59.236 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.092 * * * [progress]: [2/2] Setting up program. 0.098 * [progress]: [Phase 2 of 3] Improving. 0.098 * * * * [progress]: [ 1 / 1 ] simplifiying candidate # 0.098 * [simplify]: Simplifying: (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) 0.098 * * [simplify]: iteration 0: 13 enodes 0.105 * * [simplify]: iteration 1: 31 enodes 0.141 * * [simplify]: iteration 2: 62 enodes 0.162 * * [simplify]: iteration 3: 124 enodes 0.201 * * [simplify]: iteration 4: 328 enodes 0.488 * * [simplify]: iteration 5: 970 enodes 1.697 * * [simplify]: iteration 6: 2753 enodes 2.805 * * [simplify]: iteration complete: 5000 enodes 2.805 * * [simplify]: Extracting #0: cost 1 inf + 0 2.806 * * [simplify]: Extracting #1: cost 218 inf + 0 2.808 * * [simplify]: Extracting #2: cost 583 inf + 1 2.811 * * [simplify]: Extracting #3: cost 872 inf + 91 2.816 * * [simplify]: Extracting #4: cost 882 inf + 7092 2.826 * * [simplify]: Extracting #5: cost 661 inf + 35266 2.898 * * [simplify]: Extracting #6: cost 372 inf + 225053 3.043 * * [simplify]: Extracting #7: cost 38 inf + 563892 3.255 * * [simplify]: Extracting #8: cost 0 inf + 582786 3.426 * * [simplify]: Extracting #9: cost 0 inf + 575286 3.647 * [simplify]: Simplified to: (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)) 3.657 * * [progress]: iteration 1 / 4 3.657 * * * [progress]: picking best candidate 3.668 * * * * [pick]: Picked # 3.668 * * * [progress]: localizing error 3.710 * * * [progress]: generating rewritten candidates 3.711 * * * * [progress]: [ 1 / 3 ] rewriting at (2 1) 3.738 * * * * [progress]: [ 2 / 3 ] rewriting at (2 1 1) 3.759 * * * * [progress]: [ 3 / 3 ] rewriting at (2) 3.822 * * * [progress]: generating series expansions 3.822 * * * * [progress]: [ 1 / 3 ] generating series at (2 1) 3.822 * [backup-simplify]: Simplify (pow (* (* n 2) PI) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 3.822 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 3.822 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 3.822 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 3.822 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 3.822 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 3.823 * [taylor]: Taking taylor expansion of 1/2 in k 3.823 * [backup-simplify]: Simplify 1/2 into 1/2 3.823 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 3.823 * [taylor]: Taking taylor expansion of 1/2 in k 3.823 * [backup-simplify]: Simplify 1/2 into 1/2 3.823 * [taylor]: Taking taylor expansion of k in k 3.823 * [backup-simplify]: Simplify 0 into 0 3.823 * [backup-simplify]: Simplify 1 into 1 3.823 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 3.823 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 3.823 * [taylor]: Taking taylor expansion of 2 in k 3.823 * [backup-simplify]: Simplify 2 into 2 3.823 * [taylor]: Taking taylor expansion of (* n PI) in k 3.823 * [taylor]: Taking taylor expansion of n in k 3.823 * [backup-simplify]: Simplify n into n 3.823 * [taylor]: Taking taylor expansion of PI in k 3.823 * [backup-simplify]: Simplify PI into PI 3.823 * [backup-simplify]: Simplify (* n PI) into (* n PI) 3.823 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 3.823 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 3.824 * [backup-simplify]: Simplify (* 1/2 0) into 0 3.824 * [backup-simplify]: Simplify (- 0) into 0 3.824 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 3.824 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 3.824 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 3.825 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 3.825 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 3.825 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 3.825 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 3.825 * [taylor]: Taking taylor expansion of 1/2 in n 3.825 * [backup-simplify]: Simplify 1/2 into 1/2 3.825 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 3.825 * [taylor]: Taking taylor expansion of 1/2 in n 3.825 * [backup-simplify]: Simplify 1/2 into 1/2 3.825 * [taylor]: Taking taylor expansion of k in n 3.825 * [backup-simplify]: Simplify k into k 3.825 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 3.825 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 3.825 * [taylor]: Taking taylor expansion of 2 in n 3.825 * [backup-simplify]: Simplify 2 into 2 3.825 * [taylor]: Taking taylor expansion of (* n PI) in n 3.825 * [taylor]: Taking taylor expansion of n in n 3.825 * [backup-simplify]: Simplify 0 into 0 3.825 * [backup-simplify]: Simplify 1 into 1 3.825 * [taylor]: Taking taylor expansion of PI in n 3.825 * [backup-simplify]: Simplify PI into PI 3.825 * [backup-simplify]: Simplify (* 0 PI) into 0 3.826 * [backup-simplify]: Simplify (* 2 0) into 0 3.827 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.828 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 3.829 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 3.829 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 3.829 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 3.829 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 3.830 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 3.831 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 3.832 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 3.832 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 3.832 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 3.832 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 3.832 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 3.832 * [taylor]: Taking taylor expansion of 1/2 in n 3.832 * [backup-simplify]: Simplify 1/2 into 1/2 3.832 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 3.832 * [taylor]: Taking taylor expansion of 1/2 in n 3.832 * [backup-simplify]: Simplify 1/2 into 1/2 3.832 * [taylor]: Taking taylor expansion of k in n 3.832 * [backup-simplify]: Simplify k into k 3.832 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 3.832 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 3.832 * [taylor]: Taking taylor expansion of 2 in n 3.832 * [backup-simplify]: Simplify 2 into 2 3.832 * [taylor]: Taking taylor expansion of (* n PI) in n 3.832 * [taylor]: Taking taylor expansion of n in n 3.832 * [backup-simplify]: Simplify 0 into 0 3.832 * [backup-simplify]: Simplify 1 into 1 3.832 * [taylor]: Taking taylor expansion of PI in n 3.832 * [backup-simplify]: Simplify PI into PI 3.832 * [backup-simplify]: Simplify (* 0 PI) into 0 3.832 * [backup-simplify]: Simplify (* 2 0) into 0 3.833 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.834 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 3.835 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 3.835 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 3.835 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 3.835 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 3.836 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 3.837 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 3.838 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 3.838 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 3.838 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 3.838 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 3.838 * [taylor]: Taking taylor expansion of 1/2 in k 3.838 * [backup-simplify]: Simplify 1/2 into 1/2 3.838 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 3.838 * [taylor]: Taking taylor expansion of 1/2 in k 3.838 * [backup-simplify]: Simplify 1/2 into 1/2 3.838 * [taylor]: Taking taylor expansion of k in k 3.838 * [backup-simplify]: Simplify 0 into 0 3.838 * [backup-simplify]: Simplify 1 into 1 3.838 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 3.838 * [taylor]: Taking taylor expansion of (log n) in k 3.838 * [taylor]: Taking taylor expansion of n in k 3.838 * [backup-simplify]: Simplify n into n 3.838 * [backup-simplify]: Simplify (log n) into (log n) 3.838 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 3.838 * [taylor]: Taking taylor expansion of (* 2 PI) in k 3.838 * [taylor]: Taking taylor expansion of 2 in k 3.838 * [backup-simplify]: Simplify 2 into 2 3.838 * [taylor]: Taking taylor expansion of PI in k 3.838 * [backup-simplify]: Simplify PI into PI 3.838 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 3.839 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 3.839 * [backup-simplify]: Simplify (* 1/2 0) into 0 3.839 * [backup-simplify]: Simplify (- 0) into 0 3.840 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 3.840 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 3.841 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 3.842 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 3.843 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 3.844 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 3.844 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 3.845 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 3.846 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 3.846 * [backup-simplify]: Simplify (- 0) into 0 3.846 * [backup-simplify]: Simplify (+ 0 0) into 0 3.847 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 3.848 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 3.849 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 3.849 * [taylor]: Taking taylor expansion of 0 in k 3.849 * [backup-simplify]: Simplify 0 into 0 3.849 * [backup-simplify]: Simplify 0 into 0 3.850 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 3.850 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 3.852 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 3.852 * [backup-simplify]: Simplify (+ 0 0) into 0 3.853 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 3.854 * [backup-simplify]: Simplify (- 1/2) into -1/2 3.854 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 3.856 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 3.859 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 3.862 * [backup-simplify]: Simplify (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 3.864 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 3.865 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 3.869 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 3.869 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 3.870 * [backup-simplify]: Simplify (- 0) into 0 3.870 * [backup-simplify]: Simplify (+ 0 0) into 0 3.872 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 3.874 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 3.876 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 3.876 * [taylor]: Taking taylor expansion of 0 in k 3.876 * [backup-simplify]: Simplify 0 into 0 3.876 * [backup-simplify]: Simplify 0 into 0 3.876 * [backup-simplify]: Simplify 0 into 0 3.878 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 3.879 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 3.881 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 3.881 * [backup-simplify]: Simplify (+ 0 0) into 0 3.882 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 3.882 * [backup-simplify]: Simplify (- 0) into 0 3.882 * [backup-simplify]: Simplify (+ 0 0) into 0 3.884 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 3.886 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 3.889 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 3.901 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) 3.901 * [backup-simplify]: Simplify (pow (* (* (/ 1 n) 2) PI) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 3.901 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 3.901 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 3.901 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 3.901 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 3.901 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 3.901 * [taylor]: Taking taylor expansion of 1/2 in k 3.901 * [backup-simplify]: Simplify 1/2 into 1/2 3.901 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 3.901 * [taylor]: Taking taylor expansion of 1/2 in k 3.901 * [backup-simplify]: Simplify 1/2 into 1/2 3.901 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.901 * [taylor]: Taking taylor expansion of k in k 3.901 * [backup-simplify]: Simplify 0 into 0 3.901 * [backup-simplify]: Simplify 1 into 1 3.902 * [backup-simplify]: Simplify (/ 1 1) into 1 3.902 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 3.902 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 3.902 * [taylor]: Taking taylor expansion of 2 in k 3.902 * [backup-simplify]: Simplify 2 into 2 3.902 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.902 * [taylor]: Taking taylor expansion of PI in k 3.902 * [backup-simplify]: Simplify PI into PI 3.902 * [taylor]: Taking taylor expansion of n in k 3.902 * [backup-simplify]: Simplify n into n 3.902 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 3.902 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 3.902 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 3.902 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 3.903 * [backup-simplify]: Simplify (- 1/2) into -1/2 3.903 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 3.903 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 3.903 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 3.903 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 3.903 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 3.903 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 3.903 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 3.903 * [taylor]: Taking taylor expansion of 1/2 in n 3.903 * [backup-simplify]: Simplify 1/2 into 1/2 3.903 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 3.903 * [taylor]: Taking taylor expansion of 1/2 in n 3.903 * [backup-simplify]: Simplify 1/2 into 1/2 3.903 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.903 * [taylor]: Taking taylor expansion of k in n 3.903 * [backup-simplify]: Simplify k into k 3.903 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.903 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 3.903 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 3.903 * [taylor]: Taking taylor expansion of 2 in n 3.903 * [backup-simplify]: Simplify 2 into 2 3.903 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.903 * [taylor]: Taking taylor expansion of PI in n 3.903 * [backup-simplify]: Simplify PI into PI 3.903 * [taylor]: Taking taylor expansion of n in n 3.903 * [backup-simplify]: Simplify 0 into 0 3.903 * [backup-simplify]: Simplify 1 into 1 3.904 * [backup-simplify]: Simplify (/ PI 1) into PI 3.904 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 3.905 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 3.905 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 3.905 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 3.905 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 3.906 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 3.907 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 3.908 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 3.908 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 3.908 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 3.908 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 3.908 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 3.908 * [taylor]: Taking taylor expansion of 1/2 in n 3.908 * [backup-simplify]: Simplify 1/2 into 1/2 3.908 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 3.908 * [taylor]: Taking taylor expansion of 1/2 in n 3.908 * [backup-simplify]: Simplify 1/2 into 1/2 3.908 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.908 * [taylor]: Taking taylor expansion of k in n 3.908 * [backup-simplify]: Simplify k into k 3.908 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.908 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 3.908 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 3.908 * [taylor]: Taking taylor expansion of 2 in n 3.908 * [backup-simplify]: Simplify 2 into 2 3.908 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.908 * [taylor]: Taking taylor expansion of PI in n 3.908 * [backup-simplify]: Simplify PI into PI 3.908 * [taylor]: Taking taylor expansion of n in n 3.908 * [backup-simplify]: Simplify 0 into 0 3.908 * [backup-simplify]: Simplify 1 into 1 3.908 * [backup-simplify]: Simplify (/ PI 1) into PI 3.909 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 3.909 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 3.909 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 3.910 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 3.910 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 3.911 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 3.911 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 3.912 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 3.912 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 3.912 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 3.912 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 3.912 * [taylor]: Taking taylor expansion of 1/2 in k 3.912 * [backup-simplify]: Simplify 1/2 into 1/2 3.912 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 3.912 * [taylor]: Taking taylor expansion of 1/2 in k 3.912 * [backup-simplify]: Simplify 1/2 into 1/2 3.912 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.912 * [taylor]: Taking taylor expansion of k in k 3.912 * [backup-simplify]: Simplify 0 into 0 3.912 * [backup-simplify]: Simplify 1 into 1 3.913 * [backup-simplify]: Simplify (/ 1 1) into 1 3.913 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 3.913 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 3.913 * [taylor]: Taking taylor expansion of (* 2 PI) in k 3.913 * [taylor]: Taking taylor expansion of 2 in k 3.913 * [backup-simplify]: Simplify 2 into 2 3.913 * [taylor]: Taking taylor expansion of PI in k 3.913 * [backup-simplify]: Simplify PI into PI 3.913 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 3.914 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 3.914 * [taylor]: Taking taylor expansion of (log n) in k 3.914 * [taylor]: Taking taylor expansion of n in k 3.914 * [backup-simplify]: Simplify n into n 3.914 * [backup-simplify]: Simplify (log n) into (log n) 3.914 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 3.914 * [backup-simplify]: Simplify (- 1/2) into -1/2 3.915 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 3.915 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 3.915 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 3.916 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 3.917 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 3.918 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 3.918 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 3.919 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 3.921 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 3.921 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 3.922 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 3.922 * [backup-simplify]: Simplify (- 0) into 0 3.922 * [backup-simplify]: Simplify (+ 0 0) into 0 3.924 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 3.925 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 3.927 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 3.927 * [taylor]: Taking taylor expansion of 0 in k 3.927 * [backup-simplify]: Simplify 0 into 0 3.927 * [backup-simplify]: Simplify 0 into 0 3.927 * [backup-simplify]: Simplify 0 into 0 3.929 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.930 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 3.933 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 3.933 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 3.934 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 3.934 * [backup-simplify]: Simplify (- 0) into 0 3.935 * [backup-simplify]: Simplify (+ 0 0) into 0 3.936 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 3.938 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 3.940 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 3.940 * [taylor]: Taking taylor expansion of 0 in k 3.940 * [backup-simplify]: Simplify 0 into 0 3.940 * [backup-simplify]: Simplify 0 into 0 3.940 * [backup-simplify]: Simplify 0 into 0 3.940 * [backup-simplify]: Simplify 0 into 0 3.942 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.943 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 3.949 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 3.950 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 3.951 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 3.952 * [backup-simplify]: Simplify (- 0) into 0 3.952 * [backup-simplify]: Simplify (+ 0 0) into 0 3.954 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 3.955 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 3.958 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 3.958 * [taylor]: Taking taylor expansion of 0 in k 3.958 * [backup-simplify]: Simplify 0 into 0 3.958 * [backup-simplify]: Simplify 0 into 0 3.960 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 3.960 * [backup-simplify]: Simplify (pow (* (* (/ 1 (- n)) 2) PI) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 3.960 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 3.960 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 3.960 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 3.960 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 3.960 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 3.960 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 3.960 * [taylor]: Taking taylor expansion of 1/2 in k 3.960 * [backup-simplify]: Simplify 1/2 into 1/2 3.960 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.960 * [taylor]: Taking taylor expansion of k in k 3.960 * [backup-simplify]: Simplify 0 into 0 3.960 * [backup-simplify]: Simplify 1 into 1 3.961 * [backup-simplify]: Simplify (/ 1 1) into 1 3.961 * [taylor]: Taking taylor expansion of 1/2 in k 3.961 * [backup-simplify]: Simplify 1/2 into 1/2 3.961 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 3.961 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 3.961 * [taylor]: Taking taylor expansion of -2 in k 3.961 * [backup-simplify]: Simplify -2 into -2 3.961 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.961 * [taylor]: Taking taylor expansion of PI in k 3.961 * [backup-simplify]: Simplify PI into PI 3.961 * [taylor]: Taking taylor expansion of n in k 3.961 * [backup-simplify]: Simplify n into n 3.961 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 3.961 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 3.961 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 3.962 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 3.962 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 3.962 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 3.963 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) 3.963 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 3.963 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 3.963 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 3.963 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 3.963 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 3.963 * [taylor]: Taking taylor expansion of 1/2 in n 3.963 * [backup-simplify]: Simplify 1/2 into 1/2 3.963 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.963 * [taylor]: Taking taylor expansion of k in n 3.963 * [backup-simplify]: Simplify k into k 3.963 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.963 * [taylor]: Taking taylor expansion of 1/2 in n 3.963 * [backup-simplify]: Simplify 1/2 into 1/2 3.963 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 3.963 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 3.963 * [taylor]: Taking taylor expansion of -2 in n 3.963 * [backup-simplify]: Simplify -2 into -2 3.963 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.963 * [taylor]: Taking taylor expansion of PI in n 3.963 * [backup-simplify]: Simplify PI into PI 3.963 * [taylor]: Taking taylor expansion of n in n 3.963 * [backup-simplify]: Simplify 0 into 0 3.963 * [backup-simplify]: Simplify 1 into 1 3.964 * [backup-simplify]: Simplify (/ PI 1) into PI 3.964 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 3.965 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 3.965 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 3.966 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 3.967 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 3.968 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 3.969 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 3.970 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 3.970 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 3.970 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 3.970 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 3.970 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 3.970 * [taylor]: Taking taylor expansion of 1/2 in n 3.970 * [backup-simplify]: Simplify 1/2 into 1/2 3.970 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.970 * [taylor]: Taking taylor expansion of k in n 3.970 * [backup-simplify]: Simplify k into k 3.970 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.970 * [taylor]: Taking taylor expansion of 1/2 in n 3.970 * [backup-simplify]: Simplify 1/2 into 1/2 3.970 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 3.970 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 3.970 * [taylor]: Taking taylor expansion of -2 in n 3.970 * [backup-simplify]: Simplify -2 into -2 3.970 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.970 * [taylor]: Taking taylor expansion of PI in n 3.970 * [backup-simplify]: Simplify PI into PI 3.970 * [taylor]: Taking taylor expansion of n in n 3.970 * [backup-simplify]: Simplify 0 into 0 3.970 * [backup-simplify]: Simplify 1 into 1 3.971 * [backup-simplify]: Simplify (/ PI 1) into PI 3.971 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 3.972 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 3.972 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 3.972 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 3.973 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 3.973 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 3.974 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 3.974 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 3.974 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 3.974 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 3.974 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 3.974 * [taylor]: Taking taylor expansion of 1/2 in k 3.974 * [backup-simplify]: Simplify 1/2 into 1/2 3.974 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.974 * [taylor]: Taking taylor expansion of k in k 3.974 * [backup-simplify]: Simplify 0 into 0 3.974 * [backup-simplify]: Simplify 1 into 1 3.975 * [backup-simplify]: Simplify (/ 1 1) into 1 3.975 * [taylor]: Taking taylor expansion of 1/2 in k 3.975 * [backup-simplify]: Simplify 1/2 into 1/2 3.975 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 3.975 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 3.975 * [taylor]: Taking taylor expansion of (* -2 PI) in k 3.975 * [taylor]: Taking taylor expansion of -2 in k 3.975 * [backup-simplify]: Simplify -2 into -2 3.975 * [taylor]: Taking taylor expansion of PI in k 3.975 * [backup-simplify]: Simplify PI into PI 3.975 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 3.976 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 3.976 * [taylor]: Taking taylor expansion of (log n) in k 3.976 * [taylor]: Taking taylor expansion of n in k 3.976 * [backup-simplify]: Simplify n into n 3.976 * [backup-simplify]: Simplify (log n) into (log n) 3.976 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 3.976 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 3.976 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 3.977 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 3.978 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 3.979 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 3.979 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 3.980 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 3.980 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 3.981 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 3.982 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 3.982 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 3.982 * [backup-simplify]: Simplify (+ 0 0) into 0 3.983 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 3.984 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 3.985 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 3.985 * [taylor]: Taking taylor expansion of 0 in k 3.985 * [backup-simplify]: Simplify 0 into 0 3.985 * [backup-simplify]: Simplify 0 into 0 3.985 * [backup-simplify]: Simplify 0 into 0 3.986 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.986 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 3.988 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 3.988 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 3.989 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 3.989 * [backup-simplify]: Simplify (+ 0 0) into 0 3.990 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 3.991 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 3.993 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 3.993 * [taylor]: Taking taylor expansion of 0 in k 3.993 * [backup-simplify]: Simplify 0 into 0 3.993 * [backup-simplify]: Simplify 0 into 0 3.993 * [backup-simplify]: Simplify 0 into 0 3.993 * [backup-simplify]: Simplify 0 into 0 3.993 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.994 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 3.998 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0 3.998 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 3.998 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 3.999 * [backup-simplify]: Simplify (+ 0 0) into 0 4.000 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 4.001 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 4.003 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 4.003 * [taylor]: Taking taylor expansion of 0 in k 4.003 * [backup-simplify]: Simplify 0 into 0 4.003 * [backup-simplify]: Simplify 0 into 0 4.004 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 4.004 * * * * [progress]: [ 2 / 3 ] generating series at (2 1 1) 4.004 * [backup-simplify]: Simplify (* (* n 2) PI) into (* 2 (* n PI)) 4.004 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 4.004 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 4.004 * [taylor]: Taking taylor expansion of 2 in n 4.004 * [backup-simplify]: Simplify 2 into 2 4.004 * [taylor]: Taking taylor expansion of (* n PI) in n 4.004 * [taylor]: Taking taylor expansion of n in n 4.004 * [backup-simplify]: Simplify 0 into 0 4.004 * [backup-simplify]: Simplify 1 into 1 4.004 * [taylor]: Taking taylor expansion of PI in n 4.004 * [backup-simplify]: Simplify PI into PI 4.004 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 4.004 * [taylor]: Taking taylor expansion of 2 in n 4.004 * [backup-simplify]: Simplify 2 into 2 4.004 * [taylor]: Taking taylor expansion of (* n PI) in n 4.004 * [taylor]: Taking taylor expansion of n in n 4.004 * [backup-simplify]: Simplify 0 into 0 4.004 * [backup-simplify]: Simplify 1 into 1 4.004 * [taylor]: Taking taylor expansion of PI in n 4.004 * [backup-simplify]: Simplify PI into PI 4.004 * [backup-simplify]: Simplify (* 0 PI) into 0 4.005 * [backup-simplify]: Simplify (* 2 0) into 0 4.005 * [backup-simplify]: Simplify 0 into 0 4.006 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.007 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 4.011 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 4.012 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 4.013 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 4.013 * [backup-simplify]: Simplify 0 into 0 4.014 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 4.016 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 4.016 * [backup-simplify]: Simplify 0 into 0 4.017 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 4.018 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 4.019 * [backup-simplify]: Simplify 0 into 0 4.020 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 4.022 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 4.022 * [backup-simplify]: Simplify 0 into 0 4.023 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 4.025 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 4.025 * [backup-simplify]: Simplify 0 into 0 4.027 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 4.029 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 4.029 * [backup-simplify]: Simplify 0 into 0 4.029 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 4.030 * [backup-simplify]: Simplify (* (* (/ 1 n) 2) PI) into (* 2 (/ PI n)) 4.030 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 4.030 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 4.030 * [taylor]: Taking taylor expansion of 2 in n 4.030 * [backup-simplify]: Simplify 2 into 2 4.030 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.030 * [taylor]: Taking taylor expansion of PI in n 4.030 * [backup-simplify]: Simplify PI into PI 4.030 * [taylor]: Taking taylor expansion of n in n 4.030 * [backup-simplify]: Simplify 0 into 0 4.030 * [backup-simplify]: Simplify 1 into 1 4.030 * [backup-simplify]: Simplify (/ PI 1) into PI 4.030 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 4.030 * [taylor]: Taking taylor expansion of 2 in n 4.030 * [backup-simplify]: Simplify 2 into 2 4.030 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.030 * [taylor]: Taking taylor expansion of PI in n 4.030 * [backup-simplify]: Simplify PI into PI 4.030 * [taylor]: Taking taylor expansion of n in n 4.031 * [backup-simplify]: Simplify 0 into 0 4.031 * [backup-simplify]: Simplify 1 into 1 4.031 * [backup-simplify]: Simplify (/ PI 1) into PI 4.032 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 4.032 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 4.033 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.034 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 4.034 * [backup-simplify]: Simplify 0 into 0 4.035 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.036 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 4.036 * [backup-simplify]: Simplify 0 into 0 4.037 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.038 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.038 * [backup-simplify]: Simplify 0 into 0 4.039 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.041 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 4.041 * [backup-simplify]: Simplify 0 into 0 4.042 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.043 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 4.043 * [backup-simplify]: Simplify 0 into 0 4.044 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.046 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 4.046 * [backup-simplify]: Simplify 0 into 0 4.047 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 4.047 * [backup-simplify]: Simplify (* (* (/ 1 (- n)) 2) PI) into (* -2 (/ PI n)) 4.047 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 4.047 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 4.047 * [taylor]: Taking taylor expansion of -2 in n 4.047 * [backup-simplify]: Simplify -2 into -2 4.047 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.047 * [taylor]: Taking taylor expansion of PI in n 4.047 * [backup-simplify]: Simplify PI into PI 4.047 * [taylor]: Taking taylor expansion of n in n 4.047 * [backup-simplify]: Simplify 0 into 0 4.047 * [backup-simplify]: Simplify 1 into 1 4.048 * [backup-simplify]: Simplify (/ PI 1) into PI 4.048 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 4.048 * [taylor]: Taking taylor expansion of -2 in n 4.048 * [backup-simplify]: Simplify -2 into -2 4.048 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.048 * [taylor]: Taking taylor expansion of PI in n 4.048 * [backup-simplify]: Simplify PI into PI 4.048 * [taylor]: Taking taylor expansion of n in n 4.048 * [backup-simplify]: Simplify 0 into 0 4.048 * [backup-simplify]: Simplify 1 into 1 4.048 * [backup-simplify]: Simplify (/ PI 1) into PI 4.049 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 4.049 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 4.050 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.051 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 4.051 * [backup-simplify]: Simplify 0 into 0 4.053 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.054 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 4.054 * [backup-simplify]: Simplify 0 into 0 4.055 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.056 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.056 * [backup-simplify]: Simplify 0 into 0 4.057 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.059 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 4.059 * [backup-simplify]: Simplify 0 into 0 4.060 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.061 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 4.061 * [backup-simplify]: Simplify 0 into 0 4.063 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.064 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 4.064 * [backup-simplify]: Simplify 0 into 0 4.064 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 4.064 * * * * [progress]: [ 3 / 3 ] generating series at (2) 4.064 * [backup-simplify]: Simplify (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)) into (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) 4.064 * [approximate]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (n k) around 0 4.065 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 4.065 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 4.065 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.065 * [taylor]: Taking taylor expansion of k in k 4.065 * [backup-simplify]: Simplify 0 into 0 4.065 * [backup-simplify]: Simplify 1 into 1 4.065 * [backup-simplify]: Simplify (/ 1 1) into 1 4.065 * [backup-simplify]: Simplify (sqrt 0) into 0 4.066 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.066 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 4.066 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 4.066 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 4.066 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 4.066 * [taylor]: Taking taylor expansion of 1/2 in k 4.066 * [backup-simplify]: Simplify 1/2 into 1/2 4.066 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 4.066 * [taylor]: Taking taylor expansion of 1/2 in k 4.066 * [backup-simplify]: Simplify 1/2 into 1/2 4.066 * [taylor]: Taking taylor expansion of k in k 4.066 * [backup-simplify]: Simplify 0 into 0 4.066 * [backup-simplify]: Simplify 1 into 1 4.066 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 4.066 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 4.066 * [taylor]: Taking taylor expansion of 2 in k 4.066 * [backup-simplify]: Simplify 2 into 2 4.067 * [taylor]: Taking taylor expansion of (* n PI) in k 4.067 * [taylor]: Taking taylor expansion of n in k 4.067 * [backup-simplify]: Simplify n into n 4.067 * [taylor]: Taking taylor expansion of PI in k 4.067 * [backup-simplify]: Simplify PI into PI 4.067 * [backup-simplify]: Simplify (* n PI) into (* n PI) 4.067 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 4.067 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 4.067 * [backup-simplify]: Simplify (* 1/2 0) into 0 4.067 * [backup-simplify]: Simplify (- 0) into 0 4.068 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 4.068 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 4.068 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 4.068 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 4.068 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 4.068 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.068 * [taylor]: Taking taylor expansion of k in n 4.068 * [backup-simplify]: Simplify k into k 4.068 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.068 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 4.068 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.068 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 4.068 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 4.068 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 4.068 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 4.068 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 4.068 * [taylor]: Taking taylor expansion of 1/2 in n 4.068 * [backup-simplify]: Simplify 1/2 into 1/2 4.068 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 4.068 * [taylor]: Taking taylor expansion of 1/2 in n 4.068 * [backup-simplify]: Simplify 1/2 into 1/2 4.068 * [taylor]: Taking taylor expansion of k in n 4.068 * [backup-simplify]: Simplify k into k 4.068 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 4.068 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 4.068 * [taylor]: Taking taylor expansion of 2 in n 4.068 * [backup-simplify]: Simplify 2 into 2 4.068 * [taylor]: Taking taylor expansion of (* n PI) in n 4.068 * [taylor]: Taking taylor expansion of n in n 4.068 * [backup-simplify]: Simplify 0 into 0 4.068 * [backup-simplify]: Simplify 1 into 1 4.068 * [taylor]: Taking taylor expansion of PI in n 4.068 * [backup-simplify]: Simplify PI into PI 4.069 * [backup-simplify]: Simplify (* 0 PI) into 0 4.069 * [backup-simplify]: Simplify (* 2 0) into 0 4.070 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.071 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 4.072 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 4.072 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 4.072 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 4.072 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 4.073 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 4.073 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 4.074 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 4.074 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 4.074 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 4.074 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.074 * [taylor]: Taking taylor expansion of k in n 4.074 * [backup-simplify]: Simplify k into k 4.074 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.074 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 4.074 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.074 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 4.074 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 4.075 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 4.075 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 4.075 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 4.075 * [taylor]: Taking taylor expansion of 1/2 in n 4.075 * [backup-simplify]: Simplify 1/2 into 1/2 4.075 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 4.075 * [taylor]: Taking taylor expansion of 1/2 in n 4.075 * [backup-simplify]: Simplify 1/2 into 1/2 4.075 * [taylor]: Taking taylor expansion of k in n 4.075 * [backup-simplify]: Simplify k into k 4.075 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 4.075 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 4.075 * [taylor]: Taking taylor expansion of 2 in n 4.075 * [backup-simplify]: Simplify 2 into 2 4.075 * [taylor]: Taking taylor expansion of (* n PI) in n 4.075 * [taylor]: Taking taylor expansion of n in n 4.075 * [backup-simplify]: Simplify 0 into 0 4.075 * [backup-simplify]: Simplify 1 into 1 4.075 * [taylor]: Taking taylor expansion of PI in n 4.075 * [backup-simplify]: Simplify PI into PI 4.075 * [backup-simplify]: Simplify (* 0 PI) into 0 4.075 * [backup-simplify]: Simplify (* 2 0) into 0 4.076 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.077 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 4.078 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 4.078 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 4.078 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 4.078 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 4.079 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 4.080 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 4.081 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 4.081 * [backup-simplify]: Simplify (* (sqrt (/ 1 k)) (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k))) 4.081 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k))) in k 4.081 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 4.081 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 4.081 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 4.081 * [taylor]: Taking taylor expansion of 1/2 in k 4.081 * [backup-simplify]: Simplify 1/2 into 1/2 4.082 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 4.082 * [taylor]: Taking taylor expansion of 1/2 in k 4.082 * [backup-simplify]: Simplify 1/2 into 1/2 4.082 * [taylor]: Taking taylor expansion of k in k 4.082 * [backup-simplify]: Simplify 0 into 0 4.082 * [backup-simplify]: Simplify 1 into 1 4.082 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 4.082 * [taylor]: Taking taylor expansion of (log n) in k 4.082 * [taylor]: Taking taylor expansion of n in k 4.082 * [backup-simplify]: Simplify n into n 4.082 * [backup-simplify]: Simplify (log n) into (log n) 4.082 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 4.082 * [taylor]: Taking taylor expansion of (* 2 PI) in k 4.082 * [taylor]: Taking taylor expansion of 2 in k 4.082 * [backup-simplify]: Simplify 2 into 2 4.082 * [taylor]: Taking taylor expansion of PI in k 4.082 * [backup-simplify]: Simplify PI into PI 4.082 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 4.083 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 4.083 * [backup-simplify]: Simplify (* 1/2 0) into 0 4.083 * [backup-simplify]: Simplify (- 0) into 0 4.084 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 4.084 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 4.085 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 4.086 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 4.086 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 4.086 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.086 * [taylor]: Taking taylor expansion of k in k 4.086 * [backup-simplify]: Simplify 0 into 0 4.086 * [backup-simplify]: Simplify 1 into 1 4.086 * [backup-simplify]: Simplify (/ 1 1) into 1 4.086 * [backup-simplify]: Simplify (sqrt 0) into 0 4.087 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.088 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) into 0 4.088 * [backup-simplify]: Simplify 0 into 0 4.089 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 4.090 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 4.091 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 4.092 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 4.092 * [backup-simplify]: Simplify (- 0) into 0 4.092 * [backup-simplify]: Simplify (+ 0 0) into 0 4.094 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 4.095 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 4.097 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.098 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))) into 0 4.098 * [taylor]: Taking taylor expansion of 0 in k 4.098 * [backup-simplify]: Simplify 0 into 0 4.099 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 4.100 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 4.102 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 4.102 * [backup-simplify]: Simplify (+ 0 0) into 0 4.103 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 4.103 * [backup-simplify]: Simplify (- 1/2) into -1/2 4.104 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 4.105 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 4.108 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 4.113 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 0)) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 4.114 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 4.115 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 4.116 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 4.120 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 4.121 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 4.121 * [backup-simplify]: Simplify (- 0) into 0 4.121 * [backup-simplify]: Simplify (+ 0 0) into 0 4.123 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 4.125 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 4.127 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 4.127 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.128 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 4.130 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))))) into 0 4.130 * [taylor]: Taking taylor expansion of 0 in k 4.130 * [backup-simplify]: Simplify 0 into 0 4.130 * [backup-simplify]: Simplify 0 into 0 4.131 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 4.134 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.136 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 4.137 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 4.140 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 4.140 * [backup-simplify]: Simplify (+ 0 0) into 0 4.144 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 4.145 * [backup-simplify]: Simplify (- 0) into 0 4.145 * [backup-simplify]: Simplify (+ 0 0) into 0 4.147 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 4.152 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 4.161 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) +nan.0) (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 0))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) 4.166 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) 4.168 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 4.169 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 4.175 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 4.177 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 4.177 * [backup-simplify]: Simplify (- 0) into 0 4.177 * [backup-simplify]: Simplify (+ 0 0) into 0 4.179 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 4.181 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 4.184 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 4.184 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.185 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 4.187 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))))) into 0 4.187 * [taylor]: Taking taylor expansion of 0 in k 4.187 * [backup-simplify]: Simplify 0 into 0 4.187 * [backup-simplify]: Simplify 0 into 0 4.187 * [backup-simplify]: Simplify 0 into 0 4.188 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.192 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.195 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0 4.196 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.202 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 4.202 * [backup-simplify]: Simplify (+ 0 0) into 0 4.204 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 4.204 * [backup-simplify]: Simplify (- 0) into 0 4.205 * [backup-simplify]: Simplify (+ 0 0) into 0 4.207 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 4.214 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 3) 6)) (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 4.232 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) +nan.0) (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) +nan.0) (* (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 0)))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) 4.244 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) 4.263 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) (* k 1)) (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) into (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k)))))))))))))))))))))) 4.264 * [backup-simplify]: Simplify (/ (pow (* (* (/ 1 n) 2) PI) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) into (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 4.264 * [approximate]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0 4.264 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 4.264 * [taylor]: Taking taylor expansion of (sqrt k) in k 4.264 * [taylor]: Taking taylor expansion of k in k 4.264 * [backup-simplify]: Simplify 0 into 0 4.264 * [backup-simplify]: Simplify 1 into 1 4.264 * [backup-simplify]: Simplify (sqrt 0) into 0 4.266 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.266 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 4.266 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 4.266 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 4.266 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 4.266 * [taylor]: Taking taylor expansion of 1/2 in k 4.266 * [backup-simplify]: Simplify 1/2 into 1/2 4.266 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 4.266 * [taylor]: Taking taylor expansion of 1/2 in k 4.266 * [backup-simplify]: Simplify 1/2 into 1/2 4.266 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.266 * [taylor]: Taking taylor expansion of k in k 4.266 * [backup-simplify]: Simplify 0 into 0 4.266 * [backup-simplify]: Simplify 1 into 1 4.267 * [backup-simplify]: Simplify (/ 1 1) into 1 4.267 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 4.267 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 4.267 * [taylor]: Taking taylor expansion of 2 in k 4.267 * [backup-simplify]: Simplify 2 into 2 4.267 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.267 * [taylor]: Taking taylor expansion of PI in k 4.267 * [backup-simplify]: Simplify PI into PI 4.267 * [taylor]: Taking taylor expansion of n in k 4.267 * [backup-simplify]: Simplify n into n 4.267 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.267 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 4.267 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 4.267 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 4.268 * [backup-simplify]: Simplify (- 1/2) into -1/2 4.268 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 4.268 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 4.269 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 4.269 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 4.269 * [taylor]: Taking taylor expansion of (sqrt k) in n 4.269 * [taylor]: Taking taylor expansion of k in n 4.269 * [backup-simplify]: Simplify k into k 4.269 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 4.269 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 4.269 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 4.269 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 4.269 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 4.269 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 4.269 * [taylor]: Taking taylor expansion of 1/2 in n 4.269 * [backup-simplify]: Simplify 1/2 into 1/2 4.269 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 4.269 * [taylor]: Taking taylor expansion of 1/2 in n 4.269 * [backup-simplify]: Simplify 1/2 into 1/2 4.269 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.269 * [taylor]: Taking taylor expansion of k in n 4.269 * [backup-simplify]: Simplify k into k 4.269 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.269 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 4.269 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 4.269 * [taylor]: Taking taylor expansion of 2 in n 4.269 * [backup-simplify]: Simplify 2 into 2 4.269 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.269 * [taylor]: Taking taylor expansion of PI in n 4.269 * [backup-simplify]: Simplify PI into PI 4.269 * [taylor]: Taking taylor expansion of n in n 4.270 * [backup-simplify]: Simplify 0 into 0 4.270 * [backup-simplify]: Simplify 1 into 1 4.270 * [backup-simplify]: Simplify (/ PI 1) into PI 4.271 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 4.272 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 4.272 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 4.272 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 4.272 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 4.274 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 4.275 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 4.276 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 4.276 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 4.276 * [taylor]: Taking taylor expansion of (sqrt k) in n 4.276 * [taylor]: Taking taylor expansion of k in n 4.276 * [backup-simplify]: Simplify k into k 4.276 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 4.276 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 4.276 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 4.276 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 4.276 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 4.276 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 4.276 * [taylor]: Taking taylor expansion of 1/2 in n 4.277 * [backup-simplify]: Simplify 1/2 into 1/2 4.277 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 4.277 * [taylor]: Taking taylor expansion of 1/2 in n 4.277 * [backup-simplify]: Simplify 1/2 into 1/2 4.277 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.277 * [taylor]: Taking taylor expansion of k in n 4.277 * [backup-simplify]: Simplify k into k 4.277 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.277 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 4.277 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 4.277 * [taylor]: Taking taylor expansion of 2 in n 4.277 * [backup-simplify]: Simplify 2 into 2 4.277 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.277 * [taylor]: Taking taylor expansion of PI in n 4.277 * [backup-simplify]: Simplify PI into PI 4.277 * [taylor]: Taking taylor expansion of n in n 4.277 * [backup-simplify]: Simplify 0 into 0 4.277 * [backup-simplify]: Simplify 1 into 1 4.277 * [backup-simplify]: Simplify (/ PI 1) into PI 4.278 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 4.279 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 4.279 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 4.279 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 4.279 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 4.281 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 4.286 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 4.287 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 4.288 * [backup-simplify]: Simplify (* (sqrt k) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) 4.288 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) in k 4.288 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 4.288 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 4.288 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 4.288 * [taylor]: Taking taylor expansion of 1/2 in k 4.288 * [backup-simplify]: Simplify 1/2 into 1/2 4.288 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 4.288 * [taylor]: Taking taylor expansion of 1/2 in k 4.289 * [backup-simplify]: Simplify 1/2 into 1/2 4.289 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.289 * [taylor]: Taking taylor expansion of k in k 4.289 * [backup-simplify]: Simplify 0 into 0 4.289 * [backup-simplify]: Simplify 1 into 1 4.289 * [backup-simplify]: Simplify (/ 1 1) into 1 4.289 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 4.289 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 4.289 * [taylor]: Taking taylor expansion of (* 2 PI) in k 4.289 * [taylor]: Taking taylor expansion of 2 in k 4.289 * [backup-simplify]: Simplify 2 into 2 4.289 * [taylor]: Taking taylor expansion of PI in k 4.289 * [backup-simplify]: Simplify PI into PI 4.290 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 4.291 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 4.291 * [taylor]: Taking taylor expansion of (log n) in k 4.291 * [taylor]: Taking taylor expansion of n in k 4.291 * [backup-simplify]: Simplify n into n 4.291 * [backup-simplify]: Simplify (log n) into (log n) 4.291 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 4.292 * [backup-simplify]: Simplify (- 1/2) into -1/2 4.292 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 4.292 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 4.293 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 4.294 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 4.295 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 4.295 * [taylor]: Taking taylor expansion of (sqrt k) in k 4.295 * [taylor]: Taking taylor expansion of k in k 4.295 * [backup-simplify]: Simplify 0 into 0 4.295 * [backup-simplify]: Simplify 1 into 1 4.295 * [backup-simplify]: Simplify (sqrt 0) into 0 4.296 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.297 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) into 0 4.297 * [backup-simplify]: Simplify 0 into 0 4.298 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.298 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 4.299 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 4.299 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.300 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 4.300 * [backup-simplify]: Simplify (- 0) into 0 4.300 * [backup-simplify]: Simplify (+ 0 0) into 0 4.301 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 4.302 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 4.303 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 4.304 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0 4.304 * [taylor]: Taking taylor expansion of 0 in k 4.304 * [backup-simplify]: Simplify 0 into 0 4.304 * [backup-simplify]: Simplify 0 into 0 4.305 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 4.306 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 4.306 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.307 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 4.309 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 4.309 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.310 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 4.310 * [backup-simplify]: Simplify (- 0) into 0 4.310 * [backup-simplify]: Simplify (+ 0 0) into 0 4.311 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 4.312 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 4.314 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 4.314 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 4.315 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0 4.315 * [taylor]: Taking taylor expansion of 0 in k 4.315 * [backup-simplify]: Simplify 0 into 0 4.315 * [backup-simplify]: Simplify 0 into 0 4.315 * [backup-simplify]: Simplify 0 into 0 4.317 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.318 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 4.319 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 4.320 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.321 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.324 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 4.324 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.325 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 4.325 * [backup-simplify]: Simplify (- 0) into 0 4.326 * [backup-simplify]: Simplify (+ 0 0) into 0 4.327 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 4.329 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 4.332 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 4.333 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 4.335 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))) into 0 4.335 * [taylor]: Taking taylor expansion of 0 in k 4.335 * [backup-simplify]: Simplify 0 into 0 4.335 * [backup-simplify]: Simplify 0 into 0 4.335 * [backup-simplify]: Simplify 0 into 0 4.335 * [backup-simplify]: Simplify 0 into 0 4.339 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.340 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 4.341 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 4.343 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))))))) 4.343 * [backup-simplify]: Simplify (/ (pow (* (* (/ 1 (- n)) 2) PI) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) into (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) 4.344 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (n k) around 0 4.344 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 4.344 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 4.344 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 4.344 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 4.344 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 4.344 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 4.344 * [taylor]: Taking taylor expansion of 1/2 in k 4.344 * [backup-simplify]: Simplify 1/2 into 1/2 4.344 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.344 * [taylor]: Taking taylor expansion of k in k 4.344 * [backup-simplify]: Simplify 0 into 0 4.344 * [backup-simplify]: Simplify 1 into 1 4.344 * [backup-simplify]: Simplify (/ 1 1) into 1 4.344 * [taylor]: Taking taylor expansion of 1/2 in k 4.344 * [backup-simplify]: Simplify 1/2 into 1/2 4.344 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 4.344 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 4.344 * [taylor]: Taking taylor expansion of -2 in k 4.344 * [backup-simplify]: Simplify -2 into -2 4.344 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.344 * [taylor]: Taking taylor expansion of PI in k 4.344 * [backup-simplify]: Simplify PI into PI 4.344 * [taylor]: Taking taylor expansion of n in k 4.344 * [backup-simplify]: Simplify n into n 4.344 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.344 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 4.344 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 4.345 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 4.345 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 4.345 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 4.345 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) 4.345 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 4.345 * [taylor]: Taking taylor expansion of (/ -1 k) in k 4.345 * [taylor]: Taking taylor expansion of -1 in k 4.345 * [backup-simplify]: Simplify -1 into -1 4.345 * [taylor]: Taking taylor expansion of k in k 4.345 * [backup-simplify]: Simplify 0 into 0 4.345 * [backup-simplify]: Simplify 1 into 1 4.346 * [backup-simplify]: Simplify (/ -1 1) into -1 4.346 * [backup-simplify]: Simplify (sqrt 0) into 0 4.347 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 4.347 * [backup-simplify]: Simplify (/ (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) +nan.0) into (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) 4.347 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 4.347 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 4.347 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 4.347 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 4.347 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 4.347 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 4.347 * [taylor]: Taking taylor expansion of 1/2 in n 4.347 * [backup-simplify]: Simplify 1/2 into 1/2 4.347 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.347 * [taylor]: Taking taylor expansion of k in n 4.347 * [backup-simplify]: Simplify k into k 4.347 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.347 * [taylor]: Taking taylor expansion of 1/2 in n 4.347 * [backup-simplify]: Simplify 1/2 into 1/2 4.347 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 4.347 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 4.347 * [taylor]: Taking taylor expansion of -2 in n 4.347 * [backup-simplify]: Simplify -2 into -2 4.347 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.347 * [taylor]: Taking taylor expansion of PI in n 4.347 * [backup-simplify]: Simplify PI into PI 4.347 * [taylor]: Taking taylor expansion of n in n 4.347 * [backup-simplify]: Simplify 0 into 0 4.347 * [backup-simplify]: Simplify 1 into 1 4.348 * [backup-simplify]: Simplify (/ PI 1) into PI 4.348 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 4.349 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 4.349 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 4.349 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 4.350 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 4.350 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 4.351 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 4.351 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 4.351 * [taylor]: Taking taylor expansion of (/ -1 k) in n 4.351 * [taylor]: Taking taylor expansion of -1 in n 4.351 * [backup-simplify]: Simplify -1 into -1 4.351 * [taylor]: Taking taylor expansion of k in n 4.351 * [backup-simplify]: Simplify k into k 4.351 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 4.351 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 4.351 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 4.351 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 4.352 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) 4.352 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 4.352 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 4.352 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 4.352 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 4.352 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 4.352 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 4.352 * [taylor]: Taking taylor expansion of 1/2 in n 4.352 * [backup-simplify]: Simplify 1/2 into 1/2 4.352 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.352 * [taylor]: Taking taylor expansion of k in n 4.352 * [backup-simplify]: Simplify k into k 4.352 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.352 * [taylor]: Taking taylor expansion of 1/2 in n 4.352 * [backup-simplify]: Simplify 1/2 into 1/2 4.352 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 4.352 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 4.352 * [taylor]: Taking taylor expansion of -2 in n 4.352 * [backup-simplify]: Simplify -2 into -2 4.352 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.352 * [taylor]: Taking taylor expansion of PI in n 4.352 * [backup-simplify]: Simplify PI into PI 4.352 * [taylor]: Taking taylor expansion of n in n 4.352 * [backup-simplify]: Simplify 0 into 0 4.352 * [backup-simplify]: Simplify 1 into 1 4.353 * [backup-simplify]: Simplify (/ PI 1) into PI 4.353 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 4.354 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 4.354 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 4.354 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 4.355 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 4.355 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 4.356 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 4.356 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 4.356 * [taylor]: Taking taylor expansion of (/ -1 k) in n 4.356 * [taylor]: Taking taylor expansion of -1 in n 4.356 * [backup-simplify]: Simplify -1 into -1 4.356 * [taylor]: Taking taylor expansion of k in n 4.356 * [backup-simplify]: Simplify k into k 4.356 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 4.356 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 4.356 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 4.357 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 4.357 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) 4.357 * [taylor]: Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) in k 4.357 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 4.357 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 4.357 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 4.357 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 4.357 * [taylor]: Taking taylor expansion of 1/2 in k 4.357 * [backup-simplify]: Simplify 1/2 into 1/2 4.357 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.358 * [taylor]: Taking taylor expansion of k in k 4.358 * [backup-simplify]: Simplify 0 into 0 4.358 * [backup-simplify]: Simplify 1 into 1 4.358 * [backup-simplify]: Simplify (/ 1 1) into 1 4.358 * [taylor]: Taking taylor expansion of 1/2 in k 4.358 * [backup-simplify]: Simplify 1/2 into 1/2 4.358 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 4.358 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 4.358 * [taylor]: Taking taylor expansion of (* -2 PI) in k 4.358 * [taylor]: Taking taylor expansion of -2 in k 4.358 * [backup-simplify]: Simplify -2 into -2 4.358 * [taylor]: Taking taylor expansion of PI in k 4.358 * [backup-simplify]: Simplify PI into PI 4.358 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 4.359 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 4.359 * [taylor]: Taking taylor expansion of (log n) in k 4.359 * [taylor]: Taking taylor expansion of n in k 4.359 * [backup-simplify]: Simplify n into n 4.359 * [backup-simplify]: Simplify (log n) into (log n) 4.359 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 4.360 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 4.360 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 4.360 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 4.361 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 4.362 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 4.362 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 4.362 * [taylor]: Taking taylor expansion of (/ -1 k) in k 4.362 * [taylor]: Taking taylor expansion of -1 in k 4.362 * [backup-simplify]: Simplify -1 into -1 4.362 * [taylor]: Taking taylor expansion of k in k 4.362 * [backup-simplify]: Simplify 0 into 0 4.362 * [backup-simplify]: Simplify 1 into 1 4.362 * [backup-simplify]: Simplify (/ -1 1) into -1 4.362 * [backup-simplify]: Simplify (sqrt 0) into 0 4.363 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 4.364 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) +nan.0) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 4.365 * [backup-simplify]: Simplify (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 4.365 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.366 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 4.367 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 4.367 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.367 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 4.367 * [backup-simplify]: Simplify (+ 0 0) into 0 4.368 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 4.369 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 4.370 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 4.371 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0 4.371 * [taylor]: Taking taylor expansion of 0 in k 4.371 * [backup-simplify]: Simplify 0 into 0 4.371 * [backup-simplify]: Simplify 0 into 0 4.372 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 4.374 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.375 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 4.376 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 4.377 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.377 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 4.381 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 4.381 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.382 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 4.382 * [backup-simplify]: Simplify (+ 0 0) into 0 4.383 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 4.384 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 4.386 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 4.386 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.386 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 4.387 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0 4.387 * [taylor]: Taking taylor expansion of 0 in k 4.387 * [backup-simplify]: Simplify 0 into 0 4.387 * [backup-simplify]: Simplify 0 into 0 4.387 * [backup-simplify]: Simplify 0 into 0 4.388 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.390 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.392 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 4.393 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 4.397 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))) 4.397 * * * [progress]: simplifying candidates 4.397 * * * * [progress]: [ 1 / 445 ] simplifiying candidate # 4.398 * * * * [progress]: [ 2 / 445 ] simplifiying candidate # 4.398 * * * * [progress]: [ 3 / 445 ] simplifiying candidate # 4.398 * * * * [progress]: [ 4 / 445 ] simplifiying candidate # 4.398 * * * * [progress]: [ 5 / 445 ] simplifiying candidate # 4.398 * * * * [progress]: [ 6 / 445 ] simplifiying candidate # 4.398 * * * * [progress]: [ 7 / 445 ] simplifiying candidate # 4.398 * * * * [progress]: [ 8 / 445 ] simplifiying candidate # 4.398 * * * * [progress]: [ 9 / 445 ] simplifiying candidate # 4.398 * * * * [progress]: [ 10 / 445 ] simplifiying candidate # 4.398 * 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candidate # 4.402 * * * * [progress]: [ 58 / 445 ] simplifiying candidate # 4.402 * * * * [progress]: [ 59 / 445 ] simplifiying candidate # 4.402 * * * * [progress]: [ 60 / 445 ] simplifiying candidate # 4.402 * * * * [progress]: [ 61 / 445 ] simplifiying candidate # 4.402 * * * * [progress]: [ 62 / 445 ] simplifiying candidate # 4.402 * * * * [progress]: [ 63 / 445 ] simplifiying candidate # 4.402 * * * * [progress]: [ 64 / 445 ] simplifiying candidate # 4.402 * * * * [progress]: [ 65 / 445 ] simplifiying candidate # 4.403 * * * * [progress]: [ 66 / 445 ] simplifiying candidate # 4.403 * * * * [progress]: [ 67 / 445 ] simplifiying candidate #real (real->posit16 (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k)))> 4.403 * * * * [progress]: [ 68 / 445 ] simplifiying candidate # 4.403 * * * * [progress]: [ 69 / 445 ] simplifiying candidate # 4.403 * * * * [progress]: [ 70 / 445 ] simplifiying candidate # 4.403 * * * * [progress]: [ 71 / 445 ] simplifiying candidate # 4.403 * * * * 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candidate #real (real->posit16 (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt k)))> 4.404 * * * * [progress]: [ 88 / 445 ] simplifiying candidate # 4.404 * * * * [progress]: [ 89 / 445 ] simplifiying candidate # 4.404 * * * * [progress]: [ 90 / 445 ] simplifiying candidate # 4.404 * * * * [progress]: [ 91 / 445 ] simplifiying candidate # 4.404 * * * * [progress]: [ 92 / 445 ] simplifiying candidate # 4.404 * * * * [progress]: [ 93 / 445 ] simplifiying candidate # 4.404 * * * * [progress]: [ 94 / 445 ] simplifiying candidate # 4.404 * * * * [progress]: [ 95 / 445 ] simplifiying candidate # 4.405 * * * * [progress]: [ 96 / 445 ] simplifiying candidate # 4.405 * * * * [progress]: [ 97 / 445 ] simplifiying candidate # 4.405 * * * * [progress]: [ 98 / 445 ] simplifiying candidate # 4.405 * * * * [progress]: [ 99 / 445 ] simplifiying candidate # 4.405 * * * * [progress]: [ 100 / 445 ] simplifiying candidate # 4.405 * * * * [progress]: [ 101 / 445 ] simplifiying candidate # 4.405 * * * * [progress]: 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(sqrt (- 1/2 (/ k 2)))) (pow (* (* n 2) PI) 1) (pow (* (* n 2) PI) (+ (sqrt 1/2) (sqrt (/ k 2)))) (pow (* (* n 2) PI) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (pow (* (* n 2) PI) 1) (pow (* (* n 2) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (pow (* (* n 2) PI) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) (pow (* (* n 2) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (sqrt (/ k 2)) (sqrt (/ k 2)))))) (pow (* (* n 2) PI) (fma (- (sqrt (/ k 2))) (sqrt (/ k 2)) (* (sqrt (/ k 2)) (sqrt (/ k 2))))) (pow (* (* n 2) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))))))) (pow (* (* n 2) PI) (fma (- (/ (cbrt k) (cbrt 2))) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))) (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2)))))) (pow (* (* n 2) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (pow (* (* n 2) PI) (fma (- (/ (cbrt k) (sqrt 2))) (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2))))) (pow (* (* n 2) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1))))) (pow (* (* n 2) PI) (fma (- (/ (cbrt k) 2)) (/ (* (cbrt k) (cbrt k)) 1) (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1)))) (pow (* (* n 2) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2))))))) (pow (* (* n 2) PI) (fma (- (/ (sqrt k) (cbrt 2))) (/ (sqrt k) (* (cbrt 2) (cbrt 2))) (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2)))))) (pow (* (* n 2) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (pow (* (* n 2) PI) (fma (- (/ (sqrt k) (sqrt 2))) (/ (sqrt k) (sqrt 2)) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2))))) (pow (* (* n 2) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) 2) (/ (sqrt k) 1))))) (pow (* (* n 2) PI) (fma (- (/ (sqrt k) 2)) (/ (sqrt k) 1) (* (/ (sqrt k) 2) (/ (sqrt k) 1)))) (pow (* (* n 2) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2))))))) (pow (* (* n 2) PI) (fma (- (/ k (cbrt 2))) (/ 1 (* (cbrt 2) (cbrt 2))) (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2)))))) (pow (* (* n 2) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k (sqrt 2)) (/ 1 (sqrt 2)))))) (pow (* (* n 2) PI) (fma (- (/ k (sqrt 2))) (/ 1 (sqrt 2)) (* (/ k (sqrt 2)) (/ 1 (sqrt 2))))) (pow (* (* n 2) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k 2) (/ 1 1))))) (pow (* (* n 2) PI) (fma (- (/ k 2)) (/ 1 1) (* (/ k 2) (/ 1 1)))) (pow (* (* n 2) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k 2) 1)))) (pow (* (* n 2) PI) (fma (- (/ k 2)) 1 (* (/ k 2) 1))) (pow (* (* n 2) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ 1 2) k)))) (pow (* (* n 2) PI) (fma (- (/ 1 2)) k (* (/ 1 2) k))) (pow (* (* n 2) PI) (fma (sqrt 1/2) (sqrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (pow (* (* n 2) PI) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) (pow (* (* n 2) PI) (fma (sqrt 1/2) (sqrt 1/2) (- (* (sqrt (/ k 2)) (sqrt (/ k 2)))))) (pow (* (* n 2) PI) (fma (- (sqrt (/ k 2))) (sqrt (/ k 2)) (* (sqrt (/ k 2)) (sqrt (/ k 2))))) (pow (* (* n 2) PI) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))))))) (pow (* (* n 2) PI) (fma (- (/ (cbrt k) (cbrt 2))) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))) (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2)))))) (pow (* (* n 2) PI) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (pow (* (* n 2) PI) (fma (- (/ (cbrt k) (sqrt 2))) (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt 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(exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))))))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))) 4.450 * * [simplify]: iteration 0: 699 enodes 4.745 * * [simplify]: iteration 1: 1539 enodes 5.357 * * [simplify]: iteration 2: 4377 enodes 6.368 * * [simplify]: iteration complete: 5000 enodes 6.368 * * [simplify]: Extracting #0: cost 223 inf + 0 6.371 * * [simplify]: Extracting #1: cost 832 inf + 1 6.376 * * [simplify]: Extracting #2: cost 1323 inf + 1230 6.387 * * [simplify]: Extracting #3: cost 1445 inf + 38814 6.418 * * [simplify]: Extracting #4: cost 968 inf + 208564 6.518 * * [simplify]: Extracting #5: cost 510 inf + 417167 6.695 * * [simplify]: Extracting #6: cost 258 inf + 566851 6.911 * * [simplify]: Extracting #7: cost 46 inf + 704759 7.156 * * [simplify]: Extracting #8: cost 3 inf + 738606 7.379 * * [simplify]: Extracting #9: cost 0 inf + 743199 7.545 * * [simplify]: Extracting #10: cost 0 inf + 742834 7.752 * [simplify]: Simplified to: (expm1 (pow (* 2 (* PI n)) (- 1/2 (* k 1/2)))) (log1p (pow (* 2 (* PI n)) (- 1/2 (* k 1/2)))) (* (log (* 2 (* PI n))) (- 1/2 (* k 1/2))) (* (log (* 2 (* PI n))) (- 1/2 (* k 1/2))) (* (log (* 2 (* PI n))) (- 1/2 (* k 1/2))) (* (log (* 2 (* PI n))) (- 1/2 (* k 1/2))) (- 1/2 (* k 1/2)) (- 1/2 (* k 1/2)) (- 1/2 (* k 1/2)) (sqrt (* 2 (* PI n))) (pow (* 2 (* PI n)) (* k 1/2)) (pow (* 2 (* PI n)) (* (cbrt (- 1/2 (* k 1/2))) (cbrt (- 1/2 (* k 1/2))))) (pow (* 2 (* PI n)) (sqrt (- 1/2 (* k 1/2)))) (* 2 (* PI n)) (pow (* 2 (* PI n)) (+ (sqrt 1/2) (sqrt (* k 1/2)))) (pow (* 2 (* PI n)) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (* 2 (* PI n)) (pow (* 2 (* PI n)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* k 1/2)))) (pow (* 2 (* PI n)) (fma (* k 1/2) -1 (* k 1/2))) (pow (* 2 (* PI n)) (fma (* (cbrt 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(sqrt k))) (/ (pow (* 2 (* PI n)) (/ (- 1/2 (* k 1/2)) 2)) (sqrt (sqrt k))) (pow (* 2 (* PI n)) (/ (- 1/2 (* k 1/2)) 2)) (/ (pow (* 2 (* PI n)) (/ (- 1/2 (* k 1/2)) 2)) (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) (pow (* 2 (* PI n)) (- 1/2 (* k 1/2)))) (/ (pow (* 2 (* PI n)) (- 1/2 (* k 1/2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* 2 (* PI n)) (- 1/2 (* k 1/2))) (fabs (cbrt k))) (/ (pow (* 2 (* PI n)) (- 1/2 (* k 1/2))) (sqrt (sqrt k))) (pow (* 2 (* PI n)) (- 1/2 (* k 1/2))) (/ (pow (* 2 (* PI n)) (- 1/2 (* k 1/2))) (sqrt (sqrt k))) (pow (* 2 (* PI n)) (- 1/2 (* k 1/2))) (/ (sqrt k) (pow (* 2 (* PI n)) (fma (* k 1/2) -1 (* k 1/2)))) (/ (sqrt k) (pow (* 2 (* PI n)) (fma (* k 1/2) -1 (* k 1/2)))) (/ (sqrt k) (pow (* 2 (* PI n)) (* (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2))) (+ (- (/ (cbrt k) (cbrt 2))) (/ (cbrt k) (cbrt 2)))))) (/ (sqrt k) (pow (* 2 (* PI n)) (* (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (+ (- (/ (cbrt k) (sqrt 2))) (/ (cbrt k) (sqrt 2)))))) (/ (sqrt k) (pow (* 2 (* PI n)) (* (/ (cbrt k) 2) (+ (- (* (cbrt k) (cbrt k))) (* (cbrt k) (cbrt k)))))) (/ (sqrt k) (pow (* 2 (* PI n)) (* (/ (sqrt k) (* (cbrt 2) (cbrt 2))) (+ (- (/ (sqrt k) (cbrt 2))) (/ (sqrt k) (cbrt 2)))))) (/ (sqrt k) (pow (* 2 (* PI n)) (+ (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (/ (sqrt k) (pow (* 2 (* PI n)) (fma (* k 1/2) -1 (* k 1/2)))) (/ (sqrt k) (pow (* 2 (* PI n)) (+ (- (/ (/ (/ k (cbrt 2)) (cbrt 2)) (cbrt 2))) (/ (/ (/ k (cbrt 2)) (cbrt 2)) (cbrt 2))))) (/ (sqrt k) (pow (* 2 (* PI n)) (fma (/ -1 (sqrt 2)) (/ k (sqrt 2)) (/ (/ k (sqrt 2)) (sqrt 2))))) (/ (sqrt k) (pow (* 2 (* PI n)) (fma (* k 1/2) -1 (* k 1/2)))) (/ (sqrt k) (pow (* 2 (* PI n)) (fma (* k 1/2) -1 (* k 1/2)))) (/ (sqrt k) (pow (* 2 (* PI n)) (fma -1/2 k (* k 1/2)))) (/ (sqrt k) (pow (* 2 (* PI n)) (fma (* k 1/2) -1 (* k 1/2)))) (/ (sqrt k) (pow (* 2 (* PI n)) (fma (* k 1/2) -1 (* k 1/2)))) (/ (sqrt k) (pow (* 2 (* PI n)) (* (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2))) (+ (- (/ (cbrt k) (cbrt 2))) (/ (cbrt k) (cbrt 2)))))) (/ (sqrt k) (pow (* 2 (* PI n)) (* (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (+ (- (/ (cbrt k) (sqrt 2))) (/ (cbrt k) (sqrt 2)))))) (/ (sqrt k) (pow (* 2 (* PI n)) (* (/ (cbrt k) 2) (+ (- (* (cbrt k) (cbrt k))) (* (cbrt k) (cbrt k)))))) (/ (sqrt k) (pow (* 2 (* PI n)) (* (/ (sqrt k) (* (cbrt 2) (cbrt 2))) (+ (- (/ (sqrt k) (cbrt 2))) (/ (sqrt k) (cbrt 2)))))) (/ (sqrt k) (pow (* 2 (* PI n)) (+ (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (/ (sqrt k) (pow (* 2 (* PI n)) (fma (* k 1/2) -1 (* k 1/2)))) (/ (sqrt k) (pow (* 2 (* PI n)) (+ (- (/ (/ (/ k (cbrt 2)) (cbrt 2)) (cbrt 2))) (/ (/ (/ k (cbrt 2)) (cbrt 2)) (cbrt 2))))) (/ (sqrt k) (pow (* 2 (* PI n)) (fma (/ -1 (sqrt 2)) (/ k (sqrt 2)) (/ (/ k (sqrt 2)) (sqrt 2))))) (/ (sqrt k) (pow (* 2 (* PI n)) (fma (* k 1/2) -1 (* k 1/2)))) (/ (sqrt k) (pow (* 2 (* PI n)) (fma (* k 1/2) -1 (* k 1/2)))) (/ (sqrt k) (pow (* 2 (* PI n)) (fma -1/2 k (* k 1/2)))) (/ (sqrt k) (pow (* 2 (* PI n)) (fma (* k 1/2) -1 (* k 1/2)))) (/ (sqrt k) (pow (* 2 (* PI n)) (fma (* k 1/2) -1 (* k 1/2)))) (/ (sqrt k) (pow (* 2 (* PI n)) (* (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2))) (+ (- (/ (cbrt k) (cbrt 2))) (/ (cbrt k) (cbrt 2)))))) (/ (sqrt k) (pow (* 2 (* PI n)) (* (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (+ (- (/ (cbrt k) (sqrt 2))) (/ (cbrt k) (sqrt 2)))))) (/ (sqrt k) (pow (* 2 (* PI n)) (* (/ (cbrt k) 2) (+ (- (* (cbrt k) (cbrt k))) (* (cbrt k) (cbrt k)))))) (/ (sqrt k) (pow (* 2 (* PI n)) (* (/ (sqrt k) (* (cbrt 2) (cbrt 2))) (+ (- (/ (sqrt k) (cbrt 2))) (/ (sqrt k) (cbrt 2)))))) (/ (sqrt k) (pow (* 2 (* PI n)) (+ (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (/ (sqrt k) (pow (* 2 (* PI n)) (fma (* k 1/2) -1 (* k 1/2)))) (/ (sqrt k) (pow (* 2 (* PI n)) (+ (- (/ (/ (/ k (cbrt 2)) (cbrt 2)) (cbrt 2))) (/ (/ (/ k (cbrt 2)) (cbrt 2)) (cbrt 2))))) (/ (sqrt k) (pow (* 2 (* PI n)) (fma (/ -1 (sqrt 2)) (/ k (sqrt 2)) (/ (/ k (sqrt 2)) (sqrt 2))))) (/ (sqrt k) (pow (* 2 (* PI n)) (fma (* k 1/2) -1 (* k 1/2)))) (/ (sqrt k) (pow (* 2 (* PI n)) (fma (* k 1/2) -1 (* k 1/2)))) (/ (sqrt k) (pow (* 2 (* PI n)) (fma -1/2 k (* k 1/2)))) (/ (sqrt k) (pow (* 2 (* PI n)) (- (* k 1/2)))) (/ (sqrt k) (pow (* 2 (* PI n)) (- (* k 1/2)))) (/ (sqrt k) (pow PI (- 1/2 (* k 1/2)))) (/ (sqrt k) (cbrt (pow (* 2 (* PI n)) (- 1/2 (* k 1/2))))) (/ (sqrt k) (sqrt (pow (* 2 (* PI n)) (- 1/2 (* k 1/2))))) (/ (sqrt k) (pow (* 2 (* PI n)) (- 1/2 (* k 1/2)))) (/ (sqrt k) (pow (* 2 (* PI n)) (/ (- 1/2 (* k 1/2)) 2))) (* (pow (* 2 (* PI n)) (* k 1/2)) (sqrt k)) (real->posit16 (/ (pow (* 2 (* PI n)) (- 1/2 (* k 1/2))) (sqrt k))) (fma -1/2 (* k (fma (pow (* 2 (* PI n)) 1/2) (log n) (* (log (* PI 2)) (pow (* 2 (* PI n)) 1/2)))) (+ (fma (* 1/8 (* (* (* k k) (log n)) (log n))) (pow (* 2 (* PI n)) 1/2) (pow (* 2 (* PI n)) 1/2)) (fma (* (log (* PI 2)) (* (log (* PI 2)) (pow (* 2 (* PI n)) 1/2))) (* (* k k) 1/8) (* (* (log (* PI 2)) (pow (* 2 (* PI n)) 1/2)) (* (* (* k k) (log n)) 1/4))))) (exp (* (log (* 2 (* PI n))) (- 1/2 (* k 1/2)))) (exp (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1/2 (* k 1/2)))) (* 2 (* PI n)) (* 2 (* PI n)) (* 2 (* PI n)) (fma (- (* +nan.0 (log (* PI 2)))) (* (* (* k k) (log n)) (exp (* (log (* 2 (* PI n))) 1/2))) (fma (* (exp (* (log (* 2 (* PI n))) 1/2)) (* k k)) (* +nan.0 (log (* PI 2))) (fma (* +nan.0 (exp (* (log (* 2 (* PI n))) 1/2))) (- (* (* (* k k) (log n)) (log n))) (+ (- (* +nan.0 (* k (exp (* (log (* 2 (* PI n))) 1/2)))) (* +nan.0 (exp (* (log (* 2 (* PI n))) 1/2)))) (fma +nan.0 (* (exp (* (log (* 2 (* PI n))) 1/2)) (* (* k k) (* (log (* PI 2)) (log (* PI 2))))) (fma (* +nan.0 (exp (* (log (* 2 (* PI n))) 1/2))) (- (* (* k k) (log n))) (fma (* +nan.0 (exp (* (log (* 2 (* PI n))) 1/2))) (* k k) (fma (* +nan.0 (* k (exp (* (log (* 2 (* PI n))) 1/2)))) (log n) (* (- (* +nan.0 (log (* PI 2)))) (* k (exp (* (log (* 2 (* PI n))) 1/2)))))))))))) (fma (- +nan.0) (/ (/ (exp (* (log (* 2 (* PI n))) (- 1/2 (* k 1/2)))) (* k k)) k) (* +nan.0 (- (/ (exp (* (log (* 2 (* PI n))) (- 1/2 (* k 1/2)))) k) (/ (exp (* (log (* 2 (* PI n))) (- 1/2 (* k 1/2)))) (* k k))))) (fma +nan.0 (- (/ (exp (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1/2 (* k 1/2)))) k)) (* +nan.0 (- (/ (exp (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1/2 (* k 1/2)))) (* k k)) (exp (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1/2 (* k 1/2))))))) 7.894 * * * [progress]: adding candidates to table 10.802 * * [progress]: iteration 2 / 4 10.802 * * * [progress]: picking best candidate 10.841 * * * * [pick]: Picked # 10.841 * * * [progress]: localizing error 10.889 * * * [progress]: generating rewritten candidates 10.889 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 10.938 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1) 10.952 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1) 10.986 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 11.063 * * * [progress]: generating series expansions 11.063 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 11.064 * [backup-simplify]: Simplify (pow (* (* 2 PI) n) (/ (- 1 k) 2)) into (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) 11.064 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in (n k) around 0 11.064 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k 11.064 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k 11.064 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k 11.064 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k 11.064 * [taylor]: Taking taylor expansion of 1/2 in k 11.064 * [backup-simplify]: Simplify 1/2 into 1/2 11.064 * [taylor]: Taking taylor expansion of (- 1 k) in k 11.064 * [taylor]: Taking taylor expansion of 1 in k 11.064 * [backup-simplify]: Simplify 1 into 1 11.064 * [taylor]: Taking taylor expansion of k in k 11.064 * [backup-simplify]: Simplify 0 into 0 11.064 * [backup-simplify]: Simplify 1 into 1 11.064 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 11.064 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 11.064 * [taylor]: Taking taylor expansion of 2 in k 11.064 * [backup-simplify]: Simplify 2 into 2 11.064 * [taylor]: Taking taylor expansion of (* n PI) in k 11.064 * [taylor]: Taking taylor expansion of n in k 11.064 * [backup-simplify]: Simplify n into n 11.064 * [taylor]: Taking taylor expansion of PI in k 11.064 * [backup-simplify]: Simplify PI into PI 11.064 * [backup-simplify]: Simplify (* n PI) into (* n PI) 11.064 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 11.065 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 11.065 * [backup-simplify]: Simplify (- 0) into 0 11.065 * [backup-simplify]: Simplify (+ 1 0) into 1 11.065 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 11.066 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 11.066 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 11.066 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n 11.066 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n 11.066 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n 11.066 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n 11.066 * [taylor]: Taking taylor expansion of 1/2 in n 11.066 * [backup-simplify]: Simplify 1/2 into 1/2 11.066 * [taylor]: Taking taylor expansion of (- 1 k) in n 11.066 * [taylor]: Taking taylor expansion of 1 in n 11.066 * [backup-simplify]: Simplify 1 into 1 11.066 * [taylor]: Taking taylor expansion of k in n 11.066 * [backup-simplify]: Simplify k into k 11.066 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 11.066 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 11.066 * [taylor]: Taking taylor expansion of 2 in n 11.066 * [backup-simplify]: Simplify 2 into 2 11.066 * [taylor]: Taking taylor expansion of (* n PI) in n 11.066 * [taylor]: Taking taylor expansion of n in n 11.066 * [backup-simplify]: Simplify 0 into 0 11.066 * [backup-simplify]: Simplify 1 into 1 11.066 * [taylor]: Taking taylor expansion of PI in n 11.066 * [backup-simplify]: Simplify PI into PI 11.066 * [backup-simplify]: Simplify (* 0 PI) into 0 11.067 * [backup-simplify]: Simplify (* 2 0) into 0 11.068 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.069 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 11.069 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.069 * [backup-simplify]: Simplify (- k) into (- k) 11.069 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k) 11.069 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k)) 11.070 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 11.071 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) 11.072 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 11.072 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n 11.072 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n 11.072 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n 11.072 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n 11.072 * [taylor]: Taking taylor expansion of 1/2 in n 11.072 * [backup-simplify]: Simplify 1/2 into 1/2 11.072 * [taylor]: Taking taylor expansion of (- 1 k) in n 11.072 * [taylor]: Taking taylor expansion of 1 in n 11.072 * [backup-simplify]: Simplify 1 into 1 11.072 * [taylor]: Taking taylor expansion of k in n 11.072 * [backup-simplify]: Simplify k into k 11.072 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 11.072 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 11.072 * [taylor]: Taking taylor expansion of 2 in n 11.072 * [backup-simplify]: Simplify 2 into 2 11.072 * [taylor]: Taking taylor expansion of (* n PI) in n 11.072 * [taylor]: Taking taylor expansion of n in n 11.072 * [backup-simplify]: Simplify 0 into 0 11.072 * [backup-simplify]: Simplify 1 into 1 11.072 * [taylor]: Taking taylor expansion of PI in n 11.072 * [backup-simplify]: Simplify PI into PI 11.073 * [backup-simplify]: Simplify (* 0 PI) into 0 11.073 * [backup-simplify]: Simplify (* 2 0) into 0 11.074 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.075 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 11.075 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.076 * [backup-simplify]: Simplify (- k) into (- k) 11.076 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k) 11.076 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k)) 11.076 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 11.077 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) 11.078 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 11.078 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) in k 11.078 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) in k 11.078 * [taylor]: Taking taylor expansion of 1/2 in k 11.078 * [backup-simplify]: Simplify 1/2 into 1/2 11.078 * [taylor]: Taking taylor expansion of (* (- 1 k) (+ (log n) (log (* 2 PI)))) in k 11.078 * [taylor]: Taking taylor expansion of (- 1 k) in k 11.078 * [taylor]: Taking taylor expansion of 1 in k 11.078 * [backup-simplify]: Simplify 1 into 1 11.078 * [taylor]: Taking taylor expansion of k in k 11.078 * [backup-simplify]: Simplify 0 into 0 11.078 * [backup-simplify]: Simplify 1 into 1 11.078 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 11.078 * [taylor]: Taking taylor expansion of (log n) in k 11.078 * [taylor]: Taking taylor expansion of n in k 11.078 * [backup-simplify]: Simplify n into n 11.078 * [backup-simplify]: Simplify (log n) into (log n) 11.078 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 11.078 * [taylor]: Taking taylor expansion of (* 2 PI) in k 11.078 * [taylor]: Taking taylor expansion of 2 in k 11.078 * [backup-simplify]: Simplify 2 into 2 11.078 * [taylor]: Taking taylor expansion of PI in k 11.078 * [backup-simplify]: Simplify PI into PI 11.079 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.079 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.080 * [backup-simplify]: Simplify (- 0) into 0 11.080 * [backup-simplify]: Simplify (+ 1 0) into 1 11.081 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 11.081 * [backup-simplify]: Simplify (* 1 (+ (log n) (log (* 2 PI)))) into (+ (log n) (log (* 2 PI))) 11.082 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 11.083 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 11.084 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 11.084 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 11.085 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 11.086 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 11.086 * [backup-simplify]: Simplify (- 0) into 0 11.087 * [backup-simplify]: Simplify (+ 0 0) into 0 11.087 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 k))) into 0 11.088 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 11.089 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 11.090 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0 11.090 * [taylor]: Taking taylor expansion of 0 in k 11.090 * [backup-simplify]: Simplify 0 into 0 11.090 * [backup-simplify]: Simplify 0 into 0 11.091 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 11.091 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 11.092 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 11.093 * [backup-simplify]: Simplify (+ 0 0) into 0 11.093 * [backup-simplify]: Simplify (- 1) into -1 11.093 * [backup-simplify]: Simplify (+ 0 -1) into -1 11.094 * [backup-simplify]: Simplify (+ (* 1 0) (* -1 (+ (log n) (log (* 2 PI))))) into (- (+ (log (* 2 PI)) (log n))) 11.095 * [backup-simplify]: Simplify (+ (* 1/2 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 11.097 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 11.099 * [backup-simplify]: Simplify (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 11.100 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 11.101 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 11.103 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 11.103 * [backup-simplify]: Simplify (- 0) into 0 11.104 * [backup-simplify]: Simplify (+ 0 0) into 0 11.104 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0 11.106 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 11.107 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 11.110 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 11.110 * [taylor]: Taking taylor expansion of 0 in k 11.110 * [backup-simplify]: Simplify 0 into 0 11.110 * [backup-simplify]: Simplify 0 into 0 11.110 * [backup-simplify]: Simplify 0 into 0 11.112 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 11.113 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 11.116 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 11.116 * [backup-simplify]: Simplify (+ 0 0) into 0 11.117 * [backup-simplify]: Simplify (- 0) into 0 11.117 * [backup-simplify]: Simplify (+ 0 0) into 0 11.119 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 11.122 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 11.126 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 11.132 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 11.139 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) 11.140 * [backup-simplify]: Simplify (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) into (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) 11.140 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in (n k) around 0 11.140 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k 11.140 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k 11.140 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k 11.140 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k 11.140 * [taylor]: Taking taylor expansion of 1/2 in k 11.140 * [backup-simplify]: Simplify 1/2 into 1/2 11.140 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k 11.140 * [taylor]: Taking taylor expansion of 1 in k 11.140 * [backup-simplify]: Simplify 1 into 1 11.140 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.140 * [taylor]: Taking taylor expansion of k in k 11.140 * [backup-simplify]: Simplify 0 into 0 11.140 * [backup-simplify]: Simplify 1 into 1 11.140 * [backup-simplify]: Simplify (/ 1 1) into 1 11.140 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 11.140 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 11.140 * [taylor]: Taking taylor expansion of 2 in k 11.140 * [backup-simplify]: Simplify 2 into 2 11.140 * [taylor]: Taking taylor expansion of (/ PI n) in k 11.140 * [taylor]: Taking taylor expansion of PI in k 11.140 * [backup-simplify]: Simplify PI into PI 11.140 * [taylor]: Taking taylor expansion of n in k 11.140 * [backup-simplify]: Simplify n into n 11.140 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 11.140 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 11.140 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 11.141 * [backup-simplify]: Simplify (- 1) into -1 11.141 * [backup-simplify]: Simplify (+ 0 -1) into -1 11.141 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2 11.141 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 11.141 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 11.141 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n 11.141 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n 11.142 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n 11.142 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n 11.142 * [taylor]: Taking taylor expansion of 1/2 in n 11.142 * [backup-simplify]: Simplify 1/2 into 1/2 11.142 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n 11.142 * [taylor]: Taking taylor expansion of 1 in n 11.142 * [backup-simplify]: Simplify 1 into 1 11.142 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.142 * [taylor]: Taking taylor expansion of k in n 11.142 * [backup-simplify]: Simplify k into k 11.142 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.142 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 11.142 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 11.142 * [taylor]: Taking taylor expansion of 2 in n 11.142 * [backup-simplify]: Simplify 2 into 2 11.142 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.142 * [taylor]: Taking taylor expansion of PI in n 11.142 * [backup-simplify]: Simplify PI into PI 11.142 * [taylor]: Taking taylor expansion of n in n 11.142 * [backup-simplify]: Simplify 0 into 0 11.142 * [backup-simplify]: Simplify 1 into 1 11.142 * [backup-simplify]: Simplify (/ PI 1) into PI 11.142 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.143 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.143 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 11.143 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 11.143 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k))) 11.144 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 11.145 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 11.149 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 11.149 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n 11.149 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n 11.149 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n 11.149 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n 11.149 * [taylor]: Taking taylor expansion of 1/2 in n 11.149 * [backup-simplify]: Simplify 1/2 into 1/2 11.149 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n 11.149 * [taylor]: Taking taylor expansion of 1 in n 11.149 * [backup-simplify]: Simplify 1 into 1 11.149 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.149 * [taylor]: Taking taylor expansion of k in n 11.149 * [backup-simplify]: Simplify k into k 11.149 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.149 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 11.149 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 11.149 * [taylor]: Taking taylor expansion of 2 in n 11.149 * [backup-simplify]: Simplify 2 into 2 11.149 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.149 * [taylor]: Taking taylor expansion of PI in n 11.149 * [backup-simplify]: Simplify PI into PI 11.149 * [taylor]: Taking taylor expansion of n in n 11.149 * [backup-simplify]: Simplify 0 into 0 11.149 * [backup-simplify]: Simplify 1 into 1 11.150 * [backup-simplify]: Simplify (/ PI 1) into PI 11.150 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.151 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.151 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 11.151 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 11.151 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k))) 11.152 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 11.153 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 11.153 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 11.154 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k 11.154 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k 11.154 * [taylor]: Taking taylor expansion of 1/2 in k 11.154 * [backup-simplify]: Simplify 1/2 into 1/2 11.154 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k 11.154 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k 11.154 * [taylor]: Taking taylor expansion of 1 in k 11.154 * [backup-simplify]: Simplify 1 into 1 11.154 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.154 * [taylor]: Taking taylor expansion of k in k 11.154 * [backup-simplify]: Simplify 0 into 0 11.154 * [backup-simplify]: Simplify 1 into 1 11.154 * [backup-simplify]: Simplify (/ 1 1) into 1 11.154 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 11.154 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 11.154 * [taylor]: Taking taylor expansion of (* 2 PI) in k 11.154 * [taylor]: Taking taylor expansion of 2 in k 11.154 * [backup-simplify]: Simplify 2 into 2 11.154 * [taylor]: Taking taylor expansion of PI in k 11.154 * [backup-simplify]: Simplify PI into PI 11.154 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.155 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.155 * [taylor]: Taking taylor expansion of (log n) in k 11.155 * [taylor]: Taking taylor expansion of n in k 11.155 * [backup-simplify]: Simplify n into n 11.155 * [backup-simplify]: Simplify (log n) into (log n) 11.155 * [backup-simplify]: Simplify (- 1) into -1 11.156 * [backup-simplify]: Simplify (+ 0 -1) into -1 11.156 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 11.156 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 11.157 * [backup-simplify]: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n))) 11.158 * [backup-simplify]: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n))) 11.159 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 11.159 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 11.160 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 11.160 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 11.161 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 11.162 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 11.162 * [backup-simplify]: Simplify (- 0) into 0 11.162 * [backup-simplify]: Simplify (+ 0 0) into 0 11.162 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 (/ 1 k)))) into 0 11.164 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 11.165 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 11.167 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 11.167 * [taylor]: Taking taylor expansion of 0 in k 11.167 * [backup-simplify]: Simplify 0 into 0 11.167 * [backup-simplify]: Simplify 0 into 0 11.167 * [backup-simplify]: Simplify 0 into 0 11.169 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.170 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 11.173 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 11.173 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 11.174 * [backup-simplify]: Simplify (- 0) into 0 11.174 * [backup-simplify]: Simplify (+ 0 0) into 0 11.176 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0 11.177 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 11.179 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 11.181 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 11.182 * [taylor]: Taking taylor expansion of 0 in k 11.182 * [backup-simplify]: Simplify 0 into 0 11.182 * [backup-simplify]: Simplify 0 into 0 11.182 * [backup-simplify]: Simplify 0 into 0 11.182 * [backup-simplify]: Simplify 0 into 0 11.183 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.185 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 11.191 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 11.191 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 11.192 * [backup-simplify]: Simplify (- 0) into 0 11.192 * [backup-simplify]: Simplify (+ 0 0) into 0 11.194 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0 11.195 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 11.197 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 11.200 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 11.200 * [taylor]: Taking taylor expansion of 0 in k 11.200 * [backup-simplify]: Simplify 0 into 0 11.200 * [backup-simplify]: Simplify 0 into 0 11.201 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) 11.202 * [backup-simplify]: Simplify (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) into (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) 11.202 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in (n k) around 0 11.202 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k 11.202 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k 11.202 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k 11.202 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k 11.202 * [taylor]: Taking taylor expansion of 1/2 in k 11.203 * [backup-simplify]: Simplify 1/2 into 1/2 11.203 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k 11.203 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.203 * [taylor]: Taking taylor expansion of k in k 11.203 * [backup-simplify]: Simplify 0 into 0 11.203 * [backup-simplify]: Simplify 1 into 1 11.203 * [backup-simplify]: Simplify (/ 1 1) into 1 11.203 * [taylor]: Taking taylor expansion of 1 in k 11.203 * [backup-simplify]: Simplify 1 into 1 11.203 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 11.203 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 11.203 * [taylor]: Taking taylor expansion of -2 in k 11.203 * [backup-simplify]: Simplify -2 into -2 11.203 * [taylor]: Taking taylor expansion of (/ PI n) in k 11.203 * [taylor]: Taking taylor expansion of PI in k 11.203 * [backup-simplify]: Simplify PI into PI 11.203 * [taylor]: Taking taylor expansion of n in k 11.203 * [backup-simplify]: Simplify n into n 11.203 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 11.203 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 11.204 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 11.204 * [backup-simplify]: Simplify (+ 1 0) into 1 11.204 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 11.205 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 11.205 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) 11.205 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n 11.205 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n 11.205 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n 11.205 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n 11.205 * [taylor]: Taking taylor expansion of 1/2 in n 11.205 * [backup-simplify]: Simplify 1/2 into 1/2 11.205 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n 11.205 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.205 * [taylor]: Taking taylor expansion of k in n 11.205 * [backup-simplify]: Simplify k into k 11.205 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.205 * [taylor]: Taking taylor expansion of 1 in n 11.205 * [backup-simplify]: Simplify 1 into 1 11.205 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 11.205 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 11.205 * [taylor]: Taking taylor expansion of -2 in n 11.205 * [backup-simplify]: Simplify -2 into -2 11.205 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.205 * [taylor]: Taking taylor expansion of PI in n 11.205 * [backup-simplify]: Simplify PI into PI 11.205 * [taylor]: Taking taylor expansion of n in n 11.205 * [backup-simplify]: Simplify 0 into 0 11.206 * [backup-simplify]: Simplify 1 into 1 11.206 * [backup-simplify]: Simplify (/ PI 1) into PI 11.207 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 11.208 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 11.208 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 