6.704 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.077 * * * [progress]: [2/2] Setting up program. 0.079 * [progress]: [Phase 2 of 3] Improving. 0.079 * [simplify]: Simplifying using # : (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 0.080 * * [simplify]: iteration 0 : 13 enodes (cost 16 ) 0.082 * * [simplify]: iteration 1 : 29 enodes (cost 16 ) 0.086 * * [simplify]: iteration 2 : 57 enodes (cost 16 ) 0.094 * * [simplify]: iteration 3 : 114 enodes (cost 16 ) 0.117 * * [simplify]: iteration 4 : 300 enodes (cost 16 ) 0.186 * * [simplify]: iteration 5 : 859 enodes (cost 16 ) 0.520 * * [simplify]: iteration 6 : 3256 enodes (cost 16 ) 1.790 * * [simplify]: iteration done : 5000 enodes (cost 16 ) 1.790 * [simplify]: Simplified to: (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 1.791 * * [progress]: iteration 1 / 4 1.791 * * * [progress]: picking best candidate 1.793 * * * * [pick]: Picked # 1.793 * * * [progress]: localizing error 1.810 * * * [progress]: generating rewritten candidates 1.810 * * * * [progress]: [ 1 / 4 ] rewriting at (2 1) 1.813 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2) 1.823 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1) 1.830 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 1.854 * * * [progress]: generating series expansions 1.854 * * * * [progress]: [ 1 / 4 ] generating series at (2 1) 1.854 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 1.855 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 1.855 * [taylor]: Taking taylor expansion of 1.0 in k 1.855 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 1.855 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.855 * [taylor]: Taking taylor expansion of k in k 1.856 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 1.856 * [taylor]: Taking taylor expansion of 1.0 in k 1.856 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 1.856 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.856 * [taylor]: Taking taylor expansion of k in k 1.868 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 1.868 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 1.868 * [taylor]: Taking taylor expansion of 1.0 in k 1.868 * [taylor]: Taking taylor expansion of (sqrt k) in k 1.868 * [taylor]: Taking taylor expansion of k in k 1.869 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 1.869 * [taylor]: Taking taylor expansion of 1.0 in k 1.869 * [taylor]: Taking taylor expansion of (sqrt k) in k 1.869 * [taylor]: Taking taylor expansion of k in k 1.879 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 1.879 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 1.879 * [taylor]: Taking taylor expansion of 1.0 in k 1.879 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 1.879 * [taylor]: Taking taylor expansion of (/ -1 k) in k 1.879 * [taylor]: Taking taylor expansion of -1 in k 1.879 * [taylor]: Taking taylor expansion of k in k 1.881 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 1.881 * [taylor]: Taking taylor expansion of 1.0 in k 1.881 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 1.881 * [taylor]: Taking taylor expansion of (/ -1 k) in k 1.881 * [taylor]: Taking taylor expansion of -1 in k 1.881 * [taylor]: Taking taylor expansion of k in k 1.898 * * * * [progress]: [ 2 / 4 ] generating series at (2 2) 1.898 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 1.898 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 1.898 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 1.898 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 1.898 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 1.898 * [taylor]: Taking taylor expansion of 0.5 in k 1.898 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.899 * [taylor]: Taking taylor expansion of 1.0 in k 1.899 * [taylor]: Taking taylor expansion of k in k 1.899 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 1.899 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 1.899 * [taylor]: Taking taylor expansion of 2.0 in k 1.899 * [taylor]: Taking taylor expansion of (* n PI) in k 1.899 * [taylor]: Taking taylor expansion of n in k 1.899 * [taylor]: Taking taylor expansion of PI in k 1.900 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 1.900 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.900 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.900 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 1.900 * [taylor]: Taking taylor expansion of 0.5 in n 1.900 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.900 * [taylor]: Taking taylor expansion of 1.0 in n 1.900 * [taylor]: Taking taylor expansion of k in n 1.900 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.900 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.900 * [taylor]: Taking taylor expansion of 2.0 in n 1.900 * [taylor]: Taking taylor expansion of (* n PI) in n 1.900 * [taylor]: Taking taylor expansion of n in n 1.900 * [taylor]: Taking taylor expansion of PI in n 1.905 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 1.905 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.905 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.905 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 1.905 * [taylor]: Taking taylor expansion of 0.5 in n 1.905 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.905 * [taylor]: Taking taylor expansion of 1.0 in n 1.905 * [taylor]: Taking taylor expansion of k in n 1.905 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.905 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.905 * [taylor]: Taking taylor expansion of 2.0 in n 1.905 * [taylor]: Taking taylor expansion of (* n PI) in n 1.905 * [taylor]: Taking taylor expansion of n in n 1.906 * [taylor]: Taking taylor expansion of PI in n 1.911 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 1.911 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 1.911 * [taylor]: Taking taylor expansion of 0.5 in k 1.911 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 1.911 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.911 * [taylor]: Taking taylor expansion of 1.0 in k 1.911 * [taylor]: Taking taylor expansion of k in k 1.911 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 1.911 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.911 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.911 * [taylor]: Taking taylor expansion of 2.0 in k 1.911 * [taylor]: Taking taylor expansion of PI in k 1.912 * [taylor]: Taking taylor expansion of (log n) in k 1.912 * [taylor]: Taking taylor expansion of n in k 1.921 * [taylor]: Taking taylor expansion of 0 in k 1.937 * [taylor]: Taking taylor expansion of 0 in k 1.956 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 1.956 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 1.956 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 1.956 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 1.956 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 1.956 * [taylor]: Taking taylor expansion of 0.5 in k 1.956 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.956 * [taylor]: Taking taylor expansion of 1.0 in k 1.956 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.956 * [taylor]: Taking taylor expansion of k in k 1.956 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 1.956 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 1.956 * [taylor]: Taking taylor expansion of 2.0 in k 1.956 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.956 * [taylor]: Taking taylor expansion of PI in k 1.956 * [taylor]: Taking taylor expansion of n in k 1.957 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 1.957 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.958 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.958 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 1.958 * [taylor]: Taking taylor expansion of 0.5 in n 1.958 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.958 * [taylor]: Taking taylor expansion of 1.0 in n 1.958 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.958 * [taylor]: Taking taylor expansion of k in n 1.958 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.958 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.958 * [taylor]: Taking taylor expansion of 2.0 in n 1.958 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.958 * [taylor]: Taking taylor expansion of PI in n 1.958 * [taylor]: Taking taylor expansion of n in n 1.961 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 1.961 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.961 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.961 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 1.961 * [taylor]: Taking taylor expansion of 0.5 in n 1.962 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.962 * [taylor]: Taking taylor expansion of 1.0 in n 1.962 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.962 * [taylor]: Taking taylor expansion of k in n 1.962 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.962 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.962 * [taylor]: Taking taylor expansion of 2.0 in n 1.962 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.962 * [taylor]: Taking taylor expansion of PI in n 1.962 * [taylor]: Taking taylor expansion of n in n 1.965 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 1.966 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 1.966 * [taylor]: Taking taylor expansion of 0.5 in k 1.966 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 1.966 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 1.966 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.966 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.966 * [taylor]: Taking taylor expansion of 2.0 in k 1.966 * [taylor]: Taking taylor expansion of PI in k 1.967 * [taylor]: Taking taylor expansion of (log n) in k 1.967 * [taylor]: Taking taylor expansion of n in k 1.967 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.967 * [taylor]: Taking taylor expansion of 1.0 in k 1.967 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.967 * [taylor]: Taking taylor expansion of k in k 1.982 * [taylor]: Taking taylor expansion of 0 in k 1.989 * [taylor]: Taking taylor expansion of 0 in k 1.998 * [taylor]: Taking taylor expansion of 0 in k 1.999 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 1.999 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 1.999 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 1.999 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 1.999 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 1.999 * [taylor]: Taking taylor expansion of 0.5 in k 1.999 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.000 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.000 * [taylor]: Taking taylor expansion of k in k 2.000 * [taylor]: Taking taylor expansion of 1.0 in k 2.000 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 2.000 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 2.000 * [taylor]: Taking taylor expansion of -2.0 in k 2.000 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.000 * [taylor]: Taking taylor expansion of PI in k 2.000 * [taylor]: Taking taylor expansion of n in k 2.001 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 2.001 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.001 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.001 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 2.001 * [taylor]: Taking taylor expansion of 0.5 in n 2.001 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.001 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.001 * [taylor]: Taking taylor expansion of k in n 2.001 * [taylor]: Taking taylor expansion of 1.0 in n 2.001 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.001 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.001 * [taylor]: Taking taylor expansion of -2.0 in n 2.001 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.001 * [taylor]: Taking taylor expansion of PI in n 2.001 * [taylor]: Taking taylor expansion of n in n 2.005 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 2.005 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.005 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.005 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 2.005 * [taylor]: Taking taylor expansion of 0.5 in n 2.005 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.005 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.005 * [taylor]: Taking taylor expansion of k in n 2.005 * [taylor]: Taking taylor expansion of 1.0 in n 2.005 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.005 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.005 * [taylor]: Taking taylor expansion of -2.0 in n 2.005 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.005 * [taylor]: Taking taylor expansion of PI in n 2.005 * [taylor]: Taking taylor expansion of n in n 2.009 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 2.009 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 2.009 * [taylor]: Taking taylor expansion of 0.5 in k 2.009 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 2.009 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.009 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.009 * [taylor]: Taking taylor expansion of k in k 2.009 * [taylor]: Taking taylor expansion of 1.0 in k 2.009 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 2.009 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 2.009 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 2.009 * [taylor]: Taking taylor expansion of -2.0 in k 2.009 * [taylor]: Taking taylor expansion of PI in k 2.010 * [taylor]: Taking taylor expansion of (log n) in k 2.010 * [taylor]: Taking taylor expansion of n in k 2.019 * [taylor]: Taking taylor expansion of 0 in k 2.026 * [taylor]: Taking taylor expansion of 0 in k 2.035 * [taylor]: Taking taylor expansion of 0 in k 2.036 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1) 2.037 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 2.037 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.037 * [taylor]: Taking taylor expansion of 2.0 in n 2.037 * [taylor]: Taking taylor expansion of (* n PI) in n 2.037 * [taylor]: Taking taylor expansion of n in n 2.037 * [taylor]: Taking taylor expansion of PI in n 2.037 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.037 * [taylor]: Taking taylor expansion of 2.0 in n 2.037 * [taylor]: Taking taylor expansion of (* n PI) in n 2.037 * [taylor]: Taking taylor expansion of n in n 2.037 * [taylor]: Taking taylor expansion of PI in n 2.050 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 2.050 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.050 * [taylor]: Taking taylor expansion of 2.0 in n 2.050 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.050 * [taylor]: Taking taylor expansion of PI in n 2.050 * [taylor]: Taking taylor expansion of n in n 2.050 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.050 * [taylor]: Taking taylor expansion of 2.0 in n 2.050 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.050 * [taylor]: Taking taylor expansion of PI in n 2.050 * [taylor]: Taking taylor expansion of n in n 2.065 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 2.065 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.065 * [taylor]: Taking taylor expansion of -2.0 in n 2.065 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.065 * [taylor]: Taking taylor expansion of PI in n 2.065 * [taylor]: Taking taylor expansion of n in n 2.065 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.065 * [taylor]: Taking taylor expansion of -2.0 in n 2.065 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.065 * [taylor]: Taking taylor expansion of PI in n 2.065 * [taylor]: Taking taylor expansion of n in n 2.074 * * * * [progress]: [ 4 / 4 ] generating series at (2) 2.074 * [approximate]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in (k n) around 0 2.074 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in n 2.074 * [taylor]: Taking taylor expansion of 1.0 in n 2.074 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in n 2.075 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 2.075 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.075 * [taylor]: Taking taylor expansion of k in n 2.075 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 2.075 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.075 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.075 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 2.075 * [taylor]: Taking taylor expansion of 0.5 in n 2.075 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.075 * [taylor]: Taking taylor expansion of 1.0 in n 2.075 * [taylor]: Taking taylor expansion of k in n 2.075 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.075 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.075 * [taylor]: Taking taylor expansion of 2.0 in n 2.075 * [taylor]: Taking taylor expansion of (* n PI) in n 2.075 * [taylor]: Taking taylor expansion of n in n 2.075 * [taylor]: Taking taylor expansion of PI in n 2.080 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 2.080 * [taylor]: Taking taylor expansion of 1.0 in k 2.080 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 2.080 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 2.080 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.080 * [taylor]: Taking taylor expansion of k in k 2.082 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 2.082 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 2.082 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 2.082 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 2.082 * [taylor]: Taking taylor expansion of 0.5 in k 2.082 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.082 * [taylor]: Taking taylor expansion of 1.0 in k 2.082 * [taylor]: Taking taylor expansion of k in k 2.082 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 2.082 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 2.082 * [taylor]: Taking taylor expansion of 2.0 in k 2.082 * [taylor]: Taking taylor expansion of (* n PI) in k 2.082 * [taylor]: Taking taylor expansion of n in k 2.082 * [taylor]: Taking taylor expansion of PI in k 2.083 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 2.083 * [taylor]: Taking taylor expansion of 1.0 in k 2.083 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 2.083 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 2.083 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.083 * [taylor]: Taking taylor expansion of k in k 2.084 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 2.084 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 2.084 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 2.084 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 2.084 * [taylor]: Taking taylor expansion of 0.5 in k 2.084 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.084 * [taylor]: Taking taylor expansion of 1.0 in k 2.084 * [taylor]: Taking taylor expansion of k in k 2.084 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 2.084 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 2.084 * [taylor]: Taking taylor expansion of 2.0 in k 2.084 * [taylor]: Taking taylor expansion of (* n PI) in k 2.085 * [taylor]: Taking taylor expansion of n in k 2.085 * [taylor]: Taking taylor expansion of PI in k 2.086 * [taylor]: Taking taylor expansion of 0 in n 2.092 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) in n 2.092 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) in n 2.092 * [taylor]: Taking taylor expansion of +nan.0 in n 2.092 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 2.092 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 2.092 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 2.092 * [taylor]: Taking taylor expansion of 0.5 in n 2.092 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 2.092 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 2.092 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 2.092 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 2.092 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 2.092 * [taylor]: Taking taylor expansion of 1.0 in n 2.092 * [taylor]: Taking taylor expansion of (log PI) in n 2.092 * [taylor]: Taking taylor expansion of PI in n 2.094 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 2.094 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 2.094 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 2.094 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 2.094 * [taylor]: Taking taylor expansion of 1.0 in n 2.094 * [taylor]: Taking taylor expansion of (log n) in n 2.094 * [taylor]: Taking taylor expansion of n in n 2.094 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 2.094 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 2.094 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 2.094 * [taylor]: Taking taylor expansion of 1.0 in n 2.094 * [taylor]: Taking taylor expansion of (log 2.0) in n 2.094 * [taylor]: Taking taylor expansion of 2.0 in n 2.113 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))))))) in n 2.114 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))))) in n 2.114 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) in n 2.114 * [taylor]: Taking taylor expansion of +nan.0 in n 2.114 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 2.114 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 2.114 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 2.114 * [taylor]: Taking taylor expansion of 0.5 in n 2.114 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 2.114 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 2.114 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 2.114 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 2.114 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 2.114 * [taylor]: Taking taylor expansion of 1.0 in n 2.114 * [taylor]: Taking taylor expansion of (log PI) in n 2.114 * [taylor]: Taking taylor expansion of PI in n 2.116 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 2.116 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 2.116 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 2.116 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 2.116 * [taylor]: Taking taylor expansion of 1.0 in n 2.116 * [taylor]: Taking taylor expansion of (log n) in n 2.116 * [taylor]: Taking taylor expansion of n in n 2.116 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 2.116 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 2.116 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 2.116 * [taylor]: Taking taylor expansion of 1.0 in n 2.116 * [taylor]: Taking taylor expansion of (log 2.0) in n 2.116 * [taylor]: Taking taylor expansion of 2.0 in n 2.122 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))))) in n 2.122 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) in n 2.122 * [taylor]: Taking taylor expansion of +nan.0 in n 2.122 * [taylor]: Taking taylor expansion of (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))) in n 2.122 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 2.122 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 2.122 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 2.122 * [taylor]: Taking taylor expansion of 0.5 in n 2.122 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 2.122 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 2.122 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 2.122 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 2.122 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 2.122 * [taylor]: Taking taylor expansion of 1.0 in n 2.122 * [taylor]: Taking taylor expansion of (log 2.0) in n 2.122 * [taylor]: Taking taylor expansion of 2.0 in n 2.124 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 2.124 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 2.124 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 2.124 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 2.124 * [taylor]: Taking taylor expansion of 1.0 in n 2.124 * [taylor]: Taking taylor expansion of (log PI) in n 2.124 * [taylor]: Taking taylor expansion of PI in n 2.126 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 2.126 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 2.126 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 2.126 * [taylor]: Taking taylor expansion of 1.0 in n 2.126 * [taylor]: Taking taylor expansion of (log n) in n 2.126 * [taylor]: Taking taylor expansion of n in n 2.130 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.130 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.130 * [taylor]: Taking taylor expansion of 2.0 in n 2.130 * [taylor]: Taking taylor expansion of (* n PI) in n 2.130 * [taylor]: Taking taylor expansion of n in n 2.130 * [taylor]: Taking taylor expansion of PI in n 2.185 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))))) in n 2.185 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))))) in n 2.185 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) in n 2.185 * [taylor]: Taking taylor expansion of +nan.0 in n 2.185 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n 2.185 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n 2.185 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n 2.185 * [taylor]: Taking taylor expansion of 0.5 in n 2.185 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n 2.185 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n 2.185 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 2.185 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 2.185 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 2.185 * [taylor]: Taking taylor expansion of 1.0 in n 2.185 * [taylor]: Taking taylor expansion of (log 2.0) in n 2.185 * [taylor]: Taking taylor expansion of 2.0 in n 2.187 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n 2.187 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 2.187 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 2.187 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 2.187 * [taylor]: Taking taylor expansion of 1.0 in n 2.187 * [taylor]: Taking taylor expansion of (log n) in n 2.187 * [taylor]: Taking taylor expansion of n in n 2.188 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 2.188 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 2.188 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 2.188 * [taylor]: Taking taylor expansion of 1.0 in n 2.188 * [taylor]: Taking taylor expansion of (log PI) in n 2.188 * [taylor]: Taking taylor expansion of PI in n 2.193 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))) in n 2.193 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))) in n 2.194 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) in n 2.194 * [taylor]: Taking taylor expansion of +nan.0 in n 2.194 * [taylor]: Taking taylor expansion of (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))) in n 2.194 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 2.194 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 2.194 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 2.194 * [taylor]: Taking taylor expansion of 0.5 in n 2.194 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 2.194 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 2.194 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 2.194 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 2.194 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 2.194 * [taylor]: Taking taylor expansion of 1.0 in n 2.194 * [taylor]: Taking taylor expansion of (log 2.0) in n 2.194 * [taylor]: Taking taylor expansion of 2.0 in n 2.195 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 2.196 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 2.196 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 2.196 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 2.196 * [taylor]: Taking taylor expansion of 1.0 in n 2.196 * [taylor]: Taking taylor expansion of (log PI) in n 2.196 * [taylor]: Taking taylor expansion of PI in n 2.197 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 2.197 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 2.197 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 2.198 * [taylor]: Taking taylor expansion of 1.0 in n 2.198 * [taylor]: Taking taylor expansion of (log n) in n 2.198 * [taylor]: Taking taylor expansion of n in n 2.202 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.202 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.202 * [taylor]: Taking taylor expansion of 2.0 in n 2.202 * [taylor]: Taking taylor expansion of (* n PI) in n 2.202 * [taylor]: Taking taylor expansion of n in n 2.202 * [taylor]: Taking taylor expansion of PI in n 2.205 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))) in n 2.205 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) in n 2.205 * [taylor]: Taking taylor expansion of +nan.0 in n 2.205 * [taylor]: Taking taylor expansion of (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)) in n 2.205 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 2.205 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 2.205 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 2.205 * [taylor]: Taking taylor expansion of 0.5 in n 2.205 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 2.205 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 2.205 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 2.205 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 2.205 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 2.205 * [taylor]: Taking taylor expansion of 1.0 in n 2.205 * [taylor]: Taking taylor expansion of (log 2.0) in n 2.205 * [taylor]: Taking taylor expansion of 2.0 in n 2.207 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 2.207 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 2.207 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 2.207 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 2.207 * [taylor]: Taking taylor expansion of 1.0 in n 2.207 * [taylor]: Taking taylor expansion of (log PI) in n 2.207 * [taylor]: Taking taylor expansion of PI in n 2.209 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 2.209 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 2.209 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 2.209 * [taylor]: Taking taylor expansion of 1.0 in n 2.209 * [taylor]: Taking taylor expansion of (log n) in n 2.209 * [taylor]: Taking taylor expansion of n in n 2.213 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n 2.213 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.213 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.213 * [taylor]: Taking taylor expansion of 2.0 in n 2.213 * [taylor]: Taking taylor expansion of (* n PI) in n 2.213 * [taylor]: Taking taylor expansion of n in n 2.213 * [taylor]: Taking taylor expansion of PI in n 2.292 * [approximate]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in (k n) around 0 2.292 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in n 2.292 * [taylor]: Taking taylor expansion of 1.0 in n 2.292 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n 2.292 * [taylor]: Taking taylor expansion of (sqrt k) in n 2.292 * [taylor]: Taking taylor expansion of k in n 2.292 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 2.292 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.292 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.292 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 2.292 * [taylor]: Taking taylor expansion of 0.5 in n 2.292 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.292 * [taylor]: Taking taylor expansion of 1.0 in n 2.292 