53.046 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.204 * * * [progress]: [2/2] Setting up program. 0.213 * [progress]: [Phase 2 of 3] Improving. 0.213 * [simplify]: Simplifying: (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 0.213 * * [simplify]: iteration 0: 13 enodes 0.219 * * [simplify]: iteration 1: 29 enodes 0.231 * * [simplify]: iteration 2: 58 enodes 0.243 * * [simplify]: iteration 3: 114 enodes 0.267 * * [simplify]: iteration 4: 285 enodes 0.399 * * [simplify]: iteration 5: 806 enodes 1.361 * * [simplify]: iteration 6: 2693 enodes 2.244 * * [simplify]: iteration complete: 5001 enodes 2.244 * * [simplify]: Extracting #0: cost 1 inf + 0 2.244 * * [simplify]: Extracting #1: cost 108 inf + 0 2.246 * * [simplify]: Extracting #2: cost 443 inf + 1 2.249 * * [simplify]: Extracting #3: cost 1003 inf + 8 2.256 * * [simplify]: Extracting #4: cost 1325 inf + 10758 2.275 * * [simplify]: Extracting #5: cost 713 inf + 95758 2.345 * * [simplify]: Extracting #6: cost 212 inf + 355864 2.470 * * [simplify]: Extracting #7: cost 1 inf + 567087 2.635 * * [simplify]: Extracting #8: cost 0 inf + 554854 2.794 * [simplify]: Simplified to: (/ (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)) 2.795 * * [progress]: iteration 1 / 4 2.795 * * * [progress]: picking best candidate 2.804 * * * * [pick]: Picked # 2.804 * * * [progress]: localizing error 2.850 * * * [progress]: generating rewritten candidates 2.850 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 2.882 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1) 2.908 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1) 2.918 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 2.994 * * * [progress]: generating series expansions 2.994 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 2.995 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 2.995 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 2.995 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 2.995 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 2.995 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 2.995 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 2.996 * [taylor]: Taking taylor expansion of 0.5 in k 2.996 * [backup-simplify]: Simplify 0.5 into 0.5 2.996 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.996 * [taylor]: Taking taylor expansion of 1.0 in k 2.996 * [backup-simplify]: Simplify 1.0 into 1.0 2.996 * [taylor]: Taking taylor expansion of k in k 2.996 * [backup-simplify]: Simplify 0 into 0 2.996 * [backup-simplify]: Simplify 1 into 1 2.996 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 2.996 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 2.996 * [taylor]: Taking taylor expansion of 2.0 in k 2.996 * [backup-simplify]: Simplify 2.0 into 2.0 2.996 * [taylor]: Taking taylor expansion of (* n PI) in k 2.996 * [taylor]: Taking taylor expansion of n in k 2.996 * [backup-simplify]: Simplify n into n 2.996 * [taylor]: Taking taylor expansion of PI in k 2.996 * [backup-simplify]: Simplify PI into PI 2.996 * [backup-simplify]: Simplify (* n PI) into (* n PI) 2.996 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 2.996 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 2.997 * [backup-simplify]: Simplify (- 0) into 0 2.997 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.998 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 2.998 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 2.998 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 2.998 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 2.998 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.998 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.998 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 2.998 * [taylor]: Taking taylor expansion of 0.5 in n 2.998 * [backup-simplify]: Simplify 0.5 into 0.5 2.998 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.998 * [taylor]: Taking taylor expansion of 1.0 in n 2.998 * [backup-simplify]: Simplify 1.0 into 1.0 2.998 * [taylor]: Taking taylor expansion of k in n 2.998 * [backup-simplify]: Simplify k into k 2.998 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.998 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.998 * [taylor]: Taking taylor expansion of 2.0 in n 2.999 * [backup-simplify]: Simplify 2.0 into 2.0 2.999 * [taylor]: Taking taylor expansion of (* n PI) in n 2.999 * [taylor]: Taking taylor expansion of n in n 2.999 * [backup-simplify]: Simplify 0 into 0 2.999 * [backup-simplify]: Simplify 1 into 1 2.999 * [taylor]: Taking taylor expansion of PI in n 2.999 * [backup-simplify]: Simplify PI into PI 2.999 * [backup-simplify]: Simplify (* 0 PI) into 0 3.000 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.001 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.003 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.004 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.004 * [backup-simplify]: Simplify (- k) into (- k) 3.004 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 3.004 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 3.006 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.007 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 3.008 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 3.008 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 3.008 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 3.008 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 3.008 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 3.008 * [taylor]: Taking taylor expansion of 0.5 in n 3.008 * [backup-simplify]: Simplify 0.5 into 0.5 3.008 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 3.008 * [taylor]: Taking taylor expansion of 1.0 in n 3.009 * [backup-simplify]: Simplify 1.0 into 1.0 3.009 * [taylor]: Taking taylor expansion of k in n 3.009 * [backup-simplify]: Simplify k into k 3.009 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.009 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.009 * [taylor]: Taking taylor expansion of 2.0 in n 3.009 * [backup-simplify]: Simplify 2.0 into 2.0 3.009 * [taylor]: Taking taylor expansion of (* n PI) in n 3.009 * [taylor]: Taking taylor expansion of n in n 3.009 * [backup-simplify]: Simplify 0 into 0 3.009 * [backup-simplify]: Simplify 1 into 1 3.009 * [taylor]: Taking taylor expansion of PI in n 3.009 * [backup-simplify]: Simplify PI into PI 3.009 * [backup-simplify]: Simplify (* 0 PI) into 0 3.010 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.011 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.013 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.014 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.014 * [backup-simplify]: Simplify (- k) into (- k) 3.014 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 3.014 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 3.016 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.017 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 3.018 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 3.019 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 3.019 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 3.019 * [taylor]: Taking taylor expansion of 0.5 in k 3.019 * [backup-simplify]: Simplify 0.5 into 0.5 3.019 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 3.019 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 3.019 * [taylor]: Taking taylor expansion of 1.0 in k 3.019 * [backup-simplify]: Simplify 1.0 into 1.0 3.019 * [taylor]: Taking taylor expansion of k in k 3.019 * [backup-simplify]: Simplify 0 into 0 3.019 * [backup-simplify]: Simplify 1 into 1 3.019 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 3.019 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 3.019 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 3.019 * [taylor]: Taking taylor expansion of 2.0 in k 3.019 * [backup-simplify]: Simplify 2.0 into 2.0 3.019 * [taylor]: Taking taylor expansion of PI in k 3.019 * [backup-simplify]: Simplify PI into PI 3.020 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.021 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.021 * [taylor]: Taking taylor expansion of (log n) in k 3.021 * [taylor]: Taking taylor expansion of n in k 3.021 * [backup-simplify]: Simplify n into n 3.021 * [backup-simplify]: Simplify (log n) into (log n) 3.021 * [backup-simplify]: Simplify (- 0) into 0 3.022 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 3.023 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 3.024 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 3.025 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 3.026 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 3.028 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 3.029 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 3.030 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 3.032 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 3.032 * [backup-simplify]: Simplify (- 0) into 0 3.033 * [backup-simplify]: Simplify (+ 0 0) into 0 3.034 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 3.035 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.036 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 3.038 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 3.038 * [taylor]: Taking taylor expansion of 0 in k 3.038 * [backup-simplify]: Simplify 0 into 0 3.038 * [backup-simplify]: Simplify 0 into 0 3.039 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 3.041 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 3.042 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 3.042 * [backup-simplify]: Simplify (+ 0 0) into 0 3.042 * [backup-simplify]: Simplify (- 1) into -1 3.043 * [backup-simplify]: Simplify (+ 0 -1) into -1 3.044 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 3.046 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 3.050 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 3.052 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 3.054 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 3.055 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 3.058 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 3.059 * [backup-simplify]: Simplify (- 0) into 0 3.059 * [backup-simplify]: Simplify (+ 0 0) into 0 3.060 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 3.061 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.063 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 3.070 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 3.070 * [taylor]: Taking taylor expansion of 0 in k 3.070 * [backup-simplify]: Simplify 0 into 0 3.070 * [backup-simplify]: Simplify 0 into 0 3.070 * [backup-simplify]: Simplify 0 into 0 3.072 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 3.075 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 3.077 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 3.078 * [backup-simplify]: Simplify (+ 0 0) into 0 3.078 * [backup-simplify]: Simplify (- 0) into 0 3.078 * [backup-simplify]: Simplify (+ 0 0) into 0 3.079 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 3.081 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 3.083 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 3.086 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 3.093 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.25 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2))))) (+ (* 0.125 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* 0.125 (* (pow (log (* 2.0 PI)) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))))))) (+ (* 0.5 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k))) (* 0.5 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k))))) 3.093 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) 3.093 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 3.093 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 3.093 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 3.093 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 3.093 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 3.093 * [taylor]: Taking taylor expansion of 0.5 in k 3.093 * [backup-simplify]: Simplify 0.5 into 0.5 3.093 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 3.093 * [taylor]: Taking taylor expansion of 1.0 in k 3.093 * [backup-simplify]: Simplify 1.0 into 1.0 3.093 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.093 * [taylor]: Taking taylor expansion of k in k 3.093 * [backup-simplify]: Simplify 0 into 0 3.093 * [backup-simplify]: Simplify 1 into 1 3.094 * [backup-simplify]: Simplify (/ 1 1) into 1 3.094 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 3.094 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 3.094 * [taylor]: Taking taylor expansion of 2.0 in k 3.094 * [backup-simplify]: Simplify 2.0 into 2.0 3.094 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.094 * [taylor]: Taking taylor expansion of PI in k 3.094 * [backup-simplify]: Simplify PI into PI 3.094 * [taylor]: Taking taylor expansion of n in k 3.094 * [backup-simplify]: Simplify n into n 3.094 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 3.094 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 3.094 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 3.094 * [backup-simplify]: Simplify (- 1) into -1 3.094 * [backup-simplify]: Simplify (+ 0 -1) into -1 3.095 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 3.095 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 3.095 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) 3.095 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 3.095 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 3.095 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 3.095 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 3.095 * [taylor]: Taking taylor expansion of 0.5 in n 3.095 * [backup-simplify]: Simplify 0.5 into 0.5 3.095 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.095 * [taylor]: Taking taylor expansion of 1.0 in n 3.095 * [backup-simplify]: Simplify 1.0 into 1.0 3.095 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.095 * [taylor]: Taking taylor expansion of k in n 3.095 * [backup-simplify]: Simplify k into k 3.095 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.095 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.095 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.095 * [taylor]: Taking taylor expansion of 2.0 in n 3.095 * [backup-simplify]: Simplify 2.0 into 2.0 3.095 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.095 * [taylor]: Taking taylor expansion of PI in n 3.095 * [backup-simplify]: Simplify PI into PI 3.095 * [taylor]: Taking taylor expansion of n in n 3.095 * [backup-simplify]: Simplify 0 into 0 3.095 * [backup-simplify]: Simplify 1 into 1 3.096 * [backup-simplify]: Simplify (/ PI 1) into PI 3.096 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.097 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.097 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 3.097 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 3.097 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 3.098 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.099 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) 3.099 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 3.099 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 3.099 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 3.099 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 3.099 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 3.099 * [taylor]: Taking taylor expansion of 0.5 in n 3.099 * [backup-simplify]: Simplify 0.5 into 0.5 3.099 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.099 * [taylor]: Taking taylor expansion of 1.0 in n 3.099 * [backup-simplify]: Simplify 1.0 into 1.0 3.099 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.099 * [taylor]: Taking taylor expansion of k in n 3.099 * [backup-simplify]: Simplify k into k 3.100 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.100 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.100 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.100 * [taylor]: Taking taylor expansion of 2.0 in n 3.100 * [backup-simplify]: Simplify 2.0 into 2.0 3.100 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.100 * [taylor]: Taking taylor expansion of PI in n 3.100 * [backup-simplify]: Simplify PI into PI 3.100 * [taylor]: Taking taylor expansion of n in n 3.100 * [backup-simplify]: Simplify 0 into 0 3.100 * [backup-simplify]: Simplify 1 into 1 3.100 * [backup-simplify]: Simplify (/ PI 1) into PI 3.100 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.101 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.101 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 3.101 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 3.101 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 3.102 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.103 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) 3.103 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 3.104 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) in k 3.104 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) in k 3.104 * [taylor]: Taking taylor expansion of 0.5 in k 3.104 * [backup-simplify]: Simplify 0.5 into 0.5 3.104 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) in k 3.104 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 3.104 * [taylor]: Taking taylor expansion of 1.0 in k 3.104 * [backup-simplify]: Simplify 1.0 into 1.0 3.104 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.104 * [taylor]: Taking taylor expansion of k in k 3.104 * [backup-simplify]: Simplify 0 into 0 3.104 * [backup-simplify]: Simplify 1 into 1 3.104 * [backup-simplify]: Simplify (/ 1 1) into 1 3.104 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 3.104 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 3.104 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 3.104 * [taylor]: Taking taylor expansion of 2.0 in k 3.104 * [backup-simplify]: Simplify 2.0 into 2.0 3.104 * [taylor]: Taking taylor expansion of PI in k 3.104 * [backup-simplify]: Simplify PI into PI 3.104 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.105 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.105 * [taylor]: Taking taylor expansion of (log n) in k 3.105 * [taylor]: Taking taylor expansion of n in k 3.105 * [backup-simplify]: Simplify n into n 3.105 * [backup-simplify]: Simplify (log n) into (log n) 3.105 * [backup-simplify]: Simplify (- 1) into -1 3.106 * [backup-simplify]: Simplify (+ 0 -1) into -1 3.106 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 3.106 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 3.107 * [backup-simplify]: Simplify (* -1 (- (log (* 2.0 PI)) (log n))) into (* -1 (- (log (* 2.0 PI)) (log n))) 3.108 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 3.108 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 3.109 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 3.110 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 3.111 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 3.113 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 3.113 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 3.114 * [backup-simplify]: Simplify (- 0) into 0 3.114 * [backup-simplify]: Simplify (+ 0 0) into 0 3.115 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 3.117 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.118 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 3.120 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 3.120 * [taylor]: Taking taylor expansion of 0 in k 3.120 * [backup-simplify]: Simplify 0 into 0 3.120 * [backup-simplify]: Simplify 0 into 0 3.120 * [backup-simplify]: Simplify 0 into 0 3.121 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.122 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 3.126 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 3.126 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 3.126 * [backup-simplify]: Simplify (- 0) into 0 3.127 * [backup-simplify]: Simplify (+ 0 0) into 0 3.128 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 3.129 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.131 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 3.133 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 3.133 * [taylor]: Taking taylor expansion of 0 in k 3.133 * [backup-simplify]: Simplify 0 into 0 3.134 * [backup-simplify]: Simplify 0 into 0 3.134 * [backup-simplify]: Simplify 0 into 0 3.134 * [backup-simplify]: Simplify 0 into 0 3.135 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.136 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 3.142 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 3.143 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 3.143 * [backup-simplify]: Simplify (- 0) into 0 3.144 * [backup-simplify]: Simplify (+ 0 0) into 0 3.145 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 3.147 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.149 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 3.152 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 3.152 * [taylor]: Taking taylor expansion of 0 in k 3.152 * [backup-simplify]: Simplify 0 into 0 3.152 * [backup-simplify]: Simplify 0 into 0 3.153 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) 3.154 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) 3.154 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 3.154 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 3.154 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 3.154 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 3.154 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 3.154 * [taylor]: Taking taylor expansion of 0.5 in k 3.154 * [backup-simplify]: Simplify 0.5 into 0.5 3.154 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 3.155 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.155 * [taylor]: Taking taylor expansion of k in k 3.155 * [backup-simplify]: Simplify 0 into 0 3.155 * [backup-simplify]: Simplify 1 into 1 3.155 * [backup-simplify]: Simplify (/ 1 1) into 1 3.155 * [taylor]: Taking taylor expansion of 1.0 in k 3.155 * [backup-simplify]: Simplify 1.0 into 1.0 3.155 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 3.155 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 3.155 * [taylor]: Taking taylor expansion of -2.0 in k 3.155 * [backup-simplify]: Simplify -2.0 into -2.0 3.155 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.155 * [taylor]: Taking taylor expansion of PI in k 3.155 * [backup-simplify]: Simplify PI into PI 3.155 * [taylor]: Taking taylor expansion of n in k 3.155 * [backup-simplify]: Simplify n into n 3.155 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 3.155 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 3.156 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 3.156 * [backup-simplify]: Simplify (+ 1 0) into 1 3.157 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 3.157 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 3.157 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) 3.157 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 3.157 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 3.157 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 3.157 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 3.157 * [taylor]: Taking taylor expansion of 0.5 in n 3.157 * [backup-simplify]: Simplify 0.5 into 0.5 3.157 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.157 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.157 * [taylor]: Taking taylor expansion of k in n 3.157 * [backup-simplify]: Simplify k into k 3.157 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.157 * [taylor]: Taking taylor expansion of 1.0 in n 3.157 * [backup-simplify]: Simplify 1.0 into 1.0 3.157 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 3.158 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.158 * [taylor]: Taking taylor expansion of -2.0 in n 3.158 * [backup-simplify]: Simplify -2.0 into -2.0 3.158 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.158 * [taylor]: Taking taylor expansion of PI in n 3.158 * [backup-simplify]: Simplify PI into PI 3.158 * [taylor]: Taking taylor expansion of n in n 3.158 * [backup-simplify]: Simplify 0 into 0 3.158 * [backup-simplify]: Simplify 1 into 1 3.158 * [backup-simplify]: Simplify (/ PI 1) into PI 3.159 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.160 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 3.160 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 3.161 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 3.162 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.163 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) 3.165 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 3.165 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 3.165 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 3.165 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 3.165 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 3.165 * [taylor]: Taking taylor expansion of 0.5 in n 3.165 * [backup-simplify]: Simplify 0.5 into 0.5 3.165 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.165 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.165 * [taylor]: Taking taylor expansion of k in n 3.165 * [backup-simplify]: Simplify k into k 3.165 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.165 * [taylor]: Taking taylor expansion of 