11.208 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1)) 11.209 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 11.211 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 11.212 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 11.212 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n 11.212 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n 11.212 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n 11.212 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n 11.212 * [taylor]: Taking taylor expansion of 1/2 in n 11.212 * [backup-simplify]: Simplify 1/2 into 1/2 11.212 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n 11.212 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.212 * [taylor]: Taking taylor expansion of k in n 11.212 * [backup-simplify]: Simplify k into k 11.212 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.212 * [taylor]: Taking taylor expansion of 1 in n 11.212 * [backup-simplify]: Simplify 1 into 1 11.213 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 11.213 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 11.213 * [taylor]: Taking taylor expansion of -2 in n 11.213 * [backup-simplify]: Simplify -2 into -2 11.213 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.213 * [taylor]: Taking taylor expansion of PI in n 11.213 * [backup-simplify]: Simplify PI into PI 11.213 * [taylor]: Taking taylor expansion of n in n 11.213 * [backup-simplify]: Simplify 0 into 0 11.213 * [backup-simplify]: Simplify 1 into 1 11.213 * [backup-simplify]: Simplify (/ PI 1) into PI 11.214 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 11.215 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 11.215 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 11.215 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1)) 11.217 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 11.218 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 11.219 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 11.220 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k 11.220 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) in k 11.220 * [taylor]: Taking taylor expansion of 1/2 in k 11.220 * [backup-simplify]: Simplify 1/2 into 1/2 11.220 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) in k 11.220 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k 11.220 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.220 * [taylor]: Taking taylor expansion of k in k 11.220 * [backup-simplify]: Simplify 0 into 0 11.220 * [backup-simplify]: Simplify 1 into 1 11.220 * [backup-simplify]: Simplify (/ 1 1) into 1 11.220 * [taylor]: Taking taylor expansion of 1 in k 11.220 * [backup-simplify]: Simplify 1 into 1 11.220 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 11.220 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 11.220 * [taylor]: Taking taylor expansion of (* -2 PI) in k 11.220 * [taylor]: Taking taylor expansion of -2 in k 11.220 * [backup-simplify]: Simplify -2 into -2 11.220 * [taylor]: Taking taylor expansion of PI in k 11.220 * [backup-simplify]: Simplify PI into PI 11.221 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 11.222 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 11.222 * [taylor]: Taking taylor expansion of (log n) in k 11.222 * [taylor]: Taking taylor expansion of n in k 11.222 * [backup-simplify]: Simplify n into n 11.222 * [backup-simplify]: Simplify (log n) into (log n) 11.223 * [backup-simplify]: Simplify (+ 1 0) into 1 11.223 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 11.224 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 11.225 * [backup-simplify]: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n)) 11.226 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 11.228 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 11.229 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 11.230 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 11.231 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 11.233 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 11.233 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 11.233 * [backup-simplify]: Simplify (+ 0 0) into 0 11.234 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (/ 1 k) 1))) into 0 11.235 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 11.237 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 11.239 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 11.239 * [taylor]: Taking taylor expansion of 0 in k 11.239 * [backup-simplify]: Simplify 0 into 0 11.239 * [backup-simplify]: Simplify 0 into 0 11.239 * [backup-simplify]: Simplify 0 into 0 11.240 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.241 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 11.245 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 11.245 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 11.246 * [backup-simplify]: Simplify (+ 0 0) into 0 11.247 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0 11.248 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 11.250 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 11.252 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 11.252 * [taylor]: Taking taylor expansion of 0 in k 11.253 * [backup-simplify]: Simplify 0 into 0 11.253 * [backup-simplify]: Simplify 0 into 0 11.253 * [backup-simplify]: Simplify 0 into 0 11.253 * [backup-simplify]: Simplify 0 into 0 11.254 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.255 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 11.261 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0 11.261 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 11.262 * [backup-simplify]: Simplify (+ 0 0) into 0 11.263 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1))))) into 0 11.265 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 11.267 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 11.269 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 11.269 * [taylor]: Taking taylor expansion of 0 in k 11.269 * [backup-simplify]: Simplify 0 into 0 11.269 * [backup-simplify]: Simplify 0 into 0 11.271 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) 11.271 * * * * [progress]: [ 2 / 4 ] generating series at (2 1) 11.271 * [backup-simplify]: Simplify (/ 1 (sqrt k)) into (sqrt (/ 1 k)) 11.271 * [approximate]: Taking taylor expansion of (sqrt (/ 1 k)) in (k) around 0 11.271 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 11.271 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.271 * [taylor]: Taking taylor expansion of k in k 11.271 * [backup-simplify]: Simplify 0 into 0 11.271 * [backup-simplify]: Simplify 1 into 1 11.272 * [backup-simplify]: Simplify (/ 1 1) into 1 11.272 * [backup-simplify]: Simplify (sqrt 0) into 0 11.273 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.273 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 11.273 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.273 * [taylor]: Taking taylor expansion of k in k 11.273 * [backup-simplify]: Simplify 0 into 0 11.273 * [backup-simplify]: Simplify 1 into 1 11.274 * [backup-simplify]: Simplify (/ 1 1) into 1 11.274 * [backup-simplify]: Simplify (sqrt 0) into 0 11.276 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.276 * [backup-simplify]: Simplify 0 into 0 11.276 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.276 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 11.280 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 11.280 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.281 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.285 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 11.285 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.285 * [backup-simplify]: Simplify (+ (* +nan.0 (pow k 2)) (+ (* +nan.0 k) +nan.0)) into (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) 11.285 * [backup-simplify]: Simplify (/ 1 (sqrt (/ 1 k))) into (sqrt k) 11.285 * [approximate]: Taking taylor expansion of (sqrt k) in (k) around 0 11.285 * [taylor]: Taking taylor expansion of (sqrt k) in k 11.285 * [taylor]: Taking taylor expansion of k in k 11.285 * [backup-simplify]: Simplify 0 into 0 11.285 * [backup-simplify]: Simplify 1 into 1 11.286 * [backup-simplify]: Simplify (sqrt 0) into 0 11.287 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.287 * [taylor]: Taking taylor expansion of (sqrt k) in k 11.287 * [taylor]: Taking taylor expansion of k in k 11.287 * [backup-simplify]: Simplify 0 into 0 11.287 * [backup-simplify]: Simplify 1 into 1 11.287 * [backup-simplify]: Simplify (sqrt 0) into 0 11.289 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.289 * [backup-simplify]: Simplify 0 into 0 11.289 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.295 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 11.295 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.299 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 11.299 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.299 * [backup-simplify]: Simplify (+ (* +nan.0 (pow (/ 1 k) 3)) (+ (* +nan.0 (pow (/ 1 k) 2)) (* +nan.0 (/ 1 k)))) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) 11.299 * [backup-simplify]: Simplify (/ 1 (sqrt (/ 1 (- k)))) into (/ 1 (sqrt (/ -1 k))) 11.299 * [approximate]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in (k) around 0 11.299 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 11.299 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 11.299 * [taylor]: Taking taylor expansion of (/ -1 k) in k 11.299 * [taylor]: Taking taylor expansion of -1 in k 11.299 * [backup-simplify]: Simplify -1 into -1 11.299 * [taylor]: Taking taylor expansion of k in k 11.300 * [backup-simplify]: Simplify 0 into 0 11.300 * [backup-simplify]: Simplify 1 into 1 11.300 * [backup-simplify]: Simplify (/ -1 1) into -1 11.300 * [backup-simplify]: Simplify (sqrt 0) into 0 11.302 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 11.302 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0 11.302 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 11.302 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 11.302 * [taylor]: Taking taylor expansion of (/ -1 k) in k 11.302 * [taylor]: Taking taylor expansion of -1 in k 11.302 * [backup-simplify]: Simplify -1 into -1 11.302 * [taylor]: Taking taylor expansion of k in k 11.302 * [backup-simplify]: Simplify 0 into 0 11.302 * [backup-simplify]: Simplify 1 into 1 11.303 * [backup-simplify]: Simplify (/ -1 1) into -1 11.303 * [backup-simplify]: Simplify (sqrt 0) into 0 11.304 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 11.304 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0 11.304 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.305 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 11.307 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 11.308 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 11.308 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.309 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.311 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 11.313 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 11.314 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.314 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 (- k)) 2)) (+ (* (- +nan.0) (/ 1 (- k))) +nan.0)) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) 11.315 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1) 11.315 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 11.315 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 11.315 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 11.315 * [taylor]: Taking taylor expansion of 2 in n 11.315 * [backup-simplify]: Simplify 2 into 2 11.315 * [taylor]: Taking taylor expansion of (* n PI) in n 11.315 * [taylor]: Taking taylor expansion of n in n 11.315 * [backup-simplify]: Simplify 0 into 0 11.315 * [backup-simplify]: Simplify 1 into 1 11.315 * [taylor]: Taking taylor expansion of PI in n 11.315 * [backup-simplify]: Simplify PI into PI 11.315 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 11.315 * [taylor]: Taking taylor expansion of 2 in n 11.315 * [backup-simplify]: Simplify 2 into 2 11.315 * [taylor]: Taking taylor expansion of (* n PI) in n 11.315 * [taylor]: Taking taylor expansion of n in n 11.315 * [backup-simplify]: Simplify 0 into 0 11.315 * [backup-simplify]: Simplify 1 into 1 11.315 * [taylor]: Taking taylor expansion of PI in n 11.315 * [backup-simplify]: Simplify PI into PI 11.316 * [backup-simplify]: Simplify (* 0 PI) into 0 11.316 * [backup-simplify]: Simplify (* 2 0) into 0 11.316 * [backup-simplify]: Simplify 0 into 0 11.317 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.318 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 11.318 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.319 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 11.319 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 11.319 * [backup-simplify]: Simplify 0 into 0 11.320 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 11.321 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 11.321 * [backup-simplify]: Simplify 0 into 0 11.322 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 11.322 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 11.322 * [backup-simplify]: Simplify 0 into 0 11.323 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 11.324 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 11.324 * [backup-simplify]: Simplify 0 into 0 11.325 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 11.326 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 11.326 * [backup-simplify]: Simplify 0 into 0 11.327 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 11.329 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 11.329 * [backup-simplify]: Simplify 0 into 0 11.329 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 11.329 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 n)) into (* 2 (/ PI n)) 11.329 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 11.329 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 11.329 * [taylor]: Taking taylor expansion of 2 in n 11.329 * [backup-simplify]: Simplify 2 into 2 11.329 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.329 * [taylor]: Taking taylor expansion of PI in n 11.329 * [backup-simplify]: Simplify PI into PI 11.329 * [taylor]: Taking taylor expansion of n in n 11.329 * [backup-simplify]: Simplify 0 into 0 11.329 * [backup-simplify]: Simplify 1 into 1 11.330 * [backup-simplify]: Simplify (/ PI 1) into PI 11.330 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 11.330 * [taylor]: Taking taylor expansion of 2 in n 11.330 * [backup-simplify]: Simplify 2 into 2 11.330 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.330 * [taylor]: Taking taylor expansion of PI in n 11.330 * [backup-simplify]: Simplify PI into PI 11.330 * [taylor]: Taking taylor expansion of n in n 11.330 * [backup-simplify]: Simplify 0 into 0 11.330 * [backup-simplify]: Simplify 1 into 1 11.330 * [backup-simplify]: Simplify (/ PI 1) into PI 11.331 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.331 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.332 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 11.333 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 11.333 * [backup-simplify]: Simplify 0 into 0 11.334 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.335 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 11.335 * [backup-simplify]: Simplify 0 into 0 11.336 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.338 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 11.338 * [backup-simplify]: Simplify 0 into 0 11.339 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.340 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 11.340 * [backup-simplify]: Simplify 0 into 0 11.342 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.343 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 11.343 * [backup-simplify]: Simplify 0 into 0 11.345 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.346 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 11.346 * [backup-simplify]: Simplify 0 into 0 11.347 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 11.348 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (- n))) into (* -2 (/ PI n)) 11.348 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 11.348 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 11.348 * [taylor]: Taking taylor expansion of -2 in n 11.348 * [backup-simplify]: Simplify -2 into -2 11.348 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.348 * [taylor]: Taking taylor expansion of PI in n 11.348 * [backup-simplify]: Simplify PI into PI 11.348 * [taylor]: Taking taylor expansion of n in n 11.348 * [backup-simplify]: Simplify 0 into 0 11.348 * [backup-simplify]: Simplify 1 into 1 11.348 * [backup-simplify]: Simplify (/ PI 1) into PI 11.348 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 11.348 * [taylor]: Taking taylor expansion of -2 in n 11.349 * [backup-simplify]: Simplify -2 into -2 11.349 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.349 * [taylor]: Taking taylor expansion of PI in n 11.349 * [backup-simplify]: Simplify PI into PI 11.349 * [taylor]: Taking taylor expansion of n in n 11.349 * [backup-simplify]: Simplify 0 into 0 11.349 * [backup-simplify]: Simplify 1 into 1 11.349 * [backup-simplify]: Simplify (/ PI 1) into PI 11.350 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 11.350 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 11.351 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 11.352 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 11.352 * [backup-simplify]: Simplify 0 into 0 11.353 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.354 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 11.354 * [backup-simplify]: Simplify 0 into 0 11.356 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.357 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 11.357 * [backup-simplify]: Simplify 0 into 0 11.358 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.360 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 11.360 * [backup-simplify]: Simplify 0 into 0 11.361 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.362 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 11.363 * [backup-simplify]: Simplify 0 into 0 11.364 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.366 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 11.366 * [backup-simplify]: Simplify 0 into 0 11.366 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 11.368 * * * * [progress]: [ 4 / 4 ] generating series at (2) 11.368 * [backup-simplify]: Simplify (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) into (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) 11.368 * [approximate]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in (k n) around 0 11.369 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in n 11.369 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n 11.369 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n 11.369 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n 11.369 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n 11.369 * [taylor]: Taking taylor expansion of 1/2 in n 11.369 * [backup-simplify]: Simplify 1/2 into 1/2 11.369 * [taylor]: Taking taylor expansion of (- 1 k) in n 11.369 * [taylor]: Taking taylor expansion of 1 in n 11.369 * [backup-simplify]: Simplify 1 into 1 11.369 * [taylor]: Taking taylor expansion of k in n 11.369 * [backup-simplify]: Simplify k into k 11.369 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 11.369 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 11.369 * [taylor]: Taking taylor expansion of 2 in n 11.369 * [backup-simplify]: Simplify 2 into 2 11.369 * [taylor]: Taking taylor expansion of (* n PI) in n 11.369 * [taylor]: Taking taylor expansion of n in n 11.369 * [backup-simplify]: Simplify 0 into 0 11.369 * [backup-simplify]: Simplify 1 into 1 11.369 * [taylor]: Taking taylor expansion of PI in n 11.369 * [backup-simplify]: Simplify PI into PI 11.370 * [backup-simplify]: Simplify (* 0 PI) into 0 11.370 * [backup-simplify]: Simplify (* 2 0) into 0 11.372 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.373 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 11.374 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.375 * [backup-simplify]: Simplify (- k) into (- k) 11.375 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k) 11.375 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k)) 11.376 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 11.377 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) 11.378 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 11.378 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 11.378 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.378 * [taylor]: Taking taylor expansion of k in n 11.378 * [backup-simplify]: Simplify k into k 11.378 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.378 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 11.379 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 11.379 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 11.379 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k 11.379 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k 11.379 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k 11.379 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k 11.379 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k 11.379 * [taylor]: Taking taylor expansion of 1/2 in k 11.379 * [backup-simplify]: Simplify 1/2 into 1/2 11.379 * [taylor]: Taking taylor expansion of (- 1 k) in k 11.379 * [taylor]: Taking taylor expansion of 1 in k 11.379 * [backup-simplify]: Simplify 1 into 1 11.379 * [taylor]: Taking taylor expansion of k in k 11.379 * [backup-simplify]: Simplify 0 into 0 11.379 * [backup-simplify]: Simplify 1 into 1 11.379 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 11.379 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 11.379 * [taylor]: Taking taylor expansion of 2 in k 11.379 * [backup-simplify]: Simplify 2 into 2 11.379 * [taylor]: Taking taylor expansion of (* n PI) in k 11.379 * [taylor]: Taking taylor expansion of n in k 11.379 * [backup-simplify]: Simplify n into n 11.379 * [taylor]: Taking taylor expansion of PI in k 11.379 * [backup-simplify]: Simplify PI into PI 11.379 * [backup-simplify]: Simplify (* n PI) into (* n PI) 11.379 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 11.379 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 11.380 * [backup-simplify]: Simplify (- 0) into 0 11.380 * [backup-simplify]: Simplify (+ 1 0) into 1 11.381 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 11.381 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 11.381 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 11.381 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 11.381 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.381 * [taylor]: Taking taylor expansion of k in k 11.381 * [backup-simplify]: Simplify 0 into 0 11.381 * [backup-simplify]: Simplify 1 into 1 11.381 * [backup-simplify]: Simplify (/ 1 1) into 1 11.382 * [backup-simplify]: Simplify (sqrt 0) into 0 11.383 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.383 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k 11.383 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k 11.383 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k 11.383 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k 11.383 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k 11.383 * [taylor]: Taking taylor expansion of 1/2 in k 11.383 * [backup-simplify]: Simplify 1/2 into 1/2 11.383 * [taylor]: Taking taylor expansion of (- 1 k) in k 11.383 * [taylor]: Taking taylor expansion of 1 in k 11.383 * [backup-simplify]: Simplify 1 into 1 11.383 * [taylor]: Taking taylor expansion of k in k 11.384 * [backup-simplify]: Simplify 0 into 0 11.384 * [backup-simplify]: Simplify 1 into 1 11.384 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 11.384 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 11.384 * [taylor]: Taking taylor expansion of 2 in k 11.384 * [backup-simplify]: Simplify 2 into 2 11.384 * [taylor]: Taking taylor expansion of (* n PI) in k 11.384 * [taylor]: Taking taylor expansion of n in k 11.384 * [backup-simplify]: Simplify n into n 11.384 * [taylor]: Taking taylor expansion of PI in k 11.384 * [backup-simplify]: Simplify PI into PI 11.384 * [backup-simplify]: Simplify (* n PI) into (* n PI) 11.384 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 11.384 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 11.384 * [backup-simplify]: Simplify (- 0) into 0 11.385 * [backup-simplify]: Simplify (+ 1 0) into 1 11.385 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 11.385 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 11.386 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 11.386 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 11.386 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.386 * [taylor]: Taking taylor expansion of k in k 11.386 * [backup-simplify]: Simplify 0 into 0 11.386 * [backup-simplify]: Simplify 1 into 1 11.386 * [backup-simplify]: Simplify (/ 1 1) into 1 11.386 * [backup-simplify]: Simplify (sqrt 0) into 0 11.388 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.388 * [backup-simplify]: Simplify (* (pow (* 2 (* n PI)) 1/2) 0) into 0 11.388 * [taylor]: Taking taylor expansion of 0 in n 11.388 * [backup-simplify]: Simplify 0 into 0 11.388 * [backup-simplify]: Simplify 0 into 0 11.389 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 11.389 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0 11.390 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 11.391 * [backup-simplify]: Simplify (- 1) into -1 11.391 * [backup-simplify]: Simplify (+ 0 -1) into -1 11.392 * [backup-simplify]: Simplify (+ (* 1/2 -1) (* 0 1)) into -1/2 11.392 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI))))) 11.393 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1)))) into (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) 11.393 * [backup-simplify]: Simplify (+ (* (pow (* 2 (* n PI)) 1/2) +nan.0) (* (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) 0)) into (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) 11.393 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 11.393 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 11.393 * [taylor]: Taking taylor expansion of +nan.0 in n 11.393 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.393 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 11.393 * [taylor]: Taking taylor expansion of (sqrt 2) in n 11.393 * [taylor]: Taking taylor expansion of 2 in n 11.393 * [backup-simplify]: Simplify 2 into 2 11.394 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 11.394 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 11.395 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 11.395 * [taylor]: Taking taylor expansion of (* n PI) in n 11.395 * [taylor]: Taking taylor expansion of n in n 11.395 * [backup-simplify]: Simplify 0 into 0 11.395 * [backup-simplify]: Simplify 1 into 1 11.395 * [taylor]: Taking taylor expansion of PI in n 11.395 * [backup-simplify]: Simplify PI into PI 11.395 * [backup-simplify]: Simplify (* 0 PI) into 0 11.397 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.397 * [backup-simplify]: Simplify (sqrt 0) into 0 11.399 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 11.399 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 11.400 * [backup-simplify]: Simplify (* +nan.0 0) into 0 11.400 * [backup-simplify]: Simplify (- 0) into 0 11.400 * [backup-simplify]: Simplify 0 into 0 11.400 * [backup-simplify]: Simplify 0 into 0 11.401 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 11.404 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 11.405 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 11.406 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 11.408 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 1)))) 2) into 0 11.408 * [backup-simplify]: Simplify (- 0) into 0 11.409 * [backup-simplify]: Simplify (+ 0 0) into 0 11.410 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 -1) (* 0 1))) into 0 11.411 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0 11.412 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) 11.413 * [backup-simplify]: Simplify (+ (* (pow (* 2 (* n PI)) 1/2) +nan.0) (+ (* (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) +nan.0) (* (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) 0))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) 11.413 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) in n 11.413 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))) in n 11.413 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n 11.413 * [taylor]: Taking taylor expansion of +nan.0 in n 11.413 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.413 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n 11.413 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n 11.413 * [taylor]: Taking taylor expansion of (sqrt 2) in n 11.413 * [taylor]: Taking taylor expansion of 2 in n 11.413 * [backup-simplify]: Simplify 2 into 2 11.413 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 11.414 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 11.414 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 11.414 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 11.414 * [taylor]: Taking taylor expansion of 2 in n 11.414 * [backup-simplify]: Simplify 2 into 2 11.414 * [taylor]: Taking taylor expansion of (* n PI) in n 11.414 * [taylor]: Taking taylor expansion of n in n 11.414 * [backup-simplify]: Simplify 0 into 0 11.414 * [backup-simplify]: Simplify 1 into 1 11.414 * [taylor]: Taking taylor expansion of PI in n 11.414 * [backup-simplify]: Simplify PI into PI 11.415 * [backup-simplify]: Simplify (* 0 PI) into 0 11.415 * [backup-simplify]: Simplify (* 2 0) into 0 11.417 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.419 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 11.423 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.423 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 11.423 * [taylor]: Taking taylor expansion of (* n PI) in n 11.423 * [taylor]: Taking taylor expansion of n in n 11.423 * [backup-simplify]: Simplify 0 into 0 11.423 * [backup-simplify]: Simplify 1 into 1 11.423 * [taylor]: Taking taylor expansion of PI in n 11.423 * [backup-simplify]: Simplify PI into PI 11.424 * [backup-simplify]: Simplify (* 0 PI) into 0 11.425 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.426 * [backup-simplify]: Simplify (sqrt 0) into 0 11.427 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 11.427 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 11.427 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 11.427 * [taylor]: Taking taylor expansion of +nan.0 in n 11.427 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.427 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 11.427 * [taylor]: Taking taylor expansion of (sqrt 2) in n 11.427 * [taylor]: Taking taylor expansion of 2 in n 11.427 * [backup-simplify]: Simplify 2 into 2 11.428 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 11.428 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 11.428 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 11.428 * [taylor]: Taking taylor expansion of (* n PI) in n 11.429 * [taylor]: Taking taylor expansion of n in n 11.429 * [backup-simplify]: Simplify 0 into 0 11.429 * [backup-simplify]: Simplify 1 into 1 11.429 * [taylor]: Taking taylor expansion of PI in n 11.429 * [backup-simplify]: Simplify PI into PI 11.429 * [backup-simplify]: Simplify (* 0 PI) into 0 11.431 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.431 * [backup-simplify]: Simplify (sqrt 0) into 0 11.433 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 11.434 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 11.436 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 11.437 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0 11.437 * [backup-simplify]: Simplify (* +nan.0 0) into 0 11.438 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 11.438 * [backup-simplify]: Simplify (* +nan.0 0) into 0 11.439 * [backup-simplify]: Simplify (- 0) into 0 11.439 * [backup-simplify]: Simplify (+ 0 0) into 0 11.439 * [backup-simplify]: Simplify (- 0) into 0 11.439 * [backup-simplify]: Simplify 0 into 0 11.442 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 11.447 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 11.450 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 11.451 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI))) 11.451 * [backup-simplify]: Simplify 0 into 0 11.452 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.454 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 11.455 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 11.455 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 11.457 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 (* n PI)) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 (* n PI)) 1)))) 6) into 0 11.458 * [backup-simplify]: Simplify (- 0) into 0 11.458 * [backup-simplify]: Simplify (+ 0 0) into 0 11.459 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1)))) into 0 11.459 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log (* 2 (* n PI))))))) into 0 11.460 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 3) 6)) (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 3))) 11.461 * [backup-simplify]: Simplify (+ (* (pow (* 2 (* n PI)) 1/2) +nan.0) (+ (* (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) +nan.0) (+ (* (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) +nan.0) (* (* -1/48 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 3))) 0)))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))))))) 11.461 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))))))) in n 11.461 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))))))) in n 11.461 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n 11.461 * [taylor]: Taking taylor expansion of +nan.0 in n 11.461 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.461 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n 11.461 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n 11.461 * [taylor]: Taking taylor expansion of (sqrt 2) in n 11.461 * [taylor]: Taking taylor expansion of 2 in n 11.461 * [backup-simplify]: Simplify 2 into 2 11.462 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 11.462 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 11.462 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 11.462 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 11.462 * [taylor]: Taking taylor expansion of 2 in n 11.462 * [backup-simplify]: Simplify 2 into 2 11.462 * [taylor]: Taking taylor expansion of (* n PI) in n 11.462 * [taylor]: Taking taylor expansion of n in n 11.462 * [backup-simplify]: Simplify 0 into 0 11.462 * [backup-simplify]: Simplify 1 into 1 11.462 * [taylor]: Taking taylor expansion of PI in n 11.462 * [backup-simplify]: Simplify PI into PI 11.463 * [backup-simplify]: Simplify (* 0 PI) into 0 11.463 * [backup-simplify]: Simplify (* 2 0) into 0 11.464 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.465 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 11.466 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.466 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 11.466 * [taylor]: Taking taylor expansion of (* n PI) in n 11.466 * [taylor]: Taking taylor expansion of n in n 11.466 * [backup-simplify]: Simplify 0 into 0 11.466 * [backup-simplify]: Simplify 1 into 1 11.466 * [taylor]: Taking taylor expansion of PI in n 11.466 * [backup-simplify]: Simplify PI into PI 11.466 * [backup-simplify]: Simplify (* 0 PI) into 0 11.467 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.467 * [backup-simplify]: Simplify (sqrt 0) into 0 11.468 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 11.468 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))))) in n 11.468 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))))) in n 11.468 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 11.469 * [taylor]: Taking taylor expansion of +nan.0 in n 11.469 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.469 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 11.469 * [taylor]: Taking taylor expansion of (sqrt 2) in n 11.469 * [taylor]: Taking taylor expansion of 2 in n 11.469 * [backup-simplify]: Simplify 2 into 2 11.469 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 11.469 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 11.469 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 11.469 * [taylor]: Taking taylor expansion of (* n PI) in n 11.469 * [taylor]: Taking taylor expansion of n in n 11.469 * [backup-simplify]: Simplify 0 into 0 11.469 * [backup-simplify]: Simplify 1 into 1 11.469 * [taylor]: Taking taylor expansion of PI in n 11.469 * [backup-simplify]: Simplify PI into PI 11.470 * [backup-simplify]: Simplify (* 0 PI) into 0 11.471 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.471 * [backup-simplify]: Simplify (sqrt 0) into 0 11.472 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 11.472 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))) in n 11.472 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) in n 11.472 * [taylor]: Taking taylor expansion of +nan.0 in n 11.472 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.472 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))) in n 11.472 * [taylor]: Taking taylor expansion of (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) in n 11.472 * [taylor]: Taking taylor expansion of (sqrt 2) in n 11.472 * [taylor]: Taking taylor expansion of 2 in n 11.472 * [backup-simplify]: Simplify 2 into 2 11.472 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 11.473 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 11.473 * [taylor]: Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n 11.473 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 11.473 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 11.473 * [taylor]: Taking taylor expansion of 2 in n 11.473 * [backup-simplify]: Simplify 2 into 2 11.473 * [taylor]: Taking taylor expansion of (* n PI) in n 11.473 * [taylor]: Taking taylor expansion of n in n 11.473 * [backup-simplify]: Simplify 0 into 0 11.473 * [backup-simplify]: Simplify 1 into 1 11.473 * [taylor]: Taking taylor expansion of PI in n 11.473 * [backup-simplify]: Simplify PI into PI 11.473 * [backup-simplify]: Simplify (* 0 PI) into 0 11.473 * [backup-simplify]: Simplify (* 2 0) into 0 11.474 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.475 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 11.476 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.477 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 11.477 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 11.477 * [taylor]: Taking taylor expansion of (* n PI) in n 11.477 * [taylor]: Taking taylor expansion of n in n 11.477 * [backup-simplify]: Simplify 0 into 0 11.477 * [backup-simplify]: Simplify 1 into 1 11.477 * [taylor]: Taking taylor expansion of PI in n 11.477 * [backup-simplify]: Simplify PI into PI 11.478 * [backup-simplify]: Simplify (* 0 PI) into 0 11.479 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.479 * [backup-simplify]: Simplify (sqrt 0) into 0 11.480 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 11.481 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 11.482 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 11.483 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0 11.483 * [backup-simplify]: Simplify (* +nan.0 0) into 0 11.483 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 11.484 * [backup-simplify]: Simplify (* +nan.0 0) into 0 11.484 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 11.485 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 11.487 * [backup-simplify]: Simplify (* (+ (log n) (log (* 2 PI))) (+ (log n) (log (* 2 PI)))) into (pow (+ (log n) (log (* 2 PI))) 2) 11.488 * [backup-simplify]: Simplify (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) into (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 11.489 * [backup-simplify]: Simplify (* (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 0) into 0 11.489 * [backup-simplify]: Simplify (* +nan.0 0) into 0 11.489 * [backup-simplify]: Simplify (- 0) into 0 11.489 * [backup-simplify]: Simplify (+ 0 0) into 0 11.490 * [backup-simplify]: Simplify (- 0) into 0 11.490 * [backup-simplify]: Simplify (+ 0 0) into 0 11.490 * [backup-simplify]: Simplify (- 0) into 0 11.490 * [backup-simplify]: Simplify 0 into 0 11.491 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 11.491 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 11.493 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 11.493 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 11.494 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 11.496 * [backup-simplify]: Simplify (+ (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) (* +nan.0 PI)) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) 11.500 * [backup-simplify]: Simplify (+ (* +nan.0 (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) 11.502 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 11.505 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 11.507 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 11.513 * [backup-simplify]: Simplify (+ (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) (- (* +nan.0 (* (sqrt 2) PI)))) into (- (+ (* +nan.0 (* (sqrt 2) PI)) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))))) 11.521 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) PI)) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) 11.525 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) 11.526 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 11.529 * [backup-simplify]: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 11.530 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 11.533 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 (pow PI 2))) (+ (* 0 (* +nan.0 PI)) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 11.541 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) (+ (* 0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 11.546 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 11.549 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 11.563 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) (pow (* n 1) 2)) (+ (* (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) (* n k)) (* (- (* +nan.0 (* (sqrt 2) PI))) (* n 1)))) into (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))))))) 11.564 * [backup-simplify]: Simplify (* (/ 1 (sqrt (/ 1 k))) (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2))) into (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) 11.564 * [approximate]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in (k n) around 0 11.564 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in n 11.564 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n 11.564 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n 11.564 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n 11.564 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n 11.564 * [taylor]: Taking taylor expansion of 1/2 in n 11.564 * [backup-simplify]: Simplify 1/2 into 1/2 11.564 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n 11.564 * [taylor]: Taking taylor expansion of 1 in n 11.564 * [backup-simplify]: Simplify 1 into 1 11.564 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.564 * [taylor]: Taking taylor expansion of k in n 11.564 * [backup-simplify]: Simplify k into k 11.564 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.564 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 11.564 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 11.564 * [taylor]: Taking taylor expansion of 2 in n 11.564 * [backup-simplify]: Simplify 2 into 2 11.564 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.564 * [taylor]: Taking taylor expansion of PI in n 11.564 * [backup-simplify]: Simplify PI into PI 11.564 * [taylor]: Taking taylor expansion of n in n 11.564 * [backup-simplify]: Simplify 0 into 0 11.565 * [backup-simplify]: Simplify 1 into 1 11.565 * [backup-simplify]: Simplify (/ PI 1) into PI 11.565 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.566 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.566 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 11.566 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 11.566 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k))) 11.567 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 11.568 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 11.569 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 11.569 * [taylor]: Taking taylor expansion of (sqrt k) in n 11.569 * [taylor]: Taking taylor expansion of k in n 11.569 * [backup-simplify]: Simplify k into k 11.569 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 11.569 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 11.569 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k 11.569 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k 11.569 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k 11.569 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k 11.569 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k 11.569 * [taylor]: Taking taylor expansion of 1/2 in k 11.569 * [backup-simplify]: Simplify 1/2 into 1/2 11.569 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k 11.569 * [taylor]: Taking taylor expansion of 1 in k 11.569 * [backup-simplify]: Simplify 1 into 1 11.569 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.569 * [taylor]: Taking taylor expansion of k in k 11.569 * [backup-simplify]: Simplify 0 into 0 11.569 * [backup-simplify]: Simplify 1 into 1 11.569 * [backup-simplify]: Simplify (/ 1 1) into 1 11.569 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 11.569 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 11.569 * [taylor]: Taking taylor expansion of 2 in k 11.569 * [backup-simplify]: Simplify 2 into 2 11.569 * [taylor]: Taking taylor expansion of (/ PI n) in k 11.569 * [taylor]: Taking taylor expansion of PI in k 11.569 * [backup-simplify]: Simplify PI into PI 11.569 * [taylor]: Taking taylor expansion of n in k 11.569 * [backup-simplify]: Simplify n into n 11.569 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 11.570 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 11.570 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 11.570 * [backup-simplify]: Simplify (- 1) into -1 11.570 * [backup-simplify]: Simplify (+ 0 -1) into -1 11.570 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2 11.570 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 11.571 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 11.571 * [taylor]: Taking taylor expansion of (sqrt k) in k 11.571 * [taylor]: Taking taylor expansion of k in k 11.571 * [backup-simplify]: Simplify 0 into 0 11.571 * [backup-simplify]: Simplify 1 into 1 11.571 * [backup-simplify]: Simplify (sqrt 0) into 0 11.572 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.572 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k 11.572 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k 11.572 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k 11.572 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k 11.572 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k 11.572 * [taylor]: Taking taylor expansion of 1/2 in k 11.572 * [backup-simplify]: Simplify 1/2 into 1/2 11.572 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k 11.572 * [taylor]: Taking taylor expansion of 1 in k 11.572 * [backup-simplify]: Simplify 1 into 1 11.572 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.572 * [taylor]: Taking taylor expansion of k in k 11.572 * [backup-simplify]: Simplify 0 into 0 11.572 * [backup-simplify]: Simplify 1 into 1 11.572 * [backup-simplify]: Simplify (/ 1 1) into 1 11.572 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 11.572 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 11.572 * [taylor]: Taking taylor expansion of 2 in k 11.572 * [backup-simplify]: Simplify 2 into 2 11.572 * [taylor]: Taking taylor expansion of (/ PI n) in k 11.572 * [taylor]: Taking taylor expansion of PI in k 11.572 * [backup-simplify]: Simplify PI into PI 11.572 * [taylor]: Taking taylor expansion of n in k 11.572 * [backup-simplify]: Simplify n into n 11.572 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 11.573 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 11.573 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 11.573 * [backup-simplify]: Simplify (- 1) into -1 11.573 * [backup-simplify]: Simplify (+ 0 -1) into -1 11.573 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2 11.573 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 11.574 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 11.574 * [taylor]: Taking taylor expansion of (sqrt k) in k 11.574 * [taylor]: Taking taylor expansion of k in k 11.574 * [backup-simplify]: Simplify 0 into 0 11.574 * [backup-simplify]: Simplify 1 into 1 11.574 * [backup-simplify]: Simplify (sqrt 0) into 0 11.575 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.575 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 0) into 0 11.575 * [taylor]: Taking taylor expansion of 0 in n 11.575 * [backup-simplify]: Simplify 0 into 0 11.575 * [backup-simplify]: Simplify 0 into 0 11.575 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) 11.575 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n 11.575 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n 11.575 * [taylor]: Taking taylor expansion of +nan.0 in n 11.575 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.575 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n 11.575 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n 11.576 * [taylor]: Taking taylor expansion of 1/2 in n 11.576 * [backup-simplify]: Simplify 1/2 into 1/2 11.576 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n 11.576 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n 11.576 * [taylor]: Taking taylor expansion of 1 in n 11.576 * [backup-simplify]: Simplify 1 into 1 11.576 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.576 * [taylor]: Taking taylor expansion of k in n 11.576 * [backup-simplify]: Simplify k into k 11.576 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.576 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 11.576 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 11.576 * [taylor]: Taking taylor expansion of 2 in n 11.576 * [backup-simplify]: Simplify 2 into 2 11.576 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.576 * [taylor]: Taking taylor expansion of PI in n 11.576 * [backup-simplify]: Simplify PI into PI 11.576 * [taylor]: Taking taylor expansion of n in n 11.576 * [backup-simplify]: Simplify 0 into 0 11.576 * [backup-simplify]: Simplify 1 into 1 11.576 * [backup-simplify]: Simplify (/ PI 1) into PI 11.576 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.577 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.577 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 11.577 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 11.578 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 11.579 * [backup-simplify]: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) 11.580 * [backup-simplify]: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 11.581 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 11.581 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) 11.582 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 11.583 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 11.583 * [backup-simplify]: Simplify 0 into 0 11.585 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 11.586 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) 11.586 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n 11.586 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n 11.586 * [taylor]: Taking taylor expansion of +nan.0 in n 11.586 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.586 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n 11.586 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n 11.586 * [taylor]: Taking taylor expansion of 1/2 in n 11.586 * [backup-simplify]: Simplify 1/2 into 1/2 11.586 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n 11.586 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n 11.586 * [taylor]: Taking taylor expansion of 1 in n 11.586 * [backup-simplify]: Simplify 1 into 1 11.586 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.586 * [taylor]: Taking taylor expansion of k in n 11.586 * [backup-simplify]: Simplify k into k 11.586 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.586 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 11.586 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 11.586 * [taylor]: Taking taylor expansion of 2 in n 11.586 * [backup-simplify]: Simplify 2 into 2 11.586 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.586 * [taylor]: Taking taylor expansion of PI in n 11.586 * [backup-simplify]: Simplify PI into PI 11.586 * [taylor]: Taking taylor expansion of n in n 11.586 * [backup-simplify]: Simplify 0 into 0 11.586 * [backup-simplify]: Simplify 1 into 1 11.587 * [backup-simplify]: Simplify (/ PI 1) into PI 11.587 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.588 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.588 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 11.588 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 11.589 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 11.590 * [backup-simplify]: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) 11.590 * [backup-simplify]: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 11.591 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 11.592 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) 11.593 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 11.593 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 11.594 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 11.595 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 11.596 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 11.596 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 11.596 * [backup-simplify]: Simplify (- 0) into 0 11.596 * [backup-simplify]: Simplify (+ 0 0) into 0 11.597 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 11.598 * [backup-simplify]: Simplify (+ (* (- 1 (/ 1 k)) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 11.599 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into 0 11.600 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 11.601 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into 0 11.601 * [backup-simplify]: Simplify (- 0) into 0 11.601 * [backup-simplify]: Simplify 0 into 0 11.601 * [backup-simplify]: Simplify 0 into 0 11.604 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 11.604 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) 11.604 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n 11.604 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n 11.604 * [taylor]: Taking taylor expansion of +nan.0 in n 11.604 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.604 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n 11.605 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n 11.605 * [taylor]: Taking taylor expansion of 1/2 in n 11.605 * [backup-simplify]: Simplify 1/2 into 1/2 11.605 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n 11.605 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n 11.605 * [taylor]: Taking taylor expansion of 1 in n 11.605 * [backup-simplify]: Simplify 1 into 1 11.605 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.605 * [taylor]: Taking taylor expansion of k in n 11.605 * [backup-simplify]: Simplify k into k 11.605 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.605 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 11.605 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 11.605 * [taylor]: Taking taylor expansion of 2 in n 11.605 * [backup-simplify]: Simplify 2 into 2 11.605 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.605 * [taylor]: Taking taylor expansion of PI in n 11.605 * [backup-simplify]: Simplify PI into PI 11.605 * [taylor]: Taking taylor expansion of n in n 11.605 * [backup-simplify]: Simplify 0 into 0 11.605 * [backup-simplify]: Simplify 1 into 1 11.605 * [backup-simplify]: Simplify (/ PI 1) into PI 11.605 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.606 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.606 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 11.606 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 11.607 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 11.608 * [backup-simplify]: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) 11.609 * [backup-simplify]: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 11.610 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 11.610 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) 11.611 