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.292 * [taylor]: Taking taylor expansion of k in n 2.292 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.292 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.292 * [taylor]: Taking taylor expansion of 2.0 in n 2.292 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.292 * [taylor]: Taking taylor expansion of PI in n 2.292 * [taylor]: Taking taylor expansion of n in n 2.296 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 2.296 * [taylor]: Taking taylor expansion of 1.0 in k 2.296 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 2.296 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.296 * [taylor]: Taking taylor expansion of k in k 2.297 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 2.297 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 2.297 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 2.297 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 2.297 * [taylor]: Taking taylor expansion of 0.5 in k 2.297 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.297 * [taylor]: Taking taylor expansion of 1.0 in k 2.297 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.297 * [taylor]: Taking taylor expansion of k in k 2.298 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 2.298 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 2.298 * [taylor]: Taking taylor expansion of 2.0 in k 2.298 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.298 * [taylor]: Taking taylor expansion of PI in k 2.298 * [taylor]: Taking taylor expansion of n in k 2.299 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 2.299 * [taylor]: Taking taylor expansion of 1.0 in k 2.299 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 2.299 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.299 * [taylor]: Taking taylor expansion of k in k 2.300 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 2.300 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 2.300 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 2.300 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 2.300 * [taylor]: Taking taylor expansion of 0.5 in k 2.300 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.300 * [taylor]: Taking taylor expansion of 1.0 in k 2.300 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.300 * [taylor]: Taking taylor expansion of k in k 2.300 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 2.300 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 2.300 * [taylor]: Taking taylor expansion of 2.0 in k 2.300 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.300 * [taylor]: Taking taylor expansion of PI in k 2.300 * [taylor]: Taking taylor expansion of n in k 2.302 * [taylor]: Taking taylor expansion of 0 in n 2.303 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 2.303 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 2.303 * [taylor]: Taking taylor expansion of +nan.0 in n 2.303 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 2.303 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 2.303 * [taylor]: Taking taylor expansion of 0.5 in n 2.303 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 2.303 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.303 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.303 * [taylor]: Taking taylor expansion of 2.0 in n 2.303 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.303 * [taylor]: Taking taylor expansion of PI in n 2.303 * [taylor]: Taking taylor expansion of n in n 2.304 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.304 * [taylor]: Taking taylor expansion of 1.0 in n 2.304 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.304 * [taylor]: Taking taylor expansion of k in n 2.313 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 2.313 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 2.313 * [taylor]: Taking taylor expansion of +nan.0 in n 2.313 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 2.313 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 2.313 * [taylor]: Taking taylor expansion of 0.5 in n 2.313 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 2.313 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.313 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.313 * [taylor]: Taking taylor expansion of 2.0 in n 2.313 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.313 * [taylor]: Taking taylor expansion of PI in n 2.313 * [taylor]: Taking taylor expansion of n in n 2.314 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.314 * [taylor]: Taking taylor expansion of 1.0 in n 2.314 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.314 * [taylor]: Taking taylor expansion of k in n 2.336 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 2.336 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 2.336 * [taylor]: Taking taylor expansion of +nan.0 in n 2.336 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 2.336 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 2.336 * [taylor]: Taking taylor expansion of 0.5 in n 2.336 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 2.336 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.336 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.336 * [taylor]: Taking taylor expansion of 2.0 in n 2.336 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.336 * [taylor]: Taking taylor expansion of PI in n 2.336 * [taylor]: Taking taylor expansion of n in n 2.337 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.337 * [taylor]: Taking taylor expansion of 1.0 in n 2.337 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.337 * [taylor]: Taking taylor expansion of k in n 2.346 * [approximate]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in (k n) around 0 2.346 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n 2.346 * [taylor]: Taking taylor expansion of 1.0 in n 2.346 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n 2.346 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 2.346 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.346 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.346 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 2.346 * [taylor]: Taking taylor expansion of 0.5 in n 2.346 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.346 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.346 * [taylor]: Taking taylor expansion of k in n 2.346 * [taylor]: Taking taylor expansion of 1.0 in n 2.346 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.346 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.346 * [taylor]: Taking taylor expansion of -2.0 in n 2.346 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.346 * [taylor]: Taking taylor expansion of PI in n 2.346 * [taylor]: Taking taylor expansion of n in n 2.350 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 2.350 * [taylor]: Taking taylor expansion of (/ -1 k) in n 2.350 * [taylor]: Taking taylor expansion of -1 in n 2.350 * [taylor]: Taking taylor expansion of k in n 2.351 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 2.351 * [taylor]: Taking taylor expansion of 1.0 in k 2.351 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 2.351 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 2.351 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 2.351 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 2.351 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 2.351 * [taylor]: Taking taylor expansion of 0.5 in k 2.351 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.351 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.351 * [taylor]: Taking taylor expansion of k in k 2.351 * [taylor]: Taking taylor expansion of 1.0 in k 2.351 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 2.351 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 2.351 * [taylor]: Taking taylor expansion of -2.0 in k 2.351 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.351 * [taylor]: Taking taylor expansion of PI in k 2.351 * [taylor]: Taking taylor expansion of n in k 2.352 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.352 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.352 * [taylor]: Taking taylor expansion of -1 in k 2.352 * [taylor]: Taking taylor expansion of k in k 2.354 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 2.354 * [taylor]: Taking taylor expansion of 1.0 in k 2.354 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 2.354 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 2.354 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 2.354 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 2.354 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 2.354 * [taylor]: Taking taylor expansion of 0.5 in k 2.354 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.354 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.354 * [taylor]: Taking taylor expansion of k in k 2.354 * [taylor]: Taking taylor expansion of 1.0 in k 2.354 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 2.354 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 2.354 * [taylor]: Taking taylor expansion of -2.0 in k 2.355 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.355 * [taylor]: Taking taylor expansion of PI in k 2.355 * [taylor]: Taking taylor expansion of n in k 2.355 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.355 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.355 * [taylor]: Taking taylor expansion of -1 in k 2.355 * [taylor]: Taking taylor expansion of k in k 2.357 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 2.357 * [taylor]: Taking taylor expansion of +nan.0 in n 2.357 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 2.357 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 2.357 * [taylor]: Taking taylor expansion of 0.5 in n 2.357 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 2.357 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.357 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.357 * [taylor]: Taking taylor expansion of k in n 2.357 * [taylor]: Taking taylor expansion of 1.0 in n 2.357 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.357 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.357 * [taylor]: Taking taylor expansion of -2.0 in n 2.357 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.357 * [taylor]: Taking taylor expansion of PI in n 2.357 * [taylor]: Taking taylor expansion of n in n 2.366 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 2.366 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 2.366 * [taylor]: Taking taylor expansion of +nan.0 in n 2.366 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 2.366 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 2.366 * [taylor]: Taking taylor expansion of 0.5 in n 2.366 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 2.366 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.366 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.366 * [taylor]: Taking taylor expansion of k in n 2.366 * [taylor]: Taking taylor expansion of 1.0 in n 2.366 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.366 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.366 * [taylor]: Taking taylor expansion of -2.0 in n 2.366 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.366 * [taylor]: Taking taylor expansion of PI in n 2.366 * [taylor]: Taking taylor expansion of n in n 2.384 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 2.384 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 2.384 * [taylor]: Taking taylor expansion of +nan.0 in n 2.384 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 2.384 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 2.384 * [taylor]: Taking taylor expansion of 0.5 in n 2.384 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 2.384 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.384 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.384 * [taylor]: Taking taylor expansion of k in n 2.384 * [taylor]: Taking taylor expansion of 1.0 in n 2.384 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.384 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.384 * [taylor]: Taking taylor expansion of -2.0 in n 2.384 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.384 * [taylor]: Taking taylor expansion of PI in n 2.384 * [taylor]: Taking taylor expansion of n in n 2.394 * * * [progress]: simplifying candidates 2.396 * [simplify]: Simplifying using # : (expm1 (/ 1.0 (sqrt k))) (log1p (/ 1.0 (sqrt k))) (- (log 1.0) (log (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt 1)) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt 1)) (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 1) (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt 1)) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 1) (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (* (* 2.0 PI) n)) (log1p (* (* 2.0 PI) n)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (expm1 (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log1p (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (+ (- (log 1.0) (log (sqrt k))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (+ (log (/ 1.0 (sqrt k))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (* (log 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(sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (* (/ 1.0 (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) 1) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (- (+ (* +nan.0 (* (* (pow k 2) (pow (log (* 2.0 PI)) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log (* 2.0 PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (* (log (* 2.0 PI)) (log n))) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log (* 2.0 PI))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (pow (log n) 2)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow k 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* k (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))))))))))))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 2)))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))))))))) 2.421 * * [simplify]: iteration 0 : 369 enodes (cost 2880 ) 2.495 * * [simplify]: iteration 1 : 987 enodes (cost 2720 ) 2.731 * * [simplify]: iteration 2 : 3678 enodes (cost 2554 ) 3.500 * * [simplify]: iteration done : 5001 enodes (cost 2539 ) 3.502 * [simplify]: Simplified to: (expm1 (/ 1.0 (sqrt k))) (log1p (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (pow (/ 1.0 (sqrt k)) 3) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (pow (/ 1.0 (sqrt k)) 3) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (fabs (cbrt k))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 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2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (sqrt (- 1.0 k))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (* (* 2.0 PI) n) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (+ (sqrt k) (sqrt 1.0))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 3) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (* (* 2.0 PI) n)) (log1p (* (* 2.0 PI) n)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (log (* (* 2.0 PI) n)) (log (* (* 2.0 PI) n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (pow (* (* 2.0 PI) n) 3) (pow (* (* 2.0 PI) n) 3) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (pow (* (* 2.0 PI) n) 3) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* 2.0 PI) (* n PI) (expm1 (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log1p (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (exp (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (pow (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 3) (pow (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 3) (* (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (pow (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 3) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (* (/ 1.0 (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (/ 1.0 (sqrt k)) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k)) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (- (- (* +nan.0 (pow k 2)) +nan.0) (* +nan.0 k)) (- (- (/ +nan.0 k) (/ +nan.0 (pow k 3))) (/ (/ +nan.0 k) k)) (- (- (/ +nan.0 k) +nan.0) (/ (/ +nan.0 k) k)) (- (+ (fma (* 0.25 (pow k 2)) (* (pow (* (* 2.0 PI) n) 0.5) (* (log (* 2.0 PI)) (log n))) (pow (* (* 2.0 PI) n) 0.5)) (* (* 0.125 (pow k 2)) (+ (* (pow (log (* 2.0 PI)) 2) (pow (* (* 2.0 PI) n) 0.5)) (* (pow (* (* 2.0 PI) n) 0.5) (pow (log n) 2))))) (* (* 0.5 k) (+ (* (log (* 2.0 PI)) (pow (* (* 2.0 PI) n) 0.5)) (* (log n) (pow (* (* 2.0 PI) n) 0.5))))) (pow (pow (* (* 2.0 PI) n) 0.5) (- 1.0 k)) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (- (fma (* (* (pow k 2) (log (* 2.0 PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) +nan.0 (- (fma +nan.0 (* (* (pow k 2) (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5)) (- (fma (* +nan.0 (* (pow k 2) (pow (log n) 2))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (- (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (* +nan.0 (- (* (pow k 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (* k (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))) (* +nan.0 (* (* k (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))))) (* +nan.0 (* (* k (log (* 2.0 PI))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))) (* +nan.0 (* (* (pow k 2) (* (log (* 2.0 PI)) (log n))) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))))) (* +nan.0 (* (* (pow k 2) (pow (log (* 2.0 PI)) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) (- (* +nan.0 (- (/ (pow (pow (* (* 2.0 PI) n) 0.5) (- 1.0 k)) k) (/ (pow (pow (* (* 2.0 PI) n) 0.5) (- 1.0 k)) (pow k 2)))) (/ (* (pow (pow (* (* 2.0 PI) n) 0.5) (- 1.0 k)) +nan.0) (pow k 3))) (- (* +nan.0 (- (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2)) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))))) (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k))) 3.503 * * * [progress]: adding candidates to table 4.080 * * [progress]: iteration 2 / 4 4.080 * * * [progress]: picking best candidate 4.113 * * * * [pick]: Picked # 4.113 * * * [progress]: localizing error 4.131 * * * [progress]: generating rewritten candidates 4.131 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 1 1) 4.135 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1) 4.137 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 2) 4.147 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 2 1) 4.158 * * * [progress]: generating series expansions 4.159 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 1 1) 4.159 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 4.159 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 4.159 * [taylor]: Taking taylor expansion of 1.0 in k 4.159 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 4.159 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.159 * [taylor]: Taking taylor expansion of k in k 4.160 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 4.160 * [taylor]: Taking taylor expansion of 1.0 in k 4.160 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 4.160 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.161 * [taylor]: Taking taylor expansion of k in k 4.172 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 4.172 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 4.172 * [taylor]: Taking taylor expansion of 1.0 in k 4.172 * [taylor]: Taking taylor expansion of (sqrt k) in k 4.172 * [taylor]: Taking taylor expansion of k in k 4.173 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 4.173 * [taylor]: Taking taylor expansion of 1.0 in k 4.173 * [taylor]: Taking taylor expansion of (sqrt k) in k 4.173 * [taylor]: Taking taylor expansion of k in k 4.183 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 4.183 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 4.183 * [taylor]: Taking taylor expansion of 1.0 in k 4.183 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 4.183 * [taylor]: Taking taylor expansion of (/ -1 k) in k 4.184 * [taylor]: Taking taylor expansion of -1 in k 4.184 * [taylor]: Taking taylor expansion of k in k 4.185 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 4.185 * [taylor]: Taking taylor expansion of 1.0 in k 4.185 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 4.185 * [taylor]: Taking taylor expansion of (/ -1 k) in k 4.185 * [taylor]: Taking taylor expansion of -1 in k 4.185 * [taylor]: Taking taylor expansion of k in k 4.197 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1) 4.197 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 4.197 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 4.197 * [taylor]: Taking taylor expansion of 1.0 in k 4.197 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 4.197 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.197 * [taylor]: Taking taylor expansion of k in k 4.198 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 4.198 * [taylor]: Taking taylor expansion of 1.0 in k 4.198 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 4.198 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.198 * [taylor]: Taking taylor expansion of k in k 4.209 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 4.209 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 4.209 * [taylor]: Taking taylor expansion of 1.0 in k 4.209 * [taylor]: Taking taylor expansion of (sqrt k) in k 4.209 * [taylor]: Taking taylor expansion of k in k 4.210 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 4.210 * [taylor]: Taking taylor expansion of 1.0 in k 4.210 * [taylor]: Taking taylor expansion of (sqrt k) in k 4.210 * [taylor]: Taking taylor expansion of k in k 4.224 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 4.224 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 4.224 * [taylor]: Taking taylor expansion of 1.0 in k 4.224 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 4.224 * [taylor]: Taking taylor expansion of (/ -1 k) in k 4.225 * [taylor]: Taking taylor expansion of -1 in k 4.225 * [taylor]: Taking taylor expansion of k in k 4.226 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 4.226 * [taylor]: Taking taylor expansion of 1.0 in k 4.226 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 4.226 * [taylor]: Taking taylor expansion of (/ -1 k) in k 4.226 * [taylor]: Taking taylor expansion of -1 in k 4.226 * [taylor]: Taking taylor expansion of k in k 4.238 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 2) 4.238 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 4.238 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 4.238 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 4.238 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 4.239 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 4.239 * [taylor]: Taking taylor expansion of 0.5 in k 4.239 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.239 * [taylor]: Taking taylor expansion of 1.0 in k 4.239 * [taylor]: Taking taylor expansion of k in k 4.239 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 4.239 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 4.239 * [taylor]: Taking taylor expansion of 2.0 in k 4.239 * [taylor]: Taking taylor expansion of (* n PI) in k 4.239 * [taylor]: Taking taylor expansion of n in k 4.239 * [taylor]: Taking taylor expansion of PI in k 4.240 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 4.240 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 4.240 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 4.240 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 4.240 * [taylor]: Taking taylor expansion of 0.5 in n 4.240 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 4.240 * [taylor]: Taking taylor expansion of 1.0 in n 4.240 * [taylor]: Taking taylor expansion of k in n 4.240 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.240 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.240 * [taylor]: Taking taylor expansion of 2.0 in n 4.240 * [taylor]: Taking taylor expansion of (* n PI) in n 4.240 * [taylor]: Taking taylor expansion of n in n 4.240 * [taylor]: Taking taylor expansion of PI in n 4.245 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 4.245 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 4.245 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 4.245 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 4.245 * [taylor]: Taking taylor expansion of 0.5 in n 4.245 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 4.245 * [taylor]: Taking taylor expansion of 1.0 in n 4.245 * [taylor]: Taking taylor expansion of k in n 4.245 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.245 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.245 * [taylor]: Taking taylor expansion of 2.0 in n 4.246 * [taylor]: Taking taylor expansion of (* n PI) in n 4.246 * [taylor]: Taking taylor expansion of n in n 4.246 * [taylor]: Taking taylor expansion of PI in n 4.251 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 4.251 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 4.251 * [taylor]: Taking taylor expansion of 0.5 in k 4.251 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 4.251 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.251 * [taylor]: Taking taylor expansion of 1.0 in k 4.251 * [taylor]: Taking taylor expansion of k in k 4.251 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 4.251 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 4.251 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 4.251 * [taylor]: Taking taylor expansion of 2.0 in k 4.251 * [taylor]: Taking taylor expansion of PI in k 4.252 * [taylor]: Taking taylor expansion of (log n) in k 4.252 * [taylor]: Taking taylor expansion of n in k 4.261 * [taylor]: Taking taylor expansion of 0 in k 4.277 * [taylor]: Taking taylor expansion of 0 in k 4.298 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 4.298 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 4.298 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 4.298 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 4.298 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 4.298 * [taylor]: Taking taylor expansion of 0.5 in k 4.298 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.298 * [taylor]: Taking taylor expansion of 1.0 in k 4.299 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.299 * [taylor]: Taking taylor expansion of k in k 4.299 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 4.299 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 4.299 * [taylor]: Taking taylor expansion of 2.0 in k 4.299 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.299 * [taylor]: Taking taylor expansion of PI in k 4.299 * [taylor]: Taking taylor expansion of n in k 4.300 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 4.300 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 4.300 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 4.300 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 4.300 * [taylor]: Taking taylor expansion of 0.5 in n 4.300 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.300 * [taylor]: Taking taylor expansion of 1.0 in n 4.300 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.300 * [taylor]: Taking taylor expansion of k in n 4.300 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.300 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.300 * [taylor]: Taking taylor expansion of 2.0 in n 4.300 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.300 * [taylor]: Taking taylor expansion of PI in n 4.300 * [taylor]: Taking taylor expansion of n in n 4.304 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 4.304 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 4.304 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 4.304 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 4.304 * [taylor]: Taking taylor expansion of 0.5 in n 4.304 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.304 * [taylor]: Taking taylor expansion of 1.0 in n 4.304 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.304 * [taylor]: Taking taylor expansion of k in n 4.304 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.304 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.304 * [taylor]: Taking taylor expansion of 2.0 in n 4.304 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.304 * [taylor]: Taking taylor expansion of PI in n 4.304 * [taylor]: Taking taylor expansion of n in n 4.308 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 4.308 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 4.308 * [taylor]: Taking taylor expansion of 0.5 in k 4.308 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 4.308 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 4.308 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 4.308 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 4.308 * [taylor]: Taking taylor expansion of 2.0 in k 4.308 * [taylor]: Taking taylor expansion of PI in k 4.309 * [taylor]: Taking taylor expansion of (log n) in k 4.309 * [taylor]: Taking taylor expansion of n in k 4.309 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.309 * [taylor]: Taking taylor expansion of 1.0 in k 4.309 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.309 * [taylor]: Taking taylor expansion of k in k 4.319 * [taylor]: Taking taylor expansion of 0 in k 4.326 * [taylor]: Taking taylor expansion of 0 in k 4.335 * [taylor]: Taking taylor expansion of 0 in k 4.336 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 4.336 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 4.336 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 4.336 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 4.336 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 4.336 * [taylor]: Taking taylor expansion of 0.5 in k 4.336 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.336 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.336 * [taylor]: Taking taylor expansion of k in k 4.337 * [taylor]: Taking taylor expansion of 1.0 in k 4.337 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 4.337 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 4.337 * [taylor]: Taking taylor expansion of -2.0 in k 4.337 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.337 * [taylor]: Taking taylor expansion of PI in k 4.337 * [taylor]: Taking taylor expansion of n in k 4.338 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 4.338 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 4.338 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 4.338 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 4.338 * [taylor]: Taking taylor expansion of 0.5 in n 4.338 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.338 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.338 * [taylor]: Taking taylor expansion of k in n 4.338 * [taylor]: Taking taylor expansion of 1.0 in n 4.338 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.338 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.338 * [taylor]: Taking taylor expansion of -2.0 in n 4.338 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.338 * [taylor]: Taking taylor expansion of PI in n 4.338 * [taylor]: Taking taylor expansion of n in n 4.341 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 4.342 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 4.342 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 4.342 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 4.342 * [taylor]: Taking taylor expansion of 0.5 in n 4.342 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.342 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.342 * [taylor]: Taking taylor expansion of k in n 