1.0 in n 3.165 * [backup-simplify]: Simplify 1.0 into 1.0 3.165 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 3.165 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.165 * [taylor]: Taking taylor expansion of -2.0 in n 3.165 * [backup-simplify]: Simplify -2.0 into -2.0 3.165 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.165 * [taylor]: Taking taylor expansion of PI in n 3.165 * [backup-simplify]: Simplify PI into PI 3.165 * [taylor]: Taking taylor expansion of n in n 3.165 * [backup-simplify]: Simplify 0 into 0 3.165 * [backup-simplify]: Simplify 1 into 1 3.166 * [backup-simplify]: Simplify (/ PI 1) into PI 3.167 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.168 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 3.168 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 3.168 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 3.169 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.171 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) 3.172 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 3.172 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) in k 3.172 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) in k 3.172 * [taylor]: Taking taylor expansion of 0.5 in k 3.172 * [backup-simplify]: Simplify 0.5 into 0.5 3.172 * [taylor]: Taking taylor expansion of (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) in k 3.172 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 3.172 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 3.172 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 3.172 * [taylor]: Taking taylor expansion of -2.0 in k 3.172 * [backup-simplify]: Simplify -2.0 into -2.0 3.172 * [taylor]: Taking taylor expansion of PI in k 3.172 * [backup-simplify]: Simplify PI into PI 3.173 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.174 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 3.174 * [taylor]: Taking taylor expansion of (log n) in k 3.174 * [taylor]: Taking taylor expansion of n in k 3.174 * [backup-simplify]: Simplify n into n 3.174 * [backup-simplify]: Simplify (log n) into (log n) 3.174 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 3.174 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.174 * [taylor]: Taking taylor expansion of k in k 3.174 * [backup-simplify]: Simplify 0 into 0 3.174 * [backup-simplify]: Simplify 1 into 1 3.175 * [backup-simplify]: Simplify (/ 1 1) into 1 3.175 * [taylor]: Taking taylor expansion of 1.0 in k 3.175 * [backup-simplify]: Simplify 1.0 into 1.0 3.175 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 3.176 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 3.177 * [backup-simplify]: Simplify (+ 1 0) into 1 3.178 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) 1) into (- (log (* -2.0 PI)) (log n)) 3.179 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 3.180 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 3.182 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 3.183 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 3.184 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 3.186 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 3.186 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 3.186 * [backup-simplify]: Simplify (+ 0 0) into 0 3.187 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 3.189 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.190 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 3.192 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 3.192 * [taylor]: Taking taylor expansion of 0 in k 3.192 * [backup-simplify]: Simplify 0 into 0 3.192 * [backup-simplify]: Simplify 0 into 0 3.192 * [backup-simplify]: Simplify 0 into 0 3.193 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.194 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 3.198 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 3.198 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 3.199 * [backup-simplify]: Simplify (+ 0 0) into 0 3.202 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 3.204 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.206 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 3.209 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 3.209 * [taylor]: Taking taylor expansion of 0 in k 3.209 * [backup-simplify]: Simplify 0 into 0 3.209 * [backup-simplify]: Simplify 0 into 0 3.209 * [backup-simplify]: Simplify 0 into 0 3.209 * [backup-simplify]: Simplify 0 into 0 3.210 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.211 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 3.216 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 3.216 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 3.216 * [backup-simplify]: Simplify (+ 0 0) into 0 3.217 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 3.218 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.219 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 3.221 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 3.221 * [taylor]: Taking taylor expansion of 0 in k 3.221 * [backup-simplify]: Simplify 0 into 0 3.221 * [backup-simplify]: Simplify 0 into 0 3.222 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 3.222 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1) 3.222 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 3.222 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 3.222 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.222 * [taylor]: Taking taylor expansion of 2.0 in n 3.222 * [backup-simplify]: Simplify 2.0 into 2.0 3.222 * [taylor]: Taking taylor expansion of (* n PI) in n 3.222 * [taylor]: Taking taylor expansion of n in n 3.222 * [backup-simplify]: Simplify 0 into 0 3.222 * [backup-simplify]: Simplify 1 into 1 3.222 * [taylor]: Taking taylor expansion of PI in n 3.223 * [backup-simplify]: Simplify PI into PI 3.223 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.223 * [taylor]: Taking taylor expansion of 2.0 in n 3.223 * [backup-simplify]: Simplify 2.0 into 2.0 3.223 * [taylor]: Taking taylor expansion of (* n PI) in n 3.223 * [taylor]: Taking taylor expansion of n in n 3.223 * [backup-simplify]: Simplify 0 into 0 3.223 * [backup-simplify]: Simplify 1 into 1 3.223 * [taylor]: Taking taylor expansion of PI in n 3.223 * [backup-simplify]: Simplify PI into PI 3.223 * [backup-simplify]: Simplify (* 0 PI) into 0 3.223 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.223 * [backup-simplify]: Simplify 0 into 0 3.224 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.225 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.226 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.227 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 3.227 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 3.228 * [backup-simplify]: Simplify 0 into 0 3.228 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 3.229 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 3.229 * [backup-simplify]: Simplify 0 into 0 3.230 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 3.230 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 3.230 * [backup-simplify]: Simplify 0 into 0 3.231 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 3.232 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 3.232 * [backup-simplify]: Simplify 0 into 0 3.233 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 3.234 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 3.234 * [backup-simplify]: Simplify 0 into 0 3.235 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 3.236 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 3.236 * [backup-simplify]: Simplify 0 into 0 3.237 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 3.237 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 3.237 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 3.237 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.237 * [taylor]: Taking taylor expansion of 2.0 in n 3.237 * [backup-simplify]: Simplify 2.0 into 2.0 3.237 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.237 * [taylor]: Taking taylor expansion of PI in n 3.237 * [backup-simplify]: Simplify PI into PI 3.237 * [taylor]: Taking taylor expansion of n in n 3.237 * [backup-simplify]: Simplify 0 into 0 3.237 * [backup-simplify]: Simplify 1 into 1 3.238 * [backup-simplify]: Simplify (/ PI 1) into PI 3.238 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.238 * [taylor]: Taking taylor expansion of 2.0 in n 3.238 * [backup-simplify]: Simplify 2.0 into 2.0 3.238 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.238 * [taylor]: Taking taylor expansion of PI in n 3.238 * [backup-simplify]: Simplify PI into PI 3.238 * [taylor]: Taking taylor expansion of n in n 3.238 * [backup-simplify]: Simplify 0 into 0 3.238 * [backup-simplify]: Simplify 1 into 1 3.238 * [backup-simplify]: Simplify (/ PI 1) into PI 3.238 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.239 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.239 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 3.240 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 3.240 * [backup-simplify]: Simplify 0 into 0 3.240 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.241 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 3.241 * [backup-simplify]: Simplify 0 into 0 3.242 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.242 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 3.242 * [backup-simplify]: Simplify 0 into 0 3.243 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.244 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 3.244 * [backup-simplify]: Simplify 0 into 0 3.244 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.245 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 3.245 * [backup-simplify]: Simplify 0 into 0 3.246 * [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 3.247 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 3.247 * [backup-simplify]: Simplify 0 into 0 3.247 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 3.248 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 3.248 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 3.248 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.248 * [taylor]: Taking taylor expansion of -2.0 in n 3.248 * [backup-simplify]: Simplify -2.0 into -2.0 3.248 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.248 * [taylor]: Taking taylor expansion of PI in n 3.248 * [backup-simplify]: Simplify PI into PI 3.248 * [taylor]: Taking taylor expansion of n in n 3.248 * [backup-simplify]: Simplify 0 into 0 3.248 * [backup-simplify]: Simplify 1 into 1 3.248 * [backup-simplify]: Simplify (/ PI 1) into PI 3.248 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.248 * [taylor]: Taking taylor expansion of -2.0 in n 3.248 * [backup-simplify]: Simplify -2.0 into -2.0 3.248 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.248 * [taylor]: Taking taylor expansion of PI in n 3.248 * [backup-simplify]: Simplify PI into PI 3.248 * [taylor]: Taking taylor expansion of n in n 3.248 * [backup-simplify]: Simplify 0 into 0 3.248 * [backup-simplify]: Simplify 1 into 1 3.249 * [backup-simplify]: Simplify (/ PI 1) into PI 3.249 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.249 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.250 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 3.251 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 3.251 * [backup-simplify]: Simplify 0 into 0 3.252 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.253 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 3.253 * [backup-simplify]: Simplify 0 into 0 3.254 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.256 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 3.256 * [backup-simplify]: Simplify 0 into 0 3.257 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.258 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 3.258 * [backup-simplify]: Simplify 0 into 0 3.259 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.261 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 3.261 * [backup-simplify]: Simplify 0 into 0 3.262 * [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 3.264 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 3.264 * [backup-simplify]: Simplify 0 into 0 3.265 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 3.265 * * * * [progress]: [ 3 / 4 ] generating series at (2 1) 3.265 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 3.265 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 3.265 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 3.265 * [taylor]: Taking taylor expansion of 1.0 in k 3.265 * [backup-simplify]: Simplify 1.0 into 1.0 3.265 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 3.265 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.265 * [taylor]: Taking taylor expansion of k in k 3.265 * [backup-simplify]: Simplify 0 into 0 3.265 * [backup-simplify]: Simplify 1 into 1 3.266 * [backup-simplify]: Simplify (/ 1 1) into 1 3.266 * [backup-simplify]: Simplify (sqrt 0) into 0 3.268 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.268 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 3.268 * [taylor]: Taking taylor expansion of 1.0 in k 3.268 * [backup-simplify]: Simplify 1.0 into 1.0 3.268 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 3.268 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.268 * [taylor]: Taking taylor expansion of k in k 3.268 * [backup-simplify]: Simplify 0 into 0 3.268 * [backup-simplify]: Simplify 1 into 1 3.268 * [backup-simplify]: Simplify (/ 1 1) into 1 3.269 * [backup-simplify]: Simplify (sqrt 0) into 0 3.270 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.271 * [backup-simplify]: Simplify (* 1.0 0) into 0 3.271 * [backup-simplify]: Simplify 0 into 0 3.272 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 3.273 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.274 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 3.277 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 3.280 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 3.280 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.281 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.285 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 3.288 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 3.288 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.290 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) 3.290 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 3.290 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 3.290 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 3.290 * [taylor]: Taking taylor expansion of 1.0 in k 3.290 * [backup-simplify]: Simplify 1.0 into 1.0 3.290 * [taylor]: Taking taylor expansion of (sqrt k) in k 3.290 * [taylor]: Taking taylor expansion of k in k 3.290 * [backup-simplify]: Simplify 0 into 0 3.290 * [backup-simplify]: Simplify 1 into 1 3.290 * [backup-simplify]: Simplify (sqrt 0) into 0 3.292 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.292 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 3.292 * [taylor]: Taking taylor expansion of 1.0 in k 3.292 * [backup-simplify]: Simplify 1.0 into 1.0 3.292 * [taylor]: Taking taylor expansion of (sqrt k) in k 3.292 * [taylor]: Taking taylor expansion of k in k 3.292 * [backup-simplify]: Simplify 0 into 0 3.292 * [backup-simplify]: Simplify 1 into 1 3.292 * [backup-simplify]: Simplify (sqrt 0) into 0 3.294 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.294 * [backup-simplify]: Simplify (* 1.0 0) into 0 3.294 * [backup-simplify]: Simplify 0 into 0 3.296 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 3.296 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.299 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 3.301 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 3.301 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.305 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 3.307 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 3.308 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.309 * [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)))))))) 3.309 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 3.309 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 3.309 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 3.309 * [taylor]: Taking taylor expansion of 1.0 in k 3.310 * [backup-simplify]: Simplify 1.0 into 1.0 3.310 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 3.310 * [taylor]: Taking taylor expansion of (/ -1 k) in k 3.310 * [taylor]: Taking taylor expansion of -1 in k 3.310 * [backup-simplify]: Simplify -1 into -1 3.310 * [taylor]: Taking taylor expansion of k in k 3.310 * [backup-simplify]: Simplify 0 into 0 3.310 * [backup-simplify]: Simplify 1 into 1 3.310 * [backup-simplify]: Simplify (/ -1 1) into -1 3.310 * [backup-simplify]: Simplify (sqrt 0) into 0 3.312 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 3.312 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 3.312 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 3.312 * [taylor]: Taking taylor expansion of 1.0 in k 3.312 * [backup-simplify]: Simplify 1.0 into 1.0 3.312 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 3.312 * [taylor]: Taking taylor expansion of (/ -1 k) in k 3.312 * [taylor]: Taking taylor expansion of -1 in k 3.312 * [backup-simplify]: Simplify -1 into -1 3.312 * [taylor]: Taking taylor expansion of k in k 3.312 * [backup-simplify]: Simplify 0 into 0 3.312 * [backup-simplify]: Simplify 1 into 1 3.313 * [backup-simplify]: Simplify (/ -1 1) into -1 3.313 * [backup-simplify]: Simplify (sqrt 0) into 0 3.314 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 3.315 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 3.315 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.316 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 3.319 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 3.321 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 3.321 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.325 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.329 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 3.333 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 3.334 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.335 * [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))))) 3.335 * * * * [progress]: [ 4 / 4 ] generating series at (2) 3.336 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) into (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) 3.336 * [approximate]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in (k n) around 0 3.336 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in n 3.336 * [taylor]: Taking taylor expansion of 1.0 in n 3.336 * [backup-simplify]: Simplify 1.0 into 1.0 3.336 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in n 3.336 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 3.336 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 3.336 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 3.336 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 3.336 * [taylor]: Taking taylor expansion of 0.5 in n 3.336 * [backup-simplify]: Simplify 0.5 into 0.5 3.336 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 3.336 * [taylor]: Taking taylor expansion of 1.0 in n 3.336 * [backup-simplify]: Simplify 1.0 into 1.0 3.336 * [taylor]: Taking taylor expansion of k in n 3.336 * [backup-simplify]: Simplify k into k 3.336 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.336 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.336 * [taylor]: Taking taylor expansion of 2.0 in n 3.336 * [backup-simplify]: Simplify 2.0 into 2.0 3.336 * [taylor]: Taking taylor expansion of (* n PI) in n 3.336 * [taylor]: Taking taylor expansion of n in n 3.336 * [backup-simplify]: Simplify 0 into 0 3.336 * [backup-simplify]: Simplify 1 into 1 3.336 * [taylor]: Taking taylor expansion of PI in n 3.337 * [backup-simplify]: Simplify PI into PI 3.337 * [backup-simplify]: Simplify (* 0 PI) into 0 3.337 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.339 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.341 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.342 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.342 * [backup-simplify]: Simplify (- k) into (- k) 3.342 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 3.342 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 3.344 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.345 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 3.346 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 3.346 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 3.346 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.346 * [taylor]: Taking taylor expansion of k in n 3.346 * [backup-simplify]: Simplify k into k 3.346 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.346 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 3.346 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 3.347 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 3.347 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in k 3.347 * [taylor]: Taking taylor expansion of 1.0 in k 3.347 * [backup-simplify]: Simplify 1.0 into 1.0 3.347 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in k 3.347 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 3.347 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 3.347 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 3.347 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 3.347 * [taylor]: Taking taylor expansion of 0.5 in k 3.347 * [backup-simplify]: Simplify 0.5 into 0.5 3.347 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 3.347 * [taylor]: Taking taylor expansion of 1.0 in k 3.347 * [backup-simplify]: Simplify 1.0 into 1.0 3.347 * [taylor]: Taking taylor expansion of k in k 3.347 * [backup-simplify]: Simplify 0 into 0 3.347 * [backup-simplify]: Simplify 1 into 1 3.347 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 3.347 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 3.347 * [taylor]: Taking taylor expansion of 2.0 in k 3.347 * [backup-simplify]: Simplify 2.0 into 2.0 3.347 * [taylor]: Taking taylor expansion of (* n PI) in k 3.347 * [taylor]: Taking taylor expansion of n in k 3.347 * [backup-simplify]: Simplify n into n 3.347 * [taylor]: Taking taylor expansion of PI in k 3.347 * [backup-simplify]: Simplify PI into PI 3.347 * [backup-simplify]: Simplify (* n PI) into (* n PI) 3.347 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 3.348 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 3.348 * [backup-simplify]: Simplify (- 0) into 0 3.348 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 3.349 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 3.349 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 3.349 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 3.349 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 3.349 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.349 * [taylor]: Taking taylor expansion of k in k 3.349 * [backup-simplify]: Simplify 0 into 0 3.349 * [backup-simplify]: Simplify 1 into 1 3.350 * [backup-simplify]: Simplify (/ 1 1) into 1 3.350 * [backup-simplify]: Simplify (sqrt 0) into 0 3.351 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.351 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in k 3.352 * [taylor]: Taking taylor expansion of 1.0 in k 3.352 * [backup-simplify]: Simplify 1.0 into 1.0 3.352 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in k 3.352 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 3.352 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 3.352 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 3.352 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 3.352 * [taylor]: Taking taylor expansion of 0.5 in k 3.352 * [backup-simplify]: Simplify 0.5 into 0.5 3.352 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 3.352 * [taylor]: Taking taylor expansion of 1.0 in k 3.352 * [backup-simplify]: Simplify 1.0 into 1.0 3.352 * [taylor]: Taking taylor expansion of k in k 3.352 * [backup-simplify]: Simplify 0 into 0 3.352 * [backup-simplify]: Simplify 1 into 1 3.352 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 3.352 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 3.352 * [taylor]: Taking taylor expansion of 2.0 in k 3.352 * [backup-simplify]: Simplify 2.0 into 2.0 3.352 * [taylor]: Taking taylor expansion of (* n PI) in k 3.352 * [taylor]: Taking taylor expansion of n in k 3.352 * [backup-simplify]: Simplify n into n 3.352 * [taylor]: Taking taylor expansion of PI in k 3.352 * [backup-simplify]: Simplify PI into PI 3.352 * [backup-simplify]: Simplify (* n PI) into (* n PI) 3.352 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 3.353 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 3.353 * [backup-simplify]: Simplify (- 0) into 0 3.353 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 3.354 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 3.354 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 3.354 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 3.354 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 3.354 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.354 * [taylor]: Taking taylor expansion of k in k 3.354 * [backup-simplify]: Simplify 0 into 0 3.354 * [backup-simplify]: Simplify 1 into 1 3.355 * [backup-simplify]: Simplify (/ 1 1) into 1 3.355 * [backup-simplify]: Simplify (sqrt 0) into 0 3.357 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.357 * [backup-simplify]: Simplify (* (pow (* 2.0 (* n PI)) 0.5) 0) into 0 3.357 * [backup-simplify]: Simplify (* 1.0 0) into 0 3.357 * [taylor]: Taking taylor expansion of 0 in n 3.357 * [backup-simplify]: Simplify 0 into 0 3.358 * [backup-simplify]: Simplify 0 into 0 3.358 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 3.359 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* n PI))) into 0 3.359 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 1) into 0 3.360 * [backup-simplify]: Simplify (- 1) into -1 3.360 * [backup-simplify]: Simplify (+ 0 -1) into -1 3.362 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5) 3.363 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 (* n PI))))) into (- (* 0.5 (log (* 2.0 (* n PI))))) 3.363 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 1) 1)))) into (* -0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) 3.365 * [backup-simplify]: Simplify (+ (* (pow (* 2.0 (* n PI)) 0.5) +nan.0) (* (* -0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) 0)) into (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) 3.367 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) (* 0 0)) into (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 3.367 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) in n 3.367 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) in n 3.367 * [taylor]: Taking taylor expansion of +nan.0 in n 3.367 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.367 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 3.367 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 3.367 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 3.367 * [taylor]: Taking taylor expansion of 0.5 in n 3.367 * [backup-simplify]: Simplify 0.5 into 0.5 3.368 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 3.368 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 3.368 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 3.368 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 3.368 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 3.368 * [taylor]: Taking taylor expansion of 1.0 in n 3.368 * [backup-simplify]: Simplify 1.0 into 1.0 3.368 * [taylor]: Taking taylor expansion of (log PI) in n 3.368 * [taylor]: Taking taylor expansion of PI in n 3.368 * [backup-simplify]: Simplify PI into PI 3.368 * [backup-simplify]: Simplify (log PI) into (log PI) 3.369 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 3.371 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 3.371 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 3.371 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 3.371 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 3.371 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 3.371 * [taylor]: Taking taylor expansion of 1.0 in n 3.371 * [backup-simplify]: Simplify 1.0 into 1.0 3.371 * [taylor]: Taking taylor expansion of (log n) in n 3.371 * [taylor]: Taking taylor expansion of n in n 3.371 * [backup-simplify]: Simplify 0 into 0 3.371 * [backup-simplify]: Simplify 1 into 1 3.372 * [backup-simplify]: Simplify (log 1) into 0 3.372 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 3.372 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 3.372 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 3.372 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 3.372 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 3.372 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 3.372 * [taylor]: Taking taylor expansion of 1.0 in n 3.372 * [backup-simplify]: Simplify 1.0 into 1.0 3.372 * [taylor]: Taking taylor expansion of (log 2.0) in n 3.372 * [taylor]: Taking taylor expansion of 2.0 in n 3.373 * [backup-simplify]: Simplify 2.0 into 2.0 3.373 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 3.374 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 3.375 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 3.376 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0) 3.377 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 3.379 * [backup-simplify]: Simplify (log (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)) 3.380 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0))) 3.382 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 3.383 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) 3.385 * [backup-simplify]: Simplify (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) into (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) 3.386 * [backup-simplify]: Simplify (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 3.386 * [backup-simplify]: Simplify 0 into 0 3.387 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 3.391 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 3.391 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 3.392 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 3.394 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 (* n PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 2) into 0 3.395 * [backup-simplify]: Simplify (- 0) into 0 3.395 * [backup-simplify]: Simplify (+ 0 0) into 0 3.396 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0 3.397 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 (* n PI)))))) into 0 3.399 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) 3.402 * [backup-simplify]: Simplify (+ (* (pow (* 2.0 (* n PI)) 0.5) +nan.0) (+ (* (* -0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) +nan.0) (* (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) 0))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))) 3.408 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))) (+ (* 0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) (* 0 0))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))) 3.408 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))) in n 3.408 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) in n 3.408 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) in n 3.408 * [taylor]: Taking taylor expansion of +nan.0 in n 3.408 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.408 * [taylor]: Taking taylor expansion of (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI)))) in n 3.408 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 3.408 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 3.408 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 3.408 * [taylor]: Taking taylor expansion of 0.5 in n 3.408 * [backup-simplify]: Simplify 0.5 into 0.5 3.409 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 3.409 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 3.409 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 3.409 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 3.409 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 3.409 * [taylor]: Taking taylor expansion of 1.0 in n 3.409 * [backup-simplify]: Simplify 1.0 into 1.0 3.409 * [taylor]: Taking taylor expansion of (log PI) in n 3.409 * [taylor]: Taking taylor expansion of PI in n 3.409 * [backup-simplify]: Simplify PI into PI 3.409 * [backup-simplify]: Simplify (log PI) into (log PI) 3.410 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 3.412 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 3.412 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 3.412 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 3.412 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 3.412 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 3.412 * [taylor]: Taking taylor expansion of 1.0 in n 3.412 * [backup-simplify]: Simplify 1.0 into 1.0 3.412 * [taylor]: Taking taylor expansion of (log n) in n 3.412 * [taylor]: Taking taylor expansion of n in n 3.412 * [backup-simplify]: Simplify 0 into 0 3.412 * [backup-simplify]: Simplify 1 into 1 3.413 * [backup-simplify]: Simplify (log 1) into 0 3.413 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 3.413 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 3.413 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 3.413 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 3.413 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 3.413 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 3.413 * [taylor]: Taking taylor expansion of 1.0 in n 3.413 * [backup-simplify]: Simplify 1.0 into 1.0 3.414 * [taylor]: Taking taylor expansion of (log 2.0) in n 3.414 * [taylor]: Taking taylor expansion of 2.0 in n 3.414 * [backup-simplify]: Simplify 2.0 into 2.0 3.414 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 3.415 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 3.416 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 3.417 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0) 3.418 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 3.420 * [backup-simplify]: Simplify (log (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)) 3.421 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0))) 3.423 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 3.423 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.423 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.423 * [taylor]: Taking taylor expansion of 2.0 in n 3.423 * [backup-simplify]: Simplify 2.0 into 2.0 3.423 * [taylor]: Taking taylor expansion of (* n PI) in n 3.423 * [taylor]: Taking taylor expansion of n in n 3.423 * [backup-simplify]: Simplify 0 into 0 3.423 * [backup-simplify]: Simplify 1 into 1 3.423 * [taylor]: Taking taylor expansion of PI in n 3.423 * [backup-simplify]: Simplify PI into PI 3.423 * [backup-simplify]: Simplify (* 0 PI) into 0 3.424 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.425 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.427 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.428 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.428 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) in n 3.428 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) in n 3.428 * [taylor]: Taking taylor expansion of +nan.0 in n 3.428 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.428 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 3.428 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 3.428 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 3.428 * [taylor]: Taking taylor expansion of 0.5 in n 3.428 * [backup-simplify]: Simplify 0.5 into 0.5 3.428 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 3.428 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 3.428 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 3.429 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 3.429 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 3.429 * [taylor]: Taking taylor expansion of 1.0 in n 3.429 * [backup-simplify]: Simplify 1.0 into 1.0 3.429 * [taylor]: Taking taylor expansion of (log PI) in n 3.429 * [taylor]: Taking taylor expansion of PI in n 3.429 * [backup-simplify]: Simplify PI into PI 3.429 * [backup-simplify]: Simplify (log PI) into (log PI) 3.430 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 3.432 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 3.432 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 3.432 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 3.432 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 3.432 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 3.432 * [taylor]: Taking taylor expansion of 1.0 in n 3.432 * [backup-simplify]: Simplify 1.0 into 1.0 3.432 * [taylor]: Taking taylor expansion of (log n) in n 3.432 * [taylor]: Taking taylor expansion of n in n 3.432 * [backup-simplify]: Simplify 0 into 0 3.432 * [backup-simplify]: Simplify 1 into 1 3.432 * [backup-simplify]: Simplify (log 1) into 0 3.433 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 3.433 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 3.433 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 3.433 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 3.433 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 3.433 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 3.433 * [taylor]: Taking taylor expansion of 1.0 in n 3.433 * [backup-simplify]: Simplify 1.0 into 1.0 3.433 * [taylor]: Taking taylor expansion of (log 2.0) in n 3.433 * [taylor]: Taking taylor expansion of 2.0 in n 3.433 * [backup-simplify]: Simplify 2.0 into 2.0 3.434 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 3.435 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 3.436 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 3.437 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0) 3.438 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 3.439 * [backup-simplify]: Simplify (log (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)) 3.441 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0))) 3.442 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 3.444 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.446 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) (+ (log (* 2.0 PI)) (log n))) into (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n))) 3.449 * [backup-simplify]: Simplify (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n)))) into (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n)))) 3.451 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) 3.452 * [backup-simplify]: Simplify (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) into (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) 3.457 * [backup-simplify]: Simplify (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n)))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))))) 3.462 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))) into (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log (* 2.0 PI))))))))) 3.466 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log (* 2.0 PI))))))))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))))) 3.467 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0 3.467 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log 2.0))) into 0 3.468 * [backup-simplify]: Simplify (* (exp (* 1.0 (log 2.0))) (+ (* (/ (pow 0 1) 1)))) into 0 3.469 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 3.469 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 3.470 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log n))) into 0 3.470 * [backup-simplify]: Simplify (* (exp (* 1.0 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 3.471 * [backup-simplify]: Simplify (+ (* (pow n 1.0) 0) (* 0 (pow 2.0 1.0))) into 0 3.474 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 3.474 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log PI))) into 0 3.475 * [backup-simplify]: Simplify (* (exp (* 1.0 (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 3.476 * [backup-simplify]: Simplify (+ (* (pow PI 1.0) 0) (* 0 (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0))) into 0 3.478 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1)))) 1) into 0 3.479 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)))) into 0 3.480 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 3.481 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5))) into 0 3.481 * [backup-simplify]: Simplify (- 0) into 0 3.481 * [backup-simplify]: Simplify 0 into 0 3.481 * [backup-simplify]: Simplify 0 into 0 3.482 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.487 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 3.488 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 3.489 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 3.492 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 (* n PI)) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 (* n PI)) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 6) into 0 3.493 * [backup-simplify]: Simplify (- 0) into 0 3.493 * [backup-simplify]: Simplify (+ 0 0) into 0 3.494 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1.0)))) into 0 3.496 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (+ (* 0 0) (* 0 (log (* 2.0 (* n PI))))))) into 0 3.498 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 3) 6)) (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -0.020833333333333332 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 3))) 3.504 * [backup-simplify]: Simplify (+ (* (pow (* 2.0 (* n PI)) 0.5) +nan.0) (+ (* (* -0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) +nan.0) (+ (* (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) +nan.0) (* (* -0.020833333333333332 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 3))) 0)))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))))) 3.516 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))))))) (+ (* 0 (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))) (+ (* 0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) (* 0 0)))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))))) 3.516 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))))) in n 3.516 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))))) in n 3.516 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) in n 3.516 * [taylor]: Taking taylor expansion of +nan.0 in n 3.516 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.516 * [taylor]: Taking taylor expansion of (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI)))) in n 3.516 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 3.516 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 3.516 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 3.516 * [taylor]: Taking taylor expansion of 0.5 in n 3.516 * [backup-simplify]: Simplify 0.5 into 0.5 3.516 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 3.516 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 3.516 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 3.516 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 3.516 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 3.516 * [taylor]: Taking taylor expansion of 1.0 in n 3.516 * [backup-simplify]: Simplify 1.0 into 1.0 3.516 * [taylor]: Taking taylor expansion of (log PI) in n 3.516 * [taylor]: Taking taylor expansion of PI in n 3.516 * [backup-simplify]: Simplify PI into PI 3.517 * [backup-simplify]: Simplify (log PI) into (log PI) 3.518 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 3.519 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 3.519 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 3.519 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 3.519 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 3.519 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 3.519 * [taylor]: Taking taylor expansion of 1.0 in n 3.519 * [backup-simplify]: Simplify 1.0 into 1.0 3.519 * [taylor]: Taking taylor expansion of (log n) in n 3.519 * [taylor]: Taking taylor expansion of n in n 3.519 * [backup-simplify]: Simplify 0 into 0 3.519 * [backup-simplify]: Simplify 1 into 1 3.520 * [backup-simplify]: Simplify (log 1) into 0 3.520 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 3.520 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 3.520 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 3.520 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 3.520 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 3.521 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 3.521 * [taylor]: Taking taylor expansion of 1.0 in n 3.521 * [backup-simplify]: Simplify 1.0 into 1.0 3.521 * [taylor]: Taking taylor expansion of (log 2.0) in n 3.521 * [taylor]: Taking taylor expansion of 2.0 in n 3.521 * [backup-simplify]: Simplify 2.0 into 2.0 3.521 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 3.522 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 3.523 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 3.524 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0) 3.525 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 3.526 * [backup-simplify]: Simplify (log (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)) 3.527 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0))) 3.529 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 3.529 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.529 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.529 * [taylor]: Taking taylor expansion of 2.0 in n 3.529 * [backup-simplify]: Simplify 2.0 into 2.0 3.529 * [taylor]: Taking taylor expansion of (* n PI) in n 3.529 * [taylor]: Taking taylor expansion of n in n 3.529 * [backup-simplify]: Simplify 0 into 0 3.529 * [backup-simplify]: Simplify 1 into 1 3.529 * [taylor]: Taking taylor expansion of PI in n 3.529 * [backup-simplify]: Simplify PI into PI 3.530 * [backup-simplify]: Simplify (* 0 PI) into 0 3.530 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.531 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.533 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.534 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.534 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))) in n 3.534 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))) in n 3.534 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) in n 3.534 * [taylor]: Taking taylor expansion of +nan.0 in n 3.534 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.534 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n 3.534 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n 3.534 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n 3.534 * [taylor]: Taking taylor expansion of 0.5 in n 3.534 * [backup-simplify]: Simplify 0.5 into 0.5 3.534 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n 3.534 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n 3.534 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 3.534 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 3.534 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 3.535 * [taylor]: Taking taylor expansion of 1.0 in n 3.535 * [backup-simplify]: Simplify 1.0 into 1.0 3.535 * [taylor]: Taking taylor expansion of (log 2.0) in n 3.535 * [taylor]: Taking taylor expansion of 2.0 in n 3.535 * [backup-simplify]: Simplify 2.0 into 2.0 3.535 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 3.536 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 3.537 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 3.537 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n 3.537 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 3.537 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 3.537 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 3.537 * [taylor]: Taking taylor expansion of 1.0 in n 3.537 * [backup-simplify]: Simplify 1.0 into 1.0 3.537 * [taylor]: Taking taylor expansion of (log n) in n 3.537 * [taylor]: Taking taylor expansion of n in n 3.537 * [backup-simplify]: Simplify 0 into 0 3.538 * [backup-simplify]: Simplify 1 into 1 3.538 * [backup-simplify]: Simplify (log 1) into 0 3.538 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 3.538 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 3.538 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 3.538 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 3.538 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 3.539 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 3.539 * [taylor]: Taking taylor expansion of 1.0 in n 3.539 * [backup-simplify]: Simplify 1.0 into 1.0 3.539 * [taylor]: Taking taylor expansion of (log PI) in n 3.539 * [taylor]: Taking taylor expansion of PI in n 3.539 * [backup-simplify]: Simplify PI into PI 3.539 * [backup-simplify]: Simplify (log PI) into (log PI) 3.540 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 3.542 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 3.543 * [backup-simplify]: Simplify (* (pow n 1.0) (pow PI 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 3.544 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 3.545 * [backup-simplify]: Simplify (log (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0)) 3.547 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0))) 3.548 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 3.548 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))) in n 3.548 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) in n 3.548 * [taylor]: Taking taylor expansion of +nan.0 in n 3.548 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.548 * [taylor]: Taking taylor expansion of (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)) in n 3.548 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 3.548 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 3.548 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 3.548 * [taylor]: Taking taylor expansion of 0.5 in n 3.548 * [backup-simplify]: Simplify 0.5 into 0.5 3.548 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 3.549 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 3.549 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 3.549 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 3.549 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 3.549 * [taylor]: Taking taylor expansion of 1.0 in n 3.549 * [backup-simplify]: Simplify 1.0 into 1.0 3.549 * [taylor]: Taking taylor expansion of (log PI) in n 3.549 * [taylor]: Taking taylor expansion of PI in n 3.549 * [backup-simplify]: Simplify PI into PI 3.550 * [backup-simplify]: Simplify (log PI) into (log PI) 3.551 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 3.552 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 3.552 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 3.552 