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 11.612 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 11.615 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3)))))))) 11.615 * [backup-simplify]: Simplify (* (/ 1 (sqrt (/ 1 (- k)))) (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2))) into (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) 11.615 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in (k n) around 0 11.615 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in n 11.615 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n 11.615 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n 11.615 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n 11.615 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n 11.615 * [taylor]: Taking taylor expansion of 1/2 in n 11.615 * [backup-simplify]: Simplify 1/2 into 1/2 11.615 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n 11.615 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.615 * [taylor]: Taking taylor expansion of k in n 11.615 * [backup-simplify]: Simplify k into k 11.615 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.615 * [taylor]: Taking taylor expansion of 1 in n 11.615 * [backup-simplify]: Simplify 1 into 1 11.615 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 11.615 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 11.616 * [taylor]: Taking taylor expansion of -2 in n 11.616 * [backup-simplify]: Simplify -2 into -2 11.616 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.616 * [taylor]: Taking taylor expansion of PI in n 11.616 * [backup-simplify]: Simplify PI into PI 11.616 * [taylor]: Taking taylor expansion of n in n 11.616 * [backup-simplify]: Simplify 0 into 0 11.616 * [backup-simplify]: Simplify 1 into 1 11.616 * [backup-simplify]: Simplify (/ PI 1) into PI 11.616 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 11.617 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 11.617 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 11.617 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1)) 11.618 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 11.621 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 11.622 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 11.622 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 11.622 * [taylor]: Taking taylor expansion of (/ -1 k) in n 11.622 * [taylor]: Taking taylor expansion of -1 in n 11.622 * [backup-simplify]: Simplify -1 into -1 11.622 * [taylor]: Taking taylor expansion of k in n 11.622 * [backup-simplify]: Simplify k into k 11.622 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 11.622 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 11.622 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 11.623 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 11.623 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) 11.623 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in k 11.623 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k 11.623 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k 11.623 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k 11.623 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k 11.623 * [taylor]: Taking taylor expansion of 1/2 in k 11.623 * [backup-simplify]: Simplify 1/2 into 1/2 11.623 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k 11.624 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.624 * [taylor]: Taking taylor expansion of k in k 11.624 * [backup-simplify]: Simplify 0 into 0 11.624 * [backup-simplify]: Simplify 1 into 1 11.624 * [backup-simplify]: Simplify (/ 1 1) into 1 11.624 * [taylor]: Taking taylor expansion of 1 in k 11.624 * [backup-simplify]: Simplify 1 into 1 11.624 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 11.624 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 11.624 * [taylor]: Taking taylor expansion of -2 in k 11.624 * [backup-simplify]: Simplify -2 into -2 11.624 * [taylor]: Taking taylor expansion of (/ PI n) in k 11.624 * [taylor]: Taking taylor expansion of PI in k 11.624 * [backup-simplify]: Simplify PI into PI 11.624 * [taylor]: Taking taylor expansion of n in k 11.624 * [backup-simplify]: Simplify n into n 11.624 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 11.624 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 11.624 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 11.624 * [backup-simplify]: Simplify (+ 1 0) into 1 11.625 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 11.625 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 11.625 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) 11.625 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 11.625 * [taylor]: Taking taylor expansion of (/ -1 k) in k 11.625 * [taylor]: Taking taylor expansion of -1 in k 11.625 * [backup-simplify]: Simplify -1 into -1 11.625 * [taylor]: Taking taylor expansion of k in k 11.625 * [backup-simplify]: Simplify 0 into 0 11.625 * [backup-simplify]: Simplify 1 into 1 11.625 * [backup-simplify]: Simplify (/ -1 1) into -1 11.626 * [backup-simplify]: Simplify (sqrt 0) into 0 11.626 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 11.627 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) 11.627 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in k 11.627 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k 11.627 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k 11.627 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k 11.627 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k 11.627 * [taylor]: Taking taylor expansion of 1/2 in k 11.627 * [backup-simplify]: Simplify 1/2 into 1/2 11.627 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k 11.627 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.627 * [taylor]: Taking taylor expansion of k in k 11.627 * [backup-simplify]: Simplify 0 into 0 11.627 * [backup-simplify]: Simplify 1 into 1 11.627 * [backup-simplify]: Simplify (/ 1 1) into 1 11.627 * [taylor]: Taking taylor expansion of 1 in k 11.627 * [backup-simplify]: Simplify 1 into 1 11.627 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 11.627 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 11.627 * [taylor]: Taking taylor expansion of -2 in k 11.627 * [backup-simplify]: Simplify -2 into -2 11.627 * [taylor]: Taking taylor expansion of (/ PI n) in k 11.627 * [taylor]: Taking taylor expansion of PI in k 11.627 * [backup-simplify]: Simplify PI into PI 11.627 * [taylor]: Taking taylor expansion of n in k 11.627 * [backup-simplify]: Simplify n into n 11.627 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 11.627 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 11.627 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 11.628 * [backup-simplify]: Simplify (+ 1 0) into 1 11.628 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 11.628 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 11.628 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) 11.628 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 11.628 * [taylor]: Taking taylor expansion of (/ -1 k) in k 11.628 * [taylor]: Taking taylor expansion of -1 in k 11.628 * [backup-simplify]: Simplify -1 into -1 11.628 * [taylor]: Taking taylor expansion of k in k 11.628 * [backup-simplify]: Simplify 0 into 0 11.628 * [backup-simplify]: Simplify 1 into 1 11.629 * [backup-simplify]: Simplify (/ -1 1) into -1 11.629 * [backup-simplify]: Simplify (sqrt 0) into 0 11.630 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 11.630 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) 11.630 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n 11.630 * [taylor]: Taking taylor expansion of +nan.0 in n 11.630 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.630 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n 11.630 * [taylor]: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n 11.630 * [taylor]: Taking taylor expansion of 1/2 in n 11.630 * [backup-simplify]: Simplify 1/2 into 1/2 11.630 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n 11.630 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 11.630 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 11.630 * [taylor]: Taking taylor expansion of -2 in n 11.630 * [backup-simplify]: Simplify -2 into -2 11.630 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.630 * [taylor]: Taking taylor expansion of PI in n 11.630 * [backup-simplify]: Simplify PI into PI 11.630 * [taylor]: Taking taylor expansion of n in n 11.630 * [backup-simplify]: Simplify 0 into 0 11.630 * [backup-simplify]: Simplify 1 into 1 11.631 * [backup-simplify]: Simplify (/ PI 1) into PI 11.631 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 11.632 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 11.632 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n 11.632 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.632 * [taylor]: Taking taylor expansion of k in n 11.632 * [backup-simplify]: Simplify k into k 11.632 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.632 * [taylor]: Taking taylor expansion of 1 in n 11.632 * [backup-simplify]: Simplify 1 into 1 11.633 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 11.633 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 11.633 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) 11.634 * [backup-simplify]: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 11.635 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 11.636 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) 11.636 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) 11.637 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 11.639 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 11.640 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) 11.640 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n 11.640 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n 11.640 * [taylor]: Taking taylor expansion of +nan.0 in n 11.640 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.640 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n 11.640 * [taylor]: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n 11.640 * [taylor]: Taking taylor expansion of 1/2 in n 11.640 * [backup-simplify]: Simplify 1/2 into 1/2 11.640 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n 11.640 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 11.640 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 11.640 * [taylor]: Taking taylor expansion of -2 in n 11.640 * [backup-simplify]: Simplify -2 into -2 11.640 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.640 * [taylor]: Taking taylor expansion of PI in n 11.640 * [backup-simplify]: Simplify PI into PI 11.640 * [taylor]: Taking taylor expansion of n in n 11.640 * [backup-simplify]: Simplify 0 into 0 11.640 * [backup-simplify]: Simplify 1 into 1 11.640 * [backup-simplify]: Simplify (/ PI 1) into PI 11.641 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 11.641 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 11.641 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n 11.641 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.641 * [taylor]: Taking taylor expansion of k in n 11.641 * [backup-simplify]: Simplify k into k 11.641 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.641 * [taylor]: Taking taylor expansion of 1 in n 11.641 * [backup-simplify]: Simplify 1 into 1 11.642 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 11.642 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 11.643 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) 11.644 * [backup-simplify]: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 11.645 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 11.645 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) 11.646 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) 11.647 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) 11.649 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 11.649 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 11.649 * [backup-simplify]: Simplify (+ 0 0) into 0 11.650 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 11.651 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 11.653 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 11.654 * [backup-simplify]: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (/ 1 k) 1))) into 0 11.656 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into 0 11.658 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 11.660 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into 0 11.660 * [backup-simplify]: Simplify 0 into 0 11.661 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.665 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 11.667 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) 11.667 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n 11.667 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n 11.667 * [taylor]: Taking taylor expansion of +nan.0 in n 11.667 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.667 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n 11.667 * [taylor]: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n 11.667 * [taylor]: Taking taylor expansion of 1/2 in n 11.667 * [backup-simplify]: Simplify 1/2 into 1/2 11.667 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n 11.667 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 11.667 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 11.667 * [taylor]: Taking taylor expansion of -2 in n 11.667 * [backup-simplify]: Simplify -2 into -2 11.667 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.667 * [taylor]: Taking taylor expansion of PI in n 11.667 * [backup-simplify]: Simplify PI into PI 11.667 * [taylor]: Taking taylor expansion of n in n 11.667 * [backup-simplify]: Simplify 0 into 0 11.667 * [backup-simplify]: Simplify 1 into 1 11.668 * [backup-simplify]: Simplify (/ PI 1) into PI 11.668 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 11.669 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 11.670 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n 11.670 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.670 * [taylor]: Taking taylor expansion of k in n 11.670 * [backup-simplify]: Simplify k into k 11.670 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.670 * [taylor]: Taking taylor expansion of 1 in n 11.670 * [backup-simplify]: Simplify 1 into 1 11.671 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 11.671 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 11.673 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) 11.674 * [backup-simplify]: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 11.675 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 11.676 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) 11.678 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) 11.680 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) 11.684 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (* 1 (/ 1 (- k)))) (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))))))))) 11.684 * * * [progress]: simplifying candidates 11.685 * * * * [progress]: [ 1 / 196 ] simplifiying candidate # 11.685 * * * * [progress]: [ 2 / 196 ] simplifiying candidate # 11.685 * * * * [progress]: [ 3 / 196 ] simplifiying candidate # 11.685 * * * * [progress]: [ 4 / 196 ] simplifiying candidate # 11.685 * * * * [progress]: [ 5 / 196 ] simplifiying candidate # 11.685 * * * * [progress]: [ 6 / 196 ] simplifiying candidate # 11.685 * * * * [progress]: [ 7 / 196 ] simplifiying candidate # 11.685 * * * * [progress]: [ 8 / 196 ] simplifiying candidate # 11.685 * * * * [progress]: [ 9 / 196 ] simplifiying candidate # 11.685 * * * * [progress]: [ 10 / 196 ] simplifiying candidate # 11.685 * * * * [progress]: [ 11 / 196 ] simplifiying candidate # 11.685 * * * * [progress]: [ 12 / 196 ] simplifiying candidate # 11.685 * * * * [progress]: [ 13 / 196 ] simplifiying candidate # 11.686 * * * * [progress]: [ 14 / 196 ] simplifiying candidate # 11.686 * * * * [progress]: [ 15 / 196 ] simplifiying candidate # 11.686 * * * * 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simplifiying candidate # 11.687 * * * * [progress]: [ 32 / 196 ] simplifiying candidate # 11.687 * * * * [progress]: [ 33 / 196 ] simplifiying candidate # 11.687 * * * * [progress]: [ 34 / 196 ] simplifiying candidate # 11.687 * * * * [progress]: [ 35 / 196 ] simplifiying candidate # 11.687 * * * * [progress]: [ 36 / 196 ] simplifiying candidate # 11.687 * * * * [progress]: [ 37 / 196 ] simplifiying candidate # 11.687 * * * * [progress]: [ 38 / 196 ] simplifiying candidate # 11.687 * * * * [progress]: [ 39 / 196 ] simplifiying candidate # 11.687 * * * * [progress]: [ 40 / 196 ] simplifiying candidate # 11.687 * * * * [progress]: [ 41 / 196 ] simplifiying candidate # 11.688 * * * * [progress]: [ 42 / 196 ] simplifiying candidate #real (real->posit16 (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))> 11.688 * * * * [progress]: [ 43 / 196 ] simplifiying candidate # 11.688 * * * * [progress]: [ 44 / 196 ] simplifiying candidate # 11.688 * * * * [progress]: [ 45 / 196 ] simplifiying candidate # 11.688 * * * * [progress]: [ 46 / 196 ] simplifiying candidate # 11.688 * * * * [progress]: [ 47 / 196 ] simplifiying candidate # 11.688 * * * * [progress]: [ 48 / 196 ] simplifiying candidate # 11.688 * * * * [progress]: [ 49 / 196 ] simplifiying candidate # 11.688 * * * * [progress]: [ 50 / 196 ] simplifiying candidate # 11.688 * * * * [progress]: [ 51 / 196 ] simplifiying candidate # 11.688 * * * * [progress]: [ 52 / 196 ] simplifiying candidate # 11.688 * * * * [progress]: [ 53 / 196 ] simplifiying candidate # 11.688 * * * * [progress]: [ 54 / 196 ] simplifiying candidate # 11.688 * * * * [progress]: [ 55 / 196 ] simplifiying candidate # 11.688 * * * * [progress]: [ 56 / 196 ] simplifiying candidate # 11.689 * * * * [progress]: [ 57 / 196 ] simplifiying candidate # 11.689 * * * * [progress]: [ 58 / 196 ] simplifiying candidate # 11.689 * * * * [progress]: [ 59 / 196 ] simplifiying candidate # 11.689 * * * * [progress]: [ 60 / 196 ] simplifiying candidate # 11.689 * * * * [progress]: [ 61 / 196 ] simplifiying candidate # 11.689 * * * * [progress]: [ 62 / 196 ] simplifiying candidate # 11.689 * * * * [progress]: [ 63 / 196 ] simplifiying candidate # 11.689 * * * * [progress]: [ 64 / 196 ] simplifiying candidate # 11.689 * * * * [progress]: [ 65 / 196 ] simplifiying candidate # 11.689 * * * * [progress]: [ 66 / 196 ] simplifiying candidate # 11.689 * * * * [progress]: [ 67 / 196 ] simplifiying candidate # 11.689 * * * * [progress]: [ 68 / 196 ] simplifiying candidate # 11.689 * * * * [progress]: [ 69 / 196 ] simplifiying candidate # 11.689 * * * * [progress]: [ 70 / 196 ] simplifiying candidate # 11.690 * * * * [progress]: [ 71 / 196 ] simplifiying candidate # 11.690 * * * * [progress]: [ 72 / 196 ] simplifiying candidate # 11.690 * * * * [progress]: [ 73 / 196 ] simplifiying candidate # 11.690 * * * * [progress]: [ 74 / 196 ] simplifiying candidate # 11.690 * * * * [progress]: [ 75 / 196 ] simplifiying candidate # 11.690 * * * * [progress]: [ 76 / 196 ] simplifiying candidate # 11.690 * * * * [progress]: [ 77 / 196 ] simplifiying candidate # 11.690 * * * * [progress]: [ 78 / 196 ] simplifiying candidate # 11.690 * * * * [progress]: [ 79 / 196 ] simplifiying candidate # 11.690 * * * * [progress]: [ 80 / 196 ] simplifiying candidate # 11.690 * * * * [progress]: [ 81 / 196 ] simplifiying candidate # 11.690 * * * * [progress]: [ 82 / 196 ] simplifiying candidate # 11.690 * * * * [progress]: [ 83 / 196 ] simplifiying candidate # 11.690 * * * * [progress]: [ 84 / 196 ] simplifiying candidate # 11.690 * * * * [progress]: [ 85 / 196 ] simplifiying candidate # 11.691 * * * * [progress]: [ 86 / 196 ] simplifiying candidate # 11.691 * * * * [progress]: [ 87 / 196 ] simplifiying candidate # 11.691 * * * * [progress]: [ 88 / 196 ] simplifiying candidate # 11.691 * * * * [progress]: [ 89 / 196 ] simplifiying candidate # 11.691 * * * * [progress]: [ 90 / 196 ] simplifiying candidate #real (real->posit16 (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))> 11.691 * * * * [progress]: [ 91 / 196 ] simplifiying candidate # 11.691 * * * * [progress]: [ 92 / 196 ] simplifiying candidate # 11.691 * * * * [progress]: [ 93 / 196 ] simplifiying candidate # 11.691 * * * * [progress]: [ 94 / 196 ] simplifiying candidate # 11.691 * * * * [progress]: [ 95 / 196 ] simplifiying candidate # 11.691 * * * * [progress]: [ 96 / 196 ] simplifiying candidate # 11.691 * * * * [progress]: [ 97 / 196 ] simplifiying candidate # 11.691 * * * * [progress]: [ 98 / 196 ] simplifiying candidate # 11.691 * * * * [progress]: [ 99 / 196 ] simplifiying candidate # 11.692 * * * * [progress]: [ 100 / 196 ] simplifiying candidate # 11.692 * * * * [progress]: [ 101 / 196 ] simplifiying candidate # 11.692 * * * * [progress]: [ 102 / 196 ] simplifiying candidate # 11.692 * * * * [progress]: [ 103 / 196 ] simplifiying candidate # 11.692 * * * * [progress]: [ 104 / 196 ] simplifiying candidate # 11.692 * * * * [progress]: [ 105 / 196 ] simplifiying candidate # 11.692 * * * * [progress]: [ 106 / 196 ] simplifiying candidate # 11.692 * * * * [progress]: [ 107 / 196 ] simplifiying candidate # 11.692 * * * * [progress]: [ 108 / 196 ] simplifiying candidate # 11.692 * * * * [progress]: [ 109 / 196 ] simplifiying candidate # 11.692 * * * * [progress]: [ 110 / 196 ] simplifiying candidate #real (real->posit16 (* (* 2 PI) n))) (/ (- 1 k) 2))))> 11.692 * * * * [progress]: [ 111 / 196 ] simplifiying candidate # 11.692 * * * * [progress]: [ 112 / 196 ] simplifiying candidate # 11.692 * * * * [progress]: [ 113 / 196 ] simplifiying candidate # 11.692 * * * * [progress]: [ 114 / 196 ] simplifiying candidate # 11.693 * * * * [progress]: [ 115 / 196 ] simplifiying candidate # 11.693 * * * * [progress]: [ 116 / 196 ] simplifiying candidate # 11.693 * * * * [progress]: [ 117 / 196 ] simplifiying candidate # 11.693 * * * * [progress]: [ 118 / 196 ] simplifiying candidate # 11.693 * * * * [progress]: [ 119 / 196 ] simplifiying candidate # 11.693 * * * * [progress]: [ 120 / 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simplifiying candidate # 11.696 * * * * [progress]: [ 181 / 196 ] simplifiying candidate # 11.696 * * * * [progress]: [ 182 / 196 ] simplifiying candidate # 11.696 * * * * [progress]: [ 183 / 196 ] simplifiying candidate #real (real->posit16 (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))> 11.696 * * * * [progress]: [ 184 / 196 ] simplifiying candidate # 11.696 * * * * [progress]: [ 185 / 196 ] simplifiying candidate # 11.696 * * * * [progress]: [ 186 / 196 ] simplifiying candidate # 11.696 * * * * [progress]: [ 187 / 196 ] simplifiying candidate # 11.696 * * * * [progress]: [ 188 / 196 ] simplifiying candidate # 11.696 * * * * [progress]: [ 189 / 196 ] simplifiying candidate # 11.696 * * * * [progress]: [ 190 / 196 ] simplifiying candidate # 11.696 * * * * [progress]: [ 191 / 196 ] simplifiying candidate # 11.696 * * * * [progress]: [ 192 / 196 ] simplifiying candidate # 11.696 * * * * [progress]: [ 193 / 196 ] simplifiying candidate # 11.696 * * * * [progress]: [ 194 / 196 ] simplifiying candidate # 11.696 * * * * [progress]: [ 195 / 196 ] simplifiying candidate # 11.697 * * * * [progress]: [ 196 / 196 ] simplifiying candidate # 11.698 * [simplify]: Simplifying: (expm1 (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (log1p (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)) (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)) (* 1 (/ (- 1 k) 2)) (* 1 (/ (- 1 k) 2)) (* 1 (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ 1 2)) (pow (* (* 2 PI) n) (/ k 2)) (pow (* (* 2 PI) n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) (pow (* (* 2 PI) n) (sqrt (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2 PI) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2))) (pow (* (* 2 PI) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1)) (pow (* (* 2 PI) n) (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2 PI) n) (/ (sqrt (- 1 k)) (sqrt 2))) (pow (* (* 2 PI) n) (/ (sqrt (- 1 k)) 1)) (pow (* (* 2 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2 PI) n) (/ 1 (sqrt 2))) (pow (* (* 2 PI) n) (/ 1 1)) (pow (* (* 2 PI) n) (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2 PI) n) (/ (+ (sqrt 1) (sqrt k)) (sqrt 2))) (pow (* (* 2 PI) n) (/ (+ (sqrt 1) (sqrt k)) 1)) (pow (* (* 2 PI) n) (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2 PI) n) (/ (+ 1 (sqrt k)) (sqrt 2))) (pow (* (* 2 PI) n) (/ (+ 1 (sqrt k)) 1)) (pow (* (* 2 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2 PI) n) (/ 1 (sqrt 2))) (pow (* (* 2 PI) n) (/ 1 1)) (pow (* (* 2 PI) n) 1) (pow (* (* 2 PI) n) (- 1 k)) (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (exp (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (real->posit16 (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (expm1 (/ 1 (sqrt k))) (log1p (/ 1 (sqrt k))) (- 1/2) (- 1) (- (/ 1 2)) (- (log (sqrt k))) (- 0 (log (sqrt k))) (- (log 1) (log (sqrt k))) (log (/ 1 (sqrt k))) (exp (/ 1 (sqrt k))) (/ (* (* 1 1) 1) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k)))) (cbrt (/ 1 (sqrt k))) (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k))) (sqrt (/ 1 (sqrt k))) (sqrt (/ 1 (sqrt k))) (- 1) (- (sqrt k)) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1) (cbrt (sqrt k))) (/ (* (cbrt 1) (cbrt 1)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1) (sqrt (cbrt k))) (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k))) (/ (cbrt 1) (sqrt (sqrt k))) (/ (* (cbrt 1) (cbrt 1)) (sqrt 1)) (/ (cbrt 1) (sqrt k)) (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k))) (/ (cbrt 1) (sqrt (sqrt k))) (/ (* (cbrt 1) (cbrt 1)) 1) (/ (cbrt 1) (sqrt k)) (/ (sqrt 1) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1) (cbrt (sqrt k))) (/ (sqrt 1) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1) (sqrt (cbrt k))) (/ (sqrt 1) (sqrt (sqrt k))) (/ (sqrt 1) (sqrt (sqrt k))) (/ (sqrt 1) (sqrt 1)) (/ (sqrt 1) (sqrt k)) (/ (sqrt 1) (sqrt (sqrt k))) (/ (sqrt 1) (sqrt (sqrt k))) (/ (sqrt 1) 1) (/ (sqrt 1) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1 (cbrt (sqrt k))) (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt 1)) (/ 1 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k))) (/ 1 1) (/ 1 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt 1)) (/ 1 (sqrt (sqrt k))) (/ 1 1) (/ (sqrt k) (cbrt 1)) (/ (sqrt k) (sqrt 1)) (/ (sqrt k) 1) (real->posit16 (/ 1 (sqrt k))) (expm1 (* (* 2 PI) n)) (log1p (* (* 2 PI) n)) (* (* 2 PI) n) (* (* 2 PI) n) (+ (+ (log 2) (log PI)) (log n)) (+ (log (* 2 PI)) (log n)) (log (* (* 2 PI) n)) (exp (* (* 2 PI) n)) (* (* (* (* 2 2) 2) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2 PI) (* 2 PI)) (* 2 PI)) (* (* n n) n)) (* (cbrt (* (* 2 PI) n)) (cbrt (* (* 2 PI) n))) (cbrt (* (* 2 PI) n)) (* (* (* (* 2 PI) n) (* (* 2 PI) n)) (* (* 2 PI) n)) (sqrt (* (* 2 PI) n)) (sqrt (* (* 2 PI) n)) (* (* 2 PI) (* (cbrt n) (cbrt n))) (* (* 2 PI) (sqrt n)) (* (* 2 PI) 1) (* PI n) (real->posit16 (* (* 2 PI) n)) (expm1 (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (log1p (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (+ (- (log (sqrt k))) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2))) (+ (- (log (sqrt k))) (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2))) (+ (- (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))) (+ (- (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))) (+ (- (log (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (+ (- 0 (log (sqrt 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(* (* 2 PI) n) (/ (- 1 k) 2)))) (log (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (exp (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (/ (* (* 1 1) 1) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k))) (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (cbrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (cbrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) (cbrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (* (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* 1 (pow (* (* 2 PI) n) (/ 1 2))) (* (sqrt k) (pow (* (* 2 PI) n) (/ k 2))) (* (sqrt (/ 1 (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (sqrt (/ 1 (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (sqrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (sqrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (/ 1 (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2))) (* (/ 1 (sqrt k)) (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) (* (/ 1 (sqrt k)) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (/ 1 (sqrt k)) 1) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (cbrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (sqrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (/ (cbrt 1) (cbrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (/ (cbrt 1) (sqrt (cbrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (/ (cbrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (/ (cbrt 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (/ (cbrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (/ (cbrt 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (/ (sqrt 1) (cbrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (/ (sqrt 1) (sqrt (cbrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (/ (sqrt 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (/ (sqrt 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (/ 1 (cbrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (/ 1 (sqrt (cbrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ 1 2))) (* 1 (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (real->posit16 (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (* 2 (* n PI)) (* 2 (* n PI)) (* 2 (* n PI)) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3)))))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))))))))) 11.701 * * [simplify]: iteration 0: 353 enodes 11.855 * * [simplify]: iteration 1: 953 enodes 12.319 * * [simplify]: iteration 2: 2935 enodes 13.322 * * [simplify]: iteration complete: 5003 enodes 13.322 * * [simplify]: Extracting #0: cost 101 inf + 0 13.323 * * [simplify]: Extracting #1: cost 573 inf + 3 13.328 * * [simplify]: Extracting #2: cost 1038 inf + 5771 13.352 * * [simplify]: Extracting #3: cost 1036 inf + 65508 13.430 * * [simplify]: Extracting #4: cost 507 inf + 234741 13.521 * * [simplify]: Extracting #5: cost 132 inf + 384328 13.635 * * [simplify]: Extracting #6: cost 36 inf + 425797 13.780 * * [simplify]: Extracting #7: cost 4 inf + 436156 13.935 * * [simplify]: Extracting #8: cost 0 inf + 437112 14.064 * [simplify]: Simplified to: (expm1 (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (log1p (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (/ (log (* (* n 2) PI)) (/ 2 (- 1 k))) (/ (log (* (* n 2) PI)) (/ 2 (- 1 k))) (/ (log (* (* n 2) PI)) (/ 2 (- 1 k))) (/ (log (* (* n 2) PI)) (/ 2 (- 1 k))) (- 1/2 (/ k 2)) (- 1/2 (/ k 2)) (- 1/2 (/ k 2)) (sqrt (* (* n 2) PI)) (pow (* (* n 2) PI) (/ k 2)) (pow (* (* n 2) PI) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (pow (* (* n 2) PI) (sqrt (- 1/2 (/ k 2)))) (pow (* (* n 2) PI) (* (/ (cbrt (- 1 k)) (cbrt 2)) (/ (cbrt (- 1 k)) (cbrt 2)))) (pow (* (* n 2) PI) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2))) (pow (* (* n 2) PI) (* (cbrt (- 1 k)) (cbrt (- 1 k)))) (pow (* (* n 2) PI) (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2)))) (pow (* (* n 2) PI) (/ (sqrt (- 1 k)) (sqrt 2))) (pow (* (* n 2) PI) (sqrt (- 1 k))) (pow (* (* n 2) PI) (/ (/ 1 (cbrt 2)) (cbrt 2))) (pow (* (* n 2) PI) (/ 1 (sqrt 2))) (* (* n 2) PI) (pow (* (* n 2) PI) (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2)))) (pow (* (* n 2) PI) (/ (+ 1 (sqrt k)) (sqrt 2))) (pow (* (* n 2) PI) (+ 1 (sqrt k))) (pow (* (* n 2) PI) (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2)))) (pow (* (* n 2) PI) (/ (+ 1 (sqrt k)) (sqrt 2))) (pow (* (* n 2) PI) (+ 1 (sqrt k))) (pow (* (* n 2) PI) (/ (/ 1 (cbrt 2)) (cbrt 2))) (pow (* (* n 2) PI) (/ 1 (sqrt 2))) (* (* n 2) PI) (* (* n 2) PI) (pow (* (* n 2) PI) (- 1 k)) (pow (* PI 2) (- 1/2 (/ k 2))) (pow n (- 1/2 (/ k 2))) (/ (log (* (* n 2) PI)) (/ 2 (- 1 k))) (exp (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (pow (pow (* (* n 2) PI) (- 1/2 (/ k 2))) 3) (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (pow (* (* n 2) PI) (/ (- 1 k) 4)) (pow (* (* n 2) PI) (/ (- 1 k) 4)) (real->posit16 (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (expm1 (/ 1 (sqrt k))) (log1p (/ 1 (sqrt k))) -1/2 -1 -1/2 (- (log (sqrt k))) (- (log (sqrt k))) (- (log (sqrt k))) (- (log (sqrt k))) (exp (/ 1 (sqrt k))) (/ 1 (* k (sqrt k))) (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k)))) (cbrt (/ 1 (sqrt k))) (* (/ (/ 1 (sqrt k)) (sqrt k)) (/ 1 (sqrt k))) (sqrt (/ 1 (sqrt k))) (sqrt (/ 1 (sqrt k))) -1 (- (sqrt k)) (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (/ 1 (cbrt (sqrt k))) (/ 1 (fabs (cbrt k))) (/ 1 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k))) 1 (/ 1 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k))) 1 (/ 1 (sqrt k)) (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (/ 1 (cbrt (sqrt k))) (/ 1 (fabs (cbrt k))) (/ 1 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k))) 1 (/ 1 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k))) 1 (/ 1 (sqrt k)) (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (/ 1 (cbrt (sqrt k))) (/ 1 (fabs (cbrt k))) (/ 1 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k))) 1 (/ 1 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k))) 1 (/ 1 (sqrt k)) (/ 1 (sqrt k)) (sqrt k) (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (/ 1 (fabs (cbrt k))) (/ 1 (sqrt (sqrt k))) 1 (/ 1 (sqrt (sqrt k))) 1 (sqrt k) (sqrt k) (sqrt k) (real->posit16 (/ 1 (sqrt k))) (expm1 (* (* n 2) PI)) (log1p (* (* n 2) PI)) (* (* n 2) PI) (* (* n 2) PI) (log (* (* n 2) PI)) (log (* (* n 2) PI)) (log (* (* n 2) PI)) (* (exp (* n PI)) (exp (* n PI))) (* (* (* n (* n n)) 8) (* (* PI PI) PI)) (* (* (* (* n 2) PI) (sqrt (* (* n 2) PI))) (* (* (* n 2) PI) (sqrt (* (* n 2) PI)))) (* (cbrt (* (* n 2) PI)) (cbrt (* (* n 2) PI))) (cbrt (* (* n 2) PI)) (* (* (* (* n 2) PI) (sqrt (* (* n 2) PI))) (* (* (* n 2) PI) (sqrt (* (* n 2) PI)))) (sqrt (* (* n 2) PI)) (sqrt (* (* n 2) PI)) (* (* PI 2) (* (cbrt n) (cbrt n))) (* 2 (* (sqrt n) PI)) (* PI 2) (* n PI) (real->posit16 (* (* n 2) PI)) (expm1 (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (log1p (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (- (/ (log (* (* n 2) PI)) (/ 2 (- 1 k))) (log (sqrt k))) (- (/ (log (* (* n 2) PI)) (/ 2 (- 1 k))) (log (sqrt k))) (- (/ (log (* (* n 2) PI)) (/ 2 (- 1 k))) (log (sqrt k))) (- (/ (log (* (* n 2) PI)) (/ 2 (- 1 k))) (log (sqrt k))) (- (/ (log (* (* n 2) PI)) (/ 2 (- 1 k))) (log (sqrt k))) (- (/ (log (* (* n 2) PI)) (/ 2 (- 1 k))) (log (sqrt k))) (- (/ (log (* (* n 2) PI)) (/ 2 (- 1 k))) (log (sqrt k))) (- (/ (log (* (* n 2) PI)) (/ 2 (- 1 k))) (log (sqrt k))) (- (/ (log (* (* n 2) PI)) (/ 2 (- 1 k))) (log (sqrt k))) (- (/ (log (* (* n 2) PI)) (/ 2 (- 1 k))) (log (sqrt k))) (- (/ (log (* (* n 2) PI)) (/ 2 (- 1 k))) (log (sqrt k))) (- (/ (log (* (* n 2) PI)) (/ 2 (- 1 k))) (log (sqrt k))) (- (/ (log (* (* n 2) PI)) (/ 2 (- 1 k))) (log (sqrt k))) (- (/ (log (* (* n 2) PI)) (/ 2 (- 1 k))) (log (sqrt k))) (- (/ (log (* (* n 2) PI)) (/ 2 (- 1 k))) (log (sqrt k))) (- (/ (log (* (* n 2) PI)) (/ 2 (- 1 k))) (log (sqrt k))) (- (/ (log (* (* n 2) PI)) (/ 2 (- 1 k))) (log (sqrt k))) (- (/ (log (* (* n 2) PI)) (/ 2 (- 1 k))) (log (sqrt k))) (- (/ (log (* (* n 2) PI)) (/ 2 (- 1 k))) (log (sqrt k))) (- (/ (log (* (* n 2) PI)) (/ 2 (- 1 k))) (log (sqrt k))) (- (/ (log (* (* n 2) PI)) (/ 2 (- 1 k))) (log (sqrt k))) (exp (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (/ (pow (pow (* (* n 2) PI) (- 1/2 (/ k 2))) 3) (* k (sqrt k))) (* (* (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (* (cbrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (cbrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (* (* (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (* n 2) PI)) (* (pow (* (* n 2) PI) (/ k 2)) (sqrt k)) (* (sqrt (/ 1 (sqrt k))) (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (* (sqrt (/ 1 (sqrt k))) (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (* (sqrt (/ 1 (sqrt k))) (pow (* (* n 2) PI) (/ (- 1 k) 4))) (* (sqrt (/ 1 (sqrt k))) (pow (* (* n 2) PI) (/ (- 1 k) 4))) (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (/ (- 1 k) 4)) (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (/ (- 1 k) 4)) (sqrt (sqrt k))) (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (/ (- 1 k) 4)) (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (/ (- 1 k) 4)) (sqrt (sqrt k))) (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (/ (- 1 k) 4)) (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (/ (- 1 k) 4)) (sqrt (sqrt k))) (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (/ (- 1 k) 4)) (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (/ (- 1 k) 4)) (sqrt (sqrt k))) (/ (pow (* PI 2) (- 1/2 (/ k 2))) (sqrt k)) (* (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k)) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k)) (/ 1 (sqrt k)) (/ (pow (* (* n 2) PI) (/ (- 1 k) 4)) (sqrt k)) (* (cbrt (/ 1 (sqrt k))) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (* (sqrt (/ 1 (sqrt k))) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (cbrt (sqrt k))) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (cbrt k))) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (cbrt (sqrt k))) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (cbrt k))) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (cbrt (sqrt k))) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (cbrt k))) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)) (/ (sqrt (* (* n 2) PI)) (sqrt k)) (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (real->posit16 (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (fma (* 1/4 (* (sqrt (* (* n 2) PI)) (log (* PI 2)))) (* (* k k) (log n)) (fma (* (* k (log n)) (* k (log n))) (* 1/8 (sqrt (* (* n 2) PI))) (- (fma (* (sqrt (* (* n 2) PI)) (* (* k k) (* (log (* PI 2)) (log (* PI 2))))) 1/8 (sqrt (* (* n 2) PI))) (/ (* k (fma (log n) (sqrt (* (* n 2) PI)) (* (sqrt (* (* n 2) PI)) (log (* PI 2))))) 2)))) (sqrt (exp (* (log (* (* n 2) PI)) (- 1 k)))) (sqrt (exp (* (- 1 k) (- (log (* PI -2)) (log (/ -1 n)))))) (fma (- +nan.0) (* k k) (- +nan.0 (* +nan.0 k))) (+ (/ (- +nan.0) (* k k)) (- (/ +nan.0 k) (/ +nan.0 (* (* k k) k)))) (- (/ (- +nan.0) (* k k)) (+ +nan.0 (/ (- +nan.0) k))) (* (* n 2) PI) (* (* n 2) PI) (* (* n 2) PI) (fma (- +nan.0) (* (* n (* PI k)) (sqrt 2)) (- (fma (* n PI) (* (sqrt 2) +nan.0) (* (* (sqrt 2) +nan.0) (- (* (* (log n) k) (* n PI)) (* (* n PI) (* n PI))))) (* (* (* (* n (* PI k)) (sqrt 2)) (log (* PI 2))) +nan.0))) (- (fma +nan.0 (/ (sqrt (exp (* (log (* (* n 2) PI)) (- 1 k)))) k) (fma (- (/ (sqrt (exp (* (log (* (* n 2) PI)) (- 1 k)))) (* k k))) +nan.0 (* (/ +nan.0 k) (/ (sqrt (exp (* (log (* (* n 2) PI)) (- 1 k)))) (* k k)))))) (fma (- +nan.0) (/ (sqrt (exp (* (- 1 k) (- (log (* PI -2)) (log (/ -1 n)))))) k) (- (* (/ (sqrt (exp (* (- 1 k) (- (log (* PI -2)) (log (/ -1 n)))))) k) (/ +nan.0 k)) (* (sqrt (exp (* (- 1 k) (- (log (* PI -2)) (log (/ -1 n)))))) +nan.0))) 14.087 * * * [progress]: adding candidates to table 14.938 * * [progress]: iteration 3 / 4 14.938 * * * [progress]: picking best candidate 14.992 * * * * [pick]: Picked # 14.992 * * * [progress]: localizing error 15.051 * * * [progress]: generating rewritten candidates 15.051 * * * * [progress]: [ 1 / 4 ] rewriting at (2 1) 15.085 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 2) 15.101 * * * * [progress]: [ 3 / 4 ] rewriting at (2) 15.507 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2) 19.324 * * * [progress]: generating series expansions 19.324 * * * * [progress]: [ 1 / 4 ] generating series at (2 1) 19.325 * [backup-simplify]: Simplify (pow (* n 2) (- 1/2 (/ k 2))) into (pow (* 2 n) (- 1/2 (* 1/2 k))) 19.325 * [approximate]: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in (n k) around 0 19.325 * [taylor]: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in k 19.325 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in k 19.325 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in k 19.325 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 19.325 * [taylor]: Taking taylor expansion of 1/2 in k 19.325 * [backup-simplify]: Simplify 1/2 into 1/2 19.325 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 19.325 * [taylor]: Taking taylor expansion of 1/2 in k 19.325 * [backup-simplify]: Simplify 1/2 into 1/2 19.325 * [taylor]: Taking taylor expansion of k in k 19.325 * [backup-simplify]: Simplify 0 into 0 19.325 * [backup-simplify]: Simplify 1 into 1 19.325 * [taylor]: Taking taylor expansion of (log (* 2 n)) in k 19.325 * [taylor]: Taking taylor expansion of (* 2 n) in k 19.325 * [taylor]: Taking taylor expansion of 2 in k 19.325 * [backup-simplify]: Simplify 2 into 2 19.325 * [taylor]: Taking taylor expansion of n in k 19.325 * [backup-simplify]: Simplify n into n 19.325 * [backup-simplify]: Simplify (* 2 n) into (* 2 n) 19.325 * [backup-simplify]: Simplify (log (* 2 n)) into (log (* 2 n)) 19.326 * [backup-simplify]: Simplify (* 1/2 0) into 0 19.326 * [backup-simplify]: Simplify (- 0) into 0 19.327 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 19.327 * [backup-simplify]: Simplify (* 1/2 (log (* 2 n))) into (* 1/2 (log (* 2 n))) 19.327 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 n)))) into (pow (* 2 n) 1/2) 19.327 * [taylor]: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in n 19.327 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in n 19.327 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in n 19.327 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 19.327 * [taylor]: Taking taylor expansion of 1/2 in n 19.327 * [backup-simplify]: Simplify 1/2 into 1/2 19.327 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 19.327 * [taylor]: Taking taylor expansion of 1/2 in n 19.327 * [backup-simplify]: Simplify 1/2 into 1/2 19.327 * [taylor]: Taking taylor expansion of k in n 19.327 * [backup-simplify]: Simplify k into k 19.327 * [taylor]: Taking taylor expansion of (log (* 2 n)) in n 19.327 * [taylor]: Taking taylor expansion of (* 2 n) in n 19.327 * [taylor]: Taking taylor expansion of 2 in n 19.327 * [backup-simplify]: Simplify 2 into 2 19.327 * [taylor]: Taking taylor expansion of n in n 19.327 * [backup-simplify]: Simplify 0 into 0 19.327 * [backup-simplify]: Simplify 1 into 1 19.328 * [backup-simplify]: Simplify (* 2 0) into 0 19.329 * [backup-simplify]: Simplify (+ (* 2 1) (* 0 0)) into 2 19.329 * [backup-simplify]: Simplify (log 2) into (log 2) 19.329 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 19.329 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 19.330 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 19.330 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 19.331 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log 2) (log n))) into (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) 19.331 * [backup-simplify]: Simplify (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) into (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) 19.331 * [taylor]: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in n 19.331 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in n 19.331 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in n 19.331 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 19.331 * [taylor]: Taking taylor expansion of 1/2 in n 19.331 * [backup-simplify]: Simplify 1/2 into 1/2 19.332 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 19.332 * [taylor]: Taking taylor expansion of 1/2 in n 19.332 * [backup-simplify]: Simplify 1/2 into 1/2 19.332 * [taylor]: Taking taylor expansion of k in n 19.332 * [backup-simplify]: Simplify k into k 19.332 * [taylor]: Taking taylor expansion of (log (* 2 n)) in n 19.332 * [taylor]: Taking taylor expansion of (* 2 n) in n 19.332 * [taylor]: Taking taylor expansion of 2 in n 19.332 * [backup-simplify]: Simplify 2 into 2 19.332 * [taylor]: Taking taylor expansion of n in n 19.332 * [backup-simplify]: Simplify 0 into 0 19.332 * [backup-simplify]: Simplify 1 into 1 19.332 * [backup-simplify]: Simplify (* 2 0) into 0 19.333 * [backup-simplify]: Simplify (+ (* 2 1) (* 0 0)) into 2 19.333 * [backup-simplify]: Simplify (log 2) into (log 2) 19.333 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 19.333 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 19.334 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 19.334 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 19.335 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log 2) (log n))) into (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) 19.335 * [backup-simplify]: Simplify (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) into (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) 19.335 * [taylor]: Taking taylor expansion of (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) in k 19.336 * [taylor]: Taking taylor expansion of (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) in k 19.336 * [taylor]: Taking taylor expansion of (+ (log 2) (log n)) in k 19.336 * [taylor]: Taking taylor expansion of (log 2) in k 19.336 * [taylor]: Taking taylor expansion of 2 in k 19.336 * [backup-simplify]: Simplify 2 into 2 19.336 * [backup-simplify]: Simplify (log 2) into (log 2) 19.336 * [taylor]: Taking taylor expansion of (log n) in k 19.336 * [taylor]: Taking taylor expansion of n in k 19.336 * [backup-simplify]: Simplify n into n 19.336 * [backup-simplify]: Simplify (log n) into (log n) 19.336 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 19.336 * [taylor]: Taking taylor expansion of 1/2 in k 19.336 * [backup-simplify]: Simplify 1/2 into 1/2 19.336 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 19.336 * [taylor]: Taking taylor expansion of 1/2 in k 19.336 * [backup-simplify]: Simplify 1/2 into 1/2 19.336 * [taylor]: Taking taylor expansion of k in k 19.336 * [backup-simplify]: Simplify 0 into 0 19.336 * [backup-simplify]: Simplify 1 into 1 19.337 * [backup-simplify]: Simplify (+ (log 2) (log n)) into (+ (log 2) (log n)) 19.337 * [backup-simplify]: Simplify (* 1/2 0) into 0 19.338 * [backup-simplify]: Simplify (- 0) into 0 19.338 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 19.338 * [backup-simplify]: Simplify (* (+ (log 2) (log n)) 1/2) into (* 1/2 (+ (log 2) (log n))) 19.339 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log 2) (log n)))) into (exp (* 1/2 (+ (log 2) (log n)))) 19.339 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log 2) (log n)))) into (exp (* 1/2 (+ (log 2) (log n)))) 19.340 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 1) (* 0 0))) into 0 19.342 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 19.342 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 19.343 * [backup-simplify]: Simplify (- 0) into 0 19.343 * [backup-simplify]: Simplify (+ 0 0) into 0 19.344 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 19.345 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log 2) (log n)))) into 0 19.346 * [backup-simplify]: Simplify (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (+ (* (/ (pow 0 1) 1)))) into 0 19.346 * [taylor]: Taking taylor expansion of 0 in k 19.346 * [backup-simplify]: Simplify 0 into 0 19.346 * [backup-simplify]: Simplify 0 into 0 19.347 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 19.347 * [backup-simplify]: Simplify (- 1/2) into -1/2 19.348 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 19.349 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 19.350 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 19.351 * [backup-simplify]: Simplify (+ 0 0) into 0 19.351 * [backup-simplify]: Simplify (+ (* (+ (log 2) (log n)) -1/2) (* 0 1/2)) into (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 19.353 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) 19.354 * [backup-simplify]: Simplify (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) into (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) 19.356 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 19.359 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 19.360 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 19.360 * [backup-simplify]: Simplify (- 0) into 0 19.361 * [backup-simplify]: Simplify (+ 0 0) into 0 19.361 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 19.362 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log 2) (log n))))) into 0 19.364 * [backup-simplify]: Simplify (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 19.364 * [taylor]: Taking taylor expansion of 0 in k 19.364 * [backup-simplify]: Simplify 0 into 0 19.364 * [backup-simplify]: Simplify 0 into 0 19.364 * [backup-simplify]: Simplify 0 into 0 19.365 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 19.366 * [backup-simplify]: Simplify (- 0) into 0 19.366 * [backup-simplify]: Simplify (+ 0 0) into 0 19.369 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 19.371 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 19.371 * [backup-simplify]: Simplify (+ 0 0) into 0 19.372 * [backup-simplify]: Simplify (+ (* (+ (log 2) (log n)) 0) (+ (* 0 -1/2) (* 0 1/2))) into 0 19.375 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))) 19.378 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))) into (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))) 19.383 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) (* k 1)) (exp (* 1/2 (+ (log 2) (log n)))))) into (- (+ (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (* (pow (log 2) 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (pow k 2)))) (+ (* 1/4 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) (pow k 2))))) (* 1/8 (* (exp (* 1/2 (+ (log 2) (log n)))) (* (pow (log n) 2) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) k))) (* 1/2 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) k))))) 19.384 * [backup-simplify]: Simplify (pow (* (/ 1 n) 2) (- 1/2 (/ (/ 1 k) 2))) into (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) 19.384 * [approximate]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 19.384 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in k 19.384 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in k 19.384 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in k 19.384 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 19.384 * [taylor]: Taking taylor expansion of 1/2 in k 19.384 * [backup-simplify]: Simplify 1/2 into 1/2 19.384 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 19.384 * [taylor]: Taking taylor expansion of 1/2 in k 19.384 * [backup-simplify]: Simplify 1/2 into 1/2 19.384 * [taylor]: Taking taylor expansion of (/ 1 k) in k 19.384 * [taylor]: Taking taylor expansion of k in k 19.384 * [backup-simplify]: Simplify 0 into 0 19.384 * [backup-simplify]: Simplify 1 into 1 19.384 * [backup-simplify]: Simplify (/ 1 1) into 1 19.384 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in k 19.384 * [taylor]: Taking taylor expansion of (/ 2 n) in k 19.385 * [taylor]: Taking taylor expansion of 2 in k 19.385 * [backup-simplify]: Simplify 2 into 2 19.385 * [taylor]: Taking taylor expansion of n in k 19.385 * [backup-simplify]: Simplify n into n 19.385 * [backup-simplify]: Simplify (/ 2 n) into (/ 2 n) 19.385 * [backup-simplify]: Simplify (log (/ 2 n)) into (log (/ 2 n)) 19.385 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 19.386 * [backup-simplify]: Simplify (- 1/2) into -1/2 19.386 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 19.386 * [backup-simplify]: Simplify (* -1/2 (log (/ 2 n))) into (* -1/2 (log (/ 2 n))) 19.386 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) into (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) 19.386 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 19.386 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 19.386 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 19.386 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 19.386 * [taylor]: Taking taylor expansion of 1/2 in n 19.387 * [backup-simplify]: Simplify 1/2 into 1/2 19.387 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 19.387 * [taylor]: Taking taylor expansion of 1/2 in n 19.387 * [backup-simplify]: Simplify 1/2 into 1/2 19.387 * [taylor]: Taking taylor expansion of (/ 1 k) in n 19.387 * [taylor]: Taking taylor expansion of k in n 19.387 * [backup-simplify]: Simplify k into k 19.387 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 19.387 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in n 19.387 * [taylor]: Taking taylor expansion of (/ 2 n) in n 19.387 * [taylor]: Taking taylor expansion of 2 in n 19.387 * [backup-simplify]: Simplify 2 into 2 19.387 * [taylor]: Taking taylor expansion of n in n 19.387 * [backup-simplify]: Simplify 0 into 0 19.387 * [backup-simplify]: Simplify 1 into 1 19.387 * [backup-simplify]: Simplify (/ 2 1) into 2 19.388 * [backup-simplify]: Simplify (log 2) into (log 2) 19.388 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 19.388 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 19.388 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 19.389 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 19.389 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 19.390 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 19.390 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 19.390 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 19.390 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 19.390 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 19.390 * [taylor]: Taking taylor expansion of 1/2 in n 19.390 * [backup-simplify]: Simplify 1/2 into 1/2 19.390 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 19.390 * [taylor]: Taking taylor expansion of 1/2 in n 19.390 * [backup-simplify]: Simplify 1/2 into 1/2 19.390 * [taylor]: Taking taylor expansion of (/ 1 k) in n 19.390 * [taylor]: Taking taylor expansion of k in n 19.390 * [backup-simplify]: Simplify k into k 19.390 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 19.390 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in n 19.390 * [taylor]: Taking taylor expansion of (/ 2 n) in n 19.390 * [taylor]: Taking taylor expansion of 2 in n 19.390 * [backup-simplify]: Simplify 2 into 2 19.390 * [taylor]: Taking taylor expansion of n in n 19.390 * [backup-simplify]: Simplify 0 into 0 19.390 * [backup-simplify]: Simplify 1 into 1 19.391 * [backup-simplify]: Simplify (/ 2 1) into 2 19.391 * [backup-simplify]: Simplify (log 2) into (log 2) 19.391 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 19.391 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 19.391 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 19.392 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 19.392 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 19.392 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 19.393 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) in k 19.393 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) in k 19.393 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 19.393 * [taylor]: Taking taylor expansion of 1/2 in k 19.393 * [backup-simplify]: Simplify 1/2 into 1/2 19.393 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 19.393 * [taylor]: Taking taylor expansion of 1/2 in k 19.393 * [backup-simplify]: Simplify 1/2 into 1/2 19.393 * [taylor]: Taking taylor expansion of (/ 1 k) in k 19.393 * [taylor]: Taking taylor expansion of k in k 19.393 * [backup-simplify]: Simplify 0 into 0 19.393 * [backup-simplify]: Simplify 1 into 1 19.393 * [backup-simplify]: Simplify (/ 1 1) into 1 19.393 * [taylor]: Taking taylor expansion of (- (log 2) (log n)) in k 19.393 * [taylor]: Taking taylor expansion of (log 2) in k 19.393 * [taylor]: Taking taylor expansion of 2 in k 19.393 * [backup-simplify]: Simplify 2 into 2 19.393 * [backup-simplify]: Simplify (log 2) into (log 2) 19.393 * [taylor]: Taking taylor expansion of (log n) in k 19.393 * [taylor]: Taking taylor expansion of n in k 19.393 * [backup-simplify]: Simplify n into n 19.393 * [backup-simplify]: Simplify (log n) into (log n) 19.394 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 19.394 * [backup-simplify]: Simplify (- 1/2) into -1/2 19.394 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 19.394 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 19.394 * [backup-simplify]: Simplify (+ (log 2) (- (log n))) into (- (log 2) (log n)) 19.395 * [backup-simplify]: Simplify (* -1/2 (- (log 2) (log n))) into (* -1/2 (- (log 2) (log n))) 19.395 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 19.395 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 19.396 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)))) into 0 19.397 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 19.397 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 19.397 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 19.398 * [backup-simplify]: Simplify (- 0) into 0 19.398 * [backup-simplify]: Simplify (+ 0 0) into 0 19.398 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 19.399 