (log PI) k)) +nan.0) (* (* (* +nan.0 (log 2)) (* (* k k) (sqrt 2))) (sqrt PI))) (- (* (* +nan.0 (sqrt PI)) (* (* (* (* k k) (sqrt 2)) (log 2)) (log 2))) (+ (- (* (* +nan.0 (sqrt PI)) (sqrt 2)) (* (* (* (* k (* (log PI) k)) (sqrt 2)) (sqrt PI)) +nan.0)) (* (sqrt PI) (- (* (* +nan.0 (log 2)) (* (sqrt 2) k)) (* (* (sqrt 2) k) +nan.0))))))) (* (- +nan.0) (* (sqrt 2) (* (sqrt PI) (* (* (log PI) k) (* (log PI) k))))))
  (- (- (/ (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2))) (/ k +nan.0)) (* +nan.0 (- (/ (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2))) (* k (* k k))) (/ (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2))) (* k k))))))
  (- (- (/ (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2))) (/ k +nan.0)) (* +nan.0 (- (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2))) (/ (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2))) (* k k))))))
  (+ (+ (- (* (* (sqrt 2) (* (sqrt (* PI n)) k)) +nan.0) (* (* (* +nan.0 (sqrt 2)) (* k (* (log PI) k))) (sqrt (* PI n)))) (+ (- (* (sqrt (* PI n)) (* (* +nan.0 (sqrt 2)) (* (* k (log n)) k))) (* +nan.0 (* (* (* k (* (log PI) k)) (* (sqrt 2) (sqrt (* PI n)))) (log 2)))) (- (* (sqrt (* PI n)) (* (* +nan.0 (log 2)) (* (* k k) (sqrt 2)))) (+ (- (* (* (* (* (* k k) (sqrt 2)) (log 2)) (log 2)) (* (sqrt (* PI n)) +nan.0)) (* (* +nan.0 (sqrt 2)) (* (* k k) (sqrt (* PI n))))) (+ (- (* (sqrt (* PI n)) (* (* +nan.0 (sqrt 2)) (* (* k (log n)) (* k (log n))))) (* (* +nan.0 (sqrt (* PI n))) (* (* (sqrt 2) k) (log n)))) (- (* (* +nan.0 (sqrt 2)) (sqrt (* PI n))) (+ (- (* (sqrt (* PI n)) (* (* +nan.0 (log 2)) (* (sqrt 2) k))) (* (sqrt (* PI n)) (* (* +nan.0 (sqrt 2)) (* (log PI) k)))) (* +nan.0 (- (* (* (sqrt 2) (log PI)) (* (log n) (* (* k k) (sqrt (* PI n))))) (* (* (* (log PI) k) (* (log PI) k)) (* (sqrt 2) (sqrt (* PI n))))))))))))) (- (* (log 2) (* (sqrt (* PI n)) (* (* +nan.0 (sqrt 2)) (* (* k (log n)) k))))))
  (+ (- (/ (* +nan.0 (* (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2))) (exp (* (* -1/2 (- (log n))) (- 1 k))))) (* k (* k k)))) (* +nan.0 (- (/ (exp (* (* -1/2 (- (log n))) (- 1 k))) (/ (* k k) (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2))))) (/ (exp (* (* -1/2 (- (log n))) (- 1 k))) (/ k (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2))))))))
  (+ (- (/ (* +nan.0 (exp (* (- (log -1) (- (log -1) (log n))) (* (- 1 k) 1/2)))) (/ k (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2))))) (/ (* (* +nan.0 (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2)))) (exp (* (- (log -1) (- (log -1) (log n))) (* (- 1 k) 1/2)))) (* k k))) (- (* (* +nan.0 (exp (* (+ (log 2) (log PI)) (* (- 1 k) 1/2)))) (exp (* (- (log -1) (- (log -1) (log n))) (* (- 1 k) 1/2))))))
19.625 * * * [progress]: adding candidates to table
21.704 * [progress]: [Phase 3 of 3] Extracting.