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 3.552 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 3.552 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 3.552 * [taylor]: Taking taylor expansion of 1.0 in n 3.553 * [backup-simplify]: Simplify 1.0 into 1.0 3.553 * [taylor]: Taking taylor expansion of (log n) in n 3.553 * [taylor]: Taking taylor expansion of n in n 3.553 * [backup-simplify]: Simplify 0 into 0 3.553 * [backup-simplify]: Simplify 1 into 1 3.553 * [backup-simplify]: Simplify (log 1) into 0 3.553 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 3.554 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 3.554 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 3.554 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 3.554 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 3.554 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 3.554 * [taylor]: Taking taylor expansion of 1.0 in n 3.554 * [backup-simplify]: Simplify 1.0 into 1.0 3.554 * [taylor]: Taking taylor expansion of (log 2.0) in n 3.554 * [taylor]: Taking taylor expansion of 2.0 in n 3.554 * [backup-simplify]: Simplify 2.0 into 2.0 3.554 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 3.555 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 3.557 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 3.558 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0) 3.559 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 3.560 * [backup-simplify]: Simplify (log (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)) 3.561 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0))) 3.563 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 3.563 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n 3.563 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.563 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.563 * [taylor]: Taking taylor expansion of 2.0 in n 3.563 * [backup-simplify]: Simplify 2.0 into 2.0 3.563 * [taylor]: Taking taylor expansion of (* n PI) in n 3.563 * [taylor]: Taking taylor expansion of n in n 3.563 * [backup-simplify]: Simplify 0 into 0 3.563 * [backup-simplify]: Simplify 1 into 1 3.563 * [taylor]: Taking taylor expansion of PI in n 3.563 * [backup-simplify]: Simplify PI into PI 3.564 * [backup-simplify]: Simplify (* 0 PI) into 0 3.564 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.565 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.567 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.568 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.569 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.571 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.573 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) (+ (log (* 2.0 PI)) (log n))) into (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n))) 3.575 * [backup-simplify]: Simplify (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n)))) into (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n)))) 3.576 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) 3.577 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.577 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.579 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (+ (log (* 2.0 PI)) (log n))) into (pow (+ (log (* 2.0 PI)) (log n)) 2) 3.580 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) (pow (+ (log (* 2.0 PI)) (log n)) 2)) into (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (+ (log (* 2.0 PI)) (log n)) 2)) 3.582 * [backup-simplify]: Simplify (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (+ (log (* 2.0 PI)) (log n)) 2))) into (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (+ (log (* 2.0 PI)) (log n)) 2))) 3.584 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (+ (log (* 2.0 PI)) (log n)) 2)))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log n) 2)))))))) 3.589 * [backup-simplify]: Simplify (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log n) 2))))))))) into (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log n) 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))) 3.596 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log n) 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log n) 2)))))))))) 3.606 * [backup-simplify]: Simplify (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log n) 2))))))))))) into (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log n) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))))))))))) 3.616 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log n) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))))))))) into (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log n) 2))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))))))))))) 3.626 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log n) 2))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))))))))))) into (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log n) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (log n))))))))))))))) 3.641 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log n) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (log n))))))))))))))) (pow (* 1 k) 2)) (+ (* (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))))) (* 1 k)) (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))) into (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) k)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow k 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (pow (log (* 2.0 PI)) 2) (pow k 2)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) k))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log n) k))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (pow k 2)))) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (pow (log n) 2) (pow k 2))))))))))))))))))))))) 3.642 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt (/ 1 k))) (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0))) into (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) 3.642 * [approximate]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in (k n) around 0 3.642 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in n 3.642 * [taylor]: Taking taylor expansion of 1.0 in n 3.642 * [backup-simplify]: Simplify 1.0 into 1.0 3.642 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in n 3.642 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 3.642 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 3.642 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 3.642 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 3.642 * [taylor]: Taking taylor expansion of 0.5 in n 3.642 * [backup-simplify]: Simplify 0.5 into 0.5 3.642 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.642 * [taylor]: Taking taylor expansion of 1.0 in n 3.642 * [backup-simplify]: Simplify 1.0 into 1.0 3.642 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.642 * [taylor]: Taking taylor expansion of k in n 3.642 * [backup-simplify]: Simplify k into k 3.642 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.642 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.642 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.643 * [taylor]: Taking taylor expansion of 2.0 in n 3.643 * [backup-simplify]: Simplify 2.0 into 2.0 3.643 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.643 * [taylor]: Taking taylor expansion of PI in n 3.643 * [backup-simplify]: Simplify PI into PI 3.643 * [taylor]: Taking taylor expansion of n in n 3.643 * [backup-simplify]: Simplify 0 into 0 3.643 * [backup-simplify]: Simplify 1 into 1 3.643 * [backup-simplify]: Simplify (/ PI 1) into PI 3.643 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.644 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.644 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 3.644 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 3.644 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 3.645 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.646 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) 3.646 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 3.646 * [taylor]: Taking taylor expansion of (sqrt k) in n 3.646 * [taylor]: Taking taylor expansion of k in n 3.646 * [backup-simplify]: Simplify k into k 3.647 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 3.647 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 3.647 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in k 3.647 * [taylor]: Taking taylor expansion of 1.0 in k 3.647 * [backup-simplify]: Simplify 1.0 into 1.0 3.647 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in k 3.647 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 3.647 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 3.647 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 3.647 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 3.647 * [taylor]: Taking taylor expansion of 0.5 in k 3.647 * [backup-simplify]: Simplify 0.5 into 0.5 3.647 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 3.647 * [taylor]: Taking taylor expansion of 1.0 in k 3.647 * [backup-simplify]: Simplify 1.0 into 1.0 3.647 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.647 * [taylor]: Taking taylor expansion of k in k 3.647 * [backup-simplify]: Simplify 0 into 0 3.647 * [backup-simplify]: Simplify 1 into 1 3.647 * [backup-simplify]: Simplify (/ 1 1) into 1 3.647 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 3.647 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 3.647 * [taylor]: Taking taylor expansion of 2.0 in k 3.647 * [backup-simplify]: Simplify 2.0 into 2.0 3.647 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.647 * [taylor]: Taking taylor expansion of PI in k 3.647 * [backup-simplify]: Simplify PI into PI 3.647 * [taylor]: Taking taylor expansion of n in k 3.647 * [backup-simplify]: Simplify n into n 3.647 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 3.647 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 3.647 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 3.648 * [backup-simplify]: Simplify (- 1) into -1 3.648 * [backup-simplify]: Simplify (+ 0 -1) into -1 3.648 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 3.648 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 3.648 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) 3.648 * [taylor]: Taking taylor expansion of (sqrt k) in k 3.648 * [taylor]: Taking taylor expansion of k in k 3.648 * [backup-simplify]: Simplify 0 into 0 3.648 * [backup-simplify]: Simplify 1 into 1 3.649 * [backup-simplify]: Simplify (sqrt 0) into 0 3.650 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.650 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in k 3.650 * [taylor]: Taking taylor expansion of 1.0 in k 3.650 * [backup-simplify]: Simplify 1.0 into 1.0 3.650 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in k 3.650 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 3.650 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 3.650 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 3.650 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 3.650 * [taylor]: Taking taylor expansion of 0.5 in k 3.650 * [backup-simplify]: Simplify 0.5 into 0.5 3.650 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 3.650 * [taylor]: Taking taylor expansion of 1.0 in k 3.650 * [backup-simplify]: Simplify 1.0 into 1.0 3.650 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.650 * [taylor]: Taking taylor expansion of k in k 3.650 * [backup-simplify]: Simplify 0 into 0 3.650 * [backup-simplify]: Simplify 1 into 1 3.650 * [backup-simplify]: Simplify (/ 1 1) into 1 3.650 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 3.650 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 3.650 * [taylor]: Taking taylor expansion of 2.0 in k 3.650 * [backup-simplify]: Simplify 2.0 into 2.0 3.650 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.650 * [taylor]: Taking taylor expansion of PI in k 3.650 * [backup-simplify]: Simplify PI into PI 3.650 * [taylor]: Taking taylor expansion of n in k 3.650 * [backup-simplify]: Simplify n into n 3.650 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 3.650 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 3.650 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 3.651 * [backup-simplify]: Simplify (- 1) into -1 3.651 * [backup-simplify]: Simplify (+ 0 -1) into -1 3.651 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 3.651 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 3.651 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) 3.652 * [taylor]: Taking taylor expansion of (sqrt k) in k 3.652 * [taylor]: Taking taylor expansion of k in k 3.652 * [backup-simplify]: Simplify 0 into 0 3.652 * [backup-simplify]: Simplify 1 into 1 3.652 * [backup-simplify]: Simplify (sqrt 0) into 0 3.653 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.653 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) 0) into 0 3.653 * [backup-simplify]: Simplify (* 1.0 0) into 0 3.653 * [taylor]: Taking taylor expansion of 0 in n 3.653 * [backup-simplify]: Simplify 0 into 0 3.653 * [backup-simplify]: Simplify 0 into 0 3.654 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) 3.654 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) 3.654 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) in n 3.654 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))) in n 3.654 * [taylor]: Taking taylor expansion of +nan.0 in n 3.654 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.654 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) in n 3.654 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))) in n 3.654 * [taylor]: Taking taylor expansion of 0.5 in n 3.654 * [backup-simplify]: Simplify 0.5 into 0.5 3.654 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))) in n 3.654 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.654 * [taylor]: Taking taylor expansion of 1.0 in n 3.654 * [backup-simplify]: Simplify 1.0 into 1.0 3.654 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.654 * [taylor]: Taking taylor expansion of k in n 3.654 * [backup-simplify]: Simplify k into k 3.654 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.654 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.654 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.654 * [taylor]: Taking taylor expansion of 2.0 in n 3.654 * [backup-simplify]: Simplify 2.0 into 2.0 3.654 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.654 * [taylor]: Taking taylor expansion of PI in n 3.654 * [backup-simplify]: Simplify PI into PI 3.654 * [taylor]: Taking taylor expansion of n in n 3.654 * [backup-simplify]: Simplify 0 into 0 3.654 * [backup-simplify]: Simplify 1 into 1 3.655 * [backup-simplify]: Simplify (/ PI 1) into PI 3.655 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.656 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.656 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 3.656 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 3.657 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.657 * [backup-simplify]: Simplify (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) into (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) 3.658 * [backup-simplify]: Simplify (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) 3.659 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 3.660 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) 3.661 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) 3.662 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) 3.662 * [backup-simplify]: Simplify 0 into 0 3.663 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 3.664 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) 3.665 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))) (* 0 0))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) 3.665 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) in n 3.665 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))) in n 3.665 * [taylor]: Taking taylor expansion of +nan.0 in n 3.665 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.665 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) in n 3.665 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))) in n 3.665 * [taylor]: Taking taylor expansion of 0.5 in n 3.665 * [backup-simplify]: Simplify 0.5 into 0.5 3.665 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))) in n 3.665 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.665 * [taylor]: Taking taylor expansion of 1.0 in n 3.665 * [backup-simplify]: Simplify 1.0 into 1.0 3.665 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.665 * [taylor]: Taking taylor expansion of k in n 3.665 * [backup-simplify]: Simplify k into k 3.665 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.665 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.665 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.665 * [taylor]: Taking taylor expansion of 2.0 in n 3.665 * [backup-simplify]: Simplify 2.0 into 2.0 3.665 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.665 * [taylor]: Taking taylor expansion of PI in n 3.665 * [backup-simplify]: Simplify PI into PI 3.665 * [taylor]: Taking taylor expansion of n in n 3.665 * [backup-simplify]: Simplify 0 into 0 3.665 * [backup-simplify]: Simplify 1 into 1 3.665 * [backup-simplify]: Simplify (/ PI 1) into PI 3.666 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.666 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.666 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 3.666 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 3.667 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.668 * [backup-simplify]: Simplify (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) into (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) 3.669 * [backup-simplify]: Simplify (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) 3.669 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 3.670 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) 3.671 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) 3.672 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) 3.672 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 3.673 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 3.674 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 3.674 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 3.674 * [backup-simplify]: Simplify (- 0) into 0 3.674 * [backup-simplify]: Simplify (+ 0 0) into 0 3.675 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.676 * [backup-simplify]: Simplify (+ (* (- 1.0 (/ 1 k)) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 3.677 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into 0 3.678 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 3.679 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into 0 3.679 * [backup-simplify]: Simplify (- 0) into 0 3.679 * [backup-simplify]: Simplify 0 into 0 3.679 * [backup-simplify]: Simplify 0 into 0 3.682 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 3.682 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) 3.683 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))) (* 0 0)))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) 3.683 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) in n 3.683 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))) in n 3.683 * [taylor]: Taking taylor expansion of +nan.0 in n 3.683 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.683 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) in n 3.683 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))) in n 3.683 * [taylor]: Taking taylor expansion of 0.5 in n 3.683 * [backup-simplify]: Simplify 0.5 into 0.5 3.683 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))) in n 3.683 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.683 * [taylor]: Taking taylor expansion of 1.0 in n 3.683 * [backup-simplify]: Simplify 1.0 into 1.0 3.683 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.683 * [taylor]: Taking taylor expansion of k in n 3.683 * [backup-simplify]: Simplify k into k 3.683 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.683 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.683 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.683 * [taylor]: Taking taylor expansion of 2.0 in n 3.683 * [backup-simplify]: Simplify 2.0 into 2.0 3.684 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.684 * [taylor]: Taking taylor expansion of PI in n 3.684 * [backup-simplify]: Simplify PI into PI 3.684 * [taylor]: Taking taylor expansion of n in n 3.684 * [backup-simplify]: Simplify 0 into 0 3.684 * [backup-simplify]: Simplify 1 into 1 3.684 * [backup-simplify]: Simplify (/ PI 1) into PI 3.684 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.685 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.685 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 3.685 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 3.686 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.687 * [backup-simplify]: Simplify (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) into (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) 3.687 * [backup-simplify]: Simplify (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) 3.690 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 3.691 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) 3.692 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) 3.693 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) 3.695 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 3)))))))) 3.696 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt (/ 1 (- k)))) (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0))) into (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) 3.696 * [approximate]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in (k n) around 0 3.696 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n 3.696 * [taylor]: Taking taylor expansion of 1.0 in n 3.696 * [backup-simplify]: Simplify 1.0 into 1.0 3.696 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n 3.696 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 3.696 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 3.696 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 3.696 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 3.696 * [taylor]: Taking taylor expansion of 0.5 in n 3.696 * [backup-simplify]: Simplify 0.5 into 0.5 3.696 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.696 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.696 * [taylor]: Taking taylor expansion of k in n 3.696 * [backup-simplify]: Simplify k into k 3.696 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.696 * [taylor]: Taking taylor expansion of 1.0 in n 3.696 * [backup-simplify]: Simplify 1.0 into 1.0 3.696 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 3.696 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.696 * [taylor]: Taking taylor expansion of -2.0 in n 3.696 * [backup-simplify]: Simplify -2.0 into -2.0 3.697 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.697 * [taylor]: Taking taylor expansion of PI in n 3.697 * [backup-simplify]: Simplify PI into PI 3.697 * [taylor]: Taking taylor expansion of n in n 3.697 * [backup-simplify]: Simplify 0 into 0 3.697 * [backup-simplify]: Simplify 1 into 1 3.697 * [backup-simplify]: Simplify (/ PI 1) into PI 3.697 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.698 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 3.698 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 3.698 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 3.699 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.700 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) 3.700 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 3.700 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 3.700 * [taylor]: Taking taylor expansion of (/ -1 k) in n 3.700 * [taylor]: Taking taylor expansion of -1 in n 3.700 * [backup-simplify]: Simplify -1 into -1 3.700 * [taylor]: Taking taylor expansion of k in n 3.700 * [backup-simplify]: Simplify k into k 3.701 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 3.701 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 3.701 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 3.701 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 3.702 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) into (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) 3.702 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 3.702 * [taylor]: Taking taylor expansion of 1.0 in k 3.702 * [backup-simplify]: Simplify 1.0 into 1.0 3.702 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 3.702 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 3.702 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 3.702 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 3.702 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 3.702 * [taylor]: Taking taylor expansion of 0.5 in k 3.702 * [backup-simplify]: Simplify 0.5 into 0.5 3.702 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 3.702 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.702 * [taylor]: Taking taylor expansion of k in k 3.702 * [backup-simplify]: Simplify 0 into 0 3.702 * [backup-simplify]: Simplify 1 into 1 3.702 * [backup-simplify]: Simplify (/ 1 1) into 1 3.702 * [taylor]: Taking taylor expansion of 1.0 in k 3.702 * [backup-simplify]: Simplify 1.0 into 1.0 3.702 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 