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log 2) (log n)))) into 0 19.399 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 19.399 * [taylor]: Taking taylor expansion of 0 in k 19.400 * [backup-simplify]: Simplify 0 into 0 19.400 * [backup-simplify]: Simplify 0 into 0 19.400 * [backup-simplify]: Simplify 0 into 0 19.400 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)) (* 0 (/ 0 1)))) into 0 19.402 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 19.402 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 19.403 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 19.403 * [backup-simplify]: Simplify (- 0) into 0 19.403 * [backup-simplify]: Simplify (+ 0 0) into 0 19.404 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 19.405 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log 2) (log n))))) into 0 19.406 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 19.406 * [taylor]: Taking taylor expansion of 0 in k 19.406 * [backup-simplify]: Simplify 0 into 0 19.406 * [backup-simplify]: Simplify 0 into 0 19.406 * [backup-simplify]: Simplify 0 into 0 19.406 * [backup-simplify]: Simplify 0 into 0 19.406 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 19.409 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 19.409 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 19.410 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 19.410 * [backup-simplify]: Simplify (- 0) into 0 19.411 * [backup-simplify]: Simplify (+ 0 0) into 0 19.411 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 19.412 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log 2) (log n)))))) into 0 19.413 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 19.413 * [taylor]: Taking taylor expansion of 0 in k 19.413 * [backup-simplify]: Simplify 0 into 0 19.413 * [backup-simplify]: Simplify 0 into 0 19.414 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log 2) (log (/ 1 n))))) into (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) 19.414 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) 2) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) 19.414 * [approximate]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 19.414 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in k 19.414 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in k 19.414 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in k 19.414 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 19.414 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 19.414 * [taylor]: Taking taylor expansion of 1/2 in k 19.414 * [backup-simplify]: Simplify 1/2 into 1/2 19.414 * [taylor]: Taking taylor expansion of (/ 1 k) in k 19.414 * [taylor]: Taking taylor expansion of k in k 19.414 * [backup-simplify]: Simplify 0 into 0 19.414 * [backup-simplify]: Simplify 1 into 1 19.414 * [backup-simplify]: Simplify (/ 1 1) into 1 19.414 * [taylor]: Taking taylor expansion of 1/2 in k 19.414 * [backup-simplify]: Simplify 1/2 into 1/2 19.414 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in k 19.414 * [taylor]: Taking taylor expansion of (/ -2 n) in k 19.414 * [taylor]: Taking taylor expansion of -2 in k 19.414 * [backup-simplify]: Simplify -2 into -2 19.415 * [taylor]: Taking taylor expansion of n in k 19.415 * [backup-simplify]: Simplify n into n 19.415 * [backup-simplify]: Simplify (/ -2 n) into (/ -2 n) 19.415 * [backup-simplify]: Simplify (log (/ -2 n)) into (log (/ -2 n)) 19.415 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 19.415 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 19.415 * [backup-simplify]: Simplify (* 1/2 (log (/ -2 n))) into (* 1/2 (log (/ -2 n))) 19.415 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) into (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) 19.415 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 19.415 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 19.415 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 19.415 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 19.415 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 19.415 * [taylor]: Taking taylor expansion of 1/2 in n 19.415 * [backup-simplify]: Simplify 1/2 into 1/2 19.415 * [taylor]: Taking taylor expansion of (/ 1 k) in n 19.416 * [taylor]: Taking taylor expansion of k in n 19.416 * [backup-simplify]: Simplify k into k 19.416 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 19.416 * [taylor]: Taking taylor expansion of 1/2 in n 19.416 * [backup-simplify]: Simplify 1/2 into 1/2 19.416 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in n 19.416 * [taylor]: Taking taylor expansion of (/ -2 n) in n 19.416 * [taylor]: Taking taylor expansion of -2 in n 19.416 * [backup-simplify]: Simplify -2 into -2 19.416 * [taylor]: Taking taylor expansion of n in n 19.416 * [backup-simplify]: Simplify 0 into 0 19.416 * [backup-simplify]: Simplify 1 into 1 19.416 * [backup-simplify]: Simplify (/ -2 1) into -2 19.416 * [backup-simplify]: Simplify (log -2) into (log -2) 19.416 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 19.416 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 19.422 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 19.423 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 19.424 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 19.424 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 19.424 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 19.424 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 19.424 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 19.424 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 19.424 * [taylor]: Taking taylor expansion of 1/2 in n 19.424 * [backup-simplify]: Simplify 1/2 into 1/2 19.424 * [taylor]: Taking taylor expansion of (/ 1 k) in n 19.424 * [taylor]: Taking taylor expansion of k in n 19.424 * [backup-simplify]: Simplify k into k 19.424 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 19.424 * [taylor]: Taking taylor expansion of 1/2 in n 19.424 * [backup-simplify]: Simplify 1/2 into 1/2 19.424 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in n 19.424 * [taylor]: Taking taylor expansion of (/ -2 n) in n 19.424 * [taylor]: Taking taylor expansion of -2 in n 19.424 * [backup-simplify]: Simplify -2 into -2 19.424 * [taylor]: Taking taylor expansion of n in n 19.424 * [backup-simplify]: Simplify 0 into 0 19.424 * [backup-simplify]: Simplify 1 into 1 19.425 * [backup-simplify]: Simplify (/ -2 1) into -2 19.425 * [backup-simplify]: Simplify (log -2) into (log -2) 19.425 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 19.425 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 19.426 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 19.427 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 19.427 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 19.428 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) in k 19.428 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) in k 19.428 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 19.428 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 19.428 * [taylor]: Taking taylor expansion of 1/2 in k 19.428 * [backup-simplify]: Simplify 1/2 into 1/2 19.428 * [taylor]: Taking taylor expansion of (/ 1 k) in k 19.428 * [taylor]: Taking taylor expansion of k in k 19.428 * [backup-simplify]: Simplify 0 into 0 19.428 * [backup-simplify]: Simplify 1 into 1 19.428 * [backup-simplify]: Simplify (/ 1 1) into 1 19.428 * [taylor]: Taking taylor expansion of 1/2 in k 19.428 * [backup-simplify]: Simplify 1/2 into 1/2 19.428 * [taylor]: Taking taylor expansion of (- (log -2) (log n)) in k 19.429 * [taylor]: Taking taylor expansion of (log -2) in k 19.429 * [taylor]: Taking taylor expansion of -2 in k 19.429 * [backup-simplify]: Simplify -2 into -2 19.429 * [backup-simplify]: Simplify (log -2) into (log -2) 19.429 * [taylor]: Taking taylor expansion of (log n) in k 19.429 * [taylor]: Taking taylor expansion of n in k 19.429 * [backup-simplify]: Simplify n into n 19.429 * [backup-simplify]: Simplify (log n) into (log n) 19.430 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 19.430 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 19.430 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 19.431 * [backup-simplify]: Simplify (+ (log -2) (- (log n))) into (- (log -2) (log n)) 19.431 * [backup-simplify]: Simplify (* 1/2 (- (log -2) (log n))) into (* 1/2 (- (log -2) (log n))) 19.432 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 19.432 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 19.433 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -2 (/ 0 1)))) into 0 19.435 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -2 1)))) 1) into 0 19.435 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 19.435 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 19.435 * [backup-simplify]: Simplify (+ 0 0) into 0 19.436 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 19.436 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log -2) (log n)))) into 0 19.437 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 19.437 * [taylor]: Taking taylor expansion of 0 in k 19.437 * [backup-simplify]: Simplify 0 into 0 19.437 * [backup-simplify]: Simplify 0 into 0 19.437 * [backup-simplify]: Simplify 0 into 0 19.438 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -2 (/ 0 1)) (* 0 (/ 0 1)))) into 0 19.440 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -2 1)))) 2) into 0 19.440 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 19.440 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 19.441 * [backup-simplify]: Simplify (+ 0 0) into 0 19.441 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 19.442 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log -2) (log n))))) into 0 19.443 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 19.443 * [taylor]: Taking taylor expansion of 0 in k 19.443 * [backup-simplify]: Simplify 0 into 0 19.443 * [backup-simplify]: Simplify 0 into 0 19.443 * [backup-simplify]: Simplify 0 into 0 19.443 * [backup-simplify]: Simplify 0 into 0 19.444 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -2 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 19.447 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow -2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow -2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow -2 1)))) 6) into 0 19.447 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 19.448 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 19.448 * [backup-simplify]: Simplify (+ 0 0) into 0 19.449 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 19.450 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log -2) (log n)))))) into 0 19.452 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 19.452 * [taylor]: Taking taylor expansion of 0 in k 19.452 * [backup-simplify]: Simplify 0 into 0 19.452 * [backup-simplify]: Simplify 0 into 0 19.452 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -2) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) 19.452 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 2) 19.452 * [backup-simplify]: Simplify (pow PI (- 1/2 (/ k 2))) into (pow PI (- 1/2 (* 1/2 k))) 19.452 * [approximate]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in (k) around 0 19.452 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 19.452 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 19.452 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 19.452 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 19.452 * [taylor]: Taking taylor expansion of 1/2 in k 19.452 * [backup-simplify]: Simplify 1/2 into 1/2 19.452 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 19.452 * [taylor]: Taking taylor expansion of 1/2 in k 19.452 * [backup-simplify]: Simplify 1/2 into 1/2 19.452 * [taylor]: Taking taylor expansion of k in k 19.452 * [backup-simplify]: Simplify 0 into 0 19.452 * [backup-simplify]: Simplify 1 into 1 19.452 * [taylor]: Taking taylor expansion of (log PI) in k 19.453 * [taylor]: Taking taylor expansion of PI in k 19.453 * [backup-simplify]: Simplify PI into PI 19.453 * [backup-simplify]: Simplify (log PI) into (log PI) 19.453 * [backup-simplify]: Simplify (* 1/2 0) into 0 19.453 * [backup-simplify]: Simplify (- 0) into 0 19.454 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 19.454 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 19.456 * [backup-simplify]: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 19.456 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 19.456 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 19.456 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 19.456 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 19.456 * [taylor]: Taking taylor expansion of 1/2 in k 19.456 * [backup-simplify]: Simplify 1/2 into 1/2 19.456 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 19.456 * [taylor]: Taking taylor expansion of 1/2 in k 19.456 * [backup-simplify]: Simplify 1/2 into 1/2 19.456 * [taylor]: Taking taylor expansion of k in k 19.456 * [backup-simplify]: Simplify 0 into 0 19.456 * [backup-simplify]: Simplify 1 into 1 19.456 * [taylor]: Taking taylor expansion of (log PI) in k 19.456 * [taylor]: Taking taylor expansion of PI in k 19.456 * [backup-simplify]: Simplify PI into PI 19.456 * [backup-simplify]: Simplify (log PI) into (log PI) 19.456 * [backup-simplify]: Simplify (* 1/2 0) into 0 19.457 * [backup-simplify]: Simplify (- 0) into 0 19.457 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 19.457 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 19.459 * [backup-simplify]: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 19.459 * [backup-simplify]: Simplify (pow PI 1/2) into (pow PI 1/2) 19.460 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 19.461 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 19.461 * [backup-simplify]: Simplify (- 1/2) into -1/2 19.461 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 19.463 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log PI))) into (- (* 1/2 (log PI))) 19.470 * [backup-simplify]: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 1) 1)))) into (* -1/2 (* (log PI) (sqrt PI))) 19.474 * [backup-simplify]: Simplify (* -1/2 (* (log PI) (sqrt PI))) into (* -1/2 (* (log PI) (sqrt PI))) 19.478 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 19.479 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 19.480 * [backup-simplify]: Simplify (- 0) into 0 19.480 * [backup-simplify]: Simplify (+ 0 0) into 0 19.482 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log PI)))) into 0 19.494 * [backup-simplify]: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI))) 19.498 * [backup-simplify]: Simplify (* 1/8 (* (pow (log PI) 2) (sqrt PI))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI))) 19.505 * [backup-simplify]: Simplify (+ (* (* 1/8 (* (pow (log PI) 2) (sqrt PI))) (pow k 2)) (+ (* (* -1/2 (* (log PI) (sqrt PI))) k) (pow PI 1/2))) into (- (+ (pow PI 1/2) (* 1/8 (* (* (pow (log PI) 2) (pow k 2)) (sqrt PI)))) (* 1/2 (* (* (log PI) k) (sqrt PI)))) 19.505 * [backup-simplify]: Simplify (pow PI (- 1/2 (/ (/ 1 k) 2))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 19.505 * [approximate]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in (k) around 0 19.505 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 19.505 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 19.505 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 19.505 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 19.505 * [taylor]: Taking taylor expansion of 1/2 in k 19.505 * [backup-simplify]: Simplify 1/2 into 1/2 19.506 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 19.506 * [taylor]: Taking taylor expansion of 1/2 in k 19.506 * [backup-simplify]: Simplify 1/2 into 1/2 19.506 * [taylor]: Taking taylor expansion of (/ 1 k) in k 19.506 * [taylor]: Taking taylor expansion of k in k 19.506 * [backup-simplify]: Simplify 0 into 0 19.506 * [backup-simplify]: Simplify 1 into 1 19.506 * [backup-simplify]: Simplify (/ 1 1) into 1 19.506 * [taylor]: Taking taylor expansion of (log PI) in k 19.506 * [taylor]: Taking taylor expansion of PI in k 19.506 * [backup-simplify]: Simplify PI into PI 19.507 * [backup-simplify]: Simplify (log PI) into (log PI) 19.507 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 19.507 * [backup-simplify]: Simplify (- 1/2) into -1/2 19.508 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 19.509 * [backup-simplify]: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 19.509 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 19.509 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 19.509 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 19.509 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 19.509 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 19.509 * [taylor]: Taking taylor expansion of 1/2 in k 19.510 * [backup-simplify]: Simplify 1/2 into 1/2 19.510 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 19.510 * [taylor]: Taking taylor expansion of 1/2 in k 19.510 * [backup-simplify]: Simplify 1/2 into 1/2 19.510 * [taylor]: Taking taylor expansion of (/ 1 k) in k 19.510 * [taylor]: Taking taylor expansion of k in k 19.510 * [backup-simplify]: Simplify 0 into 0 19.510 * [backup-simplify]: Simplify 1 into 1 19.510 * [backup-simplify]: Simplify (/ 1 1) into 1 19.510 * [taylor]: Taking taylor expansion of (log PI) in k 19.510 * [taylor]: Taking taylor expansion of PI in k 19.510 * [backup-simplify]: Simplify PI into PI 19.511 * [backup-simplify]: Simplify (log PI) into (log PI) 19.511 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 19.511 * [backup-simplify]: Simplify (- 1/2) into -1/2 19.512 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 19.513 * [backup-simplify]: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 19.513 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 19.514 * [backup-simplify]: Simplify (pow PI (- 1/2 (* 1/2 (/ 1 k)))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 19.514 * [backup-simplify]: Simplify 0 into 0 19.514 * [backup-simplify]: Simplify 0 into 0 19.514 * [backup-simplify]: Simplify 0 into 0 19.514 * [backup-simplify]: Simplify 0 into 0 19.514 * [backup-simplify]: Simplify 0 into 0 19.514 * [backup-simplify]: Simplify 0 into 0 19.514 * [backup-simplify]: Simplify (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k))))) into (pow PI (- 1/2 (* 1/2 k))) 19.514 * [backup-simplify]: Simplify (pow PI (- 1/2 (/ (/ 1 (- k)) 2))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 19.514 * [approximate]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in (k) around 0 19.514 * [taylor]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 19.514 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 19.514 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 19.514 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 19.514 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 19.514 * [taylor]: Taking taylor expansion of 1/2 in k 19.514 * [backup-simplify]: Simplify 1/2 into 1/2 19.514 * [taylor]: Taking taylor expansion of (/ 1 k) in k 19.514 * [taylor]: Taking taylor expansion of k in k 19.514 * [backup-simplify]: Simplify 0 into 0 19.515 * [backup-simplify]: Simplify 1 into 1 19.515 * [backup-simplify]: Simplify (/ 1 1) into 1 19.515 * [taylor]: Taking taylor expansion of 1/2 in k 19.515 * [backup-simplify]: Simplify 1/2 into 1/2 19.515 * [taylor]: Taking taylor expansion of (log PI) in k 19.515 * [taylor]: Taking taylor expansion of PI in k 19.515 * [backup-simplify]: Simplify PI into PI 19.515 * [backup-simplify]: Simplify (log PI) into (log PI) 19.516 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 19.516 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 19.517 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 19.518 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 19.518 * [taylor]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 19.518 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 19.518 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 19.518 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 19.518 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 19.518 * [taylor]: Taking taylor expansion of 1/2 in k 19.518 * [backup-simplify]: Simplify 1/2 into 1/2 19.518 * [taylor]: Taking taylor expansion of (/ 1 k) in k 19.518 * [taylor]: Taking taylor expansion of k in k 19.518 * [backup-simplify]: Simplify 0 into 0 19.518 * [backup-simplify]: Simplify 1 into 1 19.519 * [backup-simplify]: Simplify (/ 1 1) into 1 19.519 * [taylor]: Taking taylor expansion of 1/2 in k 19.519 * [backup-simplify]: Simplify 1/2 into 1/2 19.519 * [taylor]: Taking taylor expansion of (log PI) in k 19.519 * [taylor]: Taking taylor expansion of PI in k 19.519 * [backup-simplify]: Simplify PI into PI 19.519 * [backup-simplify]: Simplify (log PI) into (log PI) 19.520 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 19.520 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 19.521 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 19.522 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 19.522 * [backup-simplify]: Simplify (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 19.522 * [backup-simplify]: Simplify 0 into 0 19.522 * [backup-simplify]: Simplify 0 into 0 19.522 * [backup-simplify]: Simplify 0 into 0 19.522 * [backup-simplify]: Simplify 0 into 0 19.522 * [backup-simplify]: Simplify 0 into 0 19.522 * [backup-simplify]: Simplify 0 into 0 19.522 * [backup-simplify]: Simplify (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)) into (pow PI (- 1/2 (* 1/2 k))) 19.522 * * * * [progress]: [ 3 / 4 ] generating series at (2) 19.523 * [backup-simplify]: Simplify (/ (pow (* n 2) (- 1/2 (/ k 2))) (/ (sqrt k) (pow PI (- 1/2 (/ k 2))))) into (* (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) 19.523 * [approximate]: Taking taylor expansion of (* (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in (n k) around 0 19.523 * [taylor]: Taking taylor expansion of (* (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in k 19.523 * [taylor]: Taking taylor expansion of (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) in k 19.523 * [taylor]: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in k 19.523 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in k 19.523 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in k 19.523 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 19.523 * [taylor]: Taking taylor expansion of 1/2 in k 19.523 * [backup-simplify]: Simplify 1/2 into 1/2 19.523 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 19.523 * [taylor]: Taking taylor expansion of 1/2 in k 19.523 * [backup-simplify]: Simplify 1/2 into 1/2 19.523 * [taylor]: Taking taylor expansion of k in k 19.523 * [backup-simplify]: Simplify 0 into 0 19.523 * [backup-simplify]: Simplify 1 into 1 19.523 * [taylor]: Taking taylor expansion of (log (* 2 n)) in k 19.523 * [taylor]: Taking taylor expansion of (* 2 n) in k 19.523 * [taylor]: Taking taylor expansion of 2 in k 19.523 * [backup-simplify]: Simplify 2 into 2 19.523 * [taylor]: Taking taylor expansion of n in k 19.523 * [backup-simplify]: Simplify n into n 19.523 * [backup-simplify]: Simplify (* 2 n) into (* 2 n) 19.524 * [backup-simplify]: Simplify (log (* 2 n)) into (log (* 2 n)) 19.524 * [backup-simplify]: Simplify (* 1/2 0) into 0 19.524 * [backup-simplify]: Simplify (- 0) into 0 19.525 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 19.525 * [backup-simplify]: Simplify (* 1/2 (log (* 2 n))) into (* 1/2 (log (* 2 n))) 19.525 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 n)))) into (pow (* 2 n) 1/2) 19.525 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 19.525 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 19.525 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 19.525 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 19.525 * [taylor]: Taking taylor expansion of 1/2 in k 19.525 * [backup-simplify]: Simplify 1/2 into 1/2 19.525 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 19.525 * [taylor]: Taking taylor expansion of 1/2 in k 19.525 * [backup-simplify]: Simplify 1/2 into 1/2 19.525 * [taylor]: Taking taylor expansion of k in k 19.525 * [backup-simplify]: Simplify 0 into 0 19.525 * [backup-simplify]: Simplify 1 into 1 19.525 * [taylor]: Taking taylor expansion of (log PI) in k 19.526 * [taylor]: Taking taylor expansion of PI in k 19.526 * [backup-simplify]: Simplify PI into PI 19.526 * [backup-simplify]: Simplify (log PI) into (log PI) 19.526 * [backup-simplify]: Simplify (* 1/2 0) into 0 19.527 * [backup-simplify]: Simplify (- 0) into 0 19.527 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 19.528 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 19.530 * [backup-simplify]: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 19.530 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 19.530 * [taylor]: Taking taylor expansion of (/ 1 k) in k 19.530 * [taylor]: Taking taylor expansion of k in k 19.530 * [backup-simplify]: Simplify 0 into 0 19.530 * [backup-simplify]: Simplify 1 into 1 19.531 * [backup-simplify]: Simplify (/ 1 1) into 1 19.531 * [backup-simplify]: Simplify (sqrt 0) into 0 19.532 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 19.532 * [taylor]: Taking taylor expansion of (* (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in n 19.532 * [taylor]: Taking taylor expansion of (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) in n 19.532 * [taylor]: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in n 19.532 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in n 19.533 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in n 19.533 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 19.533 * [taylor]: Taking taylor expansion of 1/2 in n 19.533 * [backup-simplify]: Simplify 1/2 into 1/2 19.533 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 19.533 * [taylor]: Taking taylor expansion of 1/2 in n 19.533 * [backup-simplify]: Simplify 1/2 into 1/2 19.533 * [taylor]: Taking taylor expansion of k in n 19.533 * [backup-simplify]: Simplify k into k 19.533 * [taylor]: Taking taylor expansion of (log (* 2 n)) in n 19.533 * [taylor]: Taking taylor expansion of (* 2 n) in n 19.533 * [taylor]: Taking taylor expansion of 2 in n 19.533 * [backup-simplify]: Simplify 2 into 2 19.533 * [taylor]: Taking taylor expansion of n in n 19.533 * [backup-simplify]: Simplify 0 into 0 19.533 * [backup-simplify]: Simplify 1 into 1 19.533 * [backup-simplify]: Simplify (* 2 0) into 0 19.534 * [backup-simplify]: Simplify (+ (* 2 1) (* 0 0)) into 2 19.534 * [backup-simplify]: Simplify (log 2) into (log 2) 19.534 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 19.535 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 19.535 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 19.535 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 19.536 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log 2) (log n))) into (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) 19.537 * [backup-simplify]: Simplify (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) into (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) 19.537 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in n 19.537 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in n 19.537 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in n 19.537 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 19.537 * [taylor]: Taking taylor expansion of 1/2 in n 19.537 * [backup-simplify]: Simplify 1/2 into 1/2 19.537 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 19.537 * [taylor]: Taking taylor expansion of 1/2 in n 19.537 * [backup-simplify]: Simplify 1/2 into 1/2 19.537 * [taylor]: Taking taylor expansion of k in n 19.537 * [backup-simplify]: Simplify k into k 19.537 * [taylor]: Taking taylor expansion of (log PI) in n 19.537 * [taylor]: Taking taylor expansion of PI in n 19.537 * [backup-simplify]: Simplify PI into PI 19.537 * [backup-simplify]: Simplify (log PI) into (log PI) 19.537 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 19.537 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 19.538 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 19.538 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (log PI)) into (* (- 1/2 (* 1/2 k)) (log PI)) 19.539 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (log PI))) into (pow PI (- 1/2 (* 1/2 k))) 19.539 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 19.539 * [taylor]: Taking taylor expansion of (/ 1 k) in n 19.539 * [taylor]: Taking taylor expansion of k in n 19.539 * [backup-simplify]: Simplify k into k 19.539 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 19.539 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 19.539 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 19.539 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 19.539 * [taylor]: Taking taylor expansion of (* (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in n 19.539 * [taylor]: Taking taylor expansion of (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) in n 19.539 * [taylor]: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in n 19.539 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in n 19.539 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in n 19.540 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 19.540 * [taylor]: Taking taylor expansion of 1/2 in n 19.540 * [backup-simplify]: Simplify 1/2 into 1/2 19.540 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 19.540 * [taylor]: Taking taylor expansion of 1/2 in n 19.540 * [backup-simplify]: Simplify 1/2 into 1/2 19.540 * [taylor]: Taking taylor expansion of k in n 19.540 * [backup-simplify]: Simplify k into k 19.540 * [taylor]: Taking taylor expansion of (log (* 2 n)) in n 19.540 * [taylor]: Taking taylor expansion of (* 2 n) in n 19.540 * [taylor]: Taking taylor expansion of 2 in n 19.540 * [backup-simplify]: Simplify 2 into 2 19.540 * [taylor]: Taking taylor expansion of n in n 19.540 * [backup-simplify]: Simplify 0 into 0 19.540 * [backup-simplify]: Simplify 1 into 1 19.540 * [backup-simplify]: Simplify (* 2 0) into 0 19.541 * [backup-simplify]: Simplify (+ (* 2 1) (* 0 0)) into 2 19.542 * [backup-simplify]: Simplify (log 2) into (log 2) 19.542 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 19.542 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 19.542 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 19.543 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 19.543 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log 2) (log n))) into (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) 19.544 * [backup-simplify]: Simplify (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) into (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) 19.544 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in n 19.544 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in n 19.544 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in n 19.544 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 19.544 * [taylor]: Taking taylor expansion of 1/2 in n 19.544 * [backup-simplify]: Simplify 1/2 into 1/2 19.544 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 19.544 * [taylor]: Taking taylor expansion of 1/2 in n 19.544 * [backup-simplify]: Simplify 1/2 into 1/2 19.544 * [taylor]: Taking taylor expansion of k in n 19.544 * [backup-simplify]: Simplify k into k 19.544 * [taylor]: Taking taylor expansion of (log PI) in n 19.544 * [taylor]: Taking taylor expansion of PI in n 19.544 * [backup-simplify]: Simplify PI into PI 19.545 * [backup-simplify]: Simplify (log PI) into (log PI) 19.545 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 19.545 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 19.545 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 19.545 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (log PI)) into (* (- 1/2 (* 1/2 k)) (log PI)) 19.546 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (log PI))) into (pow PI (- 1/2 (* 1/2 k))) 19.546 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 19.546 * [taylor]: Taking taylor expansion of (/ 1 k) in n 19.546 * [taylor]: Taking taylor expansion of k in n 19.546 * [backup-simplify]: Simplify k into k 19.546 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 19.546 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 19.546 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 19.546 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 19.547 * [backup-simplify]: Simplify (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))) into (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))) 19.548 * [backup-simplify]: Simplify (* (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) into (* (sqrt (/ 1 k)) (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))) 19.548 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))) in k 19.548 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 19.548 * [taylor]: Taking taylor expansion of (/ 1 k) in k 19.548 * [taylor]: Taking taylor expansion of k in k 19.548 * [backup-simplify]: Simplify 0 into 0 19.548 * [backup-simplify]: Simplify 1 into 1 19.549 * [backup-simplify]: Simplify (/ 1 1) into 1 19.549 * [backup-simplify]: Simplify (sqrt 0) into 0 19.550 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 19.551 * [taylor]: Taking taylor expansion of (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))) in k 19.551 * [taylor]: Taking taylor expansion of (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) in k 19.551 * [taylor]: Taking taylor expansion of (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) in k 19.551 * [taylor]: Taking taylor expansion of (+ (log 2) (log n)) in k 19.551 * [taylor]: Taking taylor expansion of (log 2) in k 19.551 * [taylor]: Taking taylor expansion of 2 in k 19.551 * [backup-simplify]: Simplify 2 into 2 19.551 * [backup-simplify]: Simplify (log 2) into (log 2) 19.551 * [taylor]: Taking taylor expansion of (log n) in k 19.551 * [taylor]: Taking taylor expansion of n in k 19.551 * [backup-simplify]: Simplify n into n 19.551 * [backup-simplify]: Simplify (log n) into (log n) 19.551 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 19.551 * [taylor]: Taking taylor expansion of 1/2 in k 19.551 * [backup-simplify]: Simplify 1/2 into 1/2 19.551 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 19.551 * [taylor]: Taking taylor expansion of 1/2 in k 19.551 * [backup-simplify]: Simplify 1/2 into 1/2 19.551 * [taylor]: Taking taylor expansion of k in k 19.551 * [backup-simplify]: Simplify 0 into 0 19.551 * [backup-simplify]: Simplify 1 into 1 19.552 * [backup-simplify]: Simplify (+ (log 2) (log n)) into (+ (log 2) (log n)) 19.552 * [backup-simplify]: Simplify (* 1/2 0) into 0 19.553 * [backup-simplify]: Simplify (- 0) into 0 19.553 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 19.554 * [backup-simplify]: Simplify (* (+ (log 2) (log n)) 1/2) into (* 1/2 (+ (log 2) (log n))) 19.554 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log 2) (log n)))) into (exp (* 1/2 (+ (log 2) (log n)))) 19.554 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 19.554 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 19.554 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 19.554 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 19.554 * [taylor]: Taking taylor expansion of 1/2 in k 19.554 * [backup-simplify]: Simplify 1/2 into 1/2 19.554 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 19.554 * [taylor]: Taking taylor expansion of 1/2 in k 19.554 * [backup-simplify]: Simplify 1/2 into 1/2 19.554 * [taylor]: Taking taylor expansion of k in k 19.554 * [backup-simplify]: Simplify 0 into 0 19.554 * [backup-simplify]: Simplify 1 into 1 19.554 * [taylor]: Taking taylor expansion of (log PI) in k 19.554 * [taylor]: Taking taylor expansion of PI in k 19.554 * [backup-simplify]: Simplify PI into PI 19.555 * [backup-simplify]: Simplify (log PI) into (log PI) 19.555 * [backup-simplify]: Simplify (* 1/2 0) into 0 19.556 * [backup-simplify]: Simplify (- 0) into 0 19.556 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 19.561 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 19.563 * [backup-simplify]: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 19.564 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (pow PI 1/2)) into (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI)) 19.565 * [backup-simplify]: Simplify (* 0 (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI))) into 0 19.565 * [backup-simplify]: Simplify 0 into 0 19.567 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 19.567 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 19.568 * [backup-simplify]: Simplify (- 0) into 0 19.568 * [backup-simplify]: Simplify (+ 0 0) into 0 19.569 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (log PI))) into 0 19.570 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 19.571 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 1) (* 0 0))) into 0 19.572 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 19.573 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 19.573 * [backup-simplify]: Simplify (- 0) into 0 19.574 * [backup-simplify]: Simplify (+ 0 0) into 0 19.575 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 19.575 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log 2) (log n)))) into 0 19.577 * [backup-simplify]: Simplify (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (+ (* (/ (pow 0 1) 1)))) into 0 19.577 * [backup-simplify]: Simplify (+ (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) 0) (* 0 (pow PI (- 1/2 (* 1/2 k))))) into 0 19.578 * [backup-simplify]: Simplify (+ (* (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))) 0) (* 0 (sqrt (/ 1 k)))) into 0 19.578 * [taylor]: Taking taylor expansion of 0 in k 19.578 * [backup-simplify]: Simplify 0 into 0 19.580 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 19.581 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 19.581 * [backup-simplify]: Simplify (- 1/2) into -1/2 19.581 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 19.584 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log PI))) into (- (* 1/2 (log PI))) 19.594 * [backup-simplify]: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 1) 1)))) into (* -1/2 (* (log PI) (sqrt PI))) 19.595 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 19.596 * [backup-simplify]: Simplify (- 1/2) into -1/2 19.596 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 19.598 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 19.599 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 19.599 * [backup-simplify]: Simplify (+ 0 0) into 0 19.600 * [backup-simplify]: Simplify (+ (* (+ (log 2) (log n)) -1/2) (* 0 1/2)) into (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 19.602 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) 19.606 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log 2) (log n)))) (* -1/2 (* (log PI) (sqrt PI)))) (* (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) (pow PI 1/2))) into (- (+ (* 1/2 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI)) (sqrt PI))) (+ (* 1/2 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log n)) (sqrt PI))) (* 1/2 (* (* (log 2) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI)))))) 19.611 * [backup-simplify]: Simplify (+ (* 0 (- (+ (* 1/2 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI)) (sqrt PI))) (+ (* 1/2 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log n)) (sqrt PI))) (* 1/2 (* (* (log 2) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI))))))) (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI)))) into (- (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI)))) 19.612 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI)))) into (- (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI)))) 19.612 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 19.613 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 19.616 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 19.617 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 19.618 * [backup-simplify]: Simplify (- 0) into 0 19.618 * [backup-simplify]: Simplify (+ 0 0) into 0 19.619 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (log PI)))) into 0 19.621 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (log PI))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 19.622 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 19.625 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 19.626 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 19.627 * [backup-simplify]: Simplify (- 0) into 0 19.627 * [backup-simplify]: Simplify (+ 0 0) into 0 19.628 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 19.629 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log 2) (log n))))) into 0 19.631 * [backup-simplify]: Simplify (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 19.632 * [backup-simplify]: Simplify (+ (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) 0) (+ (* 0 0) (* 0 (pow PI (- 1/2 (* 1/2 k)))))) into 0 19.633 * [backup-simplify]: Simplify (+ (* (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))) 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k))))) into 0 19.633 * [taylor]: Taking taylor expansion of 0 in k 19.633 * [backup-simplify]: Simplify 0 into 0 19.633 * [backup-simplify]: Simplify 0 into 0 19.636 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 19.638 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 19.638 * [backup-simplify]: Simplify (- 0) into 0 19.638 * [backup-simplify]: Simplify (+ 0 0) into 0 19.639 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log PI)))) into 0 19.647 * [backup-simplify]: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI))) 19.648 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 19.648 * [backup-simplify]: Simplify (- 0) into 0 19.648 * [backup-simplify]: Simplify (+ 0 0) into 0 19.650 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 19.651 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 19.651 * [backup-simplify]: Simplify (+ 0 0) into 0 19.652 * [backup-simplify]: Simplify (+ (* (+ (log 2) (log n)) 0) (+ (* 0 -1/2) (* 0 1/2))) into 0 19.654 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))) 19.661 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log 2) (log n)))) (* 1/8 (* (pow (log PI) 2) (sqrt PI)))) (+ (* (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) (* -1/2 (* (log PI) (sqrt PI)))) (* (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))) (pow PI 1/2)))) into (+ (* 1/4 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (sqrt PI))) (+ (* 1/4 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log PI) (log n))) (sqrt PI))) (+ (* 1/4 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI))) (sqrt PI))) (+ (* 1/8 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2)) (sqrt PI))) (+ (* 1/8 (* (* (pow (log 2) 2) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI))) (* 1/8 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log PI) 2)) (sqrt PI)))))))) 19.661 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 19.663 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 19.678 * [backup-simplify]: Simplify (+ (* 0 (+ (* 1/4 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (sqrt PI))) (+ (* 1/4 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log PI) (log n))) (sqrt PI))) (+ (* 1/4 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI))) (sqrt PI))) (+ (* 1/8 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2)) (sqrt PI))) (+ (* 1/8 (* (* (pow (log 2) 2) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI))) (* 1/8 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log PI) 2)) (sqrt PI))))))))) (+ (* +nan.0 (- (+ (* 1/2 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI)) (sqrt PI))) (+ (* 1/2 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log n)) (sqrt PI))) (* 1/2 (* (* (log 2) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI))))))) (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI))))) into (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI)) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log n)) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI))) (- (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI)))))))))) 19.684 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI)) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log n)) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI))) (- (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI)))))))))) into (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI)) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log n)) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI))) (- (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI)))))))))) 19.685 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 19.689 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 19.695 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0 19.696 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 19.696 * [backup-simplify]: Simplify (- 0) into 0 19.697 * [backup-simplify]: Simplify (+ 0 0) into 0 19.698 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log PI))))) into 0 19.700 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (log PI))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 19.702 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))) into 0 19.708 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 19.709 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 19.710 * [backup-simplify]: Simplify (- 0) into 0 19.710 * [backup-simplify]: Simplify (+ 0 0) into 0 19.711 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 19.713 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log 2) (log n)))))) into 0 19.715 * [backup-simplify]: Simplify (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 19.717 * [backup-simplify]: Simplify (+ (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow PI (- 1/2 (* 1/2 k))))))) into 0 19.718 * [backup-simplify]: Simplify (+ (* (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k)))))) into 0 19.718 * [taylor]: Taking taylor expansion of 0 in k 19.718 * [backup-simplify]: Simplify 0 into 0 19.718 * [backup-simplify]: Simplify 0 into 0 19.718 * [backup-simplify]: Simplify 0 into 0 19.724 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0 19.725 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 19.726 * [backup-simplify]: Simplify (- 0) into 0 19.726 * [backup-simplify]: Simplify (+ 0 0) into 0 19.728 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log PI))))) into 0 19.741 * [backup-simplify]: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 3) 6)) (* (/ (pow (- (* 1/2 (log PI))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (pow (log PI) 3) (sqrt PI))) 19.742 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 19.742 * [backup-simplify]: Simplify (- 0) into 0 19.743 * [backup-simplify]: Simplify (+ 0 0) into 0 19.746 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 19.748 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0 19.748 * [backup-simplify]: Simplify (+ 0 0) into 0 19.749 * [backup-simplify]: Simplify (+ (* (+ (log 2) (log n)) 0) (+ (* 0 0) (+ (* 0 -1/2) (* 0 1/2)))) into 0 19.751 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 3) 6)) (* (/ (pow (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (log 2) (pow (log n) 2))) (+ (* 1/16 (* (pow (log 2) 2) (log n))) (* 1/48 (pow (log 2) 3))))) (exp (* 1/2 (+ (log 2) (log n)))))) 19.769 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log 2) (log n)))) (* -1/48 (* (pow (log PI) 3) (sqrt PI)))) (+ (* (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) (* 1/8 (* (pow (log PI) 2) (sqrt PI)))) (+ (* (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))) (* -1/2 (* (log PI) (sqrt PI)))) (* (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (log 2) (pow (log n) 2))) (+ (* 1/16 (* (pow (log 2) 2) (log n))) (* 1/48 (pow (log 2) 3))))) (exp (* 1/2 (+ (log 2) (log n)))))) (pow PI 1/2))))) into (- (+ (* 1/16 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log PI) 2))) (sqrt PI))) (+ (* 1/16 (* (* (pow (log 2) 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI))) (sqrt PI))) (+ (* 1/16 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log PI) (pow (log n) 2))) (sqrt PI))) (+ (* 1/16 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2))) (sqrt PI))) (+ (* 1/48 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 3)) (sqrt PI))) (+ (* 1/16 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (pow (log PI) 2) (log n))) (sqrt PI))) (+ (* 1/16 (* (* (pow (log 2) 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (sqrt PI))) (+ (* 1/48 (* (* (pow (log 2) 3) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI))) (+ (* 1/48 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log PI) 3)) (sqrt PI))) (* 1/8 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log PI) (log n)))) (sqrt PI))))))))))))) 19.770 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 19.775 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 19.818 * [backup-simplify]: Simplify (+ (* 0 (- (+ (* 1/16 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log PI) 2))) (sqrt PI))) (+ (* 1/16 (* (* (pow (log 2) 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI))) (sqrt PI))) (+ (* 1/16 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log PI) (pow (log n) 2))) (sqrt PI))) (+ (* 1/16 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2))) (sqrt PI))) (+ (* 1/48 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 3)) (sqrt PI))) (+ (* 1/16 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (pow (log PI) 2) (log n))) (sqrt PI))) (+ (* 1/16 (* (* (pow (log 2) 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (sqrt PI))) (+ (* 1/48 (* (* (pow (log 2) 3) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI))) (+ (* 1/48 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log PI) 3)) (sqrt PI))) (* 1/8 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log PI) (log n)))) (sqrt PI)))))))))))))) (+ (* +nan.0 (+ (* 1/4 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (sqrt PI))) (+ (* 1/4 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log PI) (log n))) (sqrt PI))) (+ (* 1/4 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI))) (sqrt PI))) (+ (* 1/8 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2)) (sqrt PI))) (+ (* 1/8 (* (* (pow (log 2) 2) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI))) (* 1/8 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log PI) 2)) (sqrt PI))))))))) (+ (* +nan.0 (- (+ (* 1/2 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI)) (sqrt PI))) (+ (* 1/2 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log n)) (sqrt PI))) (* 1/2 (* (* (log 2) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI))))))) (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI)))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log PI) (log n))) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI)) (sqrt PI))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log PI) 2)) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log n)) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI))) (sqrt PI))) (- (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2)) (sqrt PI)))))))))))))))))))))) 19.843 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log PI) (log n))) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI)) (sqrt PI))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log PI) 2)) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log n)) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI))) (sqrt PI))) (- (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2)) (sqrt PI)))))))))))))))))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log PI) (log n))) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI)) (sqrt PI))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log PI) 2)) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log n)) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI))) (sqrt PI))) (- (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2)) (sqrt PI)))))))))))))))))))))) 19.873 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log PI) (log n))) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI)) (sqrt PI))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log PI) 2)) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log n)) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI))) (sqrt PI))) (- (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2)) (sqrt PI)))))))))))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI)) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log n)) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI))) (- (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI)))))))))) (* k 1)) (- (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI)))))) into (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (pow (log n) 2) (pow k 2))) (sqrt PI))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (pow k 2))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) k) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log PI) (pow k 2)))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log PI) k)) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log PI) (pow k 2))) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (pow k 2))) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) k)) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log PI) (* (log n) (pow k 2)))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow k 2)) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (pow (log PI) 2) (pow k 2))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) (pow k 2))) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) (pow k 2)))) (sqrt PI))) (- (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) k)) (sqrt PI)))))))))))))))))))))))))))))))) 19.874 * [backup-simplify]: Simplify (/ (pow (* (/ 1 n) 2) (- 1/2 (/ (/ 1 k) 2))) (/ (sqrt (/ 1 k)) (pow PI (- 1/2 (/ (/ 1 k) 2))))) into (* (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) 19.874 * [approximate]: Taking taylor expansion of (* (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in (n k) around 0 19.874 * [taylor]: Taking taylor expansion of (* (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in k 19.874 * [taylor]: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) in k 19.874 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 19.874 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 19.874 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 19.874 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 19.874 * [taylor]: Taking taylor expansion of 1/2 in k 19.874 * [backup-simplify]: Simplify 1/2 into 1/2 19.874 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 19.874 * [taylor]: Taking taylor expansion of 1/2 in k 19.874 * [backup-simplify]: Simplify 1/2 into 1/2 19.874 * [taylor]: Taking taylor expansion of (/ 1 k) in k 19.874 * [taylor]: Taking taylor expansion of k in k 19.874 * [backup-simplify]: Simplify 0 into 0 19.874 * [backup-simplify]: Simplify 1 into 1 19.875 * [backup-simplify]: Simplify (/ 1 1) into 1 19.875 * [taylor]: Taking taylor expansion of (log PI) in k 19.875 * [taylor]: Taking taylor expansion of PI in k 19.875 * [backup-simplify]: Simplify PI into PI 19.875 * [backup-simplify]: Simplify (log PI) into (log PI) 19.876 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 19.876 * [backup-simplify]: Simplify (- 1/2) into -1/2 19.877 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 19.877 * [backup-simplify]: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 19.878 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 19.878 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in k 19.878 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in k 19.878 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in k 19.878 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 19.878 * [taylor]: Taking taylor expansion of 1/2 in k 19.878 * [backup-simplify]: Simplify 1/2 into 1/2 19.878 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 19.878 * [taylor]: Taking taylor expansion of 1/2 in k 19.878 * [backup-simplify]: Simplify 1/2 into 1/2 19.878 * [taylor]: Taking taylor expansion of (/ 1 k) in k 19.878 * [taylor]: Taking taylor expansion of k in k 19.878 * [backup-simplify]: Simplify 0 into 0 19.878 * [backup-simplify]: Simplify 1 into 1 19.879 * [backup-simplify]: Simplify (/ 1 1) into 1 19.879 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in k 19.879 * [taylor]: Taking taylor expansion of (/ 2 n) in k 19.879 * [taylor]: Taking taylor expansion of 2 in k 19.879 * [backup-simplify]: Simplify 2 into 2 19.879 * [taylor]: Taking taylor expansion of n in k 19.879 * [backup-simplify]: Simplify n into n 19.879 * [backup-simplify]: Simplify (/ 2 n) into (/ 2 n) 19.879 * [backup-simplify]: Simplify (log (/ 2 n)) into (log (/ 2 n)) 19.879 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 19.880 * [backup-simplify]: Simplify (- 1/2) into -1/2 19.880 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 19.880 * [backup-simplify]: Simplify (* -1/2 (log (/ 2 