21.704 * * [regime]: Finding splitpoints for: (#<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (exp (log (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt k)))))> #<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))))> #<alt (λ (k n) (* (/ 1 (fabs (cbrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (cbrt k)))))> #<alt (λ (k n) (* (+ (+ (* (* (* k (log n)) (* k (log n))) (* (sqrt n) 1/8)) (* (* (* k (log n)) (sqrt n)) -1/2)) (sqrt n)) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))> #<alt (λ (k n) (/ (pow (* (sqrt n) (* (sqrt n) (* 2 PI))) (* (- 1 k) 1/2)) (sqrt k)))> #<alt (λ (k n) (* (/ (pow n (* (- 1 k) 1/2)) (sqrt (sqrt k))) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt (sqrt k)))))> #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))>)
21.705 * * * [regime-changes]: Trying 2 branch expressions: (n k)
21.705 * * * * [regimes]: Trying to branch on n from (#<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (exp (log (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt k)))))> #<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))))> #<alt (λ (k n) (* (/ 1 (fabs (cbrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (cbrt k)))))> #<alt (λ (k n) (* (+ (+ (* (* (* k (log n)) (* k (log n))) (* (sqrt n) 1/8)) (* (* (* k (log n)) (sqrt n)) -1/2)) (sqrt n)) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))> #<alt (λ (k n) (/ (pow (* (sqrt n) (* (sqrt n) (* 2 PI))) (* (- 1 k) 1/2)) (sqrt k)))> #<alt (λ (k n) (* (/ (pow n (* (- 1 k) 1/2)) (sqrt (sqrt k))) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt (sqrt k)))))> #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))>)
21.785 * * * * [regimes]: Trying to branch on k from (#<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (exp (log (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt k)))))> #<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))))> #<alt (λ (k n) (* (/ 1 (fabs (cbrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (cbrt k)))))> #<alt (λ (k n) (* (+ (+ (* (* (* k (log n)) (* k (log n))) (* (sqrt n) 1/8)) (* (* (* k (log n)) (sqrt n)) -1/2)) (sqrt n)) (/ (* (pow 2 (* (- 1 k) 1/2)) (pow PI (* (- 1 k) 1/2))) (sqrt k))))> #<alt (λ (k n) (/ (pow (* (sqrt n) (* (sqrt n) (* 2 PI))) (* (- 1 k) 1/2)) (sqrt k)))> #<alt (λ (k n) (* (/ (pow n (* (- 1 k) 1/2)) (sqrt (sqrt k))) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt (sqrt k)))))> #<alt (λ (k n) (* (pow n (* (- 1 k) 1/2)) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))>)
21.852 * * * [regime]: Found split indices: #<option (#s(si 1 255))>
21.853 * [simplify]: Simplifying:
  (* (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))))
21.853 * * [simplify]: iteration 1: (15 enodes)
21.856 * * [simplify]: iteration 2: (20 enodes)
21.859 * * [simplify]: Extracting #0: cost 1 inf + 0
21.859 * * [simplify]: Extracting #1: cost 2 inf + 0
21.859 * * [simplify]: Extracting #2: cost 3 inf + 0
21.859 * * [simplify]: Extracting #3: cost 5 inf + 0
21.859 * * [simplify]: Extracting #4: cost 8 inf + 0
21.859 * * [simplify]: Extracting #5: cost 10 inf + 42
21.859 * * [simplify]: Extracting #6: cost 11 inf + 44
21.859 * * [simplify]: Extracting #7: cost 5 inf + 214
21.859 * * [simplify]: Extracting #8: cost 1 inf + 1625
21.860 * * [simplify]: Extracting #9: cost 0 inf + 2161
21.860 * [simplify]: Simplified to:
  (* (sqrt (/ (pow (* (* PI 2) n) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (pow (* (* PI 2) n) (* (- 1 k) 1/2)) (sqrt k))))
30.513 * [regime-testing]: Baseline error score: 0.5075308645691854
30.517 * [regime-testing]: Oracle error score: 0.06772503978151716
30.526 * [regime-testing]: End program error score: 0.5075308645691854