3.702 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 3.702 * [taylor]: Taking taylor expansion of -2.0 in k 3.702 * [backup-simplify]: Simplify -2.0 into -2.0 3.702 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.702 * [taylor]: Taking taylor expansion of PI in k 3.702 * [backup-simplify]: Simplify PI into PI 3.702 * [taylor]: Taking taylor expansion of n in k 3.702 * [backup-simplify]: Simplify n into n 3.702 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 3.702 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 3.702 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 3.703 * [backup-simplify]: Simplify (+ 1 0) into 1 3.703 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 3.703 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 3.703 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) 3.703 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 3.703 * [taylor]: Taking taylor expansion of (/ -1 k) in k 3.703 * [taylor]: Taking taylor expansion of -1 in k 3.703 * [backup-simplify]: Simplify -1 into -1 3.703 * [taylor]: Taking taylor expansion of k in k 3.703 * [backup-simplify]: Simplify 0 into 0 3.703 * [backup-simplify]: Simplify 1 into 1 3.704 * [backup-simplify]: Simplify (/ -1 1) into -1 3.704 * [backup-simplify]: Simplify (sqrt 0) into 0 3.705 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 3.705 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) 3.705 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 3.705 * [taylor]: Taking taylor expansion of 1.0 in k 3.705 * [backup-simplify]: Simplify 1.0 into 1.0 3.705 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 3.705 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 3.705 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 3.705 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 3.705 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 3.705 * [taylor]: Taking taylor expansion of 0.5 in k 3.705 * [backup-simplify]: Simplify 0.5 into 0.5 3.705 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 3.705 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.705 * [taylor]: Taking taylor expansion of k in k 3.705 * [backup-simplify]: Simplify 0 into 0 3.705 * [backup-simplify]: Simplify 1 into 1 3.705 * [backup-simplify]: Simplify (/ 1 1) into 1 3.705 * [taylor]: Taking taylor expansion of 1.0 in k 3.705 * [backup-simplify]: Simplify 1.0 into 1.0 3.705 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 3.705 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 3.705 * [taylor]: Taking taylor expansion of -2.0 in k 3.705 * [backup-simplify]: Simplify -2.0 into -2.0 3.705 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.705 * [taylor]: Taking taylor expansion of PI in k 3.705 * [backup-simplify]: Simplify PI into PI 3.705 * [taylor]: Taking taylor expansion of n in k 3.705 * [backup-simplify]: Simplify n into n 3.706 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 3.706 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 3.706 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 3.706 * [backup-simplify]: Simplify (+ 1 0) into 1 3.707 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 3.707 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 3.707 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) 3.707 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 3.707 * [taylor]: Taking taylor expansion of (/ -1 k) in k 3.707 * [taylor]: Taking taylor expansion of -1 in k 3.707 * [backup-simplify]: Simplify -1 into -1 3.707 * [taylor]: Taking taylor expansion of k in k 3.707 * [backup-simplify]: Simplify 0 into 0 3.707 * [backup-simplify]: Simplify 1 into 1 3.708 * [backup-simplify]: Simplify (/ -1 1) into -1 3.708 * [backup-simplify]: Simplify (sqrt 0) into 0 3.709 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 3.710 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) 3.710 * [backup-simplify]: Simplify (* 1.0 (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) into (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) 3.710 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) in n 3.710 * [taylor]: Taking taylor expansion of +nan.0 in n 3.710 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.710 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) in n 3.711 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))) in n 3.711 * [taylor]: Taking taylor expansion of 0.5 in n 3.711 * [backup-simplify]: Simplify 0.5 into 0.5 3.711 * [taylor]: Taking taylor expansion of (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)) in n 3.711 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 3.711 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.711 * [taylor]: Taking taylor expansion of -2.0 in n 3.711 * [backup-simplify]: Simplify -2.0 into -2.0 3.711 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.711 * [taylor]: Taking taylor expansion of PI in n 3.711 * [backup-simplify]: Simplify PI into PI 3.711 * [taylor]: Taking taylor expansion of n in n 3.711 * [backup-simplify]: Simplify 0 into 0 3.711 * [backup-simplify]: Simplify 1 into 1 3.711 * [backup-simplify]: Simplify (/ PI 1) into PI 3.712 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.713 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 3.713 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.713 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.713 * [taylor]: Taking taylor expansion of k in n 3.713 * [backup-simplify]: Simplify k into k 3.713 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.713 * [taylor]: Taking taylor expansion of 1.0 in n 3.713 * [backup-simplify]: Simplify 1.0 into 1.0 3.715 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.715 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 3.716 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) into (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) 3.717 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) 3.719 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 3.720 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) 3.721 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) 3.722 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 3.725 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 3.727 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) 3.727 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) 3.727 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) in n 3.727 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) in n 3.727 * [taylor]: Taking taylor expansion of +nan.0 in n 3.727 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.727 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) in n 3.728 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))) in n 3.728 * [taylor]: Taking taylor expansion of 0.5 in n 3.728 * [backup-simplify]: Simplify 0.5 into 0.5 3.728 * [taylor]: Taking taylor expansion of (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)) in n 3.728 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 3.728 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.728 * [taylor]: Taking taylor expansion of -2.0 in n 3.728 * [backup-simplify]: Simplify -2.0 into -2.0 3.728 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.728 * [taylor]: Taking taylor expansion of PI in n 3.728 * [backup-simplify]: Simplify PI into PI 3.728 * [taylor]: Taking taylor expansion of n in n 3.728 * [backup-simplify]: Simplify 0 into 0 3.728 * [backup-simplify]: Simplify 1 into 1 3.729 * [backup-simplify]: Simplify (/ PI 1) into PI 3.729 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.730 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 3.730 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.730 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.730 * [taylor]: Taking taylor expansion of k in n 3.730 * [backup-simplify]: Simplify k into k 3.730 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.730 * [taylor]: Taking taylor expansion of 1.0 in n 3.731 * [backup-simplify]: Simplify 1.0 into 1.0 3.732 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.732 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 3.733 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) into (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) 3.734 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) 3.736 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 3.737 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) 3.738 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) 3.740 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) 3.741 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.741 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 3.742 * [backup-simplify]: Simplify (+ 0 0) into 0 3.743 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 3.743 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 3.745 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 3.746 * [backup-simplify]: Simplify (+ (* (- (log (* -2.0 PI)) (log n)) 0) (* 0 (+ (/ 1 k) 1.0))) into 0 3.747 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into 0 3.748 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 3.749 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into 0 3.749 * [backup-simplify]: Simplify 0 into 0 3.750 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.752 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 3.753 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) 3.754 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) 3.754 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) in n 3.754 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) in n 3.754 * [taylor]: Taking taylor expansion of +nan.0 in n 3.754 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.754 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) in n 3.754 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))) in n 3.754 * [taylor]: Taking taylor expansion of 0.5 in n 3.754 * [backup-simplify]: Simplify 0.5 into 0.5 3.754 * [taylor]: Taking taylor expansion of (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)) in n 3.754 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 3.754 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.754 * [taylor]: Taking taylor expansion of -2.0 in n 3.754 * [backup-simplify]: Simplify -2.0 into -2.0 3.754 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.754 * [taylor]: Taking taylor expansion of PI in n 3.754 * [backup-simplify]: Simplify PI into PI 3.754 * [taylor]: Taking taylor expansion of n in n 3.754 * [backup-simplify]: Simplify 0 into 0 3.754 * [backup-simplify]: Simplify 1 into 1 3.755 * [backup-simplify]: Simplify (/ PI 1) into PI 3.755 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.756 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 3.756 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.756 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.756 * [taylor]: Taking taylor expansion of k in n 3.756 * [backup-simplify]: Simplify k into k 3.756 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.756 * [taylor]: Taking taylor expansion of 1.0 in n 3.756 * [backup-simplify]: Simplify 1.0 into 1.0 3.757 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.757 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 3.757 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) into (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) 3.758 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) 3.759 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 3.760 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) 3.761 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) 3.761 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) 3.764 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))))) (* 1 (/ 1 (- k)))) (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0))))))) into (- (+ (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2)))))))) 3.764 * * * [progress]: simplifying candidates 3.767 * [simplify]: Simplifying: (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (- (log 1.0) (log (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt 1)) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt 1)) (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 1) (/ 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+nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) k)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow k 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (pow (log (* 2.0 PI)) 2) (pow k 2)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) k))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log n) k))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (pow k 2)))) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (pow (log n) 2) (pow k 2))))))))))))))))))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 3)))))))) (- (+ (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2)))))))) 3.770 * * [simplify]: iteration 0: 353 enodes 3.881 * * [simplify]: iteration 1: 975 enodes 4.385 * * [simplify]: iteration 2: 3261 enodes 5.406 * * [simplify]: iteration complete: 5001 enodes 5.406 * * [simplify]: Extracting #0: cost 117 inf + 0 5.408 * * [simplify]: Extracting #1: cost 590 inf + 2 5.414 * * [simplify]: Extracting #2: cost 1034 inf + 2722 5.428 * * [simplify]: Extracting #3: cost 1271 inf + 29363 5.459 * * [simplify]: Extracting #4: cost 841 inf + 157190 5.535 * * [simplify]: Extracting #5: cost 492 inf + 353948 5.633 * * [simplify]: Extracting #6: cost 429 inf + 453894 5.801 * * [simplify]: Extracting #7: cost 178 inf + 668763 5.938 * * [simplify]: Extracting #8: cost 60 inf + 770866 6.158 * * [simplify]: Extracting #9: cost 5 inf + 834102 6.344 * * [simplify]: Extracting #10: cost 0 inf + 842935 6.490 * * [simplify]: Extracting #11: cost 0 inf + 842895 6.655 * [simplify]: Simplified to: (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (* (/ (cbrt 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2.0 PI) n)))) (+ (log (/ 1.0 (sqrt k))) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n)))) (+ (log (/ 1.0 (sqrt k))) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n)))) (+ (log (/ 1.0 (sqrt k))) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n)))) (+ (log (/ 1.0 (sqrt k))) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n)))) (exp (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))))) (* (cbrt (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (cbrt (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))))) (cbrt (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))))) (sqrt (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (sqrt (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2) 2.0)) (sqrt (/ 1.0 (sqrt k)))) (* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2) 2.0)) (sqrt (/ 1.0 (sqrt k)))) (* (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2) 2.0))) (* (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2) 2.0))) (* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))) (* (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (/ 1.0 (sqrt k))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (/ (* 1.0 (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt k)) (/ 1.0 (sqrt k)) (* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2) 2.0)) (/ 1.0 (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (/ 1.0 (sqrt k)))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ (cbrt 1.0) (cbrt (sqrt k)))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ (cbrt 1.0) (sqrt (cbrt k)))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ (cbrt 1.0) (sqrt k))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ (cbrt 1.0) (sqrt k))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ (sqrt 1.0) (cbrt (sqrt k)))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ (sqrt 1.0) (sqrt (cbrt k)))) (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt 1.0)) (sqrt (sqrt k))) (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt 1.0)) (sqrt k)) (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt 1.0)) (sqrt (sqrt k))) (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt 1.0)) (sqrt k)) (/ 1.0 (/ (cbrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt (cbrt k)))) (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt (sqrt k))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))) (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt (sqrt k))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))) (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k)) (/ (* (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) 1.0) (sqrt k)) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (+ (+ (+ (* (* (* (log n) (log n)) (* (* k k) (exp (* (log (* (* 2.0 PI) n)) 0.5)))) 0.125) (exp (* (log (* (* 2.0 PI) n)) 0.5))) (* (* (log (* 2.0 PI)) (log (* 2.0 PI))) (* (* (* k k) (exp (* (log (* (* 2.0 PI) n)) 0.5))) 0.125))) (- (* (* (* 0.25 (log (* 2.0 PI))) (exp (* (log (* (* 2.0 PI) n)) 0.5))) (* (log n) (* k k))) (* (* k (+ (* (exp (* (log (* (* 2.0 PI) n)) 0.5)) (log n)) (* (log (* 2.0 PI)) (exp (* (log (* (* 2.0 PI) n)) 0.5))))) 0.5))) (exp (* 0.5 (* (- 1.0 k) (log (* (* 2.0 PI) n))))) (exp (* (* (- 1.0 k) 0.5) (- (log (* PI -2.0)) (log (/ -1 n))))) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (* (- +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 k)) +nan.0)) (- (+ (- (* k (* (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5) +nan.0)) (* (* k k) (* (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5) +nan.0))) (- (* (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5) (* +nan.0 (* (log n) (* k k)))) (- (* +nan.0 (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5)) (+ (- (* (* (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5) (* (* k (log (* 2.0 PI))) (* k (log (* 2.0 PI))))) +nan.0) (* +nan.0 (* (* (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5) (log (* 2.0 PI))) (* (log n) (* k k))))) (+ (- (* +nan.0 (* (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5) (* (log (* 2.0 PI)) k))) (* (* (* +nan.0 (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5)) (log n)) k)) (- (* (* +nan.0 (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5)) (* (* k k) (log (* 2.0 PI)))) (* +nan.0 (* (* (* k (log n)) (* k (log n))) (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5)))))))))) (- (* (/ (- +nan.0) k) (/ (exp (* 0.5 (* (- 1.0 k) (log (* (* 2.0 PI) n))))) k)) (+ (* (- +nan.0) (/ (exp (* 0.5 (* (- 1.0 k) (log (* (* 2.0 PI) n))))) k)) (* (/ +nan.0 (* k k)) (/ (exp (* 0.5 (* (- 1.0 k) (log (* (* 2.0 PI) n))))) k)))) (- (+ (- (* (exp (* (* (- 1.0 k) 0.5) (- (log (* PI -2.0)) (log (/ -1 n))))) +nan.0) (/ (* (exp (* (* (- 1.0 k) 0.5) (- (log (* PI -2.0)) (log (/ -1 n))))) +nan.0) k)) (/ +nan.0 (/ (* k k) (exp (* (* (- 1.0 k) 0.5) (- (log (* PI -2.0)) (log (/ -1 n))))))))) 6.677 * * * [progress]: adding candidates to table 7.578 * * [progress]: iteration 2 / 4 7.578 * * * [progress]: picking best candidate 7.650 * * * * [pick]: Picked # 7.650 * * * [progress]: localizing error 7.696 * * * [progress]: generating rewritten candidates 7.696 * * * * [progress]: [ 1 / 4 ] rewriting at (2 1) 7.730 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1) 7.745 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2) 7.749 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 7.811 * * * [progress]: generating series expansions 7.811 * * * * [progress]: [ 1 / 4 ] generating series at (2 1) 7.812 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 7.813 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 7.813 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 7.813 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 7.813 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 7.813 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 7.813 * [taylor]: Taking taylor expansion of 0.5 in k 7.813 * [backup-simplify]: Simplify 0.5 into 0.5 7.813 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 7.813 * [taylor]: Taking taylor expansion of 1.0 in k 7.813 * [backup-simplify]: Simplify 1.0 into 1.0 7.813 * [taylor]: Taking taylor expansion of k in k 7.813 * [backup-simplify]: Simplify 0 into 0 7.813 * [backup-simplify]: Simplify 1 into 1 7.813 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 7.813 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 7.813 * [taylor]: Taking taylor expansion of 2.0 in k 7.813 * [backup-simplify]: Simplify 2.0 into 2.0 7.813 * [taylor]: Taking taylor expansion of (* n PI) in k 7.813 * [taylor]: Taking taylor expansion of n in k 7.813 * [backup-simplify]: Simplify n into n 7.813 * [taylor]: Taking taylor expansion of PI in k 7.813 * [backup-simplify]: Simplify PI into PI 7.813 * [backup-simplify]: Simplify (* n PI) into (* n PI) 7.813 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 7.814 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 7.814 * [backup-simplify]: Simplify (- 0) into 0 7.815 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 7.815 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 7.815 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 7.815 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 7.815 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 7.815 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 7.816 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 7.816 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 7.816 * [taylor]: Taking taylor expansion of 0.5 in n 7.816 * [backup-simplify]: Simplify 0.5 into 0.5 7.816 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 7.816 * [taylor]: Taking taylor expansion of 1.0 in n 7.816 * [backup-simplify]: Simplify 1.0 into 1.0 7.816 * [taylor]: Taking taylor expansion of k in n 7.816 * [backup-simplify]: Simplify k into k 7.816 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 7.816 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 7.816 * [taylor]: Taking taylor expansion of 2.0 in n 7.816 * [backup-simplify]: Simplify 2.0 into 2.0 7.816 * [taylor]: Taking taylor expansion of (* n PI) in n 7.816 * [taylor]: Taking taylor expansion of n in n 7.816 * [backup-simplify]: Simplify 0 into 0 7.816 * [backup-simplify]: Simplify 1 into 1 7.816 * [taylor]: Taking taylor expansion of PI in n 7.816 * [backup-simplify]: Simplify PI into PI 7.817 * [backup-simplify]: Simplify (* 0 PI) into 0 7.817 * [backup-simplify]: Simplify (* 2.0 0) into 0 7.819 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 7.821 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 7.822 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 7.822 * [backup-simplify]: Simplify (- k) into (- k) 7.822 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 7.822 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 7.824 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 7.825 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 7.826 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 7.826 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 7.826 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 7.826 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 7.826 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 7.826 * [taylor]: Taking taylor expansion of 0.5 in n 7.826 * [backup-simplify]: Simplify 0.5 into 0.5 7.826 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 7.826 * [taylor]: Taking taylor expansion of 1.0 in n 7.826 * [backup-simplify]: Simplify 1.0 into 1.0 7.826 * [taylor]: Taking taylor expansion of k in n 7.826 * [backup-simplify]: Simplify k into k 7.826 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 7.826 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 7.826 * [taylor]: Taking taylor expansion of 2.0 in n 7.826 * [backup-simplify]: Simplify 2.0 into 2.0 7.827 * [taylor]: Taking taylor expansion of (* n PI) in n 7.827 * [taylor]: Taking taylor expansion of n in n 7.827 * [backup-simplify]: Simplify 0 into 0 7.827 * [backup-simplify]: Simplify 1 into 1 7.827 * [taylor]: Taking taylor expansion of PI in n 7.827 * [backup-simplify]: Simplify PI into PI 7.827 * [backup-simplify]: Simplify (* 0 PI) into 0 7.828 * [backup-simplify]: Simplify (* 2.0 0) into 0 7.829 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 7.831 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 7.832 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 7.832 * [backup-simplify]: Simplify (- k) into (- k) 7.832 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 7.832 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 7.834 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 7.835 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 7.836 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 7.836 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 7.836 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 7.836 * [taylor]: Taking taylor expansion of 0.5 in k 7.836 * [backup-simplify]: Simplify 0.5 into 0.5 7.836 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 7.836 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 7.837 * [taylor]: Taking taylor expansion of 1.0 in k 7.837 * [backup-simplify]: Simplify 1.0 into 1.0 7.837 * [taylor]: Taking taylor expansion of k in k 7.837 * [backup-simplify]: Simplify 0 into 0 7.837 * [backup-simplify]: Simplify 1 into 1 7.837 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 7.837 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 7.837 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 