4.342 * [taylor]: Taking taylor expansion of 1.0 in n 4.342 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.342 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.342 * [taylor]: Taking taylor expansion of -2.0 in n 4.342 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.342 * [taylor]: Taking taylor expansion of PI in n 4.342 * [taylor]: Taking taylor expansion of n in n 4.345 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 4.345 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 4.345 * [taylor]: Taking taylor expansion of 0.5 in k 4.346 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 4.346 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.346 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.346 * [taylor]: Taking taylor expansion of k in k 4.346 * [taylor]: Taking taylor expansion of 1.0 in k 4.346 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 4.346 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 4.346 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 4.346 * [taylor]: Taking taylor expansion of -2.0 in k 4.346 * [taylor]: Taking taylor expansion of PI in k 4.347 * [taylor]: Taking taylor expansion of (log n) in k 4.347 * [taylor]: Taking taylor expansion of n in k 4.356 * [taylor]: Taking taylor expansion of 0 in k 4.363 * [taylor]: Taking taylor expansion of 0 in k 4.371 * [taylor]: Taking taylor expansion of 0 in k 4.372 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 2 1) 4.373 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 4.373 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.373 * [taylor]: Taking taylor expansion of 2.0 in n 4.373 * [taylor]: Taking taylor expansion of (* n PI) in n 4.373 * [taylor]: Taking taylor expansion of n in n 4.373 * [taylor]: Taking taylor expansion of PI in n 4.373 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.373 * [taylor]: Taking taylor expansion of 2.0 in n 4.373 * [taylor]: Taking taylor expansion of (* n PI) in n 4.373 * [taylor]: Taking taylor expansion of n in n 4.373 * [taylor]: Taking taylor expansion of PI in n 4.388 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 4.388 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.388 * [taylor]: Taking taylor expansion of 2.0 in n 4.388 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.388 * [taylor]: Taking taylor expansion of PI in n 4.388 * [taylor]: Taking taylor expansion of n in n 4.389 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.389 * [taylor]: Taking taylor expansion of 2.0 in n 4.389 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.389 * [taylor]: Taking taylor expansion of PI in n 4.389 * [taylor]: Taking taylor expansion of n in n 4.397 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 4.398 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.398 * [taylor]: Taking taylor expansion of -2.0 in n 4.398 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.398 * [taylor]: Taking taylor expansion of PI in n 4.398 * [taylor]: Taking taylor expansion of n in n 4.398 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.398 * [taylor]: Taking taylor expansion of -2.0 in n 4.398 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.398 * [taylor]: Taking taylor expansion of PI in n 4.398 * [taylor]: Taking taylor expansion of n in n 4.407 * * * [progress]: simplifying candidates 4.409 * [simplify]: Simplifying using # : (expm1 (/ 1.0 (sqrt k))) (log1p (/ 1.0 (sqrt k))) (- (log 1.0) (log (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt 1)) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt 1)) (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 1) (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt 1)) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 1) (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (expm1 (/ 1.0 (sqrt k))) (log1p (/ 1.0 (sqrt k))) (- (log 1.0) (log (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt 1)) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt 1)) (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 1) (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt 1)) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 1) (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (* (* 2.0 PI) n)) (log1p (* (* 2.0 PI) n)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) 4.416 * * [simplify]: iteration 0 : 240 enodes (cost 1698 ) 4.463 * * [simplify]: iteration 1 : 589 enodes (cost 1576 ) 4.589 * * [simplify]: iteration 2 : 2011 enodes (cost 1464 ) 5.084 * * [simplify]: iteration done : 5000 enodes (cost 1454 ) 5.085 * [simplify]: Simplified to: (expm1 (/ 1.0 (sqrt k))) (log1p (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (pow (/ 1.0 (sqrt k)) 3) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (pow (/ 1.0 (sqrt k)) 3) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (fabs (cbrt k))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (fabs (cbrt k))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 1) (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (fabs (cbrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 1) (/ 1.0 (sqrt (sqrt k))) 1.0 (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (expm1 (/ 1.0 (sqrt k))) (log1p (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (pow (/ 1.0 (sqrt k)) 3) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (pow (/ 1.0 (sqrt k)) 3) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (fabs (cbrt k))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (fabs (cbrt k))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 1) (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (fabs (cbrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 1) (/ 1.0 (sqrt (sqrt k))) 1.0 (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* 2.0 (* n PI)) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (sqrt (- 1.0 k))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (* (* 2.0 PI) n) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* 2.0 (* n PI)) (+ (sqrt 1.0) (sqrt k))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 3) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (* (* 2.0 PI) n)) (log1p (* (* 2.0 PI) n)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (log (* (* 2.0 PI) n)) (log (* (* 2.0 PI) n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (pow (* (* 2.0 PI) n) 3) (pow (* (* 2.0 PI) n) 3) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (pow (* (* 2.0 PI) n) 3) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* 2.0 PI) (* n PI) (- (fma +nan.0 (pow k 2) (- +nan.0)) (* +nan.0 k)) (- (- (/ +nan.0 k) (/ +nan.0 (pow k 3))) (/ (/ +nan.0 k) k)) (- (- (/ +nan.0 k) +nan.0) (/ (/ +nan.0 k) k)) (- (fma +nan.0 (pow k 2) (- +nan.0)) (* +nan.0 k)) (- (- (/ +nan.0 k) (/ +nan.0 (pow k 3))) (/ (/ +nan.0 k) k)) (- (- (/ +nan.0 k) +nan.0) (/ (/ +nan.0 k) k)) (+ (* (* 0.125 (pow k 2)) (+ (* (pow (* (* 2.0 PI) n) 0.5) (pow (log (* 2.0 PI)) 2)) (* (pow (log n) 2) (pow (* (* 2.0 PI) n) 0.5)))) (- (fma (* 0.25 (pow k 2)) (* (log n) (* (pow (* (* 2.0 PI) n) 0.5) (log (* 2.0 PI)))) (pow (* (* 2.0 PI) n) 0.5)) (* (* 0.5 k) (+ (* (pow (* (* 2.0 PI) n) 0.5) (log (* 2.0 PI))) (* (pow (* (* 2.0 PI) n) 0.5) (log n)))))) (pow (pow (* (* 2.0 PI) n) 0.5) (- 1.0 k)) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (* (* 2.0 PI) n) 5.086 * * * [progress]: adding candidates to table 5.564 * * [progress]: iteration 3 / 4 5.565 * * * [progress]: picking best candidate 5.604 * * * * [pick]: Picked # 5.604 * * * [progress]: localizing error 5.623 * * * [progress]: generating rewritten candidates 5.623 * * * * [progress]: [ 1 / 4 ] rewriting at (2 1) 5.641 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1) 5.645 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2) 5.655 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1) 5.698 * * * [progress]: generating series expansions 5.698 * * * * [progress]: [ 1 / 4 ] generating series at (2 1) 5.698 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 5.698 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 5.698 * [taylor]: Taking taylor expansion of 1.0 in k 5.698 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 5.698 * [taylor]: Taking taylor expansion of (/ 1 k) in k 5.698 * [taylor]: Taking taylor expansion of k in k 5.700 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 5.700 * [taylor]: Taking taylor expansion of 1.0 in k 5.700 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 5.700 * [taylor]: Taking taylor expansion of (/ 1 k) in k 5.700 * [taylor]: Taking taylor expansion of k in k 5.711 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 5.711 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 5.711 * [taylor]: Taking taylor expansion of 1.0 in k 5.712 * [taylor]: Taking taylor expansion of (sqrt k) in k 5.712 * [taylor]: Taking taylor expansion of k in k 5.713 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 5.713 * [taylor]: Taking taylor expansion of 1.0 in k 5.713 * [taylor]: Taking taylor expansion of (sqrt k) in k 5.713 * [taylor]: Taking taylor expansion of k in k 5.723 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 5.723 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 5.723 * [taylor]: Taking taylor expansion of 1.0 in k 5.723 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 5.723 * [taylor]: Taking taylor expansion of (/ -1 k) in k 5.723 * [taylor]: Taking taylor expansion of -1 in k 5.723 * [taylor]: Taking taylor expansion of k in k 5.725 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 5.725 * [taylor]: Taking taylor expansion of 1.0 in k 5.725 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 5.725 * [taylor]: Taking taylor expansion of (/ -1 k) in k 5.725 * [taylor]: Taking taylor expansion of -1 in k 5.725 * [taylor]: Taking taylor expansion of k in k 5.736 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1) 5.736 * [approximate]: Taking taylor expansion of (* 1.0 (pow (/ 1 k) 1/4)) in (k) around 0 5.736 * [taylor]: Taking taylor expansion of (* 1.0 (pow (/ 1 k) 1/4)) in k 5.736 * [taylor]: Taking taylor expansion of 1.0 in k 5.736 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k 5.736 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k 5.736 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k 5.736 * [taylor]: Taking taylor expansion of 1/4 in k 5.736 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 5.736 * [taylor]: Taking taylor expansion of (/ 1 k) in k 5.736 * [taylor]: Taking taylor expansion of k in k 5.737 * [taylor]: Taking taylor expansion of (* 1.0 (pow (/ 1 k) 1/4)) in k 5.737 * [taylor]: Taking taylor expansion of 1.0 in k 5.737 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k 5.737 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k 5.737 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k 5.737 * [taylor]: Taking taylor expansion of 1/4 in k 5.737 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 5.737 * [taylor]: Taking taylor expansion of (/ 1 k) in k 5.737 * [taylor]: Taking taylor expansion of k in k 5.798 * [approximate]: Taking taylor expansion of (* 1.0 (pow k 1/4)) in (k) around 0 5.798 * [taylor]: Taking taylor expansion of (* 1.0 (pow k 1/4)) in k 5.798 * [taylor]: Taking taylor expansion of 1.0 in k 5.798 * [taylor]: Taking taylor expansion of (pow k 1/4) in k 5.798 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k 5.798 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k 5.798 * [taylor]: Taking taylor expansion of 1/4 in k 5.798 * [taylor]: Taking taylor expansion of (log k) in k 5.798 * [taylor]: Taking taylor expansion of k in k 5.799 * [taylor]: Taking taylor expansion of (* 1.0 (pow k 1/4)) in k 5.799 * [taylor]: Taking taylor expansion of 1.0 in k 5.799 * [taylor]: Taking taylor expansion of (pow k 1/4) in k 5.799 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k 5.799 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k 5.799 * [taylor]: Taking taylor expansion of 1/4 in k 5.799 * [taylor]: Taking taylor expansion of (log k) in k 5.799 * [taylor]: Taking taylor expansion of k in k 5.856 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) in (k) around 0 5.856 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) in k 5.856 * [taylor]: Taking taylor expansion of 1.0 in k 5.856 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in k 5.856 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 5.856 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 5.856 * [taylor]: Taking taylor expansion of (/ -1 k) in k 5.856 * [taylor]: Taking taylor expansion of -1 in k 5.856 * [taylor]: Taking taylor expansion of k in k 5.863 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) in k 5.863 * [taylor]: Taking taylor expansion of 1.0 in k 5.863 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in k 5.863 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 5.863 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 5.863 * [taylor]: Taking taylor expansion of (/ -1 k) in k 5.863 * [taylor]: Taking taylor expansion of -1 in k 5.863 * [taylor]: Taking taylor expansion of k in k 5.900 * * * * [progress]: [ 3 / 4 ] generating series at (2 2) 5.901 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 5.901 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 5.901 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 5.901 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 5.901 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 5.901 * [taylor]: Taking taylor expansion of 0.5 in k 5.901 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 5.901 * [taylor]: Taking taylor expansion of 1.0 in k 5.901 * [taylor]: Taking taylor expansion of k in k 5.901 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 5.901 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 5.901 * [taylor]: Taking taylor expansion of 2.0 in k 5.901 * [taylor]: Taking taylor expansion of (* n PI) in k 5.901 * [taylor]: Taking taylor expansion of n in k 5.901 * [taylor]: Taking taylor expansion of PI in k 5.902 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 5.902 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 5.902 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 5.902 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 5.902 * [taylor]: Taking taylor expansion of 0.5 in n 5.902 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 5.902 * [taylor]: Taking taylor expansion of 1.0 in n 5.902 * [taylor]: Taking taylor expansion of k in n 5.902 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 5.902 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 5.902 * [taylor]: Taking taylor expansion of 2.0 in n 5.902 * [taylor]: Taking taylor expansion of (* n PI) in n 5.902 * [taylor]: Taking taylor expansion of n in n 5.902 * [taylor]: Taking taylor expansion of PI in n 5.907 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 5.907 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 5.907 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 5.907 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 5.907 * [taylor]: Taking taylor expansion of 0.5 in n 5.907 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 5.907 * [taylor]: Taking taylor expansion of 1.0 in n 5.907 * [taylor]: Taking taylor expansion of k in n 5.907 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 5.907 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 5.907 * [taylor]: Taking taylor expansion of 2.0 in n 5.907 * [taylor]: Taking taylor expansion of (* n PI) in n 5.907 * [taylor]: Taking taylor expansion of n in n 5.908 * [taylor]: Taking taylor expansion of PI in n 5.913 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 5.913 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 5.913 * [taylor]: Taking taylor expansion of 0.5 in k 5.913 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 5.913 