n))) into (* -1/2 (log (/ 2 n))) 19.880 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) into (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) 19.880 * [taylor]: Taking taylor expansion of (sqrt k) in k 19.880 * [taylor]: Taking taylor expansion of k in k 19.880 * [backup-simplify]: Simplify 0 into 0 19.880 * [backup-simplify]: Simplify 1 into 1 19.881 * [backup-simplify]: Simplify (sqrt 0) into 0 19.882 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 19.882 * [taylor]: Taking taylor expansion of (* (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in n 19.882 * [taylor]: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) in n 19.882 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in n 19.882 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in n 19.882 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in n 19.882 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 19.882 * [taylor]: Taking taylor expansion of 1/2 in n 19.882 * [backup-simplify]: Simplify 1/2 into 1/2 19.882 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 19.883 * [taylor]: Taking taylor expansion of 1/2 in n 19.883 * [backup-simplify]: Simplify 1/2 into 1/2 19.883 * [taylor]: Taking taylor expansion of (/ 1 k) in n 19.883 * [taylor]: Taking taylor expansion of k in n 19.883 * [backup-simplify]: Simplify k into k 19.883 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 19.883 * [taylor]: Taking taylor expansion of (log PI) in n 19.883 * [taylor]: Taking taylor expansion of PI in n 19.883 * [backup-simplify]: Simplify PI into PI 19.883 * [backup-simplify]: Simplify (log PI) into (log PI) 19.884 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 19.884 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 19.884 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 19.884 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) into (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) 19.885 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 19.885 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 19.885 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 19.885 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 19.885 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 19.885 * [taylor]: Taking taylor expansion of 1/2 in n 19.885 * [backup-simplify]: Simplify 1/2 into 1/2 19.885 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 19.885 * [taylor]: Taking taylor expansion of 1/2 in n 19.885 * [backup-simplify]: Simplify 1/2 into 1/2 19.885 * [taylor]: Taking taylor expansion of (/ 1 k) in n 19.885 * [taylor]: Taking taylor expansion of k in n 19.885 * [backup-simplify]: Simplify k into k 19.885 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 19.885 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in n 19.885 * [taylor]: Taking taylor expansion of (/ 2 n) in n 19.885 * [taylor]: Taking taylor expansion of 2 in n 19.885 * [backup-simplify]: Simplify 2 into 2 19.885 * [taylor]: Taking taylor expansion of n in n 19.885 * [backup-simplify]: Simplify 0 into 0 19.885 * [backup-simplify]: Simplify 1 into 1 19.886 * [backup-simplify]: Simplify (/ 2 1) into 2 19.886 * [backup-simplify]: Simplify (log 2) into (log 2) 19.886 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 19.886 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 19.886 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 19.887 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 19.887 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 19.888 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 19.888 * [taylor]: Taking taylor expansion of (sqrt k) in n 19.888 * [taylor]: Taking taylor expansion of k in n 19.888 * [backup-simplify]: Simplify k into k 19.888 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 19.888 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 19.888 * [taylor]: Taking taylor expansion of (* (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in n 19.888 * [taylor]: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) in n 19.888 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in n 19.888 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in n 19.888 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in n 19.888 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 19.888 * [taylor]: Taking taylor expansion of 1/2 in n 19.888 * [backup-simplify]: Simplify 1/2 into 1/2 19.888 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 19.888 * [taylor]: Taking taylor expansion of 1/2 in n 19.888 * [backup-simplify]: Simplify 1/2 into 1/2 19.889 * [taylor]: Taking taylor expansion of (/ 1 k) in n 19.889 * [taylor]: Taking taylor expansion of k in n 19.889 * [backup-simplify]: Simplify k into k 19.889 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 19.889 * [taylor]: Taking taylor expansion of (log PI) in n 19.889 * [taylor]: Taking taylor expansion of PI in n 19.889 * [backup-simplify]: Simplify PI into PI 19.889 * [backup-simplify]: Simplify (log PI) into (log PI) 19.889 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 19.889 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 19.889 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 19.890 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) into (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) 19.890 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 19.890 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 19.890 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 19.890 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 19.890 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 19.890 * [taylor]: Taking taylor expansion of 1/2 in n 19.890 * [backup-simplify]: Simplify 1/2 into 1/2 19.890 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 19.891 * [taylor]: Taking taylor expansion of 1/2 in n 19.891 * [backup-simplify]: Simplify 1/2 into 1/2 19.891 * [taylor]: Taking taylor expansion of (/ 1 k) in n 19.891 * [taylor]: Taking taylor expansion of k in n 19.891 * [backup-simplify]: Simplify k into k 19.891 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 19.891 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in n 19.891 * [taylor]: Taking taylor expansion of (/ 2 n) in n 19.891 * [taylor]: Taking taylor expansion of 2 in n 19.891 * [backup-simplify]: Simplify 2 into 2 19.891 * [taylor]: Taking taylor expansion of n in n 19.891 * [backup-simplify]: Simplify 0 into 0 19.891 * [backup-simplify]: Simplify 1 into 1 19.891 * [backup-simplify]: Simplify (/ 2 1) into 2 19.892 * [backup-simplify]: Simplify (log 2) into (log 2) 19.892 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 19.892 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 19.892 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 19.893 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 19.893 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 19.893 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 19.894 * [taylor]: Taking taylor expansion of (sqrt k) in n 19.894 * [taylor]: Taking taylor expansion of k in n 19.894 * [backup-simplify]: Simplify k into k 19.894 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 19.894 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 19.894 * [backup-simplify]: Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) into (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) 19.895 * [backup-simplify]: Simplify (* (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) (sqrt k)) into (* (sqrt k) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) 19.895 * [taylor]: Taking taylor expansion of (* (sqrt k) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) in k 19.895 * [taylor]: Taking taylor expansion of (sqrt k) in k 19.895 * [taylor]: Taking taylor expansion of k in k 19.895 * [backup-simplify]: Simplify 0 into 0 19.895 * [backup-simplify]: Simplify 1 into 1 19.896 * [backup-simplify]: Simplify (sqrt 0) into 0 19.897 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 19.897 * [taylor]: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) in k 19.897 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 19.897 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 19.897 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 19.897 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 19.897 * [taylor]: Taking taylor expansion of 1/2 in k 19.897 * [backup-simplify]: Simplify 1/2 into 1/2 19.897 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 19.897 * [taylor]: Taking taylor expansion of 1/2 in k 19.897 * [backup-simplify]: Simplify 1/2 into 1/2 19.897 * [taylor]: Taking taylor expansion of (/ 1 k) in k 19.897 * [taylor]: Taking taylor expansion of k in k 19.897 * [backup-simplify]: Simplify 0 into 0 19.897 * [backup-simplify]: Simplify 1 into 1 19.898 * [backup-simplify]: Simplify (/ 1 1) into 1 19.898 * [taylor]: Taking taylor expansion of (log PI) in k 19.898 * [taylor]: Taking taylor expansion of PI in k 19.898 * [backup-simplify]: Simplify PI into PI 19.898 * [backup-simplify]: Simplify (log PI) into (log PI) 19.898 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 19.899 * [backup-simplify]: Simplify (- 1/2) into -1/2 19.899 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 19.900 * [backup-simplify]: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 19.901 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 19.901 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) in k 19.901 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) in k 19.901 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 19.901 * [taylor]: Taking taylor expansion of 1/2 in k 19.901 * [backup-simplify]: Simplify 1/2 into 1/2 19.901 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 19.901 * [taylor]: Taking taylor expansion of 1/2 in k 19.901 * [backup-simplify]: Simplify 1/2 into 1/2 19.901 * [taylor]: Taking taylor expansion of (/ 1 k) in k 19.901 * [taylor]: Taking taylor expansion of k in k 19.901 * [backup-simplify]: Simplify 0 into 0 19.901 * [backup-simplify]: Simplify 1 into 1 19.902 * [backup-simplify]: Simplify (/ 1 1) into 1 19.902 * [taylor]: Taking taylor expansion of (- (log 2) (log n)) in k 19.902 * [taylor]: Taking taylor expansion of (log 2) in k 19.902 * [taylor]: Taking taylor expansion of 2 in k 19.902 * [backup-simplify]: Simplify 2 into 2 19.902 * [backup-simplify]: Simplify (log 2) into (log 2) 19.902 * [taylor]: Taking taylor expansion of (log n) in k 19.902 * [taylor]: Taking taylor expansion of n in k 19.902 * [backup-simplify]: Simplify n into n 19.902 * [backup-simplify]: Simplify (log n) into (log n) 19.903 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 19.903 * [backup-simplify]: Simplify (- 1/2) into -1/2 19.903 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 19.903 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 19.904 * [backup-simplify]: Simplify (+ (log 2) (- (log n))) into (- (log 2) (log n)) 19.904 * [backup-simplify]: Simplify (* -1/2 (- (log 2) (log n))) into (* -1/2 (- (log 2) (log n))) 19.904 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 19.905 * [backup-simplify]: Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) into (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) 19.906 * [backup-simplify]: Simplify (* 0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) into 0 19.906 * [backup-simplify]: Simplify 0 into 0 19.907 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)))) into 0 19.908 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 19.908 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 19.908 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 19.909 * [backup-simplify]: Simplify (- 0) into 0 19.909 * [backup-simplify]: Simplify (+ 0 0) into 0 19.910 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 19.910 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log 2) (log n)))) into 0 19.912 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 19.913 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 19.913 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 19.914 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 19.914 * [backup-simplify]: Simplify (- 0) into 0 19.915 * [backup-simplify]: Simplify (+ 0 0) into 0 19.915 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (log PI))) into 0 19.917 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 19.917 * [backup-simplify]: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) into 0 19.918 * [backup-simplify]: Simplify (+ (* (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) 0) (* 0 (sqrt k))) into 0 19.918 * [taylor]: Taking taylor expansion of 0 in k 19.918 * [backup-simplify]: Simplify 0 into 0 19.918 * [backup-simplify]: Simplify 0 into 0 19.920 * [backup-simplify]: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) into 0 19.921 * [backup-simplify]: Simplify (+ (* 0 0) (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) into (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) 19.922 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) into (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) 19.923 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 19.924 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)) (* 0 (/ 0 1)))) into 0 19.926 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 19.927 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 19.927 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 19.928 * [backup-simplify]: Simplify (- 0) into 0 19.928 * [backup-simplify]: Simplify (+ 0 0) into 0 19.929 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 19.930 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log 2) (log n))))) into 0 19.932 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 19.935 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 19.935 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 19.936 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 19.936 * [backup-simplify]: Simplify (- 0) into 0 19.937 * [backup-simplify]: Simplify (+ 0 0) into 0 19.938 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (log PI)))) into 0 19.939 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 19.940 * [backup-simplify]: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) into 0 19.941 * [backup-simplify]: Simplify (+ (* (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) 0) (+ (* 0 0) (* 0 (sqrt k)))) into 0 19.941 * [taylor]: Taking taylor expansion of 0 in k 19.941 * [backup-simplify]: Simplify 0 into 0 19.941 * [backup-simplify]: Simplify 0 into 0 19.941 * [backup-simplify]: Simplify 0 into 0 19.942 * [backup-simplify]: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) into 0 19.946 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 19.947 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))))) into (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) 19.948 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) into (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) 19.949 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 19.950 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 19.958 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 19.959 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 19.960 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 19.961 * [backup-simplify]: Simplify (- 0) into 0 19.961 * [backup-simplify]: Simplify (+ 0 0) into 0 19.962 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 19.964 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log 2) (log n)))))) into 0 19.966 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 19.971 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0 19.971 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 19.972 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 19.972 * [backup-simplify]: Simplify (- 0) into 0 19.972 * [backup-simplify]: Simplify (+ 0 0) into 0 19.973 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log PI))))) into 0 19.974 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 19.975 * [backup-simplify]: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))))) into 0 19.976 * [backup-simplify]: Simplify (+ (* (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt k))))) into 0 19.976 * [taylor]: Taking taylor expansion of 0 in k 19.976 * [backup-simplify]: Simplify 0 into 0 19.976 * [backup-simplify]: Simplify 0 into 0 19.976 * [backup-simplify]: Simplify 0 into 0 19.976 * [backup-simplify]: Simplify 0 into 0 19.977 * [backup-simplify]: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))))) into 0 19.980 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 19.981 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (+ (* +nan.0 0) (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))))) into (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) 19.982 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) into (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) 19.984 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k))))) (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log 2) (log (/ 1 n)))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k))))) (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log 2) (log (/ 1 n)))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k))))) (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log 2) (log (/ 1 n)))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (* (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))) (pow k 2))) (- (+ (* +nan.0 (/ (* (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))) k)) (- (* +nan.0 (/ (* (pow PI (- 1/2 (* 1/2 k))) (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k))))) (pow k 3)))))))) 19.984 * [backup-simplify]: Simplify (/ (pow (* (/ 1 (- n)) 2) (- 1/2 (/ (/ 1 (- k)) 2))) (/ (sqrt (/ 1 (- k))) (pow PI (- 1/2 (/ (/ 1 (- k)) 2))))) into (/ (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) 19.984 * [approximate]: Taking taylor expansion of (/ (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) in (n k) around 0 19.984 * [taylor]: Taking taylor expansion of (/ (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) in k 19.984 * [taylor]: Taking taylor expansion of (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in k 19.984 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in k 19.984 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in k 19.984 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in k 19.984 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 19.984 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 19.984 * [taylor]: Taking taylor expansion of 1/2 in k 19.984 * [backup-simplify]: Simplify 1/2 into 1/2 19.984 * [taylor]: Taking taylor expansion of (/ 1 k) in k 19.984 * [taylor]: Taking taylor expansion of k in k 19.984 * [backup-simplify]: Simplify 0 into 0 19.984 * [backup-simplify]: Simplify 1 into 1 19.984 * [backup-simplify]: Simplify (/ 1 1) into 1 19.984 * [taylor]: Taking taylor expansion of 1/2 in k 19.984 * [backup-simplify]: Simplify 1/2 into 1/2 19.984 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in k 19.984 * [taylor]: Taking taylor expansion of (/ -2 n) in k 19.984 * [taylor]: Taking taylor expansion of -2 in k 19.984 * [backup-simplify]: Simplify -2 into -2 19.984 * [taylor]: Taking taylor expansion of n in k 19.984 * [backup-simplify]: Simplify n into n 19.985 * [backup-simplify]: Simplify (/ -2 n) into (/ -2 n) 19.985 * [backup-simplify]: Simplify (log (/ -2 n)) into (log (/ -2 n)) 19.985 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 19.985 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 19.985 * [backup-simplify]: Simplify (* 1/2 (log (/ -2 n))) into (* 1/2 (log (/ -2 n))) 19.985 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) into (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) 19.985 * [taylor]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 19.985 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 19.985 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 19.985 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 19.985 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 19.985 * [taylor]: Taking taylor expansion of 1/2 in k 19.985 * [backup-simplify]: Simplify 1/2 into 1/2 19.985 * [taylor]: Taking taylor expansion of (/ 1 k) in k 19.985 * [taylor]: Taking taylor expansion of k in k 19.985 * [backup-simplify]: Simplify 0 into 0 19.985 * [backup-simplify]: Simplify 1 into 1 19.986 * [backup-simplify]: Simplify (/ 1 1) into 1 19.986 * [taylor]: Taking taylor expansion of 1/2 in k 19.986 * [backup-simplify]: Simplify 1/2 into 1/2 19.986 * [taylor]: Taking taylor expansion of (log PI) in k 19.986 * [taylor]: Taking taylor expansion of PI in k 19.986 * [backup-simplify]: Simplify PI into PI 19.986 * [backup-simplify]: Simplify (log PI) into (log PI) 19.986 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 19.987 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 19.988 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 19.989 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 19.989 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 19.989 * [taylor]: Taking taylor expansion of (/ -1 k) in k 19.989 * [taylor]: Taking taylor expansion of -1 in k 19.989 * [backup-simplify]: Simplify -1 into -1 19.989 * [taylor]: Taking taylor expansion of k in k 19.989 * [backup-simplify]: Simplify 0 into 0 19.989 * [backup-simplify]: Simplify 1 into 1 19.989 * [backup-simplify]: Simplify (/ -1 1) into -1 19.990 * [backup-simplify]: Simplify (sqrt 0) into 0 19.991 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 19.992 * [backup-simplify]: Simplify (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 19.992 * [backup-simplify]: Simplify (/ (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) +nan.0) into (* +nan.0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 19.992 * [taylor]: Taking taylor expansion of (/ (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) in n 19.992 * [taylor]: Taking taylor expansion of (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in n 19.992 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 19.992 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 19.992 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 19.993 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 19.993 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 19.993 * [taylor]: Taking taylor expansion of 1/2 in n 19.993 * [backup-simplify]: Simplify 1/2 into 1/2 19.993 * [taylor]: Taking taylor expansion of (/ 1 k) in n 19.993 * [taylor]: Taking taylor expansion of k in n 19.993 * [backup-simplify]: Simplify k into k 19.993 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 19.993 * [taylor]: Taking taylor expansion of 1/2 in n 19.993 * [backup-simplify]: Simplify 1/2 into 1/2 19.993 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in n 19.993 * [taylor]: Taking taylor expansion of (/ -2 n) in n 19.993 * [taylor]: Taking taylor expansion of -2 in n 19.993 * [backup-simplify]: Simplify -2 into -2 19.993 * [taylor]: Taking taylor expansion of n in n 19.993 * [backup-simplify]: Simplify 0 into 0 19.993 * [backup-simplify]: Simplify 1 into 1 19.994 * [backup-simplify]: Simplify (/ -2 1) into -2 19.994 * [backup-simplify]: Simplify (log -2) into (log -2) 19.994 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 19.995 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 19.995 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 19.996 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 19.997 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 19.997 * [taylor]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in n 19.997 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in n 19.997 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in n 19.997 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 19.997 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 19.997 * [taylor]: Taking taylor expansion of 1/2 in n 19.997 * [backup-simplify]: Simplify 1/2 into 1/2 19.997 * [taylor]: Taking taylor expansion of (/ 1 k) in n 19.997 * [taylor]: Taking taylor expansion of k in n 19.997 * [backup-simplify]: Simplify k into k 19.997 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 19.997 * [taylor]: Taking taylor expansion of 1/2 in n 19.997 * [backup-simplify]: Simplify 1/2 into 1/2 19.997 * [taylor]: Taking taylor expansion of (log PI) in n 19.997 * [taylor]: Taking taylor expansion of PI in n 19.997 * [backup-simplify]: Simplify PI into PI 19.998 * [backup-simplify]: Simplify (log PI) into (log PI) 19.998 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 19.998 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 19.998 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) 19.999 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 19.999 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 19.999 * [taylor]: Taking taylor expansion of (/ -1 k) in n 19.999 * [taylor]: Taking taylor expansion of -1 in n 19.999 * [backup-simplify]: Simplify -1 into -1 19.999 * [taylor]: Taking taylor expansion of k in n 19.999 * [backup-simplify]: Simplify k into k 19.999 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 19.999 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 19.999 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 20.000 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 20.000 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 20.001 * [backup-simplify]: Simplify (/ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) into (/ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) 20.001 * [taylor]: Taking taylor expansion of (/ (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) in n 20.001 * [taylor]: Taking taylor expansion of (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in n 20.001 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 20.001 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 20.001 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 20.001 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 20.001 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 20.001 * [taylor]: Taking taylor expansion of 1/2 in n 20.002 * [backup-simplify]: Simplify 1/2 into 1/2 20.002 * [taylor]: Taking taylor expansion of (/ 1 k) in n 20.002 * [taylor]: Taking taylor expansion of k in n 20.002 * [backup-simplify]: Simplify k into k 20.002 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 20.002 * [taylor]: Taking taylor expansion of 1/2 in n 20.002 * [backup-simplify]: Simplify 1/2 into 1/2 20.002 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in n 20.002 * [taylor]: Taking taylor expansion of (/ -2 n) in n 20.002 * [taylor]: Taking taylor expansion of -2 in n 20.002 * [backup-simplify]: Simplify -2 into -2 20.002 * [taylor]: Taking taylor expansion of n in n 20.002 * [backup-simplify]: Simplify 0 into 0 20.002 * [backup-simplify]: Simplify 1 into 1 20.002 * [backup-simplify]: Simplify (/ -2 1) into -2 20.003 * [backup-simplify]: Simplify (log -2) into (log -2) 20.003 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 20.003 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 20.004 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 20.005 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 20.006 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 20.006 * [taylor]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in n 20.006 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in n 20.006 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in n 20.006 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 20.006 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 20.006 * [taylor]: Taking taylor expansion of 1/2 in n 20.006 * [backup-simplify]: Simplify 1/2 into 1/2 20.006 * [taylor]: Taking taylor expansion of (/ 1 k) in n 20.006 * [taylor]: Taking taylor expansion of k in n 20.006 * [backup-simplify]: Simplify k into k 20.006 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 20.006 * [taylor]: Taking taylor expansion of 1/2 in n 20.006 * [backup-simplify]: Simplify 1/2 into 1/2 20.006 * [taylor]: Taking taylor expansion of (log PI) in n 20.006 * [taylor]: Taking taylor expansion of PI in n 20.006 * [backup-simplify]: Simplify PI into PI 20.007 * [backup-simplify]: Simplify (log PI) into (log PI) 20.007 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 20.007 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 20.008 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) 20.008 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 20.008 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 20.008 * [taylor]: Taking taylor expansion of (/ -1 k) in n 20.008 * [taylor]: Taking taylor expansion of -1 in n 20.008 * [backup-simplify]: Simplify -1 into -1 20.008 * [taylor]: Taking taylor expansion of k in n 20.008 * [backup-simplify]: Simplify k into k 20.008 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 20.008 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 20.009 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 20.009 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 20.009 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 20.010 * [backup-simplify]: Simplify (/ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) into (/ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) 20.010 * [taylor]: Taking taylor expansion of (/ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) in k 20.010 * [taylor]: Taking taylor expansion of (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in k 20.010 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) in k 20.010 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) in k 20.010 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 20.010 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 20.011 * [taylor]: Taking taylor expansion of 1/2 in k 20.011 * [backup-simplify]: Simplify 1/2 into 1/2 20.011 * [taylor]: Taking taylor expansion of (/ 1 k) in k 20.011 * [taylor]: Taking taylor expansion of k in k 20.011 * [backup-simplify]: Simplify 0 into 0 20.011 * [backup-simplify]: Simplify 1 into 1 20.011 * [backup-simplify]: Simplify (/ 1 1) into 1 20.011 * [taylor]: Taking taylor expansion of 1/2 in k 20.011 * [backup-simplify]: Simplify 1/2 into 1/2 20.011 * [taylor]: Taking taylor expansion of (- (log -2) (log n)) in k 20.011 * [taylor]: Taking taylor expansion of (log -2) in k 20.011 * [taylor]: Taking taylor expansion of -2 in k 20.011 * [backup-simplify]: Simplify -2 into -2 20.012 * [backup-simplify]: Simplify (log -2) into (log -2) 20.012 * [taylor]: Taking taylor expansion of (log n) in k 20.012 * [taylor]: Taking taylor expansion of n in k 20.012 * [backup-simplify]: Simplify n into n 20.012 * [backup-simplify]: Simplify (log n) into (log n) 20.012 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 20.013 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 20.013 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 20.013 * [backup-simplify]: Simplify (+ (log -2) (- (log n))) into (- (log -2) (log n)) 20.014 * [backup-simplify]: Simplify (* 1/2 (- (log -2) (log n))) into (* 1/2 (- (log -2) (log n))) 20.014 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 20.014 * [taylor]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 20.014 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 20.015 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 20.015 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 20.015 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 20.015 * [taylor]: Taking taylor expansion of 1/2 in k 20.015 * [backup-simplify]: Simplify 1/2 into 1/2 20.015 * [taylor]: Taking taylor expansion of (/ 1 k) in k 20.015 * [taylor]: Taking taylor expansion of k in k 20.015 * [backup-simplify]: Simplify 0 into 0 20.015 * [backup-simplify]: Simplify 1 into 1 20.015 * [backup-simplify]: Simplify (/ 1 1) into 1 20.015 * [taylor]: Taking taylor expansion of 1/2 in k 20.015 * [backup-simplify]: Simplify 1/2 into 1/2 20.015 * [taylor]: Taking taylor expansion of (log PI) in k 20.015 * [taylor]: Taking taylor expansion of PI in k 20.015 * [backup-simplify]: Simplify PI into PI 20.016 * [backup-simplify]: Simplify (log PI) into (log PI) 20.016 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 20.017 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 20.018 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 20.018 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 20.018 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 20.018 * [taylor]: Taking taylor expansion of (/ -1 k) in k 20.018 * [taylor]: Taking taylor expansion of -1 in k 20.018 * [backup-simplify]: Simplify -1 into -1 20.018 * [taylor]: Taking taylor expansion of k in k 20.018 * [backup-simplify]: Simplify 0 into 0 20.018 * [backup-simplify]: Simplify 1 into 1 20.019 * [backup-simplify]: Simplify (/ -1 1) into -1 20.019 * [backup-simplify]: Simplify (sqrt 0) into 0 20.021 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 20.022 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 20.022 * [backup-simplify]: Simplify (/ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) +nan.0) into (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 20.023 * [backup-simplify]: Simplify (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 20.024 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 20.024 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 20.024 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 20.024 * [backup-simplify]: Simplify (+ 0 0) into 0 20.025 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (log PI))) into 0 20.026 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 20.026 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -2 (/ 0 1)))) into 0 20.027 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -2 1)))) 1) into 0 20.027 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 20.027 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 20.028 * [backup-simplify]: Simplify (+ 0 0) into 0 20.028 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 20.029 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log -2) (log n)))) into 0 20.029 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 20.030 * [backup-simplify]: Simplify (+ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 0) (* 0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into 0 20.030 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0 20.030 * [taylor]: Taking taylor expansion of 0 in k 20.030 * [backup-simplify]: Simplify 0 into 0 20.031 * [backup-simplify]: Simplify 0 into 0 20.031 * [backup-simplify]: Simplify (+ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 0) (* 0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into 0 20.032 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 20.033 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 20.034 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 20.035 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 20.037 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 20.037 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 20.037 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 20.038 * [backup-simplify]: Simplify (+ 0 0) into 0 20.038 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (log PI)))) into 0 20.039 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 20.040 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -2 (/ 0 1)) (* 0 (/ 0 1)))) into 0 20.042 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -2 1)))) 2) into 0 20.042 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 20.042 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 20.043 * [backup-simplify]: Simplify (+ 0 0) into 0 20.043 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 20.044 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log -2) (log n))))) into 0 20.045 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 20.045 * [backup-simplify]: Simplify (+ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 0) (+ (* 0 0) (* 0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into 0 20.046 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 20.046 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 20.047 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0 20.047 * [taylor]: Taking taylor expansion of 0 in k 20.047 * [backup-simplify]: Simplify 0 into 0 20.047 * [backup-simplify]: Simplify 0 into 0 20.047 * [backup-simplify]: Simplify 0 into 0 20.048 * [backup-simplify]: Simplify (+ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 0) (+ (* 0 0) (* 0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into 0 20.048 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 20.051 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 20.053 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 20.053 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 20.055 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -2) (log (/ 1 (- n)))))) (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -2) (log (/ 1 (- n)))))) (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))))) (* (/ 1 (- k)) 1)) (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -2) (log (/ 1 (- n)))))) (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)))))) into (- (+ (* +nan.0 (* (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (pow PI (- 1/2 (* 1/2 k))))) (- (+ (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (pow PI (- 1/2 (* 1/2 k)))) k)) (- (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (pow PI (- 1/2 (* 1/2 k)))) (pow k 2)))))))) 20.055 * * * * [progress]: [ 4 / 4 ] generating series at (2 2) 20.055 * [backup-simplify]: Simplify (/ (sqrt k) (pow PI (- 1/2 (/ k 2)))) into (* (/ 1 (pow PI (- 1/2 (* 1/2 k)))) (sqrt k)) 20.055 * [approximate]: Taking taylor expansion of (* (/ 1 (pow PI (- 1/2 (* 1/2 k)))) (sqrt k)) in (k) around 0 20.055 * [taylor]: Taking taylor expansion of (* (/ 1 (pow PI (- 1/2 (* 1/2 k)))) (sqrt k)) in k 20.055 * [taylor]: Taking taylor expansion of (/ 1 (pow PI (- 1/2 (* 1/2 k)))) in k 20.055 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 20.055 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 20.055 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 20.055 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 20.055 * [taylor]: Taking taylor expansion of 1/2 in k 20.055 * [backup-simplify]: Simplify 1/2 into 1/2 20.055 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 20.055 * [taylor]: Taking taylor expansion of 1/2 in k 20.055 * [backup-simplify]: Simplify 1/2 into 1/2 20.055 * [taylor]: Taking taylor expansion of k in k 20.055 * [backup-simplify]: Simplify 0 into 0 20.055 * [backup-simplify]: Simplify 1 into 1 20.055 * [taylor]: Taking taylor expansion of (log PI) in k 20.056 * [taylor]: Taking taylor expansion of PI in k 20.056 * [backup-simplify]: Simplify PI into PI 20.056 * [backup-simplify]: Simplify (log PI) into (log PI) 20.056 * [backup-simplify]: Simplify (* 1/2 0) into 0 20.056 * [backup-simplify]: Simplify (- 0) into 0 20.057 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 20.057 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 20.058 * [backup-simplify]: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 20.060 * [backup-simplify]: Simplify (/ 1 (pow PI 1/2)) into (sqrt (/ 1 PI)) 20.060 * [taylor]: Taking taylor expansion of (sqrt k) in k 20.060 * [taylor]: Taking taylor expansion of k in k 20.060 * [backup-simplify]: Simplify 0 into 0 20.060 * [backup-simplify]: Simplify 1 into 1 20.060 * [backup-simplify]: Simplify (sqrt 0) into 0 20.061 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 20.061 * [taylor]: Taking taylor expansion of (* (/ 1 (pow PI (- 1/2 (* 1/2 k)))) (sqrt k)) in k 20.061 * [taylor]: Taking taylor expansion of (/ 1 (pow PI (- 1/2 (* 1/2 k)))) in k 20.061 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 20.062 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 20.062 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 20.062 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 20.062 * [taylor]: Taking taylor expansion of 1/2 in k 20.062 * [backup-simplify]: Simplify 1/2 into 1/2 20.062 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 20.062 * [taylor]: Taking taylor expansion of 1/2 in k 20.062 * [backup-simplify]: Simplify 1/2 into 1/2 20.062 * [taylor]: Taking taylor expansion of k in k 20.062 * [backup-simplify]: Simplify 0 into 0 20.062 * [backup-simplify]: Simplify 1 into 1 20.062 * [taylor]: Taking taylor expansion of (log PI) in k 20.062 * [taylor]: Taking taylor expansion of PI in k 20.062 * [backup-simplify]: Simplify PI into PI 20.063 * [backup-simplify]: Simplify (log PI) into (log PI) 20.063 * [backup-simplify]: Simplify (* 1/2 0) into 0 20.064 * [backup-simplify]: Simplify (- 0) into 0 20.064 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 20.065 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 20.067 * [backup-simplify]: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 20.068 * [backup-simplify]: Simplify (/ 1 (pow PI 1/2)) into (sqrt (/ 1 PI)) 20.068 * [taylor]: Taking taylor expansion of (sqrt k) in k 20.068 * [taylor]: Taking taylor expansion of k in k 20.068 * [backup-simplify]: Simplify 0 into 0 20.068 * [backup-simplify]: Simplify 1 into 1 20.069 * [backup-simplify]: Simplify (sqrt 0) into 0 20.070 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 20.071 * [backup-simplify]: Simplify (* (sqrt (/ 1 PI)) 0) into 0 20.071 * [backup-simplify]: Simplify 0 into 0 20.073 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 20.073 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 20.077 * [backup-simplify]: Simplify (- 1/2) into -1/2 20.077 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 20.080 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log PI))) into (- (* 1/2 (log PI))) 20.090 * [backup-simplify]: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 1) 1)))) into (* -1/2 (* (log PI) (sqrt PI))) 20.102 * [backup-simplify]: Simplify (- (+ (* (sqrt (/ 1 PI)) (/ (* -1/2 (* (log PI) (sqrt PI))) (pow PI 1/2))))) into (* 1/2 (* (log PI) (sqrt (/ 1 PI)))) 20.107 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 PI)) +nan.0) (* (* 1/2 (* (log PI) (sqrt (/ 1 PI)))) 0)) into (- (* +nan.0 (sqrt (/ 1 PI)))) 20.110 * [backup-simplify]: Simplify (- (* +nan.0 (sqrt (/ 1 PI)))) into (- (* +nan.0 (sqrt (/ 1 PI)))) 20.114 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 20.117 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 20.118 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 20.119 * [backup-simplify]: Simplify (- 0) into 0 20.119 * [backup-simplify]: Simplify (+ 0 0) into 0 20.121 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log PI)))) into 0 20.134 * [backup-simplify]: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI))) 20.160 * [backup-simplify]: Simplify (- (+ (* (sqrt (/ 1 PI)) (/ (* 1/8 (* (pow (log PI) 2) (sqrt PI))) (pow PI 1/2))) (* (* 1/2 (* (log PI) (sqrt (/ 1 PI)))) (/ (* -1/2 (* (log PI) (sqrt PI))) (pow PI 1/2))))) into (* 1/8 (* (pow (log PI) 2) (sqrt (/ 1 PI)))) 20.168 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 PI)) +nan.0) (+ (* (* 1/2 (* (log PI) (sqrt (/ 1 PI)))) +nan.0) (* (* 1/8 (* (pow (log PI) 2) (sqrt (/ 1 PI)))) 0))) into (- (+ (* +nan.0 (* (log PI) (sqrt (/ 1 PI)))) (- (* +nan.0 (sqrt (/ 1 PI)))))) 20.174 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (log PI) (sqrt (/ 1 PI)))) (- (* +nan.0 (sqrt (/ 1 PI)))))) into (- (+ (* +nan.0 (* (log PI) (sqrt (/ 1 PI)))) (- (* +nan.0 (sqrt (/ 1 PI)))))) 20.177 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 20.180 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0 20.180 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 20.181 * [backup-simplify]: Simplify (- 0) into 0 20.181 * [backup-simplify]: Simplify (+ 0 0) into 0 20.182 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log PI))))) into 0 20.195 * [backup-simplify]: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 3) 6)) (* (/ (pow (- (* 1/2 (log PI))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (pow (log PI) 3) (sqrt PI))) 20.235 * [backup-simplify]: Simplify (- (+ (* (sqrt (/ 1 PI)) (/ (* -1/48 (* (pow (log PI) 3) (sqrt PI))) (pow PI 1/2))) (* (* 1/2 (* (log PI) (sqrt (/ 1 PI)))) (/ (* 1/8 (* (pow (log PI) 2) (sqrt PI))) (pow PI 1/2))) (* (* 1/8 (* (pow (log PI) 2) (sqrt (/ 1 PI)))) (/ (* -1/2 (* (log PI) (sqrt PI))) (pow PI 1/2))))) into (* 1/48 (* (pow (log PI) 3) (sqrt (/ 1 PI)))) 20.253 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 PI)) +nan.0) (+ (* (* 1/2 (* (log PI) (sqrt (/ 1 PI)))) +nan.0) (+ (* (* 1/8 (* (pow (log PI) 2) (sqrt (/ 1 PI)))) +nan.0) (* (* 1/48 (* (pow (log PI) 3) (sqrt (/ 1 PI)))) 0)))) into (- (+ (* +nan.0 (* (pow (log PI) 2) (sqrt (/ 1 PI)))) (- (+ (* +nan.0 (* (log PI) (sqrt (/ 1 PI)))) (- (* +nan.0 (sqrt (/ 1 PI)))))))) 20.274 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (pow (log PI) 2) (sqrt (/ 1 PI)))) (- (+ (* +nan.0 (* (log PI) (sqrt (/ 1 PI)))) (- (* +nan.0 (sqrt (/ 1 PI)))))))) into (- (+ (* +nan.0 (* (pow (log PI) 2) (sqrt (/ 1 PI)))) (- (+ (* +nan.0 (* (log PI) (sqrt (/ 1 PI)))) (- (* +nan.0 (sqrt (/ 1 PI)))))))) 20.297 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (pow (log PI) 2) (sqrt (/ 1 PI)))) (- (+ (* +nan.0 (* (log PI) (sqrt (/ 1 PI)))) (- (* +nan.0 (sqrt (/ 1 PI)))))))) (pow k 3)) (+ (* (- (+ (* +nan.0 (* (log PI) (sqrt (/ 1 PI)))) (- (* +nan.0 (sqrt (/ 1 PI)))))) (pow k 2)) (* (- (* +nan.0 (sqrt (/ 1 PI)))) k))) into (- (+ (* +nan.0 (* (sqrt (/ 1 PI)) (pow k 3))) (- (+ (* +nan.0 (* (* (log PI) (pow k 3)) (sqrt (/ 1 PI)))) (- (+ (* +nan.0 (* (* (pow (log PI) 2) (pow k 3)) (sqrt (/ 1 PI)))) (- (+ (* +nan.0 (* (sqrt (/ 1 PI)) k)) (- (+ (* +nan.0 (* (* (log PI) (pow k 2)) (sqrt (/ 1 PI)))) (- (* +nan.0 (* (sqrt (/ 1 PI)) (pow k 2)))))))))))))) 20.298 * [backup-simplify]: Simplify (/ (sqrt (/ 1 k)) (pow PI (- 1/2 (/ (/ 1 k) 2)))) into (* (/ 1 (pow PI (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) 20.298 * [approximate]: Taking taylor expansion of (* (/ 1 (pow PI (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in (k) around 0 20.298 * [taylor]: Taking taylor expansion of (* (/ 1 (pow PI (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in k 20.298 * [taylor]: Taking taylor expansion of (/ 1 (pow PI (- 1/2 (* 1/2 (/ 1 k))))) in k 20.298 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 20.298 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 20.298 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 20.298 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 20.298 * [taylor]: Taking taylor expansion of 1/2 in k 20.298 * [backup-simplify]: Simplify 1/2 into 1/2 20.298 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 20.298 * [taylor]: Taking taylor expansion of 1/2 in k 20.298 * [backup-simplify]: Simplify 1/2 into 1/2 20.298 * [taylor]: Taking taylor expansion of (/ 1 k) in k 20.298 * [taylor]: Taking taylor expansion of k in k 20.298 * [backup-simplify]: Simplify 0 into 0 20.298 * [backup-simplify]: Simplify 1 into 1 20.298 * [backup-simplify]: Simplify (/ 1 1) into 1 20.298 * [taylor]: Taking taylor expansion of (log PI) in k 20.298 * [taylor]: Taking taylor expansion of PI in k 20.298 * [backup-simplify]: Simplify PI into PI 20.298 * [backup-simplify]: Simplify (log PI) into (log PI) 20.299 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 20.299 * [backup-simplify]: Simplify (- 1/2) into -1/2 20.299 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 20.300 * [backup-simplify]: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 20.300 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 20.300 * [backup-simplify]: Simplify (/ 1 (pow PI (- 1/2 (* 1/2 (/ 1 k))))) into (/ 1 (pow PI (- 1/2 (* 1/2 (/ 1 k))))) 20.300 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 20.300 * [taylor]: Taking taylor expansion of (/ 1 k) in k 20.300 * [taylor]: Taking taylor expansion of k in k 20.300 * [backup-simplify]: Simplify 0 into 0 20.300 * [backup-simplify]: Simplify 1 into 1 20.301 * [backup-simplify]: Simplify (/ 1 1) into 1 20.301 * [backup-simplify]: Simplify (sqrt 0) into 0 20.302 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 20.302 * [taylor]: Taking taylor expansion of (* (/ 1 (pow PI (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in k 20.302 * [taylor]: Taking taylor expansion of (/ 1 (pow PI (- 1/2 (* 1/2 (/ 1 k))))) in k 20.302 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 20.302 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 20.302 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 20.302 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 20.302 * [taylor]: Taking taylor expansion of 1/2 in k 20.302 * [backup-simplify]: Simplify 1/2 into 1/2 20.302 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 20.302 * [taylor]: Taking taylor expansion of 1/2 in k 20.302 * [backup-simplify]: Simplify 1/2 into 1/2 20.302 * [taylor]: Taking taylor expansion of (/ 1 k) in k 20.302 * [taylor]: Taking taylor expansion of k in k 20.302 * [backup-simplify]: Simplify 0 into 0 20.302 * [backup-simplify]: Simplify 1 into 1 20.302 * [backup-simplify]: Simplify (/ 1 1) into 1 20.302 * [taylor]: Taking taylor expansion of (log PI) in k 20.302 * [taylor]: Taking taylor expansion of PI in k 20.302 * [backup-simplify]: Simplify PI into PI 20.303 * [backup-simplify]: Simplify (log PI) into (log PI) 20.303 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 20.303 * [backup-simplify]: Simplify (- 1/2) into -1/2 20.304 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 20.304 * [backup-simplify]: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 20.304 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 20.305 * [backup-simplify]: Simplify (/ 1 (pow PI (- 1/2 (* 1/2 (/ 1 k))))) into (/ 1 (pow PI (- 1/2 (* 1/2 (/ 1 k))))) 20.305 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 20.305 * [taylor]: Taking taylor expansion of (/ 1 k) in k 20.305 * [taylor]: Taking taylor expansion of k in k 20.305 * [backup-simplify]: Simplify 0 into 0 20.305 * [backup-simplify]: Simplify 1 into 1 20.305 * [backup-simplify]: Simplify (/ 1 1) into 1 20.305 * [backup-simplify]: Simplify (sqrt 0) into 0 20.306 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 20.306 * [backup-simplify]: Simplify (* (/ 1 (pow PI (- 1/2 (* 1/2 (/ 1 k))))) 0) into 0 20.306 * [backup-simplify]: Simplify 0 into 0 20.306 * [backup-simplify]: Simplify (- (+ (* (/ 1 (pow PI (- 1/2 (* 1/2 (/ 1 k))))) (/ 0 (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 20.307 * [backup-simplify]: Simplify (+ (* (/ 1 (pow PI (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (* 0 0)) into (- (* +nan.0 (/ 1 (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) 20.307 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) into (- (* +nan.0 (/ 1 (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) 20.307 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 20.309 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 20.310 * [backup-simplify]: Simplify (- (+ (* (/ 1 (pow PI (- 1/2 (* 1/2 (/ 1 k))))) (/ 0 (pow PI (- 1/2 (* 1/2 (/ 1 k)))))) (* 0 (/ 0 (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 20.310 * [backup-simplify]: Simplify (+ (* (/ 1 (pow PI (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (/ 1 (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) 20.310 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) into (- (* +nan.0 (/ 1 (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) 20.311 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 20.315 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 20.316 * [backup-simplify]: Simplify (- (+ (* (/ 1 (pow PI (- 1/2 (* 1/2 (/ 1 k))))) (/ 0 (pow PI (- 1/2 (* 1/2 (/ 1 k)))))) (* 0 (/ 0 (pow PI (- 1/2 (* 1/2 (/ 1 k)))))) (* 0 (/ 0 (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 20.317 * [backup-simplify]: Simplify (+ (* (/ 1 (pow PI (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (/ 1 (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) 20.317 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) into (- (* +nan.0 (/ 1 (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) 20.318 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (/ 1 (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))))) (pow (/ 1 k) 2)) (+ (* (- (* +nan.0 (/ 1 (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))))) (/ 1 k)) (- (* +nan.0 (/ 1 (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))))))) into (- (+ (* +nan.0 (/ 1 (pow PI (- 1/2 (* 1/2 k))))) (- (+ (* +nan.0 (/ 1 (* (pow PI (- 1/2 (* 1/2 k))) k))) (- (* +nan.0 (/ 1 (* (pow PI (- 1/2 (* 1/2 k))) (pow k 2))))))))) 20.319 * [backup-simplify]: Simplify (/ (sqrt (/ 1 (- k))) (pow PI (- 1/2 (/ (/ 1 (- k)) 2)))) into (/ (sqrt (/ -1 k)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 20.319 * [approximate]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in (k) around 0 20.319 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in k 20.319 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 20.319 * [taylor]: Taking taylor expansion of (/ -1 k) in k 20.319 * [taylor]: Taking taylor expansion of -1 in k 20.319 * [backup-simplify]: Simplify -1 into -1 20.319 * [taylor]: Taking taylor expansion of k in k 20.319 * [backup-simplify]: Simplify 0 into 0 20.319 * [backup-simplify]: Simplify 1 into 1 20.319 * [backup-simplify]: Simplify (/ -1 1) into -1 20.320 * [backup-simplify]: Simplify (sqrt 0) into 0 20.321 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 20.321 * [taylor]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 20.321 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 20.321 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 20.321 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 20.321 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 20.321 * [taylor]: Taking taylor expansion of 1/2 in k 20.321 * [backup-simplify]: Simplify 1/2 into 1/2 20.321 * [taylor]: Taking taylor expansion of (/ 1 k) in k 20.321 * [taylor]: Taking taylor expansion of k in k 20.322 * [backup-simplify]: Simplify 0 into 0 20.322 * [backup-simplify]: Simplify 1 into 1 20.322 * [backup-simplify]: Simplify (/ 1 1) into 1 20.322 * [taylor]: Taking taylor expansion of 1/2 in k 20.322 * [backup-simplify]: Simplify 1/2 into 1/2 20.322 * [taylor]: Taking taylor expansion of (log PI) in k 20.322 * [taylor]: Taking taylor expansion of PI in k 20.322 * [backup-simplify]: Simplify PI into PI 20.325 * [backup-simplify]: Simplify (log PI) into (log PI) 20.326 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 20.327 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 20.328 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 20.329 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 20.329 * [backup-simplify]: Simplify (/ +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (/ +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 20.329 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in k 20.329 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 20.329 * [taylor]: Taking taylor expansion of (/ -1 k) in k 20.329 * [taylor]: Taking taylor expansion of -1 in k 20.329 * [backup-simplify]: Simplify -1 into -1 20.329 * [taylor]: Taking taylor expansion of k in k 20.329 * [backup-simplify]: Simplify 0 into 0 20.329 * [backup-simplify]: Simplify 1 into 1 20.330 * [backup-simplify]: Simplify (/ -1 1) into -1 20.330 * [backup-simplify]: Simplify (sqrt 0) into 0 20.331 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 20.331 * [taylor]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 20.331 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 20.332 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 20.332 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 20.332 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 20.332 * [taylor]: Taking taylor expansion of 1/2 in k 20.332 * [backup-simplify]: Simplify 1/2 into 1/2 20.332 * [taylor]: Taking taylor expansion of (/ 1 k) in k 20.332 * [taylor]: Taking taylor expansion of k in k 20.332 * [backup-simplify]: Simplify 0 into 0 20.332 * [backup-simplify]: Simplify 1 into 1 20.332 * [backup-simplify]: Simplify (/ 1 1) into 1 20.332 * [taylor]: Taking taylor expansion of 1/2 in k 20.332 * [backup-simplify]: Simplify 1/2 into 1/2 20.332 * [taylor]: Taking taylor expansion of (log PI) in k 20.332 * [taylor]: Taking taylor expansion of PI in k 20.332 * [backup-simplify]: Simplify PI into PI 20.333 * [backup-simplify]: Simplify (log PI) into (log PI) 20.333 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 20.335 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 20.336 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 20.336 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 20.337 * [backup-simplify]: Simplify (/ +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (/ +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 20.337 * [backup-simplify]: Simplify (/ +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (/ +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 20.338 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 20.341 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 20.342 * [backup-simplify]: Simplify (- (/ +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (+ (* (/ +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (/ 0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) into (- (* +nan.0 (/ 1 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 20.342 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (- (* +nan.0 (/ 1 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 20.343 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 20.347 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 20.348 * [backup-simplify]: Simplify (- (/ +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (+ (* (/ +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (/ 0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) (* (- (* +nan.0 (/ 1 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) (/ 0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) into (- (* +nan.0 (/ 1 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 20.349 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (- (* +nan.0 (/ 1 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 20.350 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (/ 1 (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))))) (pow (/ 1 (- k)) 2)) (+ (* (- (* +nan.0 (/ 1 (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))))) (/ 1 (- k))) (/ +nan.0 (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))))) into (- (+ (* +nan.0 (/ 1 (pow PI (- 1/2 (* 1/2 k))))) (- (+ (* +nan.0 (/ 1 (* (pow PI (- 1/2 (* 1/2 k))) k))) (- (* +nan.0 (/ 1 (* (pow PI (- 1/2 (* 1/2 k))) (pow k 2))))))))) 20.350 * * * [progress]: simplifying candidates 20.350 * * * * [progress]: [ 1 / 14352 ] simplifiying candidate # 20.350 * * * * [progress]: [ 2 / 14352 ] simplifiying candidate # 20.350 * * * * [progress]: [ 3 / 14352 ] simplifiying candidate # 20.351 * * * * [progress]: [ 4 / 14352 ] simplifiying candidate # 20.351 * * * * [progress]: [ 5 / 14352 ] simplifiying candidate # 20.351 * * * * [progress]: [ 6 / 14352 ] simplifiying candidate # 20.351 * * * * [progress]: [ 7 / 14352 ] simplifiying candidate # 20.351 * * * * [progress]: [ 8 / 14352 ] simplifiying candidate # 20.351 * * * * [progress]: [ 9 / 14352 ] simplifiying candidate # 20.351 * * * * [progress]: [ 10 / 14352 ] simplifiying candidate # 20.351 * * * * [progress]: [ 11 / 14352 ] simplifiying candidate # 20.351 * * * * [progress]: [ 12 / 14352 ] simplifiying candidate # 20.351 * * * * [progress]: [ 13 / 14352 ] simplifiying candidate # 20.352 * * * * [progress]: [ 14 / 14352 ] simplifiying candidate # 20.352 * * * * [progress]: [ 15 / 14352 ] simplifiying candidate # 20.352 * * * * [progress]: [ 16 / 14352 ] simplifiying candidate # 20.352 * * * * [progress]: [ 17 / 14352 ] simplifiying candidate # 20.352 * * * * [progress]: [ 18 / 14352 ] simplifiying candidate # 20.352 * * * * [progress]: [ 19 / 14352 ] simplifiying candidate # 20.352 * * * * [progress]: [ 20 / 14352 ] simplifiying candidate # 20.352 * * * * [progress]: [ 21 / 14352 ] simplifiying candidate # 20.352 * * * * [progress]: [ 22 / 14352 ] simplifiying candidate # 20.353 * * * * [progress]: [ 23 / 14352 ] simplifiying candidate # 20.353 * * * * [progress]: [ 24 / 14352 ] simplifiying candidate # 20.353 * * * * [progress]: [ 25 / 14352 ] simplifiying candidate # 20.353 * * * * [progress]: [ 26 / 14352 ] simplifiying candidate # 20.353 * * * * [progress]: [ 27 / 14352 ] simplifiying candidate # 20.353 * * * * [progress]: [ 28 / 14352 ] simplifiying candidate # 20.353 * * * * [progress]: [ 29 / 14352 ] simplifiying candidate # 20.353 * * * * [progress]: [ 30 / 14352 ] simplifiying candidate # 20.354 * * * * [progress]: [ 31 / 14352 ] simplifiying candidate # 20.354 * * * * [progress]: [ 32 / 14352 ] simplifiying candidate # 20.354 * * * * [progress]: [ 33 / 14352 ] simplifiying candidate # 20.354 * * * * [progress]: [ 34 / 14352 ] simplifiying candidate # 20.354 * * * * [progress]: [ 35 / 14352 ] simplifiying candidate # 20.354 * * * * [progress]: [ 36 / 14352 ] simplifiying candidate # 20.354 * * * * [progress]: [ 37 / 14352 ] simplifiying candidate # 20.354 * * * * [progress]: [ 38 / 14352 ] simplifiying candidate # 20.355 * * * * [progress]: [ 39 / 14352 ] simplifiying candidate # 20.355 * * * * [progress]: [ 40 / 14352 ] simplifiying candidate # 20.355 * * * * [progress]: [ 41 / 14352 ] simplifiying candidate # 20.355 * * * * [progress]: [ 42 / 14352 ] simplifiying candidate # 20.355 * * * * [progress]: [ 43 / 14352 ] simplifiying candidate # 20.355 * * * * [progress]: [ 44 / 14352 ] simplifiying candidate # 20.355 * * * * [progress]: [ 45 / 14352 ] simplifiying candidate # 20.355 * * * * [progress]: [ 46 / 14352 ] simplifiying candidate # 20.355 * * * * [progress]: [ 47 / 14352 ] simplifiying candidate # 20.356 * * * * [progress]: [ 48 / 14352 ] simplifiying candidate # 20.356 * * * * [progress]: [ 49 / 14352 ] simplifiying candidate # 20.356 * * * * [progress]: [ 50 / 14352 ] simplifiying candidate # 20.356 * * * * [progress]: [ 51 / 14352 ] simplifiying candidate # 20.356 * * * * [progress]: [ 52 / 14352 ] simplifiying candidate # 20.356 * * * * [progress]: [ 53 / 14352 ] simplifiying candidate # 20.356 * * * * [progress]: [ 54 / 14352 ] simplifiying candidate # 20.356 * * * * [progress]: [ 55 / 14352 ] simplifiying candidate # 20.356 * * * * [progress]: [ 56 / 14352 ] simplifiying candidate # 20.357 * * * * [progress]: [ 57 / 14352 ] simplifiying candidate # 20.357 * * * * [progress]: [ 58 / 14352 ] simplifiying candidate # 20.357 * * * * [progress]: [ 59 / 14352 ] simplifiying candidate # 20.357 * * * * [progress]: [ 60 / 14352 ] simplifiying candidate # 20.357 * * * * [progress]: [ 61 / 14352 ] simplifiying candidate # 20.357 * * * * [progress]: [ 62 / 14352 ] simplifiying candidate # 20.357 * * * * [progress]: [ 63 / 14352 ] simplifiying candidate # 20.357 * * * * [progress]: [ 64 / 14352 ] simplifiying candidate # 20.357 * * * * [progress]: [ 65 / 14352 ] simplifiying candidate #real (real->posit16 (pow (* n 2) (- 1/2 (/ k 2))))) (/ (sqrt k) (pow PI (- 1/2 (/ k 2))))))> 20.357 * * * * [progress]: [ 66 / 14352 ] simplifiying candidate # 20.358 * * * * [progress]: [ 67 / 14352 ] simplifiying candidate # 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candidate # 20.364 * * * * [progress]: [ 127 / 14352 ] simplifiying candidate # 20.365 * * * * [progress]: [ 128 / 14352 ] simplifiying candidate # 20.365 * * * * [progress]: [ 129 / 14352 ] simplifiying candidate # 20.365 * * * * [progress]: [ 130 / 14352 ] simplifiying candidate #real (real->posit16 (pow PI (- 1/2 (/ k 2))))))))> 20.365 * * * * [progress]: [ 131 / 14352 ] simplifiying candidate # 20.365 * * * * [progress]: [ 132 / 14352 ] simplifiying candidate # 20.365 * * * * [progress]: [ 133 / 14352 ] simplifiying candidate # 20.365 * * * * [progress]: [ 134 / 14352 ] simplifiying candidate # 20.365 * * * * [progress]: [ 135 / 14352 ] simplifiying candidate # 20.365 * * * * [progress]: [ 136 / 14352 ] simplifiying candidate # 20.365 * * * * [progress]: [ 137 / 14352 ] simplifiying candidate # 20.366 * * * * [progress]: [ 138 / 14352 ] simplifiying candidate # 20.366 * * * * [progress]: [ 139 / 14352 ] simplifiying candidate # 20.366 * * * * [progress]: [ 140 / 14352 ] 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simplifiying candidate # 21.970 * * * * [progress]: [ 14298 / 14352 ] simplifiying candidate # 21.970 * * * * [progress]: [ 14299 / 14352 ] simplifiying candidate # 21.970 * * * * [progress]: [ 14300 / 14352 ] simplifiying candidate # 21.971 * * * * [progress]: [ 14301 / 14352 ] simplifiying candidate # 21.971 * * * * [progress]: [ 14302 / 14352 ] simplifiying candidate # 21.971 * * * * [progress]: [ 14303 / 14352 ] simplifiying candidate # 21.971 * * * * [progress]: [ 14304 / 14352 ] simplifiying candidate # 21.971 * * * * [progress]: [ 14305 / 14352 ] simplifiying candidate # 21.971 * * * * [progress]: [ 14306 / 14352 ] simplifiying candidate # 21.971 * * * * [progress]: [ 14307 / 14352 ] simplifiying candidate # 21.971 * * * * [progress]: [ 14308 / 14352 ] simplifiying candidate # 21.971 * * * * [progress]: [ 14309 / 14352 ] simplifiying candidate # 21.972 * * * * [progress]: [ 14310 / 14352 ] simplifiying candidate # 21.972 * * * * [progress]: [ 14311 / 14352 ] simplifiying 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* * * [progress]: [ 14326 / 14352 ] simplifiying candidate # 21.973 * * * * [progress]: [ 14327 / 14352 ] simplifiying candidate # 21.974 * * * * [progress]: [ 14328 / 14352 ] simplifiying candidate # 21.974 * * * * [progress]: [ 14329 / 14352 ] simplifiying candidate # 21.974 * * * * [progress]: [ 14330 / 14352 ] simplifiying candidate # 21.976 * * * * [progress]: [ 14331 / 14352 ] simplifiying candidate # 21.976 * * * * [progress]: [ 14332 / 14352 ] simplifiying candidate # 21.976 * * * * [progress]: [ 14333 / 14352 ] simplifiying candidate # 21.976 * * * * [progress]: [ 14334 / 14352 ] simplifiying candidate # 21.976 * * * * [progress]: [ 14335 / 14352 ] simplifiying candidate # 21.976 * * * * [progress]: [ 14336 / 14352 ] simplifiying candidate # 21.976 * * * * [progress]: [ 14337 / 14352 ] simplifiying candidate # 21.977 * * * * [progress]: [ 14338 / 14352 ] simplifiying candidate # 21.977 * * * * [progress]: [ 14339 / 14352 ] simplifiying candidate # 21.977 * * * * [progress]: [ 14340 / 14352 ] simplifiying candidate #real (real->posit16 (/ (sqrt k) (pow PI (- 1/2 (/ k 2))))))))> 21.977 * * * * [progress]: [ 14341 / 14352 ] simplifiying candidate # 21.977 * * * * [progress]: [ 14342 / 14352 ] simplifiying candidate # 21.977 * * * * [progress]: [ 14343 / 14352 ] simplifiying candidate # 21.977 * * * * [progress]: [ 14344 / 14352 ] simplifiying candidate # 21.977 * * * * [progress]: [ 14345 / 14352 ] simplifiying candidate # 21.977 * * * * [progress]: [ 14346 / 14352 ] simplifiying candidate # 21.978 * * * * [progress]: [ 14347 / 14352 ] simplifiying candidate # 21.978 * * * * [progress]: [ 14348 / 14352 ] simplifiying candidate # 21.978 * * * * [progress]: [ 14349 / 14352 ] simplifiying candidate # 21.978 * * * * [progress]: [ 14350 / 14352 ] simplifiying candidate # 21.978 * * * * [progress]: [ 14351 / 14352 ] simplifiying candidate # 21.978 * * * * [progress]: [ 14352 / 14352 ] simplifiying candidate # 22.749 * [simplify]: Simplifying: (expm1 (pow (* n 2) (- 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(- (+ (* +nan.0 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) k)) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log PI) (* (log n) (pow k 2)))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow k 2)) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (pow (log PI) 2) (pow k 2))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) (pow k 2))) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) (pow k 2)))) (sqrt PI))) (- (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) k)) (sqrt PI)))))))))))))))))))))))))))))))) (- (+ (* +nan.0 (/ (* (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))) (pow k 2))) (- (+ (* +nan.0 (/ (* (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))) k)) (- (* +nan.0 (/ (* (pow PI (- 1/2 (* 1/2 k))) (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k))))) (pow k 3)))))))) (- (+ (* +nan.0 (* (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (pow PI (- 1/2 (* 1/2 k))))) (- (+ (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (pow PI (- 1/2 (* 1/2 k)))) k)) (- (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (pow PI (- 1/2 (* 1/2 k)))) (pow k 2)))))))) (- (+ (* +nan.0 (* (sqrt (/ 1 PI)) (pow k 3))) (- (+ (* +nan.0 (* (* (log PI) (pow k 3)) (sqrt (/ 1 PI)))) (- (+ (* +nan.0 (* (* (pow (log PI) 2) (pow k 3)) (sqrt (/ 1 PI)))) (- (+ (* +nan.0 (* (sqrt (/ 1 PI)) k)) (- (+ (* +nan.0 (* (* (log PI) (pow k 2)) (sqrt (/ 1 PI)))) (- (* +nan.0 (* (sqrt (/ 1 PI)) (pow k 2)))))))))))))) (- (+ (* +nan.0 (/ 1 (pow PI (- 1/2 (* 1/2 k))))) (- (+ (* +nan.0 (/ 1 (* (pow PI (- 1/2 (* 1/2 k))) k))) (- (* +nan.0 (/ 1 (* (pow PI (- 1/2 (* 1/2 k))) (pow k 2))))))))) (- (+ (* +nan.0 (/ 1 (pow PI (- 1/2 (* 1/2 k))))) (- (+ (* +nan.0 (/ 1 (* (pow PI (- 1/2 (* 1/2 k))) k))) (- (* +nan.0 (/ 1 (* (pow PI (- 1/2 (* 1/2 k))) (pow k 2))))))))) 23.990 * * [simplify]: iteration 0: 13534 enodes 28.557 * * [simplify]: iteration complete: 13534 enodes 28.579 * * [simplify]: Extracting #0: cost 13202 inf + 0 28.616 * * [simplify]: Extracting #1: cost 13300 inf + 0 28.673 * * [simplify]: Extracting #2: cost 13359 inf + 1526 28.714 * * [simplify]: Extracting #3: cost 13312 inf + 24588 28.780 * * [simplify]: Extracting #4: cost 12851 inf + 348234 28.968 * * [simplify]: Extracting #5: cost 11474 inf + 1577773 29.451 * * [simplify]: Extracting #6: cost 9222 inf + 3945113 30.231 * * [simplify]: Extracting #7: cost 5653 inf + 8035141 31.690 * * [simplify]: Extracting #8: cost 2447 inf + 11886634 33.334 * * [simplify]: Extracting #9: cost 530 inf + 14263804 35.044 * * [simplify]: Extracting #10: cost 66 inf + 14852162 36.772 * * [simplify]: Extracting #11: cost 31 inf + 14901342 39.204 * * [simplify]: Extracting #12: cost 34 inf + 14903606 40.986 * * [simplify]: Extracting #13: cost 33 inf + 14905664 42.858 * * [simplify]: Extracting #14: cost 33 inf + 14907178 44.588 * * [simplify]: Extracting #15: cost 30 inf + 14909973 46.388 * * [simplify]: Extracting #16: cost 27 inf + 14913550 48.003 * * [simplify]: Extracting #17: cost 27 inf + 14915131 49.612 * * [simplify]: Extracting #18: cost 28 inf + 14917402 51.180 * * [simplify]: Extracting #19: cost 27 inf + 14921078 52.882 * * [simplify]: Extracting #20: cost 26 inf + 14923864 54.774 * * [simplify]: Extracting #21: cost 25 inf + 14926852 56.686 * * [simplify]: Extracting #22: cost 27 inf + 14928678 58.531 * * [simplify]: Extracting #23: cost 30 inf + 14928678 60.217 * * [simplify]: Extracting #24: cost 28 inf + 14931098 61.947 * * [simplify]: Extracting #25: cost 29 inf + 14931873 63.730 * * [simplify]: Extracting #26: cost 31 inf + 14932689 65.388 * * [simplify]: Extracting #27: cost 32 inf + 14933554 67.204 * * [simplify]: Extracting #28: cost 31 inf + 14935870 69.062 * * [simplify]: Extracting #29: cost 32 inf + 14936856 71.043 * * [simplify]: Extracting #30: cost 32 inf + 14937561 72.839 * * [simplify]: Extracting #31: cost 29 inf + 14939258 74.694 * * [simplify]: Extracting #32: cost 25 inf + 14942952 76.496 * * [simplify]: Extracting #33: cost 22 inf + 14947510 78.344 * * [simplify]: Extracting #34: cost 19 inf + 14953388 80.191 * * [simplify]: Extracting #35: cost 17 inf + 14957880 82.092 * * [simplify]: Extracting #36: cost 14 inf + 14965398 83.923 * * [simplify]: Extracting #37: cost 11 inf + 14974036 85.779 * * [simplify]: Extracting #38: cost 8 inf + 14983594 87.349 * * [simplify]: Extracting #39: cost 7 inf + 14986980 88.953 * * [simplify]: Extracting #40: cost 3 inf + 15001994 90.540 * * [simplify]: Extracting #41: cost 0 inf + 15014842 92.635 * [simplify]: Simplified to: (expm1 (pow (* n 2) (- 1/2 (/ k 2)))) (log1p (pow (* n 2) (- 1/2 (/ k 2)))) (* (+ (log n) (log 2)) (- 1/2 (/ k 2))) (* (log (* n 2)) (- 1/2 (/ k 2))) (* (log (* n 2)) (- 1/2 (/ k 2))) (* 1 (- 1/2 (/ k 2))) (* 1 (- 1/2 (/ k 2))) (pow (* 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(- 1/2 (/ k 2))) (sqrt (cbrt k))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) (/ (sqrt k) (pow PI 1/2)) (real->posit16 (/ (sqrt k) (pow PI (- 1/2 (/ k 2))))) (- (+ (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (* (pow (log 2) 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (pow k 2)))) (+ (* 1/4 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) (pow k 2))))) (* 1/8 (* (exp (* 1/2 (+ (log 2) (log n)))) (* (pow (log n) 2) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) k))) (* 1/2 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) k))))) (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (- (+ (pow PI 1/2) (* 1/8 (* (* (pow (log PI) 2) (pow k 2)) (sqrt PI)))) (* 1/2 (* (* (log PI) k) (sqrt PI)))) (pow PI (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (pow (log n) 2) (pow k 2))) (sqrt PI))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (pow k 2))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) k) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log PI) (pow k 2)))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log PI) k)) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log PI) (pow k 2))) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (pow k 2))) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) k)) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log PI) (* (log n) (pow k 2)))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow k 2)) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (pow (log PI) 2) (pow k 2))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) (pow k 2))) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) (pow k 2)))) (sqrt PI))) (- (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) k)) (sqrt PI)))))))))))))))))))))))))))))))) (- (+ (* +nan.0 (/ (* (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))) (pow k 2))) (- (+ (* +nan.0 (/ (* (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))) k)) (- (* +nan.0 (/ (* (pow PI (- 1/2 (* 1/2 k))) (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k))))) (pow k 3)))))))) (- (+ (* +nan.0 (* (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (pow PI (- 1/2 (* 1/2 k))))) (- (+ (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (pow PI (- 1/2 (* 1/2 k)))) k)) (- (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (pow PI (- 1/2 (* 1/2 k)))) (pow k 2)))))))) (- (+ (* +nan.0 (* (sqrt (/ 1 PI)) (pow k 3))) (- (+ (* +nan.0 (* (* (log PI) (pow k 3)) (sqrt (/ 1 PI)))) (- (+ (* +nan.0 (* (* (pow (log PI) 2) (pow k 3)) (sqrt (/ 1 PI)))) (- (+ (* +nan.0 (* (sqrt (/ 1 PI)) k)) (- (+ (* +nan.0 (* (* (log PI) (pow k 2)) (sqrt (/ 1 PI)))) (- (* +nan.0 (* (sqrt (/ 1 PI)) (pow k 2)))))))))))))) (- (+ (* +nan.0 (/ 1 (pow PI (- 1/2 (* 1/2 k))))) (- (+ (* +nan.0 (/ 1 (* (pow PI (- 1/2 (* 1/2 k))) k))) (- (* +nan.0 (/ 1 (* (pow PI (- 1/2 (* 1/2 k))) (pow k 2))))))))) (- (+ (* +nan.0 (/ 1 (pow PI (- 1/2 (* 1/2 k))))) (- (+ (* +nan.0 (/ 1 (* (pow PI (- 1/2 (* 1/2 k))) k))) (- (* +nan.0 (/ 1 (* (pow PI (- 1/2 (* 1/2 k))) (pow k 2))))))))) 99.326 * * * [progress]: adding candidates to table 233.708 * * [progress]: iteration 4 / 4 233.709 * * * [progress]: picking best candidate 233.729 * * * * [pick]: Picked # 233.729 * * * [progress]: localizing error 233.771 * * * [progress]: generating rewritten candidates 233.771 * * * * [progress]: [ 1 / 4 ] rewriting at (2 1 2 2) 233.773 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1) 233.786 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 2) 233.795 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1) 234.118 * * * [progress]: generating series expansions 234.118 * * * * [progress]: [ 1 / 4 ] generating series at (2 1 2 2) 234.118 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1) 234.118 * [backup-simplify]: Simplify (pow n (- 1/2 (/ k 2))) into (pow n (- 1/2 (* 1/2 k))) 234.118 * [approximate]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in (n k) around 0 234.118 * [taylor]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in k 234.118 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in k 234.118 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in k 234.118 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 234.118 * [taylor]: Taking taylor expansion of 1/2 in k 234.118 * [backup-simplify]: Simplify 1/2 into 1/2 234.118 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 234.118 * [taylor]: Taking taylor expansion of 1/2 in k 234.118 * [backup-simplify]: Simplify 1/2 into 1/2 234.118 * [taylor]: Taking taylor expansion of k in k 234.118 * [backup-simplify]: Simplify 0 into 0 234.118 * [backup-simplify]: Simplify 1 into 1 234.118 * [taylor]: Taking taylor expansion of (log n) in k 234.118 * [taylor]: Taking taylor expansion of n in k 234.118 * [backup-simplify]: Simplify n into n 234.118 * [backup-simplify]: Simplify (log n) into (log n) 234.119 * [backup-simplify]: Simplify (* 1/2 0) into 0 234.119 * [backup-simplify]: Simplify (- 0) into 0 234.119 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 234.119 * [backup-simplify]: Simplify (* 1/2 (log n)) into (* 1/2 (log n)) 234.119 * [backup-simplify]: Simplify (exp (* 1/2 (log n))) into (pow n 1/2) 234.119 * [taylor]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in n 234.120 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in n 234.120 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in n 234.120 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 234.120 * [taylor]: Taking taylor expansion of 1/2 in n 234.120 * [backup-simplify]: Simplify 1/2 into 1/2 234.120 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 234.120 * [taylor]: Taking taylor expansion of 1/2 in n 234.120 * [backup-simplify]: Simplify 1/2 into 1/2 234.120 * [taylor]: Taking taylor expansion of k in n 234.120 * [backup-simplify]: Simplify k into k 234.120 * [taylor]: Taking taylor expansion of (log n) in n 234.120 * [taylor]: Taking taylor expansion of n in n 234.120 * [backup-simplify]: Simplify 0 into 0 234.120 * [backup-simplify]: Simplify 1 into 1 234.120 * [backup-simplify]: Simplify (log 1) into 0 234.120 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 234.120 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 234.120 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 234.120 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 234.121 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (log n)) into (* (- 1/2 (* 1/2 k)) (log n)) 234.121 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (log n))) into (pow n (- 1/2 (* 1/2 k))) 234.121 * [taylor]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in n 234.121 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in n 234.121 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in n 234.121 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 234.121 * [taylor]: Taking taylor expansion of 1/2 in n 234.121 * [backup-simplify]: Simplify 1/2 into 1/2 234.121 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 234.121 * [taylor]: Taking taylor expansion of 1/2 in n 234.121 * [backup-simplify]: Simplify 1/2 into 1/2 234.121 * [taylor]: Taking taylor expansion of k in n 234.121 * [backup-simplify]: Simplify k into k 234.121 * [taylor]: Taking taylor expansion of (log n) in n 234.121 * [taylor]: Taking taylor expansion of n in n 234.121 * [backup-simplify]: Simplify 0 into 0 234.121 * [backup-simplify]: Simplify 1 into 1 234.121 * [backup-simplify]: Simplify (log 1) into 0 234.121 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 234.121 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 234.121 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 234.122 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 234.122 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (log n)) into (* (- 1/2 (* 1/2 k)) (log n)) 234.122 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (log n))) into (pow n (- 1/2 (* 1/2 k))) 234.122 * [taylor]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in k 234.122 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in k 234.122 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in k 234.122 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 234.122 * [taylor]: Taking taylor expansion of 1/2 in k 234.122 * [backup-simplify]: Simplify 1/2 into 1/2 234.122 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 234.122 * [taylor]: Taking taylor expansion of 1/2 in k 234.122 * [backup-simplify]: Simplify 1/2 into 1/2 234.122 * [taylor]: Taking taylor expansion of k in k 234.122 * [backup-simplify]: Simplify 0 into 0 234.122 * [backup-simplify]: Simplify 1 into 1 234.122 * [taylor]: Taking taylor expansion of (log n) in k 234.122 * [taylor]: Taking taylor expansion of n in k 234.122 * [backup-simplify]: Simplify n into n 234.122 * [backup-simplify]: Simplify (log n) into (log n) 234.122 * [backup-simplify]: Simplify (* 1/2 0) into 0 234.123 * [backup-simplify]: Simplify (- 0) into 0 234.123 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 234.123 * [backup-simplify]: Simplify (* 1/2 (log n)) into (* 1/2 (log n)) 234.123 * [backup-simplify]: Simplify (exp (* 1/2 (log n))) into (pow n 1/2) 234.123 * [backup-simplify]: Simplify (pow n 1/2) into (pow n 1/2) 234.124 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 234.124 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 234.124 * [backup-simplify]: Simplify (- 0) into 0 234.125 * [backup-simplify]: Simplify (+ 0 0) into 0 234.125 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 234.125 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (log n))) into 0 234.125 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 234.125 * [taylor]: Taking taylor expansion of 0 in k 234.125 * [backup-simplify]: Simplify 0 into 0 234.126 * [backup-simplify]: Simplify 0 into 0 234.126 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 234.126 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 234.127 * [backup-simplify]: Simplify (- 1/2) into -1/2 234.127 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 234.127 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log n))) into (- (* 1/2 (log n))) 234.127 * [backup-simplify]: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 1) 1)))) into (* -1/2 (* (sqrt n) (log n))) 234.128 * [backup-simplify]: Simplify (* -1/2 (* (sqrt n) (log n))) into (* -1/2 (* (sqrt n) (log n))) 234.129 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 234.130 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 234.130 * [backup-simplify]: Simplify (- 0) into 0 234.130 * [backup-simplify]: Simplify (+ 0 0) into 0 234.130 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 234.131 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (log n)))) into 0 234.131 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (log n))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 234.131 * [taylor]: Taking taylor expansion of 0 in k 234.131 * [backup-simplify]: Simplify 0 into 0 234.131 * [backup-simplify]: Simplify 0 into 0 234.132 * [backup-simplify]: Simplify 0 into 0 234.133 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 234.133 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 234.133 * [backup-simplify]: Simplify (- 0) into 0 234.134 * [backup-simplify]: Simplify (+ 0 0) into 0 234.134 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log n)))) into 0 234.135 * [backup-simplify]: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt n) (pow (log n) 2))) 234.135 * [backup-simplify]: Simplify (* 1/8 (* (sqrt n) (pow (log n) 2))) into (* 1/8 (* (sqrt n) (pow (log n) 2))) 234.135 * [backup-simplify]: Simplify (+ (* (* 1/8 (* (sqrt n) (pow (log n) 2))) (pow (* k 1) 2)) (+ (* (* -1/2 (* (sqrt n) (log n))) (* k 1)) (pow n 1/2))) into (- (+ (pow n 1/2) (* 1/8 (* (sqrt n) (* (pow (log n) 2) (pow k 2))))) (* 1/2 (* (sqrt n) (* (log n) k)))) 234.135 * [backup-simplify]: Simplify (pow (/ 1 n) (- 1/2 (/ (/ 1 k) 2))) into (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) 234.135 * [approximate]: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 234.136 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in k 234.136 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in k 234.136 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in k 234.136 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 234.136 * [taylor]: Taking taylor expansion of 1/2 in k 234.136 * [backup-simplify]: Simplify 1/2 into 1/2 234.136 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 234.136 * [taylor]: Taking taylor expansion of 1/2 in k 234.136 * [backup-simplify]: Simplify 1/2 into 1/2 234.136 * [taylor]: Taking taylor expansion of (/ 1 k) in k 234.136 * [taylor]: Taking taylor expansion of k in k 234.136 * [backup-simplify]: Simplify 0 into 0 234.136 * [backup-simplify]: Simplify 1 into 1 234.136 * [backup-simplify]: Simplify (/ 1 1) into 1 234.136 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in k 234.136 * [taylor]: Taking taylor expansion of (/ 1 n) in k 234.136 * [taylor]: Taking taylor expansion of n in k 234.136 * [backup-simplify]: Simplify n into n 234.136 * [backup-simplify]: Simplify (/ 1 n) into (/ 1 n) 234.136 * [backup-simplify]: Simplify (log (/ 1 n)) into (log (/ 1 n)) 234.136 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 234.137 * [backup-simplify]: Simplify (- 1/2) into -1/2 234.137 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 234.137 * [backup-simplify]: Simplify (* -1/2 (log (/ 1 n))) into (* -1/2 (log (/ 1 n))) 234.137 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) into (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) 234.137 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 234.137 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in n 234.137 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in n 234.137 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 234.137 * [taylor]: Taking taylor expansion of 1/2 in n 234.137 * [backup-simplify]: Simplify 1/2 into 1/2 234.137 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 234.137 * [taylor]: Taking taylor expansion of 1/2 in n 234.137 * [backup-simplify]: Simplify 1/2 into 1/2 234.137 * [taylor]: Taking taylor expansion of (/ 1 k) in n 234.137 * [taylor]: Taking taylor expansion of k in n 234.137 * [backup-simplify]: Simplify k into k 234.137 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 234.137 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 234.137 * [taylor]: Taking taylor expansion of (/ 1 n) in n 234.137 * [taylor]: Taking taylor expansion of n in n 234.137 * [backup-simplify]: Simplify 0 into 0 234.137 * [backup-simplify]: Simplify 1 into 1 234.138 * [backup-simplify]: Simplify (/ 1 1) into 1 234.138 * [backup-simplify]: Simplify (log 1) into 0 234.138 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 234.138 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 234.138 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 234.138 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 234.139 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log n))) into (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))) 234.139 * [backup-simplify]: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 234.139 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 234.139 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in n 234.139 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in n 234.139 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 234.139 * [taylor]: Taking taylor expansion of 1/2 in n 234.139 * [backup-simplify]: Simplify 1/2 into 1/2 234.139 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 234.139 * [taylor]: Taking taylor expansion of 1/2 in n 234.139 * [backup-simplify]: Simplify 1/2 into 1/2 234.139 * [taylor]: Taking taylor expansion of (/ 1 k) in n 234.139 * [taylor]: Taking taylor expansion of k in n 234.139 * [backup-simplify]: Simplify k into k 234.139 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 234.139 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 234.139 * [taylor]: Taking taylor expansion of (/ 1 n) in n 234.139 * [taylor]: Taking taylor expansion of n in n 234.139 * [backup-simplify]: Simplify 0 into 0 234.139 * [backup-simplify]: Simplify 1 into 1 234.139 * [backup-simplify]: Simplify (/ 1 1) into 1 234.139 * [backup-simplify]: Simplify (log 1) into 0 234.139 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 234.139 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 234.140 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 234.140 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 234.140 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log n))) into (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))) 234.140 * [backup-simplify]: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 234.140 * [taylor]: Taking taylor expansion of (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) in k 234.140 * [taylor]: Taking taylor expansion of (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))) in k 234.140 * [taylor]: Taking taylor expansion of -1 in k 234.140 * [backup-simplify]: Simplify -1 into -1 234.140 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log n)) in k 234.140 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 234.140 * [taylor]: Taking taylor expansion of 1/2 in k 234.140 * [backup-simplify]: Simplify 1/2 into 1/2 234.140 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 234.140 * [taylor]: Taking taylor expansion of 1/2 in k 234.140 * [backup-simplify]: Simplify 1/2 into 1/2 234.140 * [taylor]: Taking taylor expansion of (/ 1 k) in k 234.140 * [taylor]: Taking taylor expansion of k in k 234.140 * [backup-simplify]: Simplify 0 into 0 234.140 * [backup-simplify]: Simplify 1 into 1 234.141 * [backup-simplify]: Simplify (/ 1 1) into 1 234.141 * [taylor]: Taking taylor expansion of (log n) in k 234.141 * [taylor]: Taking taylor expansion of n in k 234.141 * [backup-simplify]: Simplify n into n 234.141 * [backup-simplify]: Simplify (log n) into (log n) 234.141 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 234.141 * [backup-simplify]: Simplify (- 1/2) into -1/2 234.141 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 234.141 * [backup-simplify]: Simplify (* -1/2 (log n)) into (* -1/2 (log n)) 234.142 * [backup-simplify]: Simplify (* -1 (* -1/2 (log n))) into (* 1/2 (log n)) 234.142 * [backup-simplify]: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 234.142 * [backup-simplify]: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 234.142 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 234.143 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 234.143 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 234.143 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 234.144 * [backup-simplify]: Simplify (- 0) into 0 234.144 * [backup-simplify]: Simplify (+ 0 0) into 0 234.144 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 234.144 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log n)))) into 0 234.145 * [backup-simplify]: Simplify (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 234.145 * [taylor]: Taking taylor expansion of 0 in k 234.145 * [backup-simplify]: Simplify 0 into 0 234.145 * [backup-simplify]: Simplify 0 into 0 234.145 * [backup-simplify]: Simplify 0 into 0 234.145 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 234.147 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 234.147 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 234.148 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 234.148 * [backup-simplify]: Simplify (- 0) into 0 234.148 * [backup-simplify]: Simplify (+ 0 0) into 0 234.149 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 234.149 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log n))))) into 0 234.150 * [backup-simplify]: Simplify (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 234.150 * [taylor]: Taking taylor expansion of 0 in k 234.150 * [backup-simplify]: Simplify 0 into 0 234.150 * [backup-simplify]: Simplify 0 into 0 234.150 * [backup-simplify]: Simplify 0 into 0 234.150 * [backup-simplify]: Simplify 0 into 0 234.150 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 234.153 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 234.153 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 234.154 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 234.154 * [backup-simplify]: Simplify (- 0) into 0 234.155 * [backup-simplify]: Simplify (+ 0 0) into 0 234.155 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 234.155 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0 234.156 * [backup-simplify]: Simplify (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 234.156 * [taylor]: Taking taylor expansion of 0 in k 234.156 * [backup-simplify]: Simplify 0 into 0 234.156 * [backup-simplify]: Simplify 0 into 0 234.157 * [backup-simplify]: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (log (/ 1 n))))) into (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) 234.157 * [backup-simplify]: Simplify (pow (/ 1 (- n)) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) 234.157 * [approximate]: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 234.157 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in k 234.157 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in k 234.157 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in k 234.157 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 234.157 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 234.157 * [taylor]: Taking taylor expansion of 1/2 in k 234.157 * [backup-simplify]: Simplify 1/2 into 1/2 234.157 * [taylor]: Taking taylor expansion of (/ 1 k) in k 234.157 * [taylor]: Taking taylor expansion of k in k 234.157 * [backup-simplify]: Simplify 0 into 0 234.157 * [backup-simplify]: Simplify 1 into 1 234.157 * [backup-simplify]: Simplify (/ 1 1) into 1 234.157 * [taylor]: Taking taylor expansion of 1/2 in k 234.157 * [backup-simplify]: Simplify 1/2 into 1/2 234.157 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in k 234.157 * [taylor]: Taking taylor expansion of (/ -1 n) in k 234.157 * [taylor]: Taking taylor expansion of -1 in k 234.157 * [backup-simplify]: Simplify -1 into -1 234.157 * [taylor]: Taking taylor expansion of n in k 234.157 * [backup-simplify]: Simplify n into n 234.157 * [backup-simplify]: Simplify (/ -1 n) into (/ -1 n) 234.157 * [backup-simplify]: Simplify (log (/ -1 n)) into (log (/ -1 n)) 234.158 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 234.158 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 234.158 * [backup-simplify]: Simplify (* 1/2 (log (/ -1 n))) into (* 1/2 (log (/ -1 n))) 234.158 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) into (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) 234.158 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 234.158 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in n 234.158 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in n 234.158 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 234.158 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 234.158 * [taylor]: Taking taylor expansion of 1/2 in n 234.158 * [backup-simplify]: Simplify 1/2 into 1/2 234.158 * [taylor]: Taking taylor expansion of (/ 1 k) in n 234.158 * [taylor]: Taking taylor expansion of k in n 234.158 * [backup-simplify]: Simplify k into k 234.158 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 234.158 * [taylor]: Taking taylor expansion of 1/2 in n 234.158 * [backup-simplify]: Simplify 1/2 into 1/2 234.158 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n 234.158 * [taylor]: Taking taylor expansion of (/ -1 n) in n 234.158 * [taylor]: Taking taylor expansion of -1 in n 234.158 * [backup-simplify]: Simplify -1 into -1 234.158 * [taylor]: Taking taylor expansion of n in n 234.158 * [backup-simplify]: Simplify 0 into 0 234.158 * [backup-simplify]: Simplify 1 into 1 234.159 * [backup-simplify]: Simplify (/ -1 1) into -1 234.159 * [backup-simplify]: Simplify (log -1) into (log -1) 234.159 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 234.159 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 234.160 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 234.160 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) 234.160 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 234.160 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 234.160 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in n 234.160 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in n 234.160 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 234.160 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 234.160 * [taylor]: Taking taylor expansion of 1/2 in n 234.160 * [backup-simplify]: Simplify 1/2 into 1/2 234.160 * [taylor]: Taking taylor expansion of (/ 1 k) in n 234.160 * [taylor]: Taking taylor expansion of k in n 234.160 * [backup-simplify]: Simplify k into k 234.160 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 234.160 * [taylor]: Taking taylor expansion of 1/2 in n 234.160 * [backup-simplify]: Simplify 1/2 into 1/2 234.160 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n 234.160 * [taylor]: Taking taylor expansion of (/ -1 n) in n 234.160 * [taylor]: Taking taylor expansion of -1 in n 234.160 * [backup-simplify]: Simplify -1 into -1 234.160 * [taylor]: Taking taylor expansion of n in n 234.161 * [backup-simplify]: Simplify 0 into 0 234.161 * [backup-simplify]: Simplify 1 into 1 234.161 * [backup-simplify]: Simplify (/ -1 1) into -1 234.161 * [backup-simplify]: Simplify (log -1) into (log -1) 234.161 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 234.161 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 234.162 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 234.162 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) 234.162 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 234.162 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) in k 234.162 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) in k 234.162 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 234.162 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 234.162 * [taylor]: Taking taylor expansion of 1/2 in k 234.162 * [backup-simplify]: Simplify 1/2 into 1/2 234.163 * [taylor]: Taking taylor expansion of (/ 1 k) in k 234.163 * [taylor]: Taking taylor expansion of k in k 234.163 * [backup-simplify]: Simplify 0 into 0 234.163 * [backup-simplify]: Simplify 1 into 1 234.163 * [backup-simplify]: Simplify (/ 1 1) into 1 234.163 * [taylor]: Taking taylor expansion of 1/2 in k 234.163 * [backup-simplify]: Simplify 1/2 into 1/2 234.163 * [taylor]: Taking taylor expansion of (- (log -1) (log n)) in k 234.163 * [taylor]: Taking taylor expansion of (log -1) in k 234.163 * [taylor]: Taking taylor expansion of -1 in k 234.163 * [backup-simplify]: Simplify -1 into -1 234.163 * [backup-simplify]: Simplify (log -1) into (log -1) 234.163 * [taylor]: Taking taylor expansion of (log n) in k 234.163 * [taylor]: Taking taylor expansion of n in k 234.163 * [backup-simplify]: Simplify n into n 234.163 * [backup-simplify]: Simplify (log n) into (log n) 234.164 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 234.164 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 234.164 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 234.164 * [backup-simplify]: Simplify (+ (log -1) (- (log n))) into (- (log -1) (log n)) 234.164 * [backup-simplify]: Simplify (* 1/2 (- (log -1) (log n))) into (* 1/2 (- (log -1) (log n))) 234.165 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 234.165 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 234.166 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 234.166 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -1 1)))) 1) into 0 234.166 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 234.167 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 234.167 * [backup-simplify]: Simplify (+ 0 0) into 0 234.167 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 234.168 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log -1) (log n)))) into 0 234.169 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 234.169 * [taylor]: Taking taylor expansion of 0 in k 234.169 * [backup-simplify]: Simplify 0 into 0 234.169 * [backup-simplify]: Simplify 0 into 0 234.169 * [backup-simplify]: Simplify 0 into 0 234.169 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 234.171 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -1 1)))) 2) into 0 234.171 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 234.172 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 234.172 * [backup-simplify]: Simplify (+ 0 0) into 0 234.172 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 234.173 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log -1) (log n))))) into 0 234.174 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 234.174 * [taylor]: Taking taylor expansion of 0 in k 234.174 * [backup-simplify]: Simplify 0 into 0 234.174 * [backup-simplify]: Simplify 0 into 0 234.174 * [backup-simplify]: Simplify 0 into 0 234.174 * [backup-simplify]: Simplify 0 into 0 234.175 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 234.177 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow -1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow -1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow -1 1)))) 6) into 0 234.178 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 234.178 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 234.179 * [backup-simplify]: Simplify (+ 0 0) into 0 234.179 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 234.180 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log -1) (log n)))))) into 0 234.181 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 234.181 * [taylor]: Taking taylor expansion of 0 in k 234.181 * [backup-simplify]: Simplify 0 into 0 234.181 * [backup-simplify]: Simplify 0 into 0 234.182 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -1) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) 234.182 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 2) 234.182 * [backup-simplify]: Simplify (/ (sqrt k) (pow PI 1/2)) into (sqrt (/ k PI)) 234.182 * [approximate]: Taking taylor expansion of (sqrt (/ k PI)) in (k) around 0 234.182 * [taylor]: Taking taylor expansion of (sqrt (/ k PI)) in k 234.182 * [taylor]: Taking taylor expansion of (/ k PI) in k 234.182 * [taylor]: Taking taylor expansion of k in k 234.182 * [backup-simplify]: Simplify 0 into 0 234.182 * [backup-simplify]: Simplify 1 into 1 234.182 * [taylor]: Taking taylor expansion of PI in k 234.182 * [backup-simplify]: Simplify PI into PI 234.183 * [backup-simplify]: Simplify (/ 1 PI) into (/ 1 PI) 234.183 * [backup-simplify]: Simplify (sqrt 0) into 0 234.184 * [backup-simplify]: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI) 234.184 * [taylor]: Taking taylor expansion of (sqrt (/ k PI)) in k 234.184 * [taylor]: Taking taylor expansion of (/ k PI) in k 234.184 * [taylor]: Taking taylor expansion of k in k 234.184 * [backup-simplify]: Simplify 0 into 0 234.184 * [backup-simplify]: Simplify 1 into 1 234.184 * [taylor]: Taking taylor expansion of PI in k 234.184 * [backup-simplify]: Simplify PI into PI 234.185 * [backup-simplify]: Simplify (/ 1 PI) into (/ 1 PI) 234.185 * [backup-simplify]: Simplify (sqrt 0) into 0 234.186 * [backup-simplify]: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI) 234.186 * [backup-simplify]: Simplify 0 into 0 234.186 * [backup-simplify]: Simplify (/ +nan.0 PI) into (/ +nan.0 PI) 234.187 * [backup-simplify]: Simplify (- (/ 0 PI) (+ (* (/ 1 PI) (/ 0 PI)))) into 0 234.190 * [backup-simplify]: Simplify (/ (- 0 (pow (/ +nan.0 PI) 2) (+)) (* 2 0)) into (/ +nan.0 (pow PI 2)) 234.190 * [backup-simplify]: Simplify (/ +nan.0 (pow PI 2)) into (/ +nan.0 (pow PI 2)) 234.191 * [backup-simplify]: Simplify (- (/ 0 PI) (+ (* (/ 1 PI) (/ 0 PI)) (* 0 (/ 0 PI)))) into 0 234.196 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* (/ +nan.0 PI) (/ +nan.0 (pow PI 2)))))) (* 2 0)) into (/ +nan.0 (pow PI 3)) 234.197 * [backup-simplify]: Simplify (/ +nan.0 (pow PI 3)) into (/ +nan.0 (pow PI 3)) 234.199 * [backup-simplify]: Simplify (+ (* (/ +nan.0 (pow PI 3)) (pow k 3)) (+ (* (/ +nan.0 (pow PI 2)) (pow k 2)) (* (/ +nan.0 PI) k))) into (- (+ (* +nan.0 (/ k PI)) (- (+ (* +nan.0 (/ (pow k 2) (pow PI 2))) (- (* +nan.0 (/ (pow k 3) (pow PI 3)))))))) 234.199 * [backup-simplify]: Simplify (/ (sqrt (/ 1 k)) (pow PI 1/2)) into (sqrt (/ 1 (* PI k))) 234.199 * [approximate]: Taking taylor expansion of (sqrt (/ 1 (* PI k))) in (k) around 0 234.199 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (* PI k))) in k 234.199 * [taylor]: Taking taylor expansion of (/ 1 (* PI k)) in k 234.199 * [taylor]: Taking taylor expansion of (* PI k) in k 234.199 * [taylor]: Taking taylor expansion of PI in k 234.199 * [backup-simplify]: Simplify PI into PI 234.199 * [taylor]: Taking taylor expansion of k in k 234.199 * [backup-simplify]: Simplify 0 into 0 234.200 * [backup-simplify]: Simplify 1 into 1 234.200 * [backup-simplify]: Simplify (* PI 0) into 0 234.201 * [backup-simplify]: Simplify (+ (* PI 1) (* 0 0)) into PI 234.201 * [backup-simplify]: Simplify (/ 1 PI) into (/ 1 PI) 234.201 * [backup-simplify]: Simplify (sqrt 0) into 0 234.203 * [backup-simplify]: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI) 234.203 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (* PI k))) in k 234.203 * [taylor]: Taking taylor expansion of (/ 1 (* PI k)) in k 234.203 * [taylor]: Taking taylor expansion of (* PI k) in k 234.203 * [taylor]: Taking taylor expansion of PI in k 234.203 * [backup-simplify]: Simplify PI into PI 234.203 * [taylor]: Taking taylor expansion of k in k 234.203 * [backup-simplify]: Simplify 0 into 0 234.203 * [backup-simplify]: Simplify 1 into 1 234.203 * [backup-simplify]: Simplify (* PI 0) into 0 234.204 * [backup-simplify]: Simplify (+ (* PI 1) (* 0 0)) into PI 234.211 * [backup-simplify]: Simplify (/ 1 PI) into (/ 1 PI) 234.212 * [backup-simplify]: Simplify (sqrt 0) into 0 234.213 * [backup-simplify]: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI) 234.213 * [backup-simplify]: Simplify 0 into 0 234.213 * [backup-simplify]: Simplify (/ +nan.0 PI) into (/ +nan.0 PI) 234.214 * [backup-simplify]: Simplify (+ (* PI 0) (+ (* 0 1) (* 0 0))) into 0 234.214 * [backup-simplify]: Simplify (- (+ (* (/ 1 PI) (/ 0 PI)))) into 0 234.217 * [backup-simplify]: Simplify (/ (- 0 (pow (/ +nan.0 PI) 2) (+)) (* 2 0)) into (/ +nan.0 (pow PI 2)) 234.218 * [backup-simplify]: Simplify (/ +nan.0 (pow PI 2)) into (/ +nan.0 (pow PI 2)) 234.218 * [backup-simplify]: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 234.219 * [backup-simplify]: Simplify (- (+ (* (/ 1 PI) (/ 0 PI)) (* 0 (/ 0 PI)))) into 0 234.224 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* (/ +nan.0 PI) (/ +nan.0 (pow PI 2)))))) (* 2 0)) into (/ +nan.0 (pow PI 3)) 234.225 * [backup-simplify]: Simplify (/ +nan.0 (pow PI 3)) into (/ +nan.0 (pow PI 3)) 234.227 * [backup-simplify]: Simplify (+ (* (/ +nan.0 (pow PI 3)) (pow (/ 1 k) 2)) (+ (* (/ +nan.0 (pow PI 2)) (/ 1 k)) (/ +nan.0 PI))) into (- (+ (* +nan.0 (/ 1 (* (pow PI 2) k))) (- (+ (* +nan.0 (/ 1 PI)) (- (* +nan.0 (/ 1 (* (pow PI 3) (pow k 2))))))))) 234.227 * [backup-simplify]: Simplify (/ (sqrt (/ 1 (- k))) (pow PI 1/2)) into (* (sqrt (/ -1 k)) (sqrt (/ 1 PI))) 234.228 * [approximate]: Taking taylor expansion of (* (sqrt (/ -1 k)) (sqrt (/ 1 PI))) in (k) around 0 234.228 * [taylor]: Taking taylor expansion of (* (sqrt (/ -1 k)) (sqrt (/ 1 PI))) in k 234.228 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 234.228 * [taylor]: Taking taylor expansion of (/ -1 k) in k 234.228 * [taylor]: Taking taylor expansion of -1 in k 234.228 * [backup-simplify]: Simplify -1 into -1 234.228 * [taylor]: Taking taylor expansion of k in k 234.228 * [backup-simplify]: Simplify 0 into 0 234.228 * [backup-simplify]: Simplify 1 into 1 234.228 * [backup-simplify]: Simplify (/ -1 1) into -1 234.228 * [backup-simplify]: Simplify (sqrt 0) into 0 234.229 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 234.229 * [taylor]: Taking taylor expansion of (sqrt (/ 1 PI)) in k 234.229 * [taylor]: Taking taylor expansion of (/ 1 PI) in k 234.229 * [taylor]: Taking taylor expansion of PI in k 234.229 * [backup-simplify]: Simplify PI into PI 234.229 * [backup-simplify]: Simplify (/ 1 PI) into (/ 1 PI) 234.230 * [backup-simplify]: Simplify (sqrt (/ 1 PI)) into (sqrt (/ 1 PI)) 234.231 * [backup-simplify]: Simplify (- (+ (* (/ 1 PI) (/ 0 PI)))) into 0 234.231 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 PI)))) into 0 234.231 * [taylor]: Taking taylor expansion of (* (sqrt (/ -1 k)) (sqrt (/ 1 PI))) in k 234.231 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 234.231 * [taylor]: Taking taylor expansion of (/ -1 k) in k 234.231 * [taylor]: Taking taylor expansion of -1 in k 234.231 * [backup-simplify]: Simplify -1 into -1 234.231 * [taylor]: Taking taylor expansion of k in k 234.231 * [backup-simplify]: Simplify 0 into 0 234.231 * [backup-simplify]: Simplify 1 into 1 234.232 * [backup-simplify]: Simplify (/ -1 1) into -1 234.232 * [backup-simplify]: Simplify (sqrt 0) into 0 234.233 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 234.233 * [taylor]: Taking taylor expansion of (sqrt (/ 1 PI)) in k 234.233 * [taylor]: Taking taylor expansion of (/ 1 PI) in k 234.233 * [taylor]: Taking taylor expansion of PI in k 234.233 * [backup-simplify]: Simplify PI into PI 234.233 * [backup-simplify]: Simplify (/ 1 PI) into (/ 1 PI) 234.234 * [backup-simplify]: Simplify (sqrt (/ 1 PI)) into (sqrt (/ 1 PI)) 234.234 * [backup-simplify]: Simplify (- (+ (* (/ 1 PI) (/ 0 PI)))) into 0 234.235 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 PI)))) into 0 234.235 * [backup-simplify]: Simplify (* 0 (sqrt (/ 1 PI))) into 0 234.235 * [backup-simplify]: Simplify 0 into 0 234.237 * [backup-simplify]: Simplify (+ (* 0 0) (* +nan.0 (sqrt (/ 1 PI)))) into (- (* +nan.0 (sqrt (/ 1 PI)))) 234.239 * [backup-simplify]: Simplify (- (* +nan.0 (sqrt (/ 1 PI)))) into (- (* +nan.0 (sqrt (/ 1 PI)))) 234.240 * [backup-simplify]: Simplify (- (+ (* (/ 1 PI) (/ 0 PI)) (* 0 (/ 0 PI)))) into 0 234.241 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 PI)))) into 0 234.241 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 234.243 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 234.246 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (* +nan.0 (sqrt (/ 1 PI))))) into (- (* +nan.0 (sqrt (/ 1 PI)))) 234.247 * [backup-simplify]: Simplify (- (* +nan.0 (sqrt (/ 1 PI)))) into (- (* +nan.0 (sqrt (/ 1 PI)))) 234.248 * [backup-simplify]: Simplify (- (+ (* (/ 1 PI) (/ 0 PI)) (* 0 (/ 0 PI)) (* 0 (/ 0 PI)))) into 0 234.249 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 PI)))) into 0 234.250 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 234.252 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 234.256 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (+ (* +nan.0 0) (* +nan.0 (sqrt (/ 1 PI)))))) into (- (* +nan.0 (sqrt (/ 1 PI)))) 234.258 * [backup-simplify]: Simplify (- (* +nan.0 (sqrt (/ 1 PI)))) into (- (* +nan.0 (sqrt (/ 1 PI)))) 234.263 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (sqrt (/ 1 PI)))) (pow (/ 1 (- k)) 2)) (+ (* (- (* +nan.0 (sqrt (/ 1 PI)))) (/ 1 (- k))) (- (* +nan.0 (sqrt (/ 1 PI)))))) into (- (+ (* +nan.0 (* (sqrt (/ 1 PI)) (/ 1 k))) (- (+ (* +nan.0 (* (sqrt (/ 1 PI)) (/ 1 (pow k 2)))) (- (* +nan.0 (sqrt (/ 1 PI)))))))) 234.263 * * * * [progress]: [ 4 / 4 ] generating series at (2 1) 234.263 * [backup-simplify]: Simplify (/ (pow n (- 1/2 (/ k 2))) (/ (sqrt k) (pow PI 1/2))) into (* (pow n (- 1/2 (* 1/2 k))) (sqrt (/ PI k))) 234.263 * [approximate]: Taking taylor expansion of (* (pow n (- 1/2 (* 1/2 k))) (sqrt (/ PI k))) in (n k) around 0 234.264 * [taylor]: Taking taylor expansion of (* (pow n (- 1/2 (* 1/2 k))) (sqrt (/ PI k))) in k 234.264 * [taylor]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in k 234.264 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in k 234.264 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in k 234.264 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 234.264 * [taylor]: Taking taylor expansion of 1/2 in k 234.264 * [backup-simplify]: Simplify 1/2 into 1/2 234.264 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 234.264 * [taylor]: Taking taylor expansion of 1/2 in k 234.264 * [backup-simplify]: Simplify 1/2 into 1/2 234.264 * [taylor]: Taking taylor expansion of k in k 234.264 * [backup-simplify]: Simplify 0 into 0 234.264 * [backup-simplify]: Simplify 1 into 1 234.264 * [taylor]: Taking taylor expansion of (log n) in k 234.264 * [taylor]: Taking taylor expansion of n in k 234.264 * [backup-simplify]: Simplify n into n 234.264 * [backup-simplify]: Simplify (log n) into (log n) 234.264 * [backup-simplify]: Simplify (* 1/2 0) into 0 234.264 * [backup-simplify]: Simplify (- 0) into 0 234.265 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 234.265 * [backup-simplify]: Simplify (* 1/2 (log n)) into (* 1/2 (log n)) 234.265 * [backup-simplify]: Simplify (exp (* 1/2 (log n))) into (pow n 1/2) 234.265 * [taylor]: Taking taylor expansion of (sqrt (/ PI k)) in k 234.265 * [taylor]: Taking taylor expansion of (/ PI k) in k 234.265 * [taylor]: Taking taylor expansion of PI in k 234.265 * [backup-simplify]: Simplify PI into PI 234.265 * [taylor]: Taking taylor expansion of k in k 234.265 * [backup-simplify]: Simplify 0 into 0 234.265 * [backup-simplify]: Simplify 1 into 1 234.265 * [backup-simplify]: Simplify (/ PI 1) into PI 234.265 * [backup-simplify]: Simplify (sqrt 0) into 0 234.266 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 234.266 * [taylor]: Taking taylor expansion of (* (pow n (- 1/2 (* 1/2 k))) (sqrt (/ PI k))) in n 234.266 * [taylor]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in n 234.266 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in n 234.266 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in n 234.266 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 234.266 * [taylor]: Taking taylor expansion of 1/2 in n 234.266 * [backup-simplify]: Simplify 