7.837 * [taylor]: Taking taylor expansion of 2.0 in k 7.837 * [backup-simplify]: Simplify 2.0 into 2.0 7.837 * [taylor]: Taking taylor expansion of PI in k 7.837 * [backup-simplify]: Simplify PI into PI 7.837 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 7.838 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 7.839 * [taylor]: Taking taylor expansion of (log n) in k 7.839 * [taylor]: Taking taylor expansion of n in k 7.839 * [backup-simplify]: Simplify n into n 7.839 * [backup-simplify]: Simplify (log n) into (log n) 7.839 * [backup-simplify]: Simplify (- 0) into 0 7.839 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 7.841 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 7.842 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 7.843 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 7.844 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 7.846 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 7.847 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 7.848 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 7.849 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 7.850 * [backup-simplify]: Simplify (- 0) into 0 7.850 * [backup-simplify]: Simplify (+ 0 0) into 0 7.851 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 7.852 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 7.854 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 7.855 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 7.855 * [taylor]: Taking taylor expansion of 0 in k 7.855 * [backup-simplify]: Simplify 0 into 0 7.856 * [backup-simplify]: Simplify 0 into 0 7.856 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 7.858 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 7.859 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 7.859 * [backup-simplify]: Simplify (+ 0 0) into 0 7.860 * [backup-simplify]: Simplify (- 1) into -1 7.860 * [backup-simplify]: Simplify (+ 0 -1) into -1 7.862 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 7.864 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 7.867 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 7.870 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 7.871 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 7.872 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 7.873 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 7.874 * [backup-simplify]: Simplify (- 0) into 0 7.874 * [backup-simplify]: Simplify (+ 0 0) into 0 7.875 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 7.875 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 7.876 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 7.878 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 7.878 * [taylor]: Taking taylor expansion of 0 in k 7.878 * [backup-simplify]: Simplify 0 into 0 7.878 * [backup-simplify]: Simplify 0 into 0 7.878 * [backup-simplify]: Simplify 0 into 0 7.878 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 7.884 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 7.886 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 7.886 * [backup-simplify]: Simplify (+ 0 0) into 0 7.886 * [backup-simplify]: Simplify (- 0) into 0 7.887 * [backup-simplify]: Simplify (+ 0 0) into 0 7.888 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 7.889 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 7.892 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 7.895 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 7.902 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.25 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2))))) (+ (* 0.125 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* 0.125 (* (pow (log (* 2.0 PI)) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))))))) (+ (* 0.5 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k))) (* 0.5 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k))))) 7.902 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) 7.902 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 7.902 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 7.902 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 7.903 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 7.903 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 7.903 * [taylor]: Taking taylor expansion of 0.5 in k 7.903 * [backup-simplify]: Simplify 0.5 into 0.5 7.903 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 7.903 * [taylor]: Taking taylor expansion of 1.0 in k 7.903 * [backup-simplify]: Simplify 1.0 into 1.0 7.903 * [taylor]: Taking taylor expansion of (/ 1 k) in k 7.903 * [taylor]: Taking taylor expansion of k in k 7.903 * [backup-simplify]: Simplify 0 into 0 7.903 * [backup-simplify]: Simplify 1 into 1 7.903 * [backup-simplify]: Simplify (/ 1 1) into 1 7.903 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 7.903 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 7.903 * [taylor]: Taking taylor expansion of 2.0 in k 7.903 * [backup-simplify]: Simplify 2.0 into 2.0 7.903 * [taylor]: Taking taylor expansion of (/ PI n) in k 7.903 * [taylor]: Taking taylor expansion of PI in k 7.903 * [backup-simplify]: Simplify PI into PI 7.903 * [taylor]: Taking taylor expansion of n in k 7.903 * [backup-simplify]: Simplify n into n 7.903 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 7.903 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 7.903 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 7.903 * [backup-simplify]: Simplify (- 1) into -1 7.904 * [backup-simplify]: Simplify (+ 0 -1) into -1 7.904 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 7.904 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 7.904 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) 7.904 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 7.904 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 7.904 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 7.904 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 7.904 * [taylor]: Taking taylor expansion of 0.5 in n 7.904 * [backup-simplify]: Simplify 0.5 into 0.5 7.904 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 7.904 * [taylor]: Taking taylor expansion of 1.0 in n 7.904 * [backup-simplify]: Simplify 1.0 into 1.0 7.904 * [taylor]: Taking taylor expansion of (/ 1 k) in n 7.904 * [taylor]: Taking taylor expansion of k in n 7.904 * [backup-simplify]: Simplify k into k 7.904 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 7.905 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 7.905 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 7.905 * [taylor]: Taking taylor expansion of 2.0 in n 7.905 * [backup-simplify]: Simplify 2.0 into 2.0 7.905 * [taylor]: Taking taylor expansion of (/ PI n) in n 7.905 * [taylor]: Taking taylor expansion of PI in n 7.905 * [backup-simplify]: Simplify PI into PI 7.905 * [taylor]: Taking taylor expansion of n in n 7.905 * [backup-simplify]: Simplify 0 into 0 7.905 * [backup-simplify]: Simplify 1 into 1 7.905 * [backup-simplify]: Simplify (/ PI 1) into PI 7.905 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 7.906 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 7.906 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 7.907 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 7.907 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 7.908 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 7.909 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) 7.911 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 7.911 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 7.911 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 7.911 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 7.911 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 7.911 * [taylor]: Taking taylor expansion of 0.5 in n 7.911 * [backup-simplify]: Simplify 0.5 into 0.5 7.911 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 7.911 * [taylor]: Taking taylor expansion of 1.0 in n 7.911 * [backup-simplify]: Simplify 1.0 into 1.0 7.911 * [taylor]: Taking taylor expansion of (/ 1 k) in n 7.911 * [taylor]: Taking taylor expansion of k in n 7.911 * [backup-simplify]: Simplify k into k 7.911 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 7.911 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 7.911 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 7.911 * [taylor]: Taking taylor expansion of 2.0 in n 7.911 * [backup-simplify]: Simplify 2.0 into 2.0 7.911 * [taylor]: Taking taylor expansion of (/ PI n) in n 7.911 * [taylor]: Taking taylor expansion of PI in n 7.911 * [backup-simplify]: Simplify PI into PI 7.911 * [taylor]: Taking taylor expansion of n in n 7.911 * [backup-simplify]: Simplify 0 into 0 7.911 * [backup-simplify]: Simplify 1 into 1 7.912 * [backup-simplify]: Simplify (/ PI 1) into PI 7.912 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 7.914 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 7.914 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 7.914 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 7.914 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 7.915 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 7.917 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) 7.918 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 7.919 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) in k 7.919 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) in k 7.919 * [taylor]: Taking taylor expansion of 0.5 in k 7.919 * [backup-simplify]: Simplify 0.5 into 0.5 7.919 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) in k 7.919 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 7.919 * [taylor]: Taking taylor expansion of 1.0 in k 7.919 * [backup-simplify]: Simplify 1.0 into 1.0 7.919 * [taylor]: Taking taylor expansion of (/ 1 k) in k 7.919 * [taylor]: Taking taylor expansion of k in k 7.919 * [backup-simplify]: Simplify 0 into 0 7.919 * [backup-simplify]: Simplify 1 into 1 7.919 * [backup-simplify]: Simplify (/ 1 1) into 1 7.919 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 7.919 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 7.919 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 7.919 * [taylor]: Taking taylor expansion of 2.0 in k 7.919 * [backup-simplify]: Simplify 2.0 into 2.0 7.919 * [taylor]: Taking taylor expansion of PI in k 7.920 * [backup-simplify]: Simplify PI into PI 7.920 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 7.921 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 7.921 * [taylor]: Taking taylor expansion of (log n) in k 7.921 * [taylor]: Taking taylor expansion of n in k 7.921 * [backup-simplify]: Simplify n into n 7.921 * [backup-simplify]: Simplify (log n) into (log n) 7.922 * [backup-simplify]: Simplify (- 1) into -1 7.922 * [backup-simplify]: Simplify (+ 0 -1) into -1 7.922 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 7.923 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 7.924 * [backup-simplify]: Simplify (* -1 (- (log (* 2.0 PI)) (log n))) into (* -1 (- (log (* 2.0 PI)) (log n))) 7.926 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 7.927 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 7.928 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 7.929 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 7.930 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 7.932 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 7.932 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 7.933 * [backup-simplify]: Simplify (- 0) into 0 7.933 * [backup-simplify]: Simplify (+ 0 0) into 0 7.933 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 7.934 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 7.935 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 7.936 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 7.936 * [taylor]: Taking taylor expansion of 0 in k 7.936 * [backup-simplify]: Simplify 0 into 0 7.936 * [backup-simplify]: Simplify 0 into 0 7.936 * [backup-simplify]: Simplify 0 into 0 7.937 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 7.938 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 7.939 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 7.940 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 7.940 * [backup-simplify]: Simplify (- 0) into 0 7.940 * [backup-simplify]: Simplify (+ 0 0) into 0 7.941 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 7.941 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 7.942 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 7.944 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 7.944 * [taylor]: Taking taylor expansion of 0 in k 7.944 * [backup-simplify]: Simplify 0 into 0 7.944 * [backup-simplify]: Simplify 0 into 0 7.944 * [backup-simplify]: Simplify 0 into 0 7.944 * [backup-simplify]: Simplify 0 into 0 7.945 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 7.945 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 7.948 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 7.949 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 7.949 * [backup-simplify]: Simplify (- 0) into 0 7.949 * [backup-simplify]: Simplify (+ 0 0) into 0 7.950 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 7.951 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 7.952 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 7.954 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 7.954 * [taylor]: Taking taylor expansion of 0 in k 7.954 * [backup-simplify]: Simplify 0 into 0 7.954 * [backup-simplify]: Simplify 0 into 0 7.954 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) 7.955 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) 7.955 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 7.955 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 7.955 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 7.955 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 7.955 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 7.955 * [taylor]: Taking taylor expansion of 0.5 in k 7.955 * [backup-simplify]: Simplify 0.5 into 0.5 7.955 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 7.955 * [taylor]: Taking taylor expansion of (/ 1 k) in k 7.955 * [taylor]: Taking taylor expansion of k in k 7.955 * [backup-simplify]: Simplify 0 into 0 7.955 * [backup-simplify]: Simplify 1 into 1 7.955 * [backup-simplify]: Simplify (/ 1 1) into 1 7.955 * [taylor]: Taking taylor expansion of 1.0 in k 7.955 * [backup-simplify]: Simplify 1.0 into 1.0 7.955 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 7.955 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 7.955 * [taylor]: Taking taylor expansion of -2.0 in k 7.956 * [backup-simplify]: Simplify -2.0 into -2.0 7.956 * [taylor]: Taking taylor expansion of (/ PI n) in k 7.956 * [taylor]: Taking taylor expansion of PI in k 7.956 * [backup-simplify]: Simplify PI into PI 7.956 * [taylor]: Taking taylor expansion of n in k 7.956 * [backup-simplify]: Simplify n into n 7.956 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 7.956 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 7.956 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 7.956 * [backup-simplify]: Simplify (+ 1 0) into 1 7.956 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 7.956 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 7.956 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) 7.957 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 7.957 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 7.957 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 7.957 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 7.957 * [taylor]: Taking taylor expansion of 0.5 in n 7.957 * [backup-simplify]: Simplify 0.5 into 0.5 7.957 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 7.957 * [taylor]: Taking taylor expansion of (/ 1 k) in n 7.957 * [taylor]: Taking taylor expansion of k in n 7.957 * [backup-simplify]: Simplify k into k 7.957 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 7.957 * [taylor]: Taking taylor expansion of 1.0 in n 7.957 * [backup-simplify]: Simplify 1.0 into 1.0 7.957 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 7.957 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 7.957 * [taylor]: Taking taylor expansion of -2.0 in n 7.957 * [backup-simplify]: Simplify -2.0 into -2.0 7.957 * [taylor]: Taking taylor expansion of (/ PI n) in n 7.957 * [taylor]: Taking taylor expansion of PI in n 7.957 * [backup-simplify]: Simplify PI into PI 7.957 * [taylor]: Taking taylor expansion of n in n 7.957 * [backup-simplify]: Simplify 0 into 0 7.957 * [backup-simplify]: Simplify 1 into 1 7.957 * [backup-simplify]: Simplify (/ PI 1) into PI 7.958 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 7.958 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 7.958 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 7.958 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 7.959 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 7.960 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) 7.961 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 7.961 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 7.961 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 7.961 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 7.961 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 7.961 * [taylor]: Taking taylor expansion of 0.5 in n 7.961 * [backup-simplify]: Simplify 0.5 into 0.5 7.961 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 7.961 * [taylor]: Taking taylor expansion of (/ 1 k) in n 7.961 * [taylor]: Taking taylor expansion of k in n 7.961 * [backup-simplify]: Simplify k into k 7.961 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 7.961 * [taylor]: Taking taylor expansion of 1.0 in n 7.961 * [backup-simplify]: Simplify 1.0 into 1.0 7.961 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 7.961 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 7.961 * [taylor]: Taking taylor expansion of -2.0 in n 7.961 * [backup-simplify]: Simplify -2.0 into -2.0 7.961 * [taylor]: Taking taylor expansion of (/ PI n) in n 7.961 * [taylor]: Taking taylor expansion of PI in n 7.961 * [backup-simplify]: Simplify PI into PI 7.961 * [taylor]: Taking taylor expansion of n in n 7.961 * [backup-simplify]: Simplify 0 into 0 7.961 * [backup-simplify]: Simplify 1 into 1 7.961 * [backup-simplify]: Simplify (/ PI 1) into PI 7.962 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 7.963 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 7.963 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 7.963 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 7.965 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 7.966 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) 7.967 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 7.967 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) in k 7.967 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) in k 7.967 * [taylor]: Taking taylor expansion of 0.5 in k 7.967 * [backup-simplify]: Simplify 0.5 into 0.5 7.968 * [taylor]: Taking taylor expansion of (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) in k 7.968 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 7.968 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 7.968 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 7.968 * [taylor]: Taking taylor expansion of -2.0 in k 7.968 * [backup-simplify]: Simplify -2.0 into -2.0 7.968 * [taylor]: Taking taylor expansion of PI in k 7.968 * [backup-simplify]: Simplify PI into PI 7.968 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 7.969 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 7.969 * [taylor]: Taking taylor expansion of (log n) in k 7.969 * [taylor]: Taking taylor expansion of n in k 7.969 * [backup-simplify]: Simplify n into n 7.970 * [backup-simplify]: Simplify (log n) into (log n) 7.970 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 7.970 * [taylor]: Taking taylor expansion of (/ 1 k) in k 7.970 * [taylor]: Taking taylor expansion of k in k 7.970 * [backup-simplify]: Simplify 0 into 0 7.970 * [backup-simplify]: Simplify 1 into 1 7.970 * [backup-simplify]: Simplify (/ 1 1) into 1 7.970 * [taylor]: Taking taylor expansion of 1.0 in k 7.970 * [backup-simplify]: Simplify 1.0 into 1.0 7.970 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 7.971 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 7.972 * [backup-simplify]: Simplify (+ 1 0) into 1 7.973 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) 1) into (- (log (* -2.0 PI)) (log n)) 7.974 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 7.976 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 7.977 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 7.978 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 7.979 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 7.981 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 7.981 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 7.982 * [backup-simplify]: Simplify (+ 0 0) into 0 7.982 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 7.984 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 7.985 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 7.987 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 7.987 * [taylor]: Taking taylor expansion of 0 in k 7.987 * [backup-simplify]: Simplify 0 into 0 7.987 * [backup-simplify]: Simplify 0 into 0 7.987 * [backup-simplify]: Simplify 0 into 0 7.989 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 7.990 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 7.993 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 7.993 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 7.994 * [backup-simplify]: Simplify (+ 0 0) into 0 7.995 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 7.996 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 7.998 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 8.001 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 8.001 * [taylor]: Taking taylor expansion of 0 in k 8.001 * [backup-simplify]: Simplify 0 into 0 8.001 * [backup-simplify]: Simplify 0 into 0 8.001 * [backup-simplify]: Simplify 0 into 0 8.001 * [backup-simplify]: Simplify 0 into 0 8.007 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.009 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 8.015 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 8.015 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.016 * [backup-simplify]: Simplify (+ 0 0) into 0 8.017 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 8.019 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.021 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 8.023 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 8.023 * [taylor]: Taking taylor expansion of 0 in k 8.023 * [backup-simplify]: Simplify 0 into 0 8.023 * [backup-simplify]: Simplify 0 into 0 8.024 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 8.024 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1) 8.024 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 8.024 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 8.024 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 8.024 * [taylor]: Taking taylor expansion of 2.0 in n 8.024 * [backup-simplify]: Simplify 2.0 into 2.0 8.024 * [taylor]: Taking taylor expansion of (* n PI) in n 8.024 * [taylor]: Taking taylor expansion of n in n 8.024 * [backup-simplify]: Simplify 0 into 0 8.025 * [backup-simplify]: Simplify 1 into 1 8.025 * [taylor]: Taking taylor expansion of PI in n 8.025 * [backup-simplify]: Simplify PI into PI 8.025 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 8.025 * [taylor]: Taking taylor expansion of 2.0 in n 8.025 * [backup-simplify]: Simplify 2.0 into 2.0 8.025 * [taylor]: Taking taylor expansion of (* n PI) in n 8.025 * [taylor]: Taking taylor expansion of n in n 8.025 * [backup-simplify]: Simplify 0 into 0 8.025 * [backup-simplify]: Simplify 1 into 1 8.025 * [taylor]: Taking taylor expansion of PI in n 8.025 * [backup-simplify]: Simplify PI into PI 8.025 * [backup-simplify]: Simplify (* 0 PI) into 0 8.025 * [backup-simplify]: Simplify (* 2.0 0) into 0 8.025 * [backup-simplify]: Simplify 0 into 0 8.026 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.027 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 8.027 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.028 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 8.029 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 8.029 * [backup-simplify]: Simplify 0 into 0 8.030 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 8.030 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 8.030 * [backup-simplify]: Simplify 0 into 0 8.031 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 8.032 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 8.032 * [backup-simplify]: Simplify 0 into 0 8.033 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 8.034 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 8.034 * [backup-simplify]: Simplify 0 into 0 8.035 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 8.036 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 8.036 * [backup-simplify]: Simplify 0 into 0 8.038 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 8.039 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 8.039 * [backup-simplify]: Simplify 0 into 0 8.039 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 8.040 