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 5.913 * [taylor]: Taking taylor expansion of 1.0 in k 5.913 * [taylor]: Taking taylor expansion of k in k 5.913 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 5.913 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 5.913 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 5.913 * [taylor]: Taking taylor expansion of 2.0 in k 5.913 * [taylor]: Taking taylor expansion of PI in k 5.914 * [taylor]: Taking taylor expansion of (log n) in k 5.914 * [taylor]: Taking taylor expansion of n in k 5.924 * [taylor]: Taking taylor expansion of 0 in k 5.944 * [taylor]: Taking taylor expansion of 0 in k 5.964 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 5.964 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 5.964 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 5.964 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 5.964 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 5.964 * [taylor]: Taking taylor expansion of 0.5 in k 5.964 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 5.964 * [taylor]: Taking taylor expansion of 1.0 in k 5.964 * [taylor]: Taking taylor expansion of (/ 1 k) in k 5.964 * [taylor]: Taking taylor expansion of k in k 5.964 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 5.964 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 5.964 * [taylor]: Taking taylor expansion of 2.0 in k 5.964 * [taylor]: Taking taylor expansion of (/ PI n) in k 5.964 * [taylor]: Taking taylor expansion of PI in k 5.964 * [taylor]: Taking taylor expansion of n in k 5.965 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 5.965 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 5.965 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 5.965 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 5.965 * [taylor]: Taking taylor expansion of 0.5 in n 5.965 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 5.965 * [taylor]: Taking taylor expansion of 1.0 in n 5.965 * [taylor]: Taking taylor expansion of (/ 1 k) in n 5.965 * [taylor]: Taking taylor expansion of k in n 5.965 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 5.965 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 5.965 * [taylor]: Taking taylor expansion of 2.0 in n 5.965 * [taylor]: Taking taylor expansion of (/ PI n) in n 5.965 * [taylor]: Taking taylor expansion of PI in n 5.965 * [taylor]: Taking taylor expansion of n in n 5.969 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 5.969 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 5.969 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 5.969 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 5.969 * [taylor]: Taking taylor expansion of 0.5 in n 5.969 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 5.969 * [taylor]: Taking taylor expansion of 1.0 in n 5.969 * [taylor]: Taking taylor expansion of (/ 1 k) in n 5.969 * [taylor]: Taking taylor expansion of k in n 5.969 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 5.969 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 5.969 * [taylor]: Taking taylor expansion of 2.0 in n 5.969 * [taylor]: Taking taylor expansion of (/ PI n) in n 5.969 * [taylor]: Taking taylor expansion of PI in n 5.969 * [taylor]: Taking taylor expansion of n in n 5.973 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 5.973 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 5.973 * [taylor]: Taking taylor expansion of 0.5 in k 5.973 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 5.973 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 5.973 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 5.973 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 5.973 * [taylor]: Taking taylor expansion of 2.0 in k 5.973 * [taylor]: Taking taylor expansion of PI in k 5.974 * [taylor]: Taking taylor expansion of (log n) in k 5.974 * [taylor]: Taking taylor expansion of n in k 5.974 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 5.974 * [taylor]: Taking taylor expansion of 1.0 in k 5.974 * [taylor]: Taking taylor expansion of (/ 1 k) in k 5.974 * [taylor]: Taking taylor expansion of k in k 5.984 * [taylor]: Taking taylor expansion of 0 in k 5.991 * [taylor]: Taking taylor expansion of 0 in k 6.000 * [taylor]: Taking taylor expansion of 0 in k 6.001 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 6.002 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 6.002 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 6.002 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 6.002 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 6.002 * [taylor]: Taking taylor expansion of 0.5 in k 6.002 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 6.002 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.002 * [taylor]: Taking taylor expansion of k in k 6.002 * [taylor]: Taking taylor expansion of 1.0 in k 6.002 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 6.002 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 6.002 * [taylor]: Taking taylor expansion of -2.0 in k 6.002 * [taylor]: Taking taylor expansion of (/ PI n) in k 6.002 * [taylor]: Taking taylor expansion of PI in k 6.002 * [taylor]: Taking taylor expansion of n in k 6.003 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 6.003 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 6.003 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 6.003 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 6.003 * [taylor]: Taking taylor expansion of 0.5 in n 6.003 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 6.003 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.003 * [taylor]: Taking taylor expansion of k in n 6.003 * [taylor]: Taking taylor expansion of 1.0 in n 6.003 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 6.003 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 6.003 * [taylor]: Taking taylor expansion of -2.0 in n 6.003 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.003 * [taylor]: Taking taylor expansion of PI in n 6.003 * [taylor]: Taking taylor expansion of n in n 6.007 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 6.007 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 6.007 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 6.007 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 6.007 * [taylor]: Taking taylor expansion of 0.5 in n 6.007 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 6.007 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.007 * [taylor]: Taking taylor expansion of k in n 6.007 * [taylor]: Taking taylor expansion of 1.0 in n 6.007 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 6.007 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 6.007 * [taylor]: Taking taylor expansion of -2.0 in n 6.007 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.007 * [taylor]: Taking taylor expansion of PI in n 6.007 * [taylor]: Taking taylor expansion of n in n 6.011 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 6.011 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 6.011 * [taylor]: Taking taylor expansion of 0.5 in k 6.011 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 6.011 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 6.011 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.011 * [taylor]: Taking taylor expansion of k in k 6.012 * [taylor]: Taking taylor expansion of 1.0 in k 6.012 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 6.012 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 6.012 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 6.012 * [taylor]: Taking taylor expansion of -2.0 in k 6.012 * [taylor]: Taking taylor expansion of PI in k 6.018 * [taylor]: Taking taylor expansion of (log n) in k 6.018 * [taylor]: Taking taylor expansion of n in k 6.027 * [taylor]: Taking taylor expansion of 0 in k 6.033 * [taylor]: Taking taylor expansion of 0 in k 6.042 * [taylor]: Taking taylor expansion of 0 in k 6.043 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1) 6.044 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 6.044 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 6.044 * [taylor]: Taking taylor expansion of 2.0 in n 6.044 * [taylor]: Taking taylor expansion of (* n PI) in n 6.044 * [taylor]: Taking taylor expansion of n in n 6.044 * [taylor]: Taking taylor expansion of PI in n 6.044 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 6.044 * [taylor]: Taking taylor expansion of 2.0 in n 6.044 * [taylor]: Taking taylor expansion of (* n PI) in n 6.044 * [taylor]: Taking taylor expansion of n in n 6.044 * [taylor]: Taking taylor expansion of PI in n 6.056 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 6.056 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 6.056 * [taylor]: Taking taylor expansion of 2.0 in n 6.056 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.056 * [taylor]: Taking taylor expansion of PI in n 6.056 * [taylor]: Taking taylor expansion of n in n 6.056 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 6.056 * [taylor]: Taking taylor expansion of 2.0 in n 6.056 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.056 * [taylor]: Taking taylor expansion of PI in n 6.056 * [taylor]: Taking taylor expansion of n in n 6.065 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 6.065 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 6.065 * [taylor]: Taking taylor expansion of -2.0 in n 6.065 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.065 * [taylor]: Taking taylor expansion of PI in n 6.065 * [taylor]: Taking taylor expansion of n in n 6.065 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 6.065 * [taylor]: Taking taylor expansion of -2.0 in n 6.066 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.066 * [taylor]: Taking taylor expansion of PI in n 6.066 * [taylor]: Taking taylor expansion of n in n 6.074 * * * [progress]: simplifying candidates 6.082 * [simplify]: Simplifying using # : (expm1 (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (log1p (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (- (- (log 1.0) (log (sqrt (sqrt k)))) (log (sqrt (sqrt k)))) (- (log (/ 1.0 (sqrt (sqrt k)))) (log (sqrt (sqrt k)))) (log (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (exp (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (/ (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k)))) (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k)))) (/ (* (* (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt k)))) (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k)))) (* (cbrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (cbrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))))) (cbrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (* (* (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (sqrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (sqrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (- (/ 1.0 (sqrt (sqrt k)))) (- (sqrt (sqrt k))) (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k)))) (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (sqrt 1))) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt 1)) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) 1) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt 1))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt 1)) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) 1) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt 1))) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt 1)) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) 1) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt (cbrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (sqrt 1))) (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt 1)) (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) 1) (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (cbrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (cbrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt (cbrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (sqrt 1))) (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt 1)) (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) 1) (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt 1))) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt 1)) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) 1) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt 1))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt 1))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (cbrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt 1))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt (cbrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt 1))) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt 1))) (sqrt (sqrt 1))) (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt 1))) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt 1))) (sqrt 1)) (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt 1))) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt 1))) 1) (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) 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(+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) 6.118 * * [simplify]: iteration 0 : 566 enodes (cost 9021 ) 6.228 * * [simplify]: iteration 1 : 1367 enodes (cost 7999 ) 6.511 * * [simplify]: iteration 2 : 4331 enodes (cost 7284 ) 7.396 * * [simplify]: iteration done : 5000 enodes (cost 7284 ) 7.399 * [simplify]: Simplified to: (expm1 (/ 1.0 (sqrt k))) (log1p (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (pow (/ 1.0 (sqrt k)) 3) (pow (/ 1.0 (sqrt k)) 3) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt 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2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* 2.0 (* n PI)) (sqrt (- 1.0 k))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (* (* 2.0 PI) n) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* 2.0 (* n PI)) (+ (sqrt k) (sqrt 1.0))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 3) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (* (* 2.0 PI) n)) (log1p (* (* 2.0 PI) n)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (log (* (* 2.0 PI) n)) (log (* (* 2.0 PI) n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (pow (* (* 2.0 PI) n) 3) (pow (* (* 2.0 PI) n) 3) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (pow (* (* 2.0 PI) n) 3) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* 2.0 PI) (* PI n) (- (fma +nan.0 k (- (- (* +nan.0 (pow k 2)) +nan.0)))) (+ (/ (- +nan.0) (pow k 2)) (- (/ +nan.0 k) (/ +nan.0 (pow k 3)))) (+ (/ (- +nan.0) (pow k 2)) (- (/ +nan.0 k) +nan.0)) (* 1.0 (pow (/ 1 k) 1/4)) (* 1.0 (pow (/ 1 k) 1/4)) (+ (- (* 1.0 (sqrt +nan.0)) (/ +nan.0 (* (sqrt +nan.0) (pow k 2)))) (- (/ +nan.0 (* (sqrt +nan.0) k)) (/ +nan.0 (* (pow (sqrt +nan.0) 3) (pow k 2))))) (+ (* (* 0.125 (pow k 2)) (+ (* (pow (* (* 2.0 PI) n) 0.5) (pow (log (* 2.0 PI)) 2)) (* (pow (log n) 2) (pow (* (* 2.0 PI) n) 0.5)))) (- (fma (* (pow k 2) (* (log n) (* (log (* 2.0 PI)) (pow (* (* 2.0 PI) n) 0.5)))) 0.25 (pow (* (* 2.0 PI) n) 0.5)) (* 0.5 (* k (+ (* (log (* 2.0 PI)) (pow (* (* 2.0 PI) n) 0.5)) (* (pow (* (* 2.0 PI) n) 0.5) (log n))))))) (pow (pow (* (* 2.0 PI) n) 0.5) (- 1.0 k)) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (* (* 2.0 PI) n) 7.403 * * * [progress]: adding candidates to table 8.315 * * [progress]: iteration 4 / 4 8.315 * * * [progress]: picking best candidate 8.357 * * * * [pick]: Picked # 8.358 * * * [progress]: localizing error 8.376 * * * [progress]: generating rewritten candidates 8.376 * * * * [progress]: [ 1 / 4 ] rewriting at (2 1 1) 8.437 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1) 8.460 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2) 8.470 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1 1) 8.497 * * * [progress]: generating series expansions 8.497 * * * * [progress]: [ 1 / 4 ] generating series at (2 1 1) 8.498 * [approximate]: Taking taylor expansion of (* 1.0 (pow (/ 1 k) 1/4)) in (k) around 0 8.498 * [taylor]: Taking taylor expansion of (* 1.0 (pow (/ 1 k) 1/4)) in k 8.498 * [taylor]: Taking taylor expansion of 1.0 in k 8.498 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k 8.498 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k 8.498 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k 8.498 * [taylor]: Taking taylor expansion of 1/4 in k 8.498 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 8.498 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.498 * [taylor]: Taking taylor expansion of k in k 8.499 * [taylor]: Taking taylor expansion of (* 1.0 (pow (/ 1 k) 1/4)) in k 8.499 * [taylor]: Taking taylor expansion of 1.0 in k 8.499 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k 8.499 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k 8.499 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k 8.499 * [taylor]: Taking taylor expansion of 1/4 in k 8.499 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 8.499 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.499 * [taylor]: Taking taylor expansion of k in k 8.557 * [approximate]: Taking taylor expansion of (* 1.0 (pow k 1/4)) in (k) around 0 8.557 * [taylor]: Taking taylor expansion of (* 1.0 (pow k 1/4)) in k 8.557 * [taylor]: Taking taylor expansion of 1.0 in k 8.557 * [taylor]: Taking taylor expansion of (pow k 1/4) in k 8.557 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k 8.557 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k 8.557 * [taylor]: Taking taylor expansion of 1/4 in k 8.557 * [taylor]: Taking taylor expansion of (log k) in k 8.557 * [taylor]: Taking taylor expansion of k in k 8.557 * [taylor]: Taking taylor expansion of (* 1.0 (pow k 1/4)) in k 8.557 * [taylor]: Taking taylor expansion of 1.0 in k 8.557 * [taylor]: Taking taylor expansion of (pow k 1/4) in k 8.558 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k 8.558 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k 8.558 * [taylor]: Taking taylor expansion of 1/4 in k 8.558 * [taylor]: Taking taylor expansion of (log k) in k 8.558 * [taylor]: Taking taylor expansion of k in k 8.616 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) in (k) around 0 8.617 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) in k 8.617 * [taylor]: Taking taylor expansion of 1.0 in k 8.617 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in k 8.617 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 8.617 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 8.617 * [taylor]: Taking taylor expansion of (/ -1 k) in k 8.617 * [taylor]: Taking taylor expansion of -1 in k 8.617 * [taylor]: Taking taylor expansion of k in k 8.623 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) in k 8.623 * [taylor]: Taking taylor expansion of 1.0 in k 8.623 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in k 8.623 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 8.623 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 8.623 * [taylor]: Taking taylor expansion of (/ -1 k) in k 8.623 * [taylor]: Taking taylor expansion of -1 in k 8.623 * [taylor]: Taking taylor expansion of k in k 8.666 * * * * [progress]: [ 2 / 4 ] generating series at (2 1) 8.666 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 8.666 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 8.666 * [taylor]: Taking taylor expansion of 1.0 in k 8.666 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 8.666 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.666 * [taylor]: Taking taylor expansion of k in k 8.668 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 8.668 * [taylor]: Taking taylor expansion of 1.0 in k 8.668 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 8.668 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.668 * [taylor]: Taking taylor expansion of k in k 8.679 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 8.679 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 8.679 * [taylor]: Taking taylor expansion of 1.0 in k 8.679 * [taylor]: Taking taylor expansion of (sqrt k) in k 8.679 * [taylor]: Taking taylor expansion of k in k 8.680 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 8.680 * [taylor]: Taking taylor expansion of 1.0 in k 8.680 * [taylor]: Taking taylor expansion of (sqrt k) in k 8.680 * [taylor]: Taking taylor expansion of k in k 8.691 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 8.691 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 8.691 * [taylor]: Taking taylor expansion of 1.0 in k 8.691 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 8.691 * [taylor]: Taking taylor expansion of (/ -1 k) in k 8.691 * [taylor]: Taking taylor expansion of -1 in k 8.691 * [taylor]: Taking taylor expansion of k in k 8.692 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 8.692 * [taylor]: Taking taylor expansion of 1.0 in k 8.692 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 8.692 * [taylor]: Taking taylor expansion of (/ -1 k) in k 8.692 * [taylor]: Taking taylor expansion of -1 in k 8.693 * [taylor]: Taking taylor expansion of k in k 8.704 * * * * [progress]: [ 3 / 4 ] generating series at (2 2) 8.705 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 8.705 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 8.705 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 8.705 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 8.705 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 8.705 * [taylor]: Taking taylor expansion of 0.5 in k 8.705 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 8.705 * [taylor]: Taking taylor expansion of 1.0 in k 8.705 * [taylor]: Taking taylor expansion of k in k 8.705 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 8.705 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 8.705 * [taylor]: Taking taylor expansion of 2.0 in k 8.705 * [taylor]: Taking taylor expansion of (* n PI) in k 8.705 * [taylor]: Taking taylor expansion of n in k 8.705 * [taylor]: Taking taylor expansion of PI in k 8.706 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 8.706 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 8.706 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 8.706 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 8.706 * [taylor]: Taking taylor expansion of 0.5 in n 8.706 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 8.706 * [taylor]: Taking taylor expansion of 1.0 in n 8.706 * [taylor]: Taking taylor expansion of k in n 8.706 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 8.706 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 8.706 * [taylor]: Taking taylor expansion of 2.0 in n 8.706 * [taylor]: Taking taylor expansion of (* n PI) in n 8.706 * [taylor]: Taking taylor expansion of n in n 8.706 * [taylor]: Taking taylor expansion of PI in n 8.711 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 8.711 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 8.712 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 8.712 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 8.712 * [taylor]: Taking taylor expansion of 0.5 in n 8.712 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 8.712 * [taylor]: Taking taylor expansion of 1.0 in n 8.712 * [taylor]: Taking taylor expansion of k in n 8.712 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 8.712 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 8.712 * [taylor]: Taking taylor expansion of 2.0 in n 8.712 * [taylor]: Taking taylor expansion of (* n PI) in n 8.712 * [taylor]: Taking taylor expansion of n in n 8.712 * [taylor]: Taking taylor expansion of PI in n 8.717 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 8.717 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 8.717 * [taylor]: Taking taylor expansion of 0.5 in k 8.717 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 8.717 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 8.717 * [taylor]: Taking taylor expansion of 1.0 in k 8.717 * [taylor]: Taking taylor expansion of k in k 8.717 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 8.717 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 8.717 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 8.717 * [taylor]: Taking taylor expansion of 2.0 in k 8.717 * [taylor]: Taking taylor expansion of PI in k 8.718 * [taylor]: Taking taylor expansion of (log n) in k 8.718 * [taylor]: Taking taylor expansion of n in k 8.734 * [taylor]: Taking taylor expansion of 0 in k 8.750 * [taylor]: Taking taylor expansion of 0 in k 8.769 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 8.769 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 8.769 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 8.769 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 8.769 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 8.769 * [taylor]: Taking taylor expansion of 0.5 in k 8.769 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 8.769 * [taylor]: Taking taylor expansion of 1.0 in k 8.769 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.769 * [taylor]: Taking taylor expansion of k in k 8.770 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 8.770 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 8.770 * [taylor]: Taking taylor expansion of 2.0 in k 8.770 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.770 * [taylor]: Taking taylor expansion of PI in k 8.770 * [taylor]: Taking taylor expansion of n in k 8.771 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 8.771 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 8.771 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 8.771 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 8.771 * [taylor]: Taking taylor expansion of 0.5 in n 8.771 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 8.771 * [taylor]: Taking taylor expansion of 1.0 in n 8.771 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.771 * [taylor]: Taking taylor expansion of k in n 8.771 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 8.771 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 8.771 * [taylor]: Taking taylor expansion of 2.0 in n 8.771 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.771 * [taylor]: Taking taylor expansion of PI in n 8.771 * [taylor]: Taking taylor expansion of n in n 8.775 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 8.775 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 8.775 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 8.775 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 8.775 * [taylor]: Taking taylor expansion of 0.5 in n 8.775 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 8.775 * [taylor]: Taking taylor expansion of 1.0 in n 8.775 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.775 * [taylor]: Taking taylor expansion of k in n 8.775 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 8.775 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 8.775 * [taylor]: Taking taylor expansion of 2.0 in n 8.775 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.775 * [taylor]: Taking taylor expansion of PI in n 8.775 * [taylor]: Taking taylor expansion of n in n 8.779 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 8.779 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 8.779 * [taylor]: Taking taylor expansion of 0.5 in k 8.779 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 8.779 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 8.779 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 8.779 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 8.779 * [taylor]: Taking taylor expansion of 2.0 in k 8.779 * [taylor]: Taking taylor expansion of PI in k 8.780 * [taylor]: Taking taylor expansion of (log n) in k 8.780 * [taylor]: Taking taylor expansion of n in k 8.780 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 8.780 * [taylor]: Taking taylor expansion of 1.0 in k 8.780 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.780 * [taylor]: Taking taylor expansion of k in k 8.790 * [taylor]: Taking taylor expansion of 0 in k 8.797 * [taylor]: Taking taylor expansion of 0 in k 8.807 * [taylor]: Taking taylor expansion of 0 in k 8.808 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 8.808 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 8.808 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 8.808 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 8.808 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 8.808 * [taylor]: Taking taylor expansion of 0.5 in k 8.808 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 8.808 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.808 * [taylor]: Taking taylor expansion of k in k 8.809 * [taylor]: Taking taylor expansion of 1.0 in k 8.809 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 8.809 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 8.809 * [taylor]: Taking taylor expansion of -2.0 in k 8.809 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.809 * [taylor]: Taking taylor expansion of PI in k 8.809 * [taylor]: Taking taylor expansion of n in k 8.809 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 8.810 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 8.810 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 8.810 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 8.810 * [taylor]: Taking taylor expansion of 0.5 in n 8.810 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 8.810 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.810 * [taylor]: Taking taylor expansion of k in n 8.810 * [taylor]: Taking taylor expansion of 1.0 in n 8.810 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 8.810 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 8.810 * [taylor]: Taking taylor expansion of -2.0 in n 8.810 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.810 * [taylor]: Taking taylor expansion of PI in n 8.810 * [taylor]: Taking taylor expansion of n in n 8.813 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 8.813 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 8.814 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 8.814 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 8.814 * [taylor]: Taking taylor expansion of 0.5 in n 8.814 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 8.814 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.814 * [taylor]: Taking taylor expansion of k in n 8.814 * [taylor]: Taking taylor expansion of 1.0 in n 8.814 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 8.814 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 8.814 * [taylor]: Taking taylor expansion of -2.0 in n 8.814 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.814 * [taylor]: Taking taylor expansion of PI in n 8.814 * [taylor]: Taking taylor expansion of n in n 8.824 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 8.824 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 8.824 * [taylor]: Taking taylor expansion of 0.5 in k 8.824 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 8.824 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 8.824 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.824 * [taylor]: Taking taylor expansion of k in k 8.824 * [taylor]: Taking taylor expansion of 1.0 in k 8.824 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 8.824 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 8.824 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 8.824 * [taylor]: Taking taylor expansion of -2.0 in k 8.824 * [taylor]: Taking taylor expansion of PI in k 8.825 * [taylor]: Taking taylor expansion of (log n) in k 8.825 * [taylor]: Taking taylor expansion of n in k 8.835 * [taylor]: Taking taylor expansion of 0 in k 8.842 * [taylor]: Taking taylor expansion of 