1/2 into 1/2 234.266 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 234.266 * [taylor]: Taking taylor expansion of 1/2 in n 234.266 * [backup-simplify]: Simplify 1/2 into 1/2 234.266 * [taylor]: Taking taylor expansion of k in n 234.266 * [backup-simplify]: Simplify k into k 234.266 * [taylor]: Taking taylor expansion of (log n) in n 234.267 * [taylor]: Taking taylor expansion of n in n 234.267 * [backup-simplify]: Simplify 0 into 0 234.267 * [backup-simplify]: Simplify 1 into 1 234.267 * [backup-simplify]: Simplify (log 1) into 0 234.267 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 234.267 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 234.267 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 234.267 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 234.267 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (log n)) into (* (- 1/2 (* 1/2 k)) (log n)) 234.267 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (log n))) into (pow n (- 1/2 (* 1/2 k))) 234.267 * [taylor]: Taking taylor expansion of (sqrt (/ PI k)) in n 234.267 * [taylor]: Taking taylor expansion of (/ PI k) in n 234.267 * [taylor]: Taking taylor expansion of PI in n 234.267 * [backup-simplify]: Simplify PI into PI 234.267 * [taylor]: Taking taylor expansion of k in n 234.267 * [backup-simplify]: Simplify k into k 234.267 * [backup-simplify]: Simplify (/ PI k) into (/ PI k) 234.267 * [backup-simplify]: Simplify (sqrt (/ PI k)) into (sqrt (/ PI k)) 234.268 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ PI k) (/ 0 k)))) into 0 234.268 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ PI k)))) into 0 234.268 * [taylor]: Taking taylor expansion of (* (pow n (- 1/2 (* 1/2 k))) (sqrt (/ PI k))) in n 234.268 * [taylor]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in n 234.268 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in n 234.268 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in n 234.268 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 234.268 * [taylor]: Taking taylor expansion of 1/2 in n 234.268 * [backup-simplify]: Simplify 1/2 into 1/2 234.268 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 234.268 * [taylor]: Taking taylor expansion of 1/2 in n 234.268 * [backup-simplify]: Simplify 1/2 into 1/2 234.268 * [taylor]: Taking taylor expansion of k in n 234.268 * [backup-simplify]: Simplify k into k 234.268 * [taylor]: Taking taylor expansion of (log n) in n 234.268 * [taylor]: Taking taylor expansion of n in n 234.268 * [backup-simplify]: Simplify 0 into 0 234.268 * [backup-simplify]: Simplify 1 into 1 234.268 * [backup-simplify]: Simplify (log 1) into 0 234.268 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 234.268 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 234.268 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 234.269 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 234.269 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (log n)) into (* (- 1/2 (* 1/2 k)) (log n)) 234.269 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (log n))) into (pow n (- 1/2 (* 1/2 k))) 234.269 * [taylor]: Taking taylor expansion of (sqrt (/ PI k)) in n 234.269 * [taylor]: Taking taylor expansion of (/ PI k) in n 234.269 * [taylor]: Taking taylor expansion of PI in n 234.269 * [backup-simplify]: Simplify PI into PI 234.269 * [taylor]: Taking taylor expansion of k in n 234.269 * [backup-simplify]: Simplify k into k 234.269 * [backup-simplify]: Simplify (/ PI k) into (/ PI k) 234.269 * [backup-simplify]: Simplify (sqrt (/ PI k)) into (sqrt (/ PI k)) 234.269 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ PI k) (/ 0 k)))) into 0 234.269 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ PI k)))) into 0 234.269 * [backup-simplify]: Simplify (* (pow n (- 1/2 (* 1/2 k))) (sqrt (/ PI k))) into (* (pow n (- 1/2 (* 1/2 k))) (sqrt (/ PI k))) 234.269 * [taylor]: Taking taylor expansion of (* (pow n (- 1/2 (* 1/2 k))) (sqrt (/ PI k))) in k 234.269 * [taylor]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in k 234.269 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in k 234.269 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in k 234.269 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 234.269 * [taylor]: Taking taylor expansion of 1/2 in k 234.269 * [backup-simplify]: Simplify 1/2 into 1/2 234.269 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 234.269 * [taylor]: Taking taylor expansion of 1/2 in k 234.269 * [backup-simplify]: Simplify 1/2 into 1/2 234.269 * [taylor]: Taking taylor expansion of k in k 234.269 * [backup-simplify]: Simplify 0 into 0 234.269 * [backup-simplify]: Simplify 1 into 1 234.269 * [taylor]: Taking taylor expansion of (log n) in k 234.269 * [taylor]: Taking taylor expansion of n in k 234.269 * [backup-simplify]: Simplify n into n 234.269 * [backup-simplify]: Simplify (log n) into (log n) 234.270 * [backup-simplify]: Simplify (* 1/2 0) into 0 234.270 * [backup-simplify]: Simplify (- 0) into 0 234.270 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 234.270 * [backup-simplify]: Simplify (* 1/2 (log n)) into (* 1/2 (log n)) 234.270 * [backup-simplify]: Simplify (exp (* 1/2 (log n))) into (pow n 1/2) 234.270 * [taylor]: Taking taylor expansion of (sqrt (/ PI k)) in k 234.270 * [taylor]: Taking taylor expansion of (/ PI k) in k 234.270 * [taylor]: Taking taylor expansion of PI in k 234.270 * [backup-simplify]: Simplify PI into PI 234.270 * [taylor]: Taking taylor expansion of k in k 234.270 * [backup-simplify]: Simplify 0 into 0 234.270 * [backup-simplify]: Simplify 1 into 1 234.271 * [backup-simplify]: Simplify (/ PI 1) into PI 234.271 * [backup-simplify]: Simplify (sqrt 0) into 0 234.272 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 234.272 * [backup-simplify]: Simplify (* (pow n 1/2) 0) into 0 234.272 * [backup-simplify]: Simplify 0 into 0 234.273 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 234.273 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 234.274 * [backup-simplify]: Simplify (- 0) into 0 234.274 * [backup-simplify]: Simplify (+ 0 0) into 0 234.274 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 234.274 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (log n))) into 0 234.275 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 234.275 * [backup-simplify]: Simplify (+ (* (pow n (- 1/2 (* 1/2 k))) 0) (* 0 (sqrt (/ PI k)))) into 0 234.275 * [taylor]: Taking taylor expansion of 0 in k 234.275 * [backup-simplify]: Simplify 0 into 0 234.275 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 234.276 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 234.276 * [backup-simplify]: Simplify (- 1/2) into -1/2 234.276 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 234.277 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log n))) into (- (* 1/2 (log n))) 234.277 * [backup-simplify]: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 1) 1)))) into (* -1/2 (* (sqrt n) (log n))) 234.277 * [backup-simplify]: Simplify (+ (* (pow n 1/2) (* +nan.0 PI)) (* (* -1/2 (* (sqrt n) (log n))) 0)) into (- (* +nan.0 (* (sqrt n) PI))) 234.277 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt n) PI))) into (- (* +nan.0 (* (sqrt n) PI))) 234.277 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ PI k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 234.278 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ PI k)))) into 0 234.280 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 234.280 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 234.281 * [backup-simplify]: Simplify (- 0) into 0 234.281 * [backup-simplify]: Simplify (+ 0 0) into 0 234.281 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 234.282 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (log n)))) into 0 234.282 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (log n))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 234.283 * [backup-simplify]: Simplify (+ (* (pow n (- 1/2 (* 1/2 k))) 0) (+ (* 0 0) (* 0 (sqrt (/ PI k))))) into 0 234.283 * [taylor]: Taking taylor expansion of 0 in k 234.283 * [backup-simplify]: Simplify 0 into 0 234.283 * [backup-simplify]: Simplify 0 into 0 234.283 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 234.286 * [backup-simplify]: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 234.287 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 234.288 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 234.288 * [backup-simplify]: Simplify (- 0) into 0 234.288 * [backup-simplify]: Simplify (+ 0 0) into 0 234.289 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log n)))) into 0 234.289 * [backup-simplify]: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt n) (pow (log n) 2))) 234.291 * [backup-simplify]: Simplify (+ (* (pow n 1/2) (* +nan.0 (pow PI 2))) (+ (* (* -1/2 (* (sqrt n) (log n))) (* +nan.0 PI)) (* (* 1/8 (* (sqrt n) (pow (log n) 2))) 0))) into (- (+ (* +nan.0 (* (sqrt n) (pow PI 2))) (- (* +nan.0 (* (sqrt n) (* PI (log n))))))) 234.291 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (sqrt n) (pow PI 2))) (- (* +nan.0 (* (sqrt n) (* PI (log n))))))) into (- (+ (* +nan.0 (* (sqrt n) (pow PI 2))) (- (* +nan.0 (* (sqrt n) (* PI (log n))))))) 234.291 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ PI k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 234.292 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ PI k)))) into 0 234.295 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 234.295 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 234.296 * [backup-simplify]: Simplify (- 0) into 0 234.296 * [backup-simplify]: Simplify (+ 0 0) into 0 234.296 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 234.297 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n))))) into 0 234.304 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (log n))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 234.305 * [backup-simplify]: Simplify (+ (* (pow n (- 1/2 (* 1/2 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt (/ PI k)))))) into 0 234.305 * [taylor]: Taking taylor expansion of 0 in k 234.305 * [backup-simplify]: Simplify 0 into 0 234.305 * [backup-simplify]: Simplify 0 into 0 234.305 * [backup-simplify]: Simplify 0 into 0 234.306 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 234.311 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* (* +nan.0 PI) (* +nan.0 (pow PI 2)))))) (* 2 0)) into (* +nan.0 (pow PI 3)) 234.313 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0 234.313 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 234.314 * [backup-simplify]: Simplify (- 0) into 0 234.314 * [backup-simplify]: Simplify (+ 0 0) into 0 234.315 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log n))))) into 0 234.316 * [backup-simplify]: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 3) 6)) (* (/ (pow (- (* 1/2 (log n))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (sqrt n) (pow (log n) 3))) 234.318 * [backup-simplify]: Simplify (+ (* (pow n 1/2) (* +nan.0 (pow PI 3))) (+ (* (* -1/2 (* (sqrt n) (log n))) (* +nan.0 (pow PI 2))) (+ (* (* 1/8 (* (sqrt n) (pow (log n) 2))) (* +nan.0 PI)) (* (* -1/48 (* (sqrt n) (pow (log n) 3))) 0)))) into (- (+ (* +nan.0 (* (sqrt n) (* PI (pow (log n) 2)))) (- (+ (* +nan.0 (* (sqrt n) (pow PI 3))) (- (* +nan.0 (* (sqrt n) (* (pow PI 2) (log n))))))))) 234.319 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (sqrt n) (* PI (pow (log n) 2)))) (- (+ (* +nan.0 (* (sqrt n) (pow PI 3))) (- (* +nan.0 (* (sqrt n) (* (pow PI 2) (log n))))))))) into (- (+ (* +nan.0 (* (sqrt n) (* PI (pow (log n) 2)))) (- (+ (* +nan.0 (* (sqrt n) (pow PI 3))) (- (* +nan.0 (* (sqrt n) (* (pow PI 2) (log n))))))))) 234.321 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (sqrt n) (* PI (pow (log n) 2)))) (- (+ (* +nan.0 (* (sqrt n) (pow PI 3))) (- (* +nan.0 (* (sqrt n) (* (pow PI 2) (log n))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (sqrt n) (pow PI 2))) (- (* +nan.0 (* (sqrt n) (* PI (log n))))))) (* k 1)) (- (* +nan.0 (* (sqrt n) PI))))) into (- (+ (* +nan.0 (* (sqrt n) (* (pow PI 2) k))) (- (+ (* +nan.0 (* (sqrt n) (* (pow PI 2) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (sqrt n) (* PI (* (pow (log n) 2) (pow k 2))))) (- (+ (* +nan.0 (* (sqrt n) PI)) (- (+ (* +nan.0 (* (sqrt n) (* PI (* (log n) k)))) (- (* +nan.0 (* (sqrt n) (* (pow PI 3) (pow k 2))))))))))))))) 234.322 * [backup-simplify]: Simplify (/ (pow (/ 1 n) (- 1/2 (/ (/ 1 k) 2))) (/ (sqrt (/ 1 k)) (pow PI 1/2))) into (* (sqrt (* PI k)) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) 234.322 * [approximate]: Taking taylor expansion of (* (sqrt (* PI k)) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0 234.322 * [taylor]: Taking taylor expansion of (* (sqrt (* PI k)) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) in k 234.322 * [taylor]: Taking taylor expansion of (sqrt (* PI k)) in k 234.322 * [taylor]: Taking taylor expansion of (* PI k) in k 234.322 * [taylor]: Taking taylor expansion of PI in k 234.322 * [backup-simplify]: Simplify PI into PI 234.322 * [taylor]: Taking taylor expansion of k in k 234.322 * [backup-simplify]: Simplify 0 into 0 234.322 * [backup-simplify]: Simplify 1 into 1 234.323 * [backup-simplify]: Simplify (* PI 0) into 0 234.323 * [backup-simplify]: Simplify (+ (* PI 1) (* 0 0)) into PI 234.324 * [backup-simplify]: Simplify (sqrt 0) into 0 234.325 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 234.325 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in k 234.325 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in k 234.325 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in k 234.325 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 234.325 * [taylor]: Taking taylor expansion of 1/2 in k 234.325 * [backup-simplify]: Simplify 1/2 into 1/2 234.325 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 234.325 * [taylor]: Taking taylor expansion of 1/2 in k 234.325 * [backup-simplify]: Simplify 1/2 into 1/2 234.325 * [taylor]: Taking taylor expansion of (/ 1 k) in k 234.325 * [taylor]: Taking taylor expansion of k in k 234.325 * [backup-simplify]: Simplify 0 into 0 234.325 * [backup-simplify]: Simplify 1 into 1 234.325 * [backup-simplify]: Simplify (/ 1 1) into 1 234.325 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in k 234.325 * [taylor]: Taking taylor expansion of (/ 1 n) in k 234.325 * [taylor]: Taking taylor expansion of n in k 234.325 * [backup-simplify]: Simplify n into n 234.325 * [backup-simplify]: Simplify (/ 1 n) into (/ 1 n) 234.325 * [backup-simplify]: Simplify (log (/ 1 n)) into (log (/ 1 n)) 234.325 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 234.326 * [backup-simplify]: Simplify (- 1/2) into -1/2 234.326 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 234.326 * [backup-simplify]: Simplify (* -1/2 (log (/ 1 n))) into (* -1/2 (log (/ 1 n))) 234.326 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) into (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) 234.326 * [taylor]: Taking taylor expansion of (* (sqrt (* PI k)) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) in n 234.326 * [taylor]: Taking taylor expansion of (sqrt (* PI k)) in n 234.326 * [taylor]: Taking taylor expansion of (* PI k) in n 234.326 * [taylor]: Taking taylor expansion of PI in n 234.326 * [backup-simplify]: Simplify PI into PI 234.326 * [taylor]: Taking taylor expansion of k in n 234.326 * [backup-simplify]: Simplify k into k 234.326 * [backup-simplify]: Simplify (* PI k) into (* PI k) 234.326 * [backup-simplify]: Simplify (sqrt (* PI k)) into (sqrt (* PI k)) 234.327 * [backup-simplify]: Simplify (+ (* PI 0) (* 0 k)) into 0 234.327 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (* PI k)))) into 0 234.327 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 234.327 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in n 234.327 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in n 234.327 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 234.327 * [taylor]: Taking taylor expansion of 1/2 in n 234.327 * [backup-simplify]: Simplify 1/2 into 1/2 234.327 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 234.327 * [taylor]: Taking taylor expansion of 1/2 in n 234.327 * [backup-simplify]: Simplify 1/2 into 1/2 234.327 * [taylor]: Taking taylor expansion of (/ 1 k) in n 234.327 * [taylor]: Taking taylor expansion of k in n 234.327 * [backup-simplify]: Simplify k into k 234.327 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 234.327 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 234.327 * [taylor]: Taking taylor expansion of (/ 1 n) in n 234.327 * [taylor]: Taking taylor expansion of n in n 234.327 * [backup-simplify]: Simplify 0 into 0 234.327 * [backup-simplify]: Simplify 1 into 1 234.327 * [backup-simplify]: Simplify (/ 1 1) into 1 234.327 * [backup-simplify]: Simplify (log 1) into 0 234.328 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 234.328 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 234.328 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 234.328 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 234.328 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log n))) into (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))) 234.328 * [backup-simplify]: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 234.328 * [taylor]: Taking taylor expansion of (* (sqrt (* PI k)) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) in n 234.328 * [taylor]: Taking taylor expansion of (sqrt (* PI k)) in n 234.328 * [taylor]: Taking taylor expansion of (* PI k) in n 234.328 * [taylor]: Taking taylor expansion of PI in n 234.328 * [backup-simplify]: Simplify PI into PI 234.328 * [taylor]: Taking taylor expansion of k in n 234.328 * [backup-simplify]: Simplify k into k 234.328 * [backup-simplify]: Simplify (* PI k) into (* PI k) 234.328 * [backup-simplify]: Simplify (sqrt (* PI k)) into (sqrt (* PI k)) 234.329 * [backup-simplify]: Simplify (+ (* PI 0) (* 0 k)) into 0 234.329 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (* PI k)))) into 0 234.329 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 234.329 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in n 234.329 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in n 234.329 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 234.329 * [taylor]: Taking taylor expansion of 1/2 in n 234.329 * [backup-simplify]: Simplify 1/2 into 1/2 234.329 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 234.329 * [taylor]: Taking taylor expansion of 1/2 in n 234.329 * [backup-simplify]: Simplify 1/2 into 1/2 234.329 * [taylor]: Taking taylor expansion of (/ 1 k) in n 234.329 * [taylor]: Taking taylor expansion of k in n 234.329 * [backup-simplify]: Simplify k into k 234.329 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 234.329 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 234.329 * [taylor]: Taking taylor expansion of (/ 1 n) in n 234.329 * [taylor]: Taking taylor expansion of n in n 234.329 * [backup-simplify]: Simplify 0 into 0 234.329 * [backup-simplify]: Simplify 1 into 1 234.329 * [backup-simplify]: Simplify (/ 1 1) into 1 234.329 * [backup-simplify]: Simplify (log 1) into 0 234.329 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 234.330 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 234.330 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 234.330 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 234.330 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log n))) into (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))) 234.330 * [backup-simplify]: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 234.330 * [backup-simplify]: Simplify (* (sqrt (* PI k)) (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))))) into (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (sqrt (* PI k))) 234.330 * [taylor]: Taking taylor expansion of (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (sqrt (* PI k))) in k 234.330 * [taylor]: Taking taylor expansion of (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) in k 234.330 * [taylor]: Taking taylor expansion of (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))) in k 234.330 * [taylor]: Taking taylor expansion of -1 in k 234.330 * [backup-simplify]: Simplify -1 into -1 234.330 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log n)) in k 234.330 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 234.330 * [taylor]: Taking taylor expansion of 1/2 in k 234.330 * [backup-simplify]: Simplify 1/2 into 1/2 234.330 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 234.330 * [taylor]: Taking taylor expansion of 1/2 in k 234.330 * [backup-simplify]: Simplify 1/2 into 1/2 234.331 * [taylor]: Taking taylor expansion of (/ 1 k) in k 234.331 * [taylor]: Taking taylor expansion of k in k 234.331 * [backup-simplify]: Simplify 0 into 0 234.331 * [backup-simplify]: Simplify 1 into 1 234.331 * [backup-simplify]: Simplify (/ 1 1) into 1 234.331 * [taylor]: Taking taylor expansion of (log n) in k 234.331 * [taylor]: Taking taylor expansion of n in k 234.331 * [backup-simplify]: Simplify n into n 234.331 * [backup-simplify]: Simplify (log n) into (log n) 234.331 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 234.331 * [backup-simplify]: Simplify (- 1/2) into -1/2 234.332 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 234.332 * [backup-simplify]: Simplify (* -1/2 (log n)) into (* -1/2 (log n)) 234.332 * [backup-simplify]: Simplify (* -1 (* -1/2 (log n))) into (* 1/2 (log n)) 234.332 * [backup-simplify]: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 234.332 * [taylor]: Taking taylor expansion of (sqrt (* PI k)) in k 234.332 * [taylor]: Taking taylor expansion of (* PI k) in k 234.332 * [taylor]: Taking taylor expansion of PI in k 234.332 * [backup-simplify]: Simplify PI into PI 234.332 * [taylor]: Taking taylor expansion of k in k 234.332 * [backup-simplify]: Simplify 0 into 0 234.332 * [backup-simplify]: Simplify 1 into 1 234.332 * [backup-simplify]: Simplify (* PI 0) into 0 234.333 * [backup-simplify]: Simplify (+ (* PI 1) (* 0 0)) into PI 234.334 * [backup-simplify]: Simplify (sqrt 0) into 0 234.334 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 234.334 * [backup-simplify]: Simplify (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 0) into 0 234.335 * [backup-simplify]: Simplify 0 into 0 234.335 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 234.336 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 234.336 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 234.336 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 234.336 * [backup-simplify]: Simplify (- 0) into 0 234.337 * [backup-simplify]: Simplify (+ 0 0) into 0 234.337 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 234.337 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log n)))) into 0 234.338 * [backup-simplify]: Simplify (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 234.338 * [backup-simplify]: Simplify (+ (* (sqrt (* PI k)) 0) (* 0 (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))))) into 0 234.338 * [taylor]: Taking taylor expansion of 0 in k 234.338 * [backup-simplify]: Simplify 0 into 0 234.338 * [backup-simplify]: Simplify 0 into 0 234.338 * [backup-simplify]: Simplify (+ (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) PI))) 234.339 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) PI))) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) PI))) 234.339 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 234.341 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 234.341 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 234.341 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 234.342 * [backup-simplify]: Simplify (- 0) into 0 234.342 * [backup-simplify]: Simplify (+ 0 0) into 0 234.342 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 234.343 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log n))))) into 0 234.344 * [backup-simplify]: Simplify (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 234.344 * [backup-simplify]: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 k))) into 0 234.345 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (* PI k)))) into 0 234.345 * [backup-simplify]: Simplify (+ (* (sqrt (* PI k)) 0) (+ (* 0 0) (* 0 (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))))))) into 0 234.345 * [taylor]: Taking taylor expansion of 0 in k 234.345 * [backup-simplify]: Simplify 0 into 0 234.345 * [backup-simplify]: Simplify 0 into 0 234.345 * [backup-simplify]: Simplify 0 into 0 234.346 * [backup-simplify]: Simplify (+ (* PI 0) (+ (* 0 1) (* 0 0))) into 0 234.348 * [backup-simplify]: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 234.350 * [backup-simplify]: Simplify (+ (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* +nan.0 (pow PI 2))) (+ (* 0 (* +nan.0 PI)) (* 0 0))) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI 2)))) 234.350 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI 2)))) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI 2)))) 234.351 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 234.353 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 234.354 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 234.354 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 234.355 * [backup-simplify]: Simplify (- 0) into 0 234.355 * [backup-simplify]: Simplify (+ 0 0) into 0 234.355 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 234.356 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0 234.357 * [backup-simplify]: Simplify (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 234.357 * [backup-simplify]: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 234.358 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (* PI k)))) into 0 234.358 * [backup-simplify]: Simplify (+ (* (sqrt (* PI k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))))))) into 0 234.358 * [taylor]: Taking taylor expansion of 0 in k 234.359 * [backup-simplify]: Simplify 0 into 0 234.359 * [backup-simplify]: Simplify 0 into 0 234.359 * [backup-simplify]: Simplify 0 into 0 234.359 * [backup-simplify]: Simplify 0 into 0 234.359 * [backup-simplify]: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 234.364 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* (* +nan.0 PI) (* +nan.0 (pow PI 2)))))) (* 2 0)) into (* +nan.0 (pow PI 3)) 234.366 * [backup-simplify]: Simplify (+ (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* +nan.0 (pow PI 3))) (+ (* 0 (* +nan.0 (pow PI 2))) (+ (* 0 (* +nan.0 PI)) (* 0 0)))) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI 3)))) 234.367 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI 3)))) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI 3)))) 234.368 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (log (/ 1 n))))) (pow PI 3)))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (log (/ 1 n))))) (pow PI 2)))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (log (/ 1 n))))) PI))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) PI) k)) (- (+ (* +nan.0 (/ (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (pow PI 3)) (pow k 3))) (- (* +nan.0 (/ (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (pow PI 2)) (pow k 2)))))))) 234.369 * [backup-simplify]: Simplify (/ (pow (/ 1 (- n)) (- 1/2 (/ (/ 1 (- k)) 2))) (/ (sqrt (/ 1 (- k))) (pow PI 1/2))) into (* (/ (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) (sqrt PI)) 234.369 * [approximate]: Taking taylor expansion of (* (/ (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) (sqrt PI)) in (n k) around 0 234.369 * [taylor]: Taking taylor expansion of (* (/ (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) (sqrt PI)) in k 234.369 * [taylor]: Taking taylor expansion of (/ (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 234.369 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in k 234.369 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in k 234.369 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in k 234.369 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 234.369 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 234.369 * [taylor]: Taking taylor expansion of 1/2 in k 234.369 * [backup-simplify]: Simplify 1/2 into 1/2 234.369 * [taylor]: Taking taylor expansion of (/ 1 k) in k 234.369 * [taylor]: Taking taylor expansion of k in k 234.369 * [backup-simplify]: Simplify 0 into 0 234.369 * [backup-simplify]: Simplify 1 into 1 234.369 * [backup-simplify]: Simplify (/ 1 1) into 1 234.369 * [taylor]: Taking taylor expansion of 1/2 in k 234.369 * [backup-simplify]: Simplify 1/2 into 1/2 234.369 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in k 234.369 * [taylor]: Taking taylor expansion of (/ -1 n) in k 234.369 * [taylor]: Taking taylor expansion of -1 in k 234.369 * [backup-simplify]: Simplify -1 into -1 234.369 * [taylor]: Taking taylor expansion of n in k 234.369 * [backup-simplify]: Simplify n into n 234.369 * [backup-simplify]: Simplify (/ -1 n) into (/ -1 n) 234.369 * [backup-simplify]: Simplify (log (/ -1 n)) into (log (/ -1 n)) 234.370 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 234.370 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 234.370 * [backup-simplify]: Simplify (* 1/2 (log (/ -1 n))) into (* 1/2 (log (/ -1 n))) 234.370 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) into (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) 234.370 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 234.370 * [taylor]: Taking taylor expansion of (/ -1 k) in k 234.370 * [taylor]: Taking taylor expansion of -1 in k 234.370 * [backup-simplify]: Simplify -1 into -1 234.370 * [taylor]: Taking taylor expansion of k in k 234.370 * [backup-simplify]: Simplify 0 into 0 234.370 * [backup-simplify]: Simplify 1 into 1 234.370 * [backup-simplify]: Simplify (/ -1 1) into -1 234.371 * [backup-simplify]: Simplify (sqrt 0) into 0 234.371 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 234.372 * [backup-simplify]: Simplify (/ (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) +nan.0) into (* +nan.0 (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2))) 234.372 * [taylor]: Taking taylor expansion of (sqrt PI) in k 234.372 * [taylor]: Taking taylor expansion of PI in k 234.372 * [backup-simplify]: Simplify PI into PI 234.372 * [backup-simplify]: Simplify (sqrt PI) into (sqrt PI) 234.373 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt PI))) into 0 234.373 * [taylor]: Taking taylor expansion of (* (/ (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) (sqrt PI)) in n 234.373 * [taylor]: Taking taylor expansion of (/ (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 234.373 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 234.373 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in n 234.373 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in n 234.373 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 234.373 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 234.373 * [taylor]: Taking taylor expansion of 1/2 in n 234.373 * [backup-simplify]: Simplify 1/2 into 1/2 234.373 * [taylor]: Taking taylor expansion of (/ 1 k) in n 234.373 * [taylor]: Taking taylor expansion of k in n 234.373 * [backup-simplify]: Simplify k into k 234.373 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 234.373 * [taylor]: Taking taylor expansion of 1/2 in n 234.373 * [backup-simplify]: Simplify 1/2 into 1/2 234.373 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n 234.373 * [taylor]: Taking taylor expansion of (/ -1 n) in n 234.373 * [taylor]: Taking taylor expansion of -1 in n 234.373 * [backup-simplify]: Simplify -1 into -1 234.373 * [taylor]: Taking taylor expansion of n in n 234.373 * [backup-simplify]: Simplify 0 into 0 234.373 * [backup-simplify]: Simplify 1 into 1 234.373 * [backup-simplify]: Simplify (/ -1 1) into -1 234.373 * [backup-simplify]: Simplify (log -1) into (log -1) 234.373 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 234.374 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 234.374 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 234.374 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) 234.375 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 234.375 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 234.375 * [taylor]: Taking taylor expansion of (/ -1 k) in n 234.375 * [taylor]: Taking taylor expansion of -1 in n 234.375 * [backup-simplify]: Simplify -1 into -1 234.375 * [taylor]: Taking taylor expansion of k in n 234.375 * [backup-simplify]: Simplify k into k 234.375 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 234.375 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 234.375 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 234.375 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 234.375 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (sqrt (/ -1 k))) 234.375 * [taylor]: Taking taylor expansion of (sqrt PI) in n 234.375 * [taylor]: Taking taylor expansion of PI in n 234.375 * [backup-simplify]: Simplify PI into PI 234.376 * [backup-simplify]: Simplify (sqrt PI) into (sqrt PI) 234.376 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt PI))) into 0 234.376 * [taylor]: Taking taylor expansion of (* (/ (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) (sqrt PI)) in n 234.376 * [taylor]: Taking taylor expansion of (/ (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 234.376 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 234.376 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in n 234.376 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in n 234.376 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 234.376 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 234.376 * [taylor]: Taking taylor expansion of 1/2 in n 234.376 * [backup-simplify]: Simplify 1/2 into 1/2 234.376 * [taylor]: Taking taylor expansion of (/ 1 k) in n 234.376 * [taylor]: Taking taylor expansion of k in n 234.376 * [backup-simplify]: Simplify k into k 234.376 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 234.376 * [taylor]: Taking taylor expansion of 1/2 in n 234.376 * [backup-simplify]: Simplify 1/2 into 1/2 234.376 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n 234.376 * [taylor]: Taking taylor expansion of (/ -1 n) in n 234.376 * [taylor]: Taking taylor expansion of -1 in n 234.376 * [backup-simplify]: Simplify -1 into -1 234.377 * [taylor]: Taking taylor expansion of n in n 234.377 * [backup-simplify]: Simplify 0 into 0 234.377 * [backup-simplify]: Simplify 1 into 1 234.377 * [backup-simplify]: Simplify (/ -1 1) into -1 234.377 * [backup-simplify]: Simplify (log -1) into (log -1) 234.377 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 234.377 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 234.378 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 234.378 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) 234.378 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 234.378 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 234.378 * [taylor]: Taking taylor expansion of (/ -1 k) in n 234.378 * [taylor]: Taking taylor expansion of -1 in n 234.378 * [backup-simplify]: Simplify -1 into -1 234.378 * [taylor]: Taking taylor expansion of k in n 234.378 * [backup-simplify]: Simplify k into k 234.378 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 234.378 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 234.379 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 234.379 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 234.379 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (sqrt (/ -1 k))) 234.379 * [taylor]: Taking taylor expansion of (sqrt PI) in n 234.379 * [taylor]: Taking taylor expansion of PI in n 234.379 * [backup-simplify]: Simplify PI into PI 234.379 * [backup-simplify]: Simplify (sqrt PI) into (sqrt PI) 234.380 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt PI))) into 0 234.380 * [backup-simplify]: Simplify (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (sqrt (/ -1 k))) (sqrt PI)) into (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (sqrt (/ -1 k))) (sqrt PI)) 234.380 * [taylor]: Taking taylor expansion of (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (sqrt (/ -1 k))) (sqrt PI)) in k 234.380 * [taylor]: Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (sqrt (/ -1 k))) in k 234.381 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) in k 234.381 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) in k 234.381 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 234.381 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 234.381 * [taylor]: Taking taylor expansion of 1/2 in k 234.381 * [backup-simplify]: Simplify 1/2 into 1/2 234.381 * [taylor]: Taking taylor expansion of (/ 1 k) in k 234.381 * [taylor]: Taking taylor expansion of k in k 234.381 * [backup-simplify]: Simplify 0 into 0 234.381 * [backup-simplify]: Simplify 1 into 1 234.381 * [backup-simplify]: Simplify (/ 1 1) into 1 234.381 * [taylor]: Taking taylor expansion of 1/2 in k 234.381 * [backup-simplify]: Simplify 1/2 into 1/2 234.381 * [taylor]: Taking taylor expansion of (- (log -1) (log n)) in k 234.381 * [taylor]: Taking taylor expansion of (log -1) in k 234.381 * [taylor]: Taking taylor expansion of -1 in k 234.381 * [backup-simplify]: Simplify -1 into -1 234.381 * [backup-simplify]: Simplify (log -1) into (log -1) 234.381 * [taylor]: Taking taylor expansion of (log n) in k 234.381 * [taylor]: Taking taylor expansion of n in k 234.381 * [backup-simplify]: Simplify n into n 234.381 * [backup-simplify]: Simplify (log n) into (log n) 234.382 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 234.382 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 234.382 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 234.382 * [backup-simplify]: Simplify (+ (log -1) (- (log n))) into (- (log -1) (log n)) 234.382 * [backup-simplify]: Simplify (* 1/2 (- (log -1) (log n))) into (* 1/2 (- (log -1) (log n))) 234.383 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 234.383 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 234.383 * [taylor]: Taking taylor expansion of (/ -1 k) in k 234.383 * [taylor]: Taking taylor expansion of -1 in k 234.383 * [backup-simplify]: Simplify -1 into -1 234.383 * [taylor]: Taking taylor expansion of k in k 234.383 * [backup-simplify]: Simplify 0 into 0 234.383 * [backup-simplify]: Simplify 1 into 1 234.383 * [backup-simplify]: Simplify (/ -1 1) into -1 234.383 * [backup-simplify]: Simplify (sqrt 0) into 0 234.384 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 234.385 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) +nan.0) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) 234.385 * [taylor]: Taking taylor expansion of (sqrt PI) in k 234.385 * [taylor]: Taking taylor expansion of PI in k 234.385 * [backup-simplify]: Simplify PI into PI 234.385 * [backup-simplify]: Simplify (sqrt PI) into (sqrt PI) 234.385 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt PI))) into 0 234.386 * [backup-simplify]: Simplify (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) (sqrt PI)) into (* +nan.0 (* (sqrt PI) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))))) 234.387 * [backup-simplify]: Simplify (* +nan.0 (* (sqrt PI) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))))) into (* +nan.0 (* (sqrt PI) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))))) 234.387 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 234.388 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -1 1)))) 1) into 0 234.388 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 234.388 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 234.389 * [backup-simplify]: Simplify (+ 0 0) into 0 234.389 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 234.389 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log -1) (log n)))) into 0 234.397 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 234.398 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0 234.398 * [backup-simplify]: Simplify (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (sqrt (/ -1 k))) 0) (* 0 (sqrt PI))) into 0 234.398 * [taylor]: Taking taylor expansion of 0 in k 234.398 * [backup-simplify]: Simplify 0 into 0 234.398 * [backup-simplify]: Simplify 0 into 0 234.399 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 234.401 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 234.402 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))))) 234.403 * [backup-simplify]: Simplify (+ (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) 0) (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))))) (sqrt PI))) into (- (* +nan.0 (* (sqrt PI) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))))) 234.403 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt PI) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))))) into (- (* +nan.0 (* (sqrt PI) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))))) 234.404 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt PI))) into 0 234.405 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 234.406 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -1 1)))) 2) into 0 234.406 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 234.407 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 234.407 * [backup-simplify]: Simplify (+ 0 0) into 0 234.408 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 234.408 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log -1) (log n))))) into 0 234.409 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 234.409 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 234.410 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 234.410 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0 234.411 * [backup-simplify]: Simplify (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (sqrt (/ -1 k))) 0) (+ (* 0 0) (* 0 (sqrt PI)))) into 0 234.411 * [taylor]: Taking taylor expansion of 0 in k 234.411 * [backup-simplify]: Simplify 0 into 0 234.411 * [backup-simplify]: Simplify 0 into 0 234.411 * [backup-simplify]: Simplify 0 into 0 234.412 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt PI))) into 0 234.413 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 234.415 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 234.416 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))))) 234.418 * [backup-simplify]: Simplify (+ (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) 0) (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))))) 0) (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))))) (sqrt PI)))) into (- (* +nan.0 (* (sqrt PI) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))))) 234.418 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt PI) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))))) into (- (* +nan.0 (* (sqrt PI) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))))) 234.421 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (sqrt PI) (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -1) (log (/ 1 (- n))))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (* (sqrt PI) (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -1) (log (/ 1 (- n))))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (* (sqrt PI) (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -1) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (* (/ (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) k) (sqrt PI))) (- (+ (* +nan.0 (* (/ (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (pow k 2)) (sqrt PI))) (- (* +nan.0 (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (sqrt PI)))))))) 234.421 * * * [progress]: simplifying candidates 234.421 * * * * [progress]: [ 1 / 2500 ] simplifiying candidate # 234.421 * * * * [progress]: [ 2 / 2500 ] simplifiying candidate # 234.421 * * * * [progress]: [ 3 / 2500 ] simplifiying candidate # 234.421 * * * * [progress]: [ 4 / 2500 ] simplifiying candidate # 234.421 * * * * [progress]: [ 5 / 2500 ] simplifiying candidate # 234.421 * * * * [progress]: [ 6 / 2500 ] simplifiying candidate # 234.421 * * * * [progress]: [ 7 / 2500 ] simplifiying candidate # 234.421 * * * * [progress]: [ 8 / 2500 ] simplifiying candidate # 234.421 * * * * [progress]: [ 9 / 2500 ] simplifiying candidate # 234.421 * * * * [progress]: [ 10 / 2500 ] simplifiying candidate # 234.421 * * * * [progress]: [ 11 / 2500 ] simplifiying candidate # 234.421 * * * * [progress]: [ 12 / 2500 ] simplifiying candidate # 234.421 * * * * [progress]: [ 13 / 2500 ] simplifiying candidate # 234.421 * * * * [progress]: [ 14 / 2500 ] simplifiying candidate # 234.421 * * * * [progress]: [ 15 / 2500 ] simplifiying candidate # 234.422 * * * * [progress]: [ 16 / 2500 ] simplifiying candidate # 234.422 * * * * [progress]: [ 17 / 2500 ] simplifiying candidate # 234.422 * * * * [progress]: [ 18 / 2500 ] simplifiying candidate # 234.422 * * * * [progress]: [ 19 / 2500 ] simplifiying candidate # 234.422 * * * * [progress]: [ 20 / 2500 ] simplifiying candidate # 234.422 * * * * [progress]: [ 21 / 2500 ] simplifiying candidate #real (real->posit16 (pow PI 1/2))))) (/ (pow 2 (- 1/2 (/ k 2))) (pow PI (/ k 2)))))> 234.422 * * * * [progress]: [ 22 / 2500 ] simplifiying candidate # 234.422 * * * * [progress]: [ 23 / 2500 ] simplifiying candidate # 234.422 * * * * [progress]: [ 24 / 2500 ] simplifiying candidate # 234.422 * * * * [progress]: [ 25 / 2500 ] simplifiying candidate # 234.422 * * * * [progress]: [ 26 / 2500 ] simplifiying candidate # 234.422 * * * * [progress]: [ 27 / 2500 ] simplifiying candidate # 234.422 * * * * [progress]: [ 28 / 2500 ] simplifiying candidate # 234.422 * * * * [progress]: [ 29 / 2500 ] simplifiying 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] simplifiying candidate # 234.425 * * * * [progress]: [ 88 / 2500 ] simplifiying candidate # 234.425 * * * * [progress]: [ 89 / 2500 ] simplifiying candidate # 234.425 * * * * [progress]: [ 90 / 2500 ] simplifiying candidate # 234.425 * * * * [progress]: [ 91 / 2500 ] simplifiying candidate # 234.425 * * * * [progress]: [ 92 / 2500 ] simplifiying candidate # 234.426 * * * * [progress]: [ 93 / 2500 ] simplifiying candidate # 234.426 * * * * [progress]: [ 94 / 2500 ] simplifiying candidate # 234.426 * * * * [progress]: [ 95 / 2500 ] simplifiying candidate # 234.426 * * * * [progress]: [ 96 / 2500 ] simplifiying candidate # 234.426 * * * * [progress]: [ 97 / 2500 ] simplifiying candidate # 234.426 * * * * [progress]: [ 98 / 2500 ] simplifiying candidate # 234.426 * * * * [progress]: [ 99 / 2500 ] simplifiying candidate # 234.426 * * * * [progress]: [ 100 / 2500 ] simplifiying candidate # 234.426 * * * * [progress]: [ 101 / 2500 ] simplifiying candidate # 234.426 * * * * [progress]: [ 102 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(/ k 2)))))> 234.429 * * * * [progress]: [ 160 / 2500 ] simplifiying candidate # 234.429 * * * * [progress]: [ 161 / 2500 ] simplifiying candidate # 234.429 * * * * [progress]: [ 162 / 2500 ] simplifiying candidate # 234.429 * * * * [progress]: [ 163 / 2500 ] simplifiying candidate # 234.429 * * * * [progress]: [ 164 / 2500 ] simplifiying candidate # 234.429 * * * * [progress]: [ 165 / 2500 ] simplifiying candidate # 234.429 * * * * [progress]: [ 166 / 2500 ] simplifiying candidate # 234.429 * * * * [progress]: [ 167 / 2500 ] simplifiying candidate # 234.429 * * * * [progress]: [ 168 / 2500 ] simplifiying candidate # 234.429 * * * * [progress]: [ 169 / 2500 ] simplifiying candidate # 234.429 * * * * [progress]: [ 170 / 2500 ] simplifiying candidate # 234.429 * * * * [progress]: [ 171 / 2500 ] simplifiying candidate # 234.429 * * * * [progress]: [ 172 / 2500 ] simplifiying candidate # 234.429 * * * * [progress]: [ 173 / 2500 ] simplifiying candidate # 234.429 * * * * [progress]: [ 174 / 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simplifiying candidate # 234.578 * * * * [progress]: [ 2475 / 2500 ] simplifiying candidate # 234.578 * * * * [progress]: [ 2476 / 2500 ] simplifiying candidate # 234.578 * * * * [progress]: [ 2477 / 2500 ] simplifiying candidate # 234.578 * * * * [progress]: [ 2478 / 2500 ] simplifiying candidate # 234.578 * * * * [progress]: [ 2479 / 2500 ] simplifiying candidate # 234.578 * * * * [progress]: [ 2480 / 2500 ] simplifiying candidate # 234.578 * * * * [progress]: [ 2481 / 2500 ] simplifiying candidate # 234.578 * * * * [progress]: [ 2482 / 2500 ] simplifiying candidate # 234.578 * * * * [progress]: [ 2483 / 2500 ] simplifiying candidate # 234.579 * * * * [progress]: [ 2484 / 2500 ] simplifiying candidate # 234.579 * * * * [progress]: [ 2485 / 2500 ] simplifiying candidate # 234.579 * * * * [progress]: [ 2486 / 2500 ] simplifiying candidate # 234.579 * * * * [progress]: [ 2487 / 2500 ] simplifiying candidate # 234.579 * * * * [progress]: [ 2488 / 2500 ] simplifiying candidate # 234.579 * * * * [progress]: [ 2489 / 2500 ] simplifiying candidate # 234.579 * * * * [progress]: [ 2490 / 2500 ] simplifiying candidate #real (real->posit16 (/ (pow n (- 1/2 (/ k 2))) (/ (sqrt k) (pow PI 1/2))))) (/ (pow 2 (- 1/2 (/ k 2))) (pow PI (/ k 2)))))> 234.579 * * * * [progress]: [ 2491 / 2500 ] simplifiying candidate # 234.579 * * * * [progress]: [ 2492 / 2500 ] simplifiying candidate # 234.579 * * * * [progress]: [ 2493 / 2500 ] simplifiying candidate # 234.579 * * * * [progress]: [ 2494 / 2500 ] simplifiying candidate # 234.579 * * * * [progress]: [ 2495 / 2500 ] simplifiying candidate # 234.579 * * * * [progress]: [ 2496 / 2500 ] simplifiying candidate # 234.579 * * * * [progress]: [ 2497 / 2500 ] simplifiying candidate # 234.579 * * * * [progress]: [ 2498 / 2500 ] simplifiying candidate # 234.579 * * * * [progress]: [ 2499 / 2500 ] simplifiying candidate # 234.579 * * * * [progress]: [ 2500 / 2500 ] simplifiying candidate # 234.643 * [simplify]: Simplifying: (expm1 (pow PI 1/2)) 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(/ (pow n (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt (sqrt k)) (pow PI 1/2))) (/ (pow n (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt (sqrt k)) (pow PI (/ 1/2 2)))) (/ (pow n (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt (sqrt k)) (pow PI (/ 1/2 2)))) (/ (pow n (/ (- 1/2 (/ k 2)) 2)) (/ 1 (pow (* (cbrt PI) (cbrt PI)) 1/2))) (/ (pow n (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (cbrt PI) 1/2))) (/ (pow n (/ (- 1/2 (/ k 2)) 2)) (/ 1 (pow (sqrt PI) 1/2))) (/ (pow n (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (sqrt PI) 1/2))) (/ (pow n (/ (- 1/2 (/ k 2)) 2)) (/ 1 (pow 1 1/2))) (/ (pow n (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow PI 1/2))) (/ (pow n (/ (- 1/2 (/ k 2)) 2)) (/ 1 (* (cbrt (pow PI 1/2)) (cbrt (pow PI 1/2))))) (/ (pow n (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (cbrt (pow PI 1/2)))) (/ (pow n (/ (- 1/2 (/ k 2)) 2)) (/ 1 (sqrt (pow PI 1/2)))) (/ (pow n (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (sqrt (pow PI 1/2)))) (/ (pow n (/ (- 1/2 (/ k 2)) 2)) (/ 1 1)) (/ (pow n (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow PI 1/2))) (/ (pow n (/ (- 1/2 (/ k 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(* (cbrt (pow PI 1/2)) (cbrt (pow PI 1/2))))) (/ (pow n (- 1/2 (/ k 2))) (/ (sqrt (sqrt k)) (sqrt (pow PI 1/2)))) (/ (pow n (- 1/2 (/ k 2))) (/ (sqrt (sqrt k)) 1)) (/ (pow n (- 1/2 (/ k 2))) (/ (sqrt (sqrt k)) (pow PI (/ 1/2 2)))) (/ (pow n (- 1/2 (/ k 2))) (/ (sqrt 1) (pow (* (cbrt PI) (cbrt PI)) 1/2))) (/ (pow n (- 1/2 (/ k 2))) (/ (sqrt 1) (pow (sqrt PI) 1/2))) (/ (pow n (- 1/2 (/ k 2))) (/ (sqrt 1) (pow 1 1/2))) (/ (pow n (- 1/2 (/ k 2))) (/ (sqrt 1) (* (cbrt (pow PI 1/2)) (cbrt (pow PI 1/2))))) (/ (pow n (- 1/2 (/ k 2))) (/ (sqrt 1) (sqrt (pow PI 1/2)))) (/ (pow n (- 1/2 (/ k 2))) (/ (sqrt 1) 1)) (/ (pow n (- 1/2 (/ k 2))) (/ (sqrt 1) (pow PI (/ 1/2 2)))) (/ (pow n (- 1/2 (/ k 2))) (/ (sqrt (sqrt k)) (pow (* (cbrt PI) (cbrt PI)) 1/2))) (/ (pow n (- 1/2 (/ k 2))) (/ (sqrt (sqrt k)) (pow (sqrt PI) 1/2))) (/ (pow n (- 1/2 (/ k 2))) (/ (sqrt (sqrt k)) (pow 1 1/2))) (/ (pow n (- 1/2 (/ k 2))) (/ (sqrt (sqrt k)) (* (cbrt (pow PI 1/2)) (cbrt (pow PI 1/2))))) (/ (pow n (- 1/2 (/ k 2))) (/ 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(pow PI 1/2)) (pow n (fma (- (/ (sqrt k) 2)) (/ (sqrt k) 1) (* (/ (sqrt k) 2) (/ (sqrt k) 1))))) (/ (/ (sqrt k) (pow PI 1/2)) (pow n (fma (- (/ k (cbrt 2))) (/ 1 (* (cbrt 2) (cbrt 2))) (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2))))))) (/ (/ (sqrt k) (pow PI 1/2)) (pow n (fma (- (/ k (sqrt 2))) (/ 1 (sqrt 2)) (* (/ k (sqrt 2)) (/ 1 (sqrt 2)))))) (/ (/ (sqrt k) (pow PI 1/2)) (pow n (fma (- (/ k 2)) (/ 1 1) (* (/ k 2) (/ 1 1))))) (/ (/ (sqrt k) (pow PI 1/2)) (pow n (fma (- (/ k 2)) 1 (* (/ k 2) 1)))) (/ (/ (sqrt k) (pow PI 1/2)) (pow n (fma (- (/ 1 2)) k (* (/ 1 2) k)))) (/ (/ (sqrt k) (pow PI 1/2)) (pow n (- (/ k 2)))) (/ (/ (sqrt k) (pow PI 1/2)) (pow n (- (/ k 2)))) (/ (/ (sqrt k) (pow PI 1/2)) (pow (cbrt n) (- 1/2 (/ k 2)))) (/ (/ (sqrt k) (pow PI 1/2)) (pow (sqrt n) (- 1/2 (/ k 2)))) (/ (/ (sqrt k) (pow PI 1/2)) (pow n (- 1/2 (/ k 2)))) (/ (/ (sqrt k) (pow PI 1/2)) (cbrt (pow n (- 1/2 (/ k 2))))) (/ (/ (sqrt k) (pow PI 1/2)) (sqrt (pow n (- 1/2 (/ k 2))))) (/ (/ (sqrt k) (pow PI 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2) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (sqrt n) (* PI (* (pow (log n) 2) (pow k 2))))) (- (+ (* +nan.0 (* (sqrt n) PI)) (- (+ (* +nan.0 (* (sqrt n) (* PI (* (log n) k)))) (- (* +nan.0 (* (sqrt n) (* (pow PI 3) (pow k 2))))))))))))))) (- (+ (* +nan.0 (/ (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) PI) k)) (- (+ (* +nan.0 (/ (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (pow PI 3)) (pow k 3))) (- (* +nan.0 (/ (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (pow PI 2)) (pow k 2)))))))) (- (+ (* +nan.0 (* (/ (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) k) (sqrt PI))) (- (+ (* +nan.0 (* (/ (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (pow k 2)) (sqrt PI))) (- (* +nan.0 (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (sqrt PI)))))))) 234.742 * * [simplify]: iteration 0: 2889 enodes 235.517 * * [simplify]: iteration complete: 5001 enodes 235.520 * * [simplify]: Extracting #0: cost 1518 inf + 0 235.526 * * [simplify]: Extracting #1: cost 2426 inf + 540 235.541 * * [simplify]: Extracting #2: cost 2565 inf + 3530 235.550 * * [simplify]: Extracting #3: cost 2614 inf + 9183 235.563 * * [simplify]: Extracting #4: cost 2393 inf + 66404 235.609 * * [simplify]: Extracting #5: cost 1707 inf + 440218 235.714 * * [simplify]: Extracting #6: cost 766 inf + 1080043 235.872 * * [simplify]: Extracting #7: cost 110 inf + 1572043 236.037 * * [simplify]: Extracting #8: cost 34 inf + 1619544 236.203 * * [simplify]: Extracting #9: cost 21 inf + 1626930 236.369 * * [simplify]: Extracting #10: cost 19 inf + 1629569 236.536 * * [simplify]: Extracting #11: cost 25 inf + 1629569 236.703 * * [simplify]: Extracting #12: cost 22 inf + 1630736 236.870 * * [simplify]: Extracting #13: cost 13 inf + 1633425 237.037 * * [simplify]: Extracting #14: cost 10 inf + 1635092 237.205 * * [simplify]: Extracting #15: cost 8 inf + 1636755 237.373 * * [simplify]: Extracting #16: cost 5 inf + 1639497 237.542 * * [simplify]: Extracting #17: cost 0 inf + 1645742 237.712 * * [simplify]: Extracting #18: cost 0 inf + 1645677 237.913 * [simplify]: Simplified to: (expm1 (sqrt PI)) (log1p (sqrt PI)) (* (log PI) 1/2) (* (log PI) 1/2) 1/2 (pow PI (* (cbrt 1/2) (cbrt 1/2))) (pow PI (sqrt 1/2)) PI (sqrt (* (cbrt PI) (cbrt PI))) (sqrt (cbrt PI)) (sqrt (sqrt PI)) (sqrt (sqrt PI)) 1 (sqrt PI) (log (sqrt PI)) (exp (sqrt PI)) (* (cbrt (sqrt PI)) (cbrt (sqrt PI))) (cbrt (sqrt PI)) (* (* (sqrt PI) (sqrt PI)) (sqrt PI)) (sqrt (sqrt PI)) (sqrt (sqrt PI)) (pow PI (/ 1/2 2)) (pow PI (/ 1/2 2)) (real->posit16 (sqrt PI)) (expm1 (pow n (- 1/2 (/ k 2)))) (log1p (pow n (- 1/2 (/ k 2)))) (* (log n) (- 1/2 (/ k 2))) (* (log n) (- 1/2 (/ k 2))) (- 1/2 (/ k 2)) (sqrt n) (pow n (/ k 2)) (pow n (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (pow n (sqrt (- 1/2 (/ k 2)))) n (pow n (+ (sqrt 1/2) (sqrt (/ k 2)))) (pow n (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) n (pow n (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (* (cbrt (/ k 2)) (- (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) 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k))) (* (- +nan.0) (* (sqrt n) (* (* (* PI PI) PI) (* k k)))))))))))))) (- (fma +nan.0 (/ (exp (- (* (- 1/2 (* 1/2 k)) (- (log n))))) (/ k PI)) (- (fma +nan.0 (/ (* (exp (- (* (- 1/2 (* 1/2 k)) (- (log n))))) (* (* PI PI) PI)) (* (* k k) k)) (* (- +nan.0) (/ (exp (- (* (- 1/2 (* 1/2 k)) (- (log n))))) (/ (* k k) (* PI PI)))))))) (- (fma +nan.0 (* (/ (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) k) (sqrt PI)) (- (fma +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (sqrt PI)) (* k k)) (* (- +nan.0) (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (sqrt PI))))))) 238.580 * * * [progress]: adding candidates to table 252.369 * [progress]: [Phase 3 of 3] Extracting. 252.369 * * [regime]: Finding splitpoints for: (# # # # # #) 252.370 * * * [regime-changes]: Trying 2 branch expressions: (n k) 252.370 * * * * [regimes]: Trying to branch on n from (# # # # # #) 252.413 * * * * [regimes]: Trying to branch on k from (# # # # # #) 252.454 * * * [regime]: Found split indices: #