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 8.040 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 8.040 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 8.040 * [taylor]: Taking taylor expansion of 2.0 in n 8.040 * [backup-simplify]: Simplify 2.0 into 2.0 8.040 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.040 * [taylor]: Taking taylor expansion of PI in n 8.040 * [backup-simplify]: Simplify PI into PI 8.040 * [taylor]: Taking taylor expansion of n in n 8.040 * [backup-simplify]: Simplify 0 into 0 8.040 * [backup-simplify]: Simplify 1 into 1 8.040 * [backup-simplify]: Simplify (/ PI 1) into PI 8.040 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 8.040 * [taylor]: Taking taylor expansion of 2.0 in n 8.040 * [backup-simplify]: Simplify 2.0 into 2.0 8.040 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.040 * [taylor]: Taking taylor expansion of PI in n 8.040 * [backup-simplify]: Simplify PI into PI 8.040 * [taylor]: Taking taylor expansion of n in n 8.040 * [backup-simplify]: Simplify 0 into 0 8.040 * [backup-simplify]: Simplify 1 into 1 8.040 * [backup-simplify]: Simplify (/ PI 1) into PI 8.041 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.041 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.042 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.042 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 8.042 * [backup-simplify]: Simplify 0 into 0 8.043 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.043 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.043 * [backup-simplify]: Simplify 0 into 0 8.044 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.045 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 8.045 * [backup-simplify]: Simplify 0 into 0 8.045 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.046 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 8.046 * [backup-simplify]: Simplify 0 into 0 8.047 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.048 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 8.048 * [backup-simplify]: Simplify 0 into 0 8.048 * [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 8.049 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 8.049 * [backup-simplify]: Simplify 0 into 0 8.050 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 8.050 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 8.050 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 8.050 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 8.050 * [taylor]: Taking taylor expansion of -2.0 in n 8.050 * [backup-simplify]: Simplify -2.0 into -2.0 8.050 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.050 * [taylor]: Taking taylor expansion of PI in n 8.050 * [backup-simplify]: Simplify PI into PI 8.050 * [taylor]: Taking taylor expansion of n in n 8.050 * [backup-simplify]: Simplify 0 into 0 8.050 * [backup-simplify]: Simplify 1 into 1 8.051 * [backup-simplify]: Simplify (/ PI 1) into PI 8.051 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 8.051 * [taylor]: Taking taylor expansion of -2.0 in n 8.051 * [backup-simplify]: Simplify -2.0 into -2.0 8.051 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.051 * [taylor]: Taking taylor expansion of PI in n 8.051 * [backup-simplify]: Simplify PI into PI 8.051 * [taylor]: Taking taylor expansion of n in n 8.051 * [backup-simplify]: Simplify 0 into 0 8.051 * [backup-simplify]: Simplify 1 into 1 8.051 * [backup-simplify]: Simplify (/ PI 1) into PI 8.051 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.052 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.052 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.053 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 8.053 * [backup-simplify]: Simplify 0 into 0 8.053 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.054 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.054 * [backup-simplify]: Simplify 0 into 0 8.056 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.057 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 8.057 * [backup-simplify]: Simplify 0 into 0 8.058 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.059 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 8.059 * [backup-simplify]: Simplify 0 into 0 8.061 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.062 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 8.062 * [backup-simplify]: Simplify 0 into 0 8.064 * [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 8.065 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 8.065 * [backup-simplify]: Simplify 0 into 0 8.066 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 8.066 * * * * [progress]: [ 3 / 4 ] generating series at (2 2) 8.066 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 8.066 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 8.066 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 8.066 * [taylor]: Taking taylor expansion of 1.0 in k 8.066 * [backup-simplify]: Simplify 1.0 into 1.0 8.066 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 8.066 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.067 * [taylor]: Taking taylor expansion of k in k 8.067 * [backup-simplify]: Simplify 0 into 0 8.067 * [backup-simplify]: Simplify 1 into 1 8.067 * [backup-simplify]: Simplify (/ 1 1) into 1 8.067 * [backup-simplify]: Simplify (sqrt 0) into 0 8.069 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.069 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 8.069 * [taylor]: Taking taylor expansion of 1.0 in k 8.069 * [backup-simplify]: Simplify 1.0 into 1.0 8.069 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 8.069 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.069 * [taylor]: Taking taylor expansion of k in k 8.069 * [backup-simplify]: Simplify 0 into 0 8.069 * [backup-simplify]: Simplify 1 into 1 8.069 * [backup-simplify]: Simplify (/ 1 1) into 1 8.070 * [backup-simplify]: Simplify (sqrt 0) into 0 8.071 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.072 * [backup-simplify]: Simplify (* 1.0 0) into 0 8.072 * [backup-simplify]: Simplify 0 into 0 8.073 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 8.073 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.074 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 8.077 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 8.080 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 8.080 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.081 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.085 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 8.087 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 8.088 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.089 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) 8.089 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 8.089 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 8.090 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 8.090 * [taylor]: Taking taylor expansion of 1.0 in k 8.090 * [backup-simplify]: Simplify 1.0 into 1.0 8.090 * [taylor]: Taking taylor expansion of (sqrt k) in k 8.090 * [taylor]: Taking taylor expansion of k in k 8.090 * [backup-simplify]: Simplify 0 into 0 8.090 * [backup-simplify]: Simplify 1 into 1 8.090 * [backup-simplify]: Simplify (sqrt 0) into 0 8.092 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.092 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 8.092 * [taylor]: Taking taylor expansion of 1.0 in k 8.092 * [backup-simplify]: Simplify 1.0 into 1.0 8.092 * [taylor]: Taking taylor expansion of (sqrt k) in k 8.092 * [taylor]: Taking taylor expansion of k in k 8.092 * [backup-simplify]: Simplify 0 into 0 8.092 * [backup-simplify]: Simplify 1 into 1 8.092 * [backup-simplify]: Simplify (sqrt 0) into 0 8.094 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.094 * [backup-simplify]: Simplify (* 1.0 0) into 0 8.094 * [backup-simplify]: Simplify 0 into 0 8.096 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 8.096 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.099 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 8.101 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 8.102 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.106 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 8.108 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 8.108 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.110 * [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)))))))) 8.110 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 8.110 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 8.110 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 8.110 * [taylor]: Taking taylor expansion of 1.0 in k 8.110 * [backup-simplify]: Simplify 1.0 into 1.0 8.110 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 8.110 * [taylor]: Taking taylor expansion of (/ -1 k) in k 8.110 * [taylor]: Taking taylor expansion of -1 in k 8.110 * [backup-simplify]: Simplify -1 into -1 8.110 * [taylor]: Taking taylor expansion of k in k 8.110 * [backup-simplify]: Simplify 0 into 0 8.110 * [backup-simplify]: Simplify 1 into 1 8.111 * [backup-simplify]: Simplify (/ -1 1) into -1 8.111 * [backup-simplify]: Simplify (sqrt 0) into 0 8.112 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 8.113 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 8.113 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 8.113 * [taylor]: Taking taylor expansion of 1.0 in k 8.113 * [backup-simplify]: Simplify 1.0 into 1.0 8.113 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 8.113 * [taylor]: Taking taylor expansion of (/ -1 k) in k 8.113 * [taylor]: Taking taylor expansion of -1 in k 8.113 * [backup-simplify]: Simplify -1 into -1 8.113 * [taylor]: Taking taylor expansion of k in k 8.113 * [backup-simplify]: Simplify 0 into 0 8.113 * [backup-simplify]: Simplify 1 into 1 8.114 * [backup-simplify]: Simplify (/ -1 1) into -1 8.114 * [backup-simplify]: Simplify (sqrt 0) into 0 8.116 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 8.116 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 8.116 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.117 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 8.118 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 8.120 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 8.120 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.121 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.123 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 8.130 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 8.131 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.131 * [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))))) 8.131 * * * * [progress]: [ 4 / 4 ] generating series at (2) 8.132 * [backup-simplify]: Simplify (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))) into (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) 8.132 * [approximate]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in (n k) around 0 8.132 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in k 8.132 * [taylor]: Taking taylor expansion of 1.0 in k 8.132 * [backup-simplify]: Simplify 1.0 into 1.0 8.132 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in k 8.132 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 8.132 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 8.132 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 8.132 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 8.132 * [taylor]: Taking taylor expansion of 0.5 in k 8.132 * [backup-simplify]: Simplify 0.5 into 0.5 8.132 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 8.132 * [taylor]: Taking taylor expansion of 1.0 in k 8.132 * [backup-simplify]: Simplify 1.0 into 1.0 8.132 * [taylor]: Taking taylor expansion of k in k 8.132 * [backup-simplify]: Simplify 0 into 0 8.132 * [backup-simplify]: Simplify 1 into 1 8.132 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 8.132 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 8.132 * [taylor]: Taking taylor expansion of 2.0 in k 8.132 * [backup-simplify]: Simplify 2.0 into 2.0 8.132 * [taylor]: Taking taylor expansion of (* n PI) in k 8.132 * [taylor]: Taking taylor expansion of n in k 8.132 * [backup-simplify]: Simplify n into n 8.132 * [taylor]: Taking taylor expansion of PI in k 8.132 * [backup-simplify]: Simplify PI into PI 8.132 * [backup-simplify]: Simplify (* n PI) into (* n PI) 8.133 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 8.133 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 8.133 * [backup-simplify]: Simplify (- 0) into 0 8.133 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 8.133 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 8.133 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 8.134 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 8.134 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 8.134 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.134 * [taylor]: Taking taylor expansion of k in k 8.134 * [backup-simplify]: Simplify 0 into 0 8.134 * [backup-simplify]: Simplify 1 into 1 8.134 * [backup-simplify]: Simplify (/ 1 1) into 1 8.134 * [backup-simplify]: Simplify (sqrt 0) into 0 8.135 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.135 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in n 8.135 * [taylor]: Taking taylor expansion of 1.0 in n 8.135 * [backup-simplify]: Simplify 1.0 into 1.0 8.135 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in n 8.135 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 8.135 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 8.135 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 8.135 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 8.135 * [taylor]: Taking taylor expansion of 0.5 in n 8.135 * [backup-simplify]: Simplify 0.5 into 0.5 8.135 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 8.135 * [taylor]: Taking taylor expansion of 1.0 in n 8.135 * [backup-simplify]: Simplify 1.0 into 1.0 8.135 * [taylor]: Taking taylor expansion of k in n 8.135 * [backup-simplify]: Simplify k into k 8.135 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 8.135 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 8.135 * [taylor]: Taking taylor expansion of 2.0 in n 8.135 * [backup-simplify]: Simplify 2.0 into 2.0 8.135 * [taylor]: Taking taylor expansion of (* n PI) in n 8.135 * [taylor]: Taking taylor expansion of n in n 8.135 * [backup-simplify]: Simplify 0 into 0 8.135 * [backup-simplify]: Simplify 1 into 1 8.135 * [taylor]: Taking taylor expansion of PI in n 8.135 * [backup-simplify]: Simplify PI into PI 8.136 * [backup-simplify]: Simplify (* 0 PI) into 0 8.136 * [backup-simplify]: Simplify (* 2.0 0) into 0 8.137 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.138 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 8.139 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.139 * [backup-simplify]: Simplify (- k) into (- k) 8.139 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 8.139 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 8.140 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.140 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 8.141 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 8.141 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 8.141 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.141 * [taylor]: Taking taylor expansion of k in n 8.141 * [backup-simplify]: Simplify k into k 8.141 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.141 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 8.141 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 8.141 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 8.141 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in n 8.141 * [taylor]: Taking taylor expansion of 1.0 in n 8.142 * [backup-simplify]: Simplify 1.0 into 1.0 8.142 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in n 8.142 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 8.142 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 8.142 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 8.142 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 8.142 * [taylor]: Taking taylor expansion of 0.5 in n 8.142 * [backup-simplify]: Simplify 0.5 into 0.5 8.142 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 8.142 * [taylor]: Taking taylor expansion of 1.0 in n 8.142 * [backup-simplify]: Simplify 1.0 into 1.0 8.142 * [taylor]: Taking taylor expansion of k in n 8.142 * [backup-simplify]: Simplify k into k 8.142 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 8.142 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 8.142 * [taylor]: Taking taylor expansion of 2.0 in n 8.142 * [backup-simplify]: Simplify 2.0 into 2.0 8.142 * [taylor]: Taking taylor expansion of (* n PI) in n 8.142 * [taylor]: Taking taylor expansion of n in n 8.142 * [backup-simplify]: Simplify 0 into 0 8.142 * [backup-simplify]: Simplify 1 into 1 8.142 * [taylor]: Taking taylor expansion of PI in n 8.142 * [backup-simplify]: Simplify PI into PI 8.142 * [backup-simplify]: Simplify (* 0 PI) into 0 8.143 * [backup-simplify]: Simplify (* 2.0 0) into 0 8.143 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.144 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 8.145 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.145 * [backup-simplify]: Simplify (- k) into (- k) 8.145 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 8.145 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 8.146 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.147 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 8.147 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 8.148 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 8.148 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.148 * [taylor]: Taking taylor expansion of k in n 8.148 * [backup-simplify]: Simplify k into k 8.148 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.148 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 8.148 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 8.148 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 8.149 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k))) into (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k))) 8.149 * [backup-simplify]: Simplify (* 1.0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k)))) into (* 1.0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k)))) 8.149 * [taylor]: Taking taylor expansion of (* 1.0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k)))) in k 8.150 * [taylor]: Taking taylor expansion of 1.0 in k 8.150 * [backup-simplify]: Simplify 1.0 into 1.0 8.150 * [taylor]: Taking taylor expansion of (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k))) in k 8.150 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 8.150 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 8.150 * [taylor]: Taking taylor expansion of 0.5 in k 8.150 * [backup-simplify]: Simplify 0.5 into 0.5 8.150 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 8.150 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 8.150 * [taylor]: Taking taylor expansion of 1.0 in k 8.150 * [backup-simplify]: Simplify 1.0 into 1.0 8.150 * [taylor]: Taking taylor expansion of k in k 8.150 * [backup-simplify]: Simplify 0 into 0 8.150 * [backup-simplify]: Simplify 1 into 1 8.150 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 8.150 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 8.150 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 8.150 * [taylor]: Taking taylor expansion of 2.0 in k 8.150 * [backup-simplify]: Simplify 2.0 into 2.0 8.150 * [taylor]: Taking taylor expansion of PI in k 8.150 * [backup-simplify]: Simplify PI into PI 8.150 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.151 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.151 * [taylor]: Taking taylor expansion of (log n) in k 8.151 * [taylor]: Taking taylor expansion of n in k 8.151 * [backup-simplify]: Simplify n into n 8.151 * [backup-simplify]: Simplify (log n) into (log n) 8.151 * [backup-simplify]: Simplify (- 0) into 0 8.151 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 8.152 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 8.153 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 8.154 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 8.154 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 8.154 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 8.154 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.154 * [taylor]: Taking taylor expansion of k in k 8.154 * [backup-simplify]: Simplify 0 into 0 8.154 * [backup-simplify]: Simplify 1 into 1 8.155 * [backup-simplify]: Simplify (/ 1 1) into 1 8.155 * [backup-simplify]: Simplify (sqrt 0) into 0 8.156 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.157 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 0) into 0 8.157 * [backup-simplify]: Simplify (* 1.0 0) into 0 8.157 * [backup-simplify]: Simplify 0 into 0 8.158 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 8.159 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 8.161 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 8.161 * [backup-simplify]: Simplify (- 0) into 0 8.162 * [backup-simplify]: Simplify (+ 0 0) into 0 8.162 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 8.164 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.165 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 8.167 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 8.169 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (* 0 (sqrt (/ 1 k)))) into 0 8.170 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k))))) into 0 8.170 * [taylor]: Taking taylor expansion of 0 in k 8.170 * [backup-simplify]: Simplify 0 into 0 8.171 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 8.173 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 8.174 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 8.174 * [backup-simplify]: Simplify (+ 0 0) into 0 8.175 * [backup-simplify]: Simplify (- 1) into -1 8.175 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.177 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 8.179 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 8.183 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 8.187 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) +nan.0) (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 0)) into (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 8.189 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 8.191 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 8.191 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.192 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 8.193 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 8.194 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 8.198 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 8.198 * [backup-simplify]: Simplify (- 0) into 0 8.199 * [backup-simplify]: Simplify (+ 0 0) into 0 8.200 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 8.201 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.203 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 8.205 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 8.207 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k))))) into 0 8.209 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k)))))) into 0 8.209 * [taylor]: Taking taylor expansion of 0 in k 8.209 * [backup-simplify]: Simplify 0 into 0 8.209 * [backup-simplify]: Simplify 0 into 0 8.210 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 8.213 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 8.214 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.218 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 8.220 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 8.220 * [backup-simplify]: Simplify (+ 0 0) into 0 8.221 * [backup-simplify]: Simplify (- 0) into 0 8.221 * [backup-simplify]: Simplify (+ 0 0) into 0 8.223 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 8.226 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 8.230 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 8.241 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) +nan.0) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) +nan.0) (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 0))) into (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))) 8.248 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0 0))) into (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))) 8.253 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))) into (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))) 8.253 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.254 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 8.256 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 8.257 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 8.265 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 8.265 * [backup-simplify]: Simplify (- 0) into 0 8.266 * [backup-simplify]: Simplify (+ 0 0) into 0 8.266 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 k))))) into 0 8.267 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.269 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n)))))) into 0 8.270 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 8.271 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k)))))) into 0 8.273 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k))))))) into 