0 in k 8.851 * [taylor]: Taking taylor expansion of 0 in k 8.852 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1 1) 8.852 * [approximate]: Taking taylor expansion of (pow (/ 1 k) 1/8) in (k) around 0 8.852 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/8) in k 8.852 * [taylor]: Taking taylor expansion of (exp (* 1/8 (log (/ 1 k)))) in k 8.852 * [taylor]: Taking taylor expansion of (* 1/8 (log (/ 1 k))) in k 8.852 * [taylor]: Taking taylor expansion of 1/8 in k 8.852 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 8.852 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.852 * [taylor]: Taking taylor expansion of k in k 8.853 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/8) in k 8.853 * [taylor]: Taking taylor expansion of (exp (* 1/8 (log (/ 1 k)))) in k 8.853 * [taylor]: Taking taylor expansion of (* 1/8 (log (/ 1 k))) in k 8.853 * [taylor]: Taking taylor expansion of 1/8 in k 8.853 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 8.853 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.853 * [taylor]: Taking taylor expansion of k in k 8.912 * [approximate]: Taking taylor expansion of (pow k 1/8) in (k) around 0 8.912 * [taylor]: Taking taylor expansion of (pow k 1/8) in k 8.912 * [taylor]: Taking taylor expansion of (exp (* 1/8 (log k))) in k 8.912 * [taylor]: Taking taylor expansion of (* 1/8 (log k)) in k 8.912 * [taylor]: Taking taylor expansion of 1/8 in k 8.912 * [taylor]: Taking taylor expansion of (log k) in k 8.912 * [taylor]: Taking taylor expansion of k in k 8.913 * [taylor]: Taking taylor expansion of (pow k 1/8) in k 8.913 * [taylor]: Taking taylor expansion of (exp (* 1/8 (log k))) in k 8.913 * [taylor]: Taking taylor expansion of (* 1/8 (log k)) in k 8.913 * [taylor]: Taking taylor expansion of 1/8 in k 8.913 * [taylor]: Taking taylor expansion of (log k) in k 8.913 * [taylor]: Taking taylor expansion of k in k 8.961 * [approximate]: Taking taylor expansion of (pow (/ 1 (sqrt (/ -1 k))) 1/4) in (k) around 0 8.961 * [taylor]: Taking taylor expansion of (pow (/ 1 (sqrt (/ -1 k))) 1/4) in k 8.961 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 (sqrt (/ -1 k)))))) in k 8.961 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 (sqrt (/ -1 k))))) in k 8.961 * [taylor]: Taking taylor expansion of 1/4 in k 8.961 * [taylor]: Taking taylor expansion of (log (/ 1 (sqrt (/ -1 k)))) in k 8.961 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 8.961 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 8.961 * [taylor]: Taking taylor expansion of (/ -1 k) in k 8.961 * [taylor]: Taking taylor expansion of -1 in k 8.961 * [taylor]: Taking taylor expansion of k in k 8.965 * [taylor]: Taking taylor expansion of (pow (/ 1 (sqrt (/ -1 k))) 1/4) in k 8.965 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 (sqrt (/ -1 k)))))) in k 8.965 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 (sqrt (/ -1 k))))) in k 8.965 * [taylor]: Taking taylor expansion of 1/4 in k 8.965 * [taylor]: Taking taylor expansion of (log (/ 1 (sqrt (/ -1 k)))) in k 8.965 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 8.965 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 8.965 * [taylor]: Taking taylor expansion of (/ -1 k) in k 8.965 * [taylor]: Taking taylor expansion of -1 in k 8.965 * [taylor]: Taking taylor expansion of k in k 9.012 * * * [progress]: simplifying candidates 9.017 * [simplify]: Simplifying using # : (expm1 (* (/ 1 (sqrt (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt (sqrt k)))))) (log1p (* (/ 1 (sqrt (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt (sqrt k)))))) (* (/ 1 (sqrt (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt (sqrt k))))) (+ (- (log (sqrt (sqrt (sqrt k))))) (- (log 1.0) (log (sqrt (sqrt (sqrt k)))))) (+ (- (log (sqrt (sqrt (sqrt k))))) (log (/ 1.0 (sqrt (sqrt (sqrt k)))))) (+ (- 0 (log (sqrt (sqrt (sqrt k))))) (- (log 1.0) (log (sqrt (sqrt (sqrt k)))))) (+ (- 0 (log (sqrt (sqrt (sqrt k))))) (log (/ 1.0 (sqrt (sqrt (sqrt k)))))) (+ (- (log 1) (log (sqrt (sqrt (sqrt k))))) (- (log 1.0) (log (sqrt (sqrt (sqrt k)))))) (+ (- (log 1) (log (sqrt (sqrt (sqrt k))))) (log (/ 1.0 (sqrt (sqrt (sqrt k)))))) (+ (log (/ 1 (sqrt (sqrt (sqrt k))))) (- (log 1.0) (log (sqrt (sqrt (sqrt k)))))) (+ (log (/ 1 (sqrt (sqrt (sqrt k))))) (log (/ 1.0 (sqrt (sqrt (sqrt k)))))) (log (* (/ 1 (sqrt (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt (sqrt k)))))) (exp (* (/ 1 (sqrt (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt (sqrt k)))))) (* (/ (* (* 1 1) 1) (* (* (sqrt (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))) (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))))) (* (/ (* (* 1 1) 1) (* (* (sqrt (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))) (* (* (/ 1.0 (sqrt (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt (sqrt k))))) (/ 1.0 (sqrt (sqrt (sqrt k)))))) (* (* (* (/ 1 (sqrt (sqrt (sqrt k)))) (/ 1 (sqrt (sqrt (sqrt k))))) (/ 1 (sqrt (sqrt (sqrt k))))) (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))))) (* (* (* (/ 1 (sqrt (sqrt (sqrt k)))) (/ 1 (sqrt (sqrt (sqrt k))))) (/ 1 (sqrt (sqrt (sqrt k))))) (* (* (/ 1.0 (sqrt (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt (sqrt k))))) (/ 1.0 (sqrt (sqrt (sqrt k)))))) (* (cbrt (* (/ 1 (sqrt (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt (sqrt k)))))) (cbrt (* (/ 1 (sqrt (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt (sqrt k))))))) (cbrt (* (/ 1 (sqrt (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt (sqrt k)))))) (* (* (* (/ 1 (sqrt (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt (sqrt k))))) (* (/ 1 (sqrt (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt (sqrt k)))))) (* (/ 1 (sqrt (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt (sqrt k)))))) (sqrt (* (/ 1 (sqrt (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt (sqrt k)))))) (sqrt (* (/ 1 (sqrt (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt (sqrt k)))))) (* 1 1.0) (* (sqrt (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (* (sqrt (/ 1 (sqrt (sqrt (sqrt k))))) (sqrt (/ 1.0 (sqrt (sqrt (sqrt k)))))) (* (sqrt (/ 1 (sqrt (sqrt (sqrt k))))) (sqrt (/ 1.0 (sqrt (sqrt (sqrt k)))))) (* (sqrt (/ 1 (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (sqrt (/ 1 (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (sqrt (/ 1 (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (sqrt (/ 1 (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (sqrt (/ 1 (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (sqrt (/ 1 (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (sqrt (/ 1 (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (sqrt (/ 1 (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ (sqrt 1) (sqrt (sqrt (sqrt (sqrt k))))) (sqrt (/ 1.0 (sqrt (sqrt (sqrt k)))))) (* (/ (sqrt 1) (sqrt (sqrt (sqrt (sqrt k))))) (sqrt (/ 1.0 (sqrt (sqrt (sqrt k)))))) (* (/ (sqrt 1) (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ (sqrt 1) (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ (sqrt 1) (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ (sqrt 1) (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ (sqrt 1) (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ (sqrt 1) (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ (sqrt 1) (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ (sqrt 1) (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ (sqrt 1) (sqrt (sqrt (sqrt (sqrt k))))) (sqrt (/ 1.0 (sqrt (sqrt (sqrt k)))))) (* (/ (sqrt 1) (sqrt (sqrt (sqrt (sqrt k))))) (sqrt (/ 1.0 (sqrt (sqrt (sqrt k)))))) (* (/ (sqrt 1) (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ (sqrt 1) (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ (sqrt 1) (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ (sqrt 1) (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ (sqrt 1) (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ (sqrt 1) (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ (sqrt 1) (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ (sqrt 1) (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ (sqrt 1) (sqrt (sqrt (sqrt (sqrt k))))) (sqrt (/ 1.0 (sqrt (sqrt (sqrt k)))))) (* (/ (sqrt 1) (sqrt (sqrt (sqrt (sqrt k))))) (sqrt (/ 1.0 (sqrt (sqrt (sqrt k)))))) (* (/ (sqrt 1) (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ (sqrt 1) (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ (sqrt 1) (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ (sqrt 1) (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ (sqrt 1) (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ (sqrt 1) (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ (sqrt 1) (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ (sqrt 1) (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ (sqrt 1) (sqrt (sqrt (sqrt (sqrt k))))) (sqrt (/ 1.0 (sqrt (sqrt (sqrt k)))))) (* (/ (sqrt 1) (sqrt (sqrt (sqrt (sqrt k))))) (sqrt (/ 1.0 (sqrt (sqrt (sqrt k)))))) (* (/ (sqrt 1) (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ (sqrt 1) (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ (sqrt 1) (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ (sqrt 1) (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ (sqrt 1) (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ (sqrt 1) (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ (sqrt 1) (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ (sqrt 1) (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) (sqrt (/ 1.0 (sqrt (sqrt (sqrt k)))))) (* (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) (sqrt (/ 1.0 (sqrt (sqrt (sqrt k)))))) (* (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) (sqrt (/ 1.0 (sqrt (sqrt (sqrt k)))))) (* (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) (sqrt (/ 1.0 (sqrt (sqrt (sqrt k)))))) (* (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) (sqrt (/ 1.0 (sqrt (sqrt (sqrt k)))))) (* (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) (sqrt (/ 1.0 (sqrt (sqrt (sqrt k)))))) (* (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) (sqrt (/ 1.0 (sqrt (sqrt (sqrt k)))))) (* (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) (sqrt (/ 1.0 (sqrt (sqrt (sqrt k)))))) (* (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ 1 (sqrt (sqrt (sqrt k)))) (* (cbrt (/ 1.0 (sqrt (sqrt (sqrt k))))) (cbrt (/ 1.0 (sqrt (sqrt (sqrt k))))))) (* (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (/ 1.0 (sqrt (sqrt (sqrt k)))))) (* (/ 1 (sqrt (sqrt (sqrt k)))) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt (sqrt k))))))) (* (/ 1 (sqrt (sqrt (sqrt k)))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))))) (* (/ 1 (sqrt (sqrt (sqrt k)))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))))) (* (/ 1 (sqrt (sqrt (sqrt k)))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt (* (cbrt k) (cbrt k))))))) (* (/ 1 (sqrt (sqrt (sqrt k)))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt (sqrt k)))))) (* (/ 1 (sqrt (sqrt (sqrt k)))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt 1))))) (* (/ 1 (sqrt (sqrt (sqrt k)))) (/ (* (cbrt 1.0) 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(exp (/ 1 (sqrt (sqrt (sqrt k))))) (/ 1 (* (sqrt (sqrt k)) (sqrt (sqrt (sqrt k))))) (* (cbrt (/ 1 (sqrt (sqrt (sqrt k))))) (cbrt (/ 1 (sqrt (sqrt (sqrt k)))))) (cbrt (/ 1 (sqrt (sqrt (sqrt k))))) (/ 1 (* (sqrt (sqrt k)) (sqrt (sqrt (sqrt k))))) (sqrt (/ 1 (sqrt (sqrt (sqrt k))))) (sqrt (/ 1 (sqrt (sqrt (sqrt k))))) -1 (- (sqrt (sqrt (sqrt k)))) (/ (/ 1 (cbrt (sqrt (sqrt (sqrt k))))) (cbrt (sqrt (sqrt (sqrt k))))) (/ 1 (cbrt (sqrt (sqrt (sqrt k))))) (/ 1 (fabs (cbrt (sqrt (sqrt k))))) (/ 1 (sqrt (cbrt (sqrt (sqrt k))))) (/ 1 (sqrt (fabs (cbrt (sqrt k))))) (/ 1 (sqrt (sqrt (cbrt (sqrt k))))) (/ 1 (sqrt (sqrt (fabs (cbrt k))))) (/ 1 (sqrt (sqrt (sqrt (cbrt k))))) (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) (/ 1 (sqrt (sqrt 1))) (/ 1 (sqrt (sqrt (sqrt k)))) (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) (/ 1 (sqrt 1)) (/ 1 (sqrt (sqrt (sqrt k)))) (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) 1 (/ 1 (sqrt (sqrt (sqrt k)))) (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) 1 (/ 1 (sqrt (sqrt (sqrt k)))) (/ (/ 1 (cbrt (sqrt (sqrt (sqrt k))))) (cbrt (sqrt (sqrt (sqrt k))))) (/ 1 (cbrt (sqrt (sqrt (sqrt k))))) (/ 1 (fabs (cbrt (sqrt (sqrt k))))) (/ 1 (sqrt (cbrt (sqrt (sqrt k))))) (/ 1 (sqrt (fabs (cbrt (sqrt k))))) (/ 1 (sqrt (sqrt (cbrt (sqrt k))))) (/ 1 (sqrt (sqrt (fabs (cbrt k))))) (/ 1 (sqrt (sqrt (sqrt (cbrt k))))) (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) (/ 1 (sqrt (sqrt 1))) (/ 1 (sqrt (sqrt (sqrt k)))) (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) (/ 1 (sqrt 1)) (/ 1 (sqrt (sqrt (sqrt k)))) (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) 1 (/ 1 (sqrt (sqrt (sqrt k)))) (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) 1 (/ 1 (sqrt (sqrt (sqrt k)))) (/ (/ 1 (cbrt (sqrt (sqrt (sqrt k))))) (cbrt (sqrt (sqrt (sqrt k))))) (/ 1 (cbrt (sqrt (sqrt (sqrt k))))) (/ 1 (fabs (cbrt (sqrt (sqrt k))))) (/ 1 (sqrt (cbrt (sqrt (sqrt k))))) (/ 1 (sqrt (fabs (cbrt (sqrt k))))) (/ 1 (sqrt (sqrt (cbrt (sqrt k))))) (/ 1 (sqrt (sqrt (fabs (cbrt k))))) (/ 1 (sqrt (sqrt (sqrt (cbrt k))))) (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) (/ 1 (sqrt (sqrt 1))) (/ 1 (sqrt (sqrt (sqrt k)))) (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) (/ 1 (sqrt 1)) (/ 1 (sqrt (sqrt (sqrt k)))) (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) 1 (/ 1 (sqrt (sqrt (sqrt k)))) (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) 1 (/ 1 (sqrt (sqrt (sqrt k)))) (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))) (/ (/ 1 (cbrt (sqrt (sqrt (sqrt k))))) (cbrt (sqrt (sqrt (sqrt k))))) (/ 1 (fabs (cbrt (sqrt (sqrt k))))) (/ 1 (sqrt (fabs (cbrt (sqrt k))))) (/ 1 (sqrt (sqrt (fabs (cbrt k))))) (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) (/ 1 (sqrt (sqrt 1))) (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) (/ 1 (sqrt 1)) (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) 1 (/ 1 (sqrt (sqrt (sqrt (sqrt k))))) 1 (sqrt (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))) (* 1.0 (pow (/ 1 k) 1/4)) (* 1.0 (pow (/ 1 k) 1/4)) (+ (- (* 1.0 (sqrt +nan.0)) (/ (/ +nan.0 (pow k 2)) (sqrt +nan.0))) (- (/ +nan.0 (* (sqrt +nan.0) k)) (/ +nan.0 (* (pow (sqrt +nan.0) 3) (pow k 2))))) (- (- (* +nan.0 k) (- (* +nan.0 (pow k 2)) +nan.0))) (+ (- (/ +nan.0 k) (/ +nan.0 (pow k 3))) (/ (- +nan.0) (pow k 2))) (+ (- (/ +nan.0 k) +nan.0) (/ (- +nan.0) (pow k 2))) (+ (* (* 0.125 (pow k 2)) (+ (* (pow (exp 0.5) (log (* (* 2.0 PI) n))) (pow (log (* 2.0 PI)) 2)) (* (pow (log n) 2) (pow (exp 0.5) (log (* (* 2.0 PI) n)))))) (- (fma 0.25 (* (* (pow k 2) (log (* 2.0 PI))) (* (log n) (pow (exp 0.5) (log (* (* 2.0 PI) n))))) (pow (exp 0.5) (log (* (* 2.0 PI) n)))) (* (* 0.5 k) (+ (* (log (* 2.0 PI)) (pow (exp 0.5) (log (* (* 2.0 PI) n)))) (* (log n) (pow (exp 0.5) (log (* (* 2.0 PI) n)))))))) (exp (* (* (log (* (* 2.0 PI) n)) 0.5) (- 1.0 k))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k -1/8) (pow (/ 1 k) 1/8) (- (pow +nan.0 1/4) (* (pow +nan.0 1/4) (- (/ +nan.0 (pow k 2)) (/ +nan.0 k)))) 9.450 * * * [progress]: adding candidates to table 10.237 * [progress]: [Phase 3 of 3] Extracting. 10.237 * * [regime]: Finding splitpoints for: (# # # # # # # # # #) 10.249 * * * [regime-changes]: Trying 4 branch expressions: ((* (* 2.0 PI) n) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) n k) 10.250 * * * * [regimes]: Trying to branch on (* (* 2.0 PI) n) from (# # # # # # # # # #) 10.311 * * * * [regimes]: Trying to branch on (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) from (# # # # # # # # # #) 10.375 * * * * [regimes]: Trying to branch on n from (# # # # # # # # # #) 10.430 * * * * [regimes]: Trying to branch on k from (# # # # # # # # # #) 10.486 * * * [regime]: Found split indices: #