0 8.273 * [taylor]: Taking taylor expansion of 0 in k 8.273 * [backup-simplify]: Simplify 0 into 0 8.273 * [backup-simplify]: Simplify 0 into 0 8.273 * [backup-simplify]: Simplify 0 into 0 8.274 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.276 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 8.277 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 8.280 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 8.282 * [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 8.282 * [backup-simplify]: Simplify (+ 0 0) into 0 8.283 * [backup-simplify]: Simplify (- 0) into 0 8.283 * [backup-simplify]: Simplify (+ 0 0) into 0 8.284 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n)))))) into 0 8.286 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))))) into 0 8.291 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 3) 6)) (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (+ (* 0.0625 (* (log (* 2.0 PI)) (pow (log n) 2))) (+ (* 0.020833333333333332 (pow (log (* 2.0 PI)) 3)) (+ (* 0.020833333333333332 (pow (log n) 3)) (* 0.0625 (* (pow (log (* 2.0 PI)) 2) (log n)))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 8.310 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) +nan.0) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) +nan.0) (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) +nan.0) (* (* -1 (* (+ (* 0.0625 (* (log (* 2.0 PI)) (pow (log n) 2))) (+ (* 0.020833333333333332 (pow (log (* 2.0 PI)) 3)) (+ (* 0.020833333333333332 (pow (log n) 3)) (* 0.0625 (* (pow (log (* 2.0 PI)) 2) (log n)))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 0)))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))))))))) 8.331 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))))))))) (+ (* 0 (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0 0)))) into (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))))))))) 8.345 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))))))))) 8.369 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))) (* k 1)) (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k))))))))))))))))))))) 8.370 * [backup-simplify]: Simplify (* (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0)) (/ 1.0 (sqrt (/ 1 k)))) into (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) 8.370 * [approximate]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in (n k) around 0 8.370 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in k 8.370 * [taylor]: Taking taylor expansion of 1.0 in k 8.370 * [backup-simplify]: Simplify 1.0 into 1.0 8.370 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in k 8.370 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 8.371 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 8.371 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 8.371 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 8.371 * [taylor]: Taking taylor expansion of 0.5 in k 8.371 * [backup-simplify]: Simplify 0.5 into 0.5 8.371 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 8.371 * [taylor]: Taking taylor expansion of 1.0 in k 8.371 * [backup-simplify]: Simplify 1.0 into 1.0 8.371 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.371 * [taylor]: Taking taylor expansion of k in k 8.371 * [backup-simplify]: Simplify 0 into 0 8.371 * [backup-simplify]: Simplify 1 into 1 8.371 * [backup-simplify]: Simplify (/ 1 1) into 1 8.371 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 8.371 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 8.371 * [taylor]: Taking taylor expansion of 2.0 in k 8.371 * [backup-simplify]: Simplify 2.0 into 2.0 8.371 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.372 * [taylor]: Taking taylor expansion of PI in k 8.372 * [backup-simplify]: Simplify PI into PI 8.372 * [taylor]: Taking taylor expansion of n in k 8.372 * [backup-simplify]: Simplify n into n 8.372 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 8.372 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 8.372 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 8.372 * [backup-simplify]: Simplify (- 1) into -1 8.373 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.373 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 8.373 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 8.373 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) 8.373 * [taylor]: Taking taylor expansion of (sqrt k) in k 8.373 * [taylor]: Taking taylor expansion of k in k 8.373 * [backup-simplify]: Simplify 0 into 0 8.374 * [backup-simplify]: Simplify 1 into 1 8.374 * [backup-simplify]: Simplify (sqrt 0) into 0 8.375 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.375 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in n 8.375 * [taylor]: Taking taylor expansion of 1.0 in n 8.375 * [backup-simplify]: Simplify 1.0 into 1.0 8.375 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in n 8.375 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 8.375 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 8.375 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 8.375 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 8.376 * [taylor]: Taking taylor expansion of 0.5 in n 8.376 * [backup-simplify]: Simplify 0.5 into 0.5 8.376 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 8.376 * [taylor]: Taking taylor expansion of 1.0 in n 8.376 * [backup-simplify]: Simplify 1.0 into 1.0 8.376 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.376 * [taylor]: Taking taylor expansion of k in n 8.376 * [backup-simplify]: Simplify k into k 8.376 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.376 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 8.376 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 8.376 * [taylor]: Taking taylor expansion of 2.0 in n 8.376 * [backup-simplify]: Simplify 2.0 into 2.0 8.376 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.376 * [taylor]: Taking taylor expansion of PI in n 8.376 * [backup-simplify]: Simplify PI into PI 8.376 * [taylor]: Taking taylor expansion of n in n 8.376 * [backup-simplify]: Simplify 0 into 0 8.376 * [backup-simplify]: Simplify 1 into 1 8.377 * [backup-simplify]: Simplify (/ PI 1) into PI 8.377 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.378 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.378 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 8.378 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 8.378 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 8.380 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.381 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) 8.382 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 8.382 * [taylor]: Taking taylor expansion of (sqrt k) in n 8.382 * [taylor]: Taking taylor expansion of k in n 8.382 * [backup-simplify]: Simplify k into k 8.382 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 8.382 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 8.382 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in n 8.382 * [taylor]: Taking taylor expansion of 1.0 in n 8.382 * [backup-simplify]: Simplify 1.0 into 1.0 8.382 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in n 8.383 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 8.383 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 8.383 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 8.383 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 8.383 * [taylor]: Taking taylor expansion of 0.5 in n 8.383 * [backup-simplify]: Simplify 0.5 into 0.5 8.383 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 8.383 * [taylor]: Taking taylor expansion of 1.0 in n 8.383 * [backup-simplify]: Simplify 1.0 into 1.0 8.383 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.383 * [taylor]: Taking taylor expansion of k in n 8.383 * [backup-simplify]: Simplify k into k 8.383 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.383 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 8.383 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 8.383 * [taylor]: Taking taylor expansion of 2.0 in n 8.383 * [backup-simplify]: Simplify 2.0 into 2.0 8.383 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.383 * [taylor]: Taking taylor expansion of PI in n 8.383 * [backup-simplify]: Simplify PI into PI 8.383 * [taylor]: Taking taylor expansion of n in n 8.383 * [backup-simplify]: Simplify 0 into 0 8.383 * [backup-simplify]: Simplify 1 into 1 8.384 * [backup-simplify]: Simplify (/ PI 1) into PI 8.384 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.385 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.385 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 8.385 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 8.385 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 8.387 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.388 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) 8.390 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 8.390 * [taylor]: Taking taylor expansion of (sqrt k) in n 8.390 * [taylor]: Taking taylor expansion of k in n 8.390 * [backup-simplify]: Simplify k into k 8.390 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 8.390 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 8.392 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k)) into (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k)) 8.393 * [backup-simplify]: Simplify (* 1.0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k))) into (* 1.0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k))) 8.393 * [taylor]: Taking taylor expansion of (* 1.0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k))) in k 8.393 * [taylor]: Taking taylor expansion of 1.0 in k 8.393 * [backup-simplify]: Simplify 1.0 into 1.0 8.393 * [taylor]: Taking taylor expansion of (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k)) in k 8.393 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) in k 8.393 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) in k 8.393 * [taylor]: Taking taylor expansion of 0.5 in k 8.393 * [backup-simplify]: Simplify 0.5 into 0.5 8.393 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) in k 8.394 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 8.394 * [taylor]: Taking taylor expansion of 1.0 in k 8.394 * [backup-simplify]: Simplify 1.0 into 1.0 8.394 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.394 * [taylor]: Taking taylor expansion of k in k 8.394 * [backup-simplify]: Simplify 0 into 0 8.394 * [backup-simplify]: Simplify 1 into 1 8.394 * [backup-simplify]: Simplify (/ 1 1) into 1 8.394 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 8.394 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 8.394 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 8.394 * [taylor]: Taking taylor expansion of 2.0 in k 8.394 * [backup-simplify]: Simplify 2.0 into 2.0 8.394 * [taylor]: Taking taylor expansion of PI in k 8.394 * [backup-simplify]: Simplify PI into PI 8.395 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.402 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.403 * [taylor]: Taking taylor expansion of (log n) in k 8.403 * [taylor]: Taking taylor expansion of n in k 8.403 * [backup-simplify]: Simplify n into n 8.403 * [backup-simplify]: Simplify (log n) into (log n) 8.403 * [backup-simplify]: Simplify (- 1) into -1 8.404 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.404 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 8.405 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 8.406 * [backup-simplify]: Simplify (* -1 (- (log (* 2.0 PI)) (log n))) into (* -1 (- (log (* 2.0 PI)) (log n))) 8.407 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 8.409 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 8.409 * [taylor]: Taking taylor expansion of (sqrt k) in k 8.409 * [taylor]: Taking taylor expansion of k in k 8.409 * [backup-simplify]: Simplify 0 into 0 8.409 * [backup-simplify]: Simplify 1 into 1 8.409 * [backup-simplify]: Simplify (sqrt 0) into 0 8.411 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.412 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 0) into 0 8.413 * [backup-simplify]: Simplify (* 1.0 0) into 0 8.413 * [backup-simplify]: Simplify 0 into 0 8.414 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.414 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 8.416 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 8.416 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 8.417 * [backup-simplify]: Simplify (- 0) into 0 8.417 * [backup-simplify]: Simplify (+ 0 0) into 0 8.418 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 8.419 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.421 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 8.422 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 8.423 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 0) (* 0 (sqrt k))) into 0 8.424 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k)))) into 0 8.424 * [taylor]: Taking taylor expansion of 0 in k 8.424 * [backup-simplify]: Simplify 0 into 0 8.424 * [backup-simplify]: Simplify 0 into 0 8.425 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) 8.426 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) 8.427 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) 8.427 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 8.428 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.429 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.430 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 8.431 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.431 * [backup-simplify]: Simplify (- 0) into 0 8.431 * [backup-simplify]: Simplify (+ 0 0) into 0 8.432 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 8.432 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.433 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 8.435 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 8.436 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (sqrt k)))) into 0 8.437 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k))))) into 0 8.437 * [taylor]: Taking taylor expansion of 0 in k 8.437 * [backup-simplify]: Simplify 0 into 0 8.437 * [backup-simplify]: Simplify 0 into 0 8.437 * [backup-simplify]: Simplify 0 into 0 8.439 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 8.440 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) 8.442 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) (* 0 0))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) 8.443 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) 8.444 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 8.444 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.445 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 8.448 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 8.448 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.449 * [backup-simplify]: Simplify (- 0) into 0 8.449 * [backup-simplify]: Simplify (+ 0 0) into 0 8.450 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 8.450 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.452 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 8.453 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 8.455 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt k))))) into 0 8.456 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k)))))) into 0 8.456 * [taylor]: Taking taylor expansion of 0 in k 8.456 * [backup-simplify]: Simplify 0 into 0 8.456 * [backup-simplify]: Simplify 0 into 0 8.456 * [backup-simplify]: Simplify 0 into 0 8.456 * [backup-simplify]: Simplify 0 into 0 8.459 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 8.460 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) 8.463 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) (* 0 0)))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) 8.464 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) 8.466 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 3)))))))) 8.467 * [backup-simplify]: Simplify (* (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0)) (/ 1.0 (sqrt (/ 1 (- k))))) into (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) 8.467 * [approximate]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in (n k) around 0 8.467 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 8.467 * [taylor]: Taking taylor expansion of 1.0 in k 8.467 * [backup-simplify]: Simplify 1.0 into 1.0 8.467 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 8.467 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 8.467 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 8.467 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 8.467 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 8.467 * [taylor]: Taking taylor expansion of 0.5 in k 8.467 * [backup-simplify]: Simplify 0.5 into 0.5 8.467 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 8.467 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.467 * [taylor]: Taking taylor expansion of k in k 8.467 * [backup-simplify]: Simplify 0 into 0 8.467 * [backup-simplify]: Simplify 1 into 1 8.468 * [backup-simplify]: Simplify (/ 1 1) into 1 8.468 * [taylor]: Taking taylor expansion of 1.0 in k 8.468 * [backup-simplify]: Simplify 1.0 into 1.0 8.468 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 8.468 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 8.468 * [taylor]: Taking taylor expansion of -2.0 in k 8.468 * [backup-simplify]: Simplify -2.0 into -2.0 8.468 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.468 * [taylor]: Taking taylor expansion of PI in k 8.468 * [backup-simplify]: Simplify PI into PI 8.468 * [taylor]: Taking taylor expansion of n in k 8.468 * [backup-simplify]: Simplify n into n 8.468 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 8.468 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 8.468 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 8.468 * [backup-simplify]: Simplify (+ 1 0) into 1 8.469 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 8.469 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 8.469 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) 8.469 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 8.469 * [taylor]: Taking taylor expansion of (/ -1 k) in k 8.469 * [taylor]: Taking taylor expansion of -1 in k 8.469 * [backup-simplify]: Simplify -1 into -1 8.469 * [taylor]: Taking taylor expansion of k in k 8.469 * [backup-simplify]: Simplify 0 into 0 8.469 * [backup-simplify]: Simplify 1 into 1 8.469 * [backup-simplify]: Simplify (/ -1 1) into -1 8.469 * [backup-simplify]: Simplify (sqrt 0) into 0 8.470 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 8.470 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) 8.470 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n 8.470 * [taylor]: Taking taylor expansion of 1.0 in n 8.470 * [backup-simplify]: Simplify 1.0 into 1.0 8.470 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n 8.471 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 8.471 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 8.471 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 8.471 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 8.471 * [taylor]: Taking taylor expansion of 0.5 in n 8.471 * [backup-simplify]: Simplify 0.5 into 0.5 8.471 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 8.471 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.471 * [taylor]: Taking taylor expansion of k in n 8.471 * [backup-simplify]: Simplify k into k 8.471 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.471 * [taylor]: Taking taylor expansion of 1.0 in n 8.471 * [backup-simplify]: Simplify 1.0 into 1.0 8.471 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 8.471 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 8.471 * [taylor]: Taking taylor expansion of -2.0 in n 8.471 * [backup-simplify]: Simplify -2.0 into -2.0 8.471 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.471 * [taylor]: Taking taylor expansion of PI in n 8.471 * [backup-simplify]: Simplify PI into PI 8.471 * [taylor]: Taking taylor expansion of n in n 8.471 * [backup-simplify]: Simplify 0 into 0 8.471 * [backup-simplify]: Simplify 1 into 1 8.471 * [backup-simplify]: Simplify (/ PI 1) into PI 8.472 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.472 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 8.472 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 8.472 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 8.473 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.474 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) 8.475 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 8.475 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 8.475 * [taylor]: Taking taylor expansion of (/ -1 k) in n 8.475 * [taylor]: Taking taylor expansion of -1 in n 8.475 * [backup-simplify]: Simplify -1 into -1 8.475 * [taylor]: Taking taylor expansion of k in n 8.475 * [backup-simplify]: Simplify k into k 8.475 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 8.475 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 8.475 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 8.475 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 8.476 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) into (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) 8.476 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n 8.476 * [taylor]: Taking taylor expansion of 1.0 in n 8.476 * [backup-simplify]: Simplify 1.0 into 1.0 8.476 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n 8.476 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 8.476 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 8.476 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 8.476 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 8.476 * [taylor]: Taking taylor expansion of 0.5 in n 8.476 * [backup-simplify]: Simplify 0.5 into 0.5 8.476 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 8.476 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.476 * [taylor]: Taking taylor expansion of k in n 8.476 * [backup-simplify]: Simplify k into k 8.476 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.476 * [taylor]: Taking taylor expansion of 1.0 in n 8.476 * [backup-simplify]: Simplify 1.0 into 1.0 8.476 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 8.476 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 8.476 * [taylor]: Taking taylor expansion of -2.0 in n 8.476 * [backup-simplify]: Simplify -2.0 into -2.0 8.476 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.476 * [taylor]: Taking taylor expansion of PI in n 8.476 * [backup-simplify]: Simplify PI into PI 8.476 * [taylor]: Taking taylor expansion of n in n 8.476 * [backup-simplify]: Simplify 0 into 0 8.476 * [backup-simplify]: Simplify 1 into 1 8.477 * [backup-simplify]: Simplify (/ PI 1) into PI 8.477 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.478 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 8.478 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 8.478 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 8.480 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.481 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) 8.482 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 8.482 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 8.482 * [taylor]: Taking taylor expansion of (/ -1 k) in n 8.482 * [taylor]: Taking taylor expansion of -1 in n 8.482 * [backup-simplify]: Simplify -1 into -1 8.482 * [taylor]: Taking taylor expansion of k in n 8.483 * [backup-simplify]: Simplify k into k 8.483 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 8.483 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 8.483 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 8.483 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 8.484 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) into (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) 8.486 * [backup-simplify]: Simplify (* 1.0 (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k)))) into (* 1.0 (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k)))) 8.486 * [taylor]: Taking taylor expansion of (* 1.0 (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k)))) in k 8.486 * [taylor]: Taking taylor expansion of 1.0 in k 8.486 * [backup-simplify]: Simplify 1.0 into 1.0 8.486 * [taylor]: Taking taylor expansion of (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) in k 8.486 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) in k 8.486 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) in k 8.486 * [taylor]: Taking taylor expansion of 0.5 in k 8.486 * [backup-simplify]: Simplify 0.5 into 0.5 8.486 * [taylor]: Taking taylor expansion of (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) in k 8.486 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 8.486 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 8.486 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 8.486 * [taylor]: Taking taylor expansion of -2.0 in k 8.486 * [backup-simplify]: Simplify -2.0 into -2.0 8.486 * [taylor]: Taking taylor expansion of PI in k 8.486 * [backup-simplify]: Simplify PI into PI 8.487 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.488 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 8.488 * [taylor]: Taking taylor expansion of (log n) in k 8.488 * [taylor]: Taking taylor expansion of n in k 8.488 * [backup-simplify]: Simplify n into n 8.488 * [backup-simplify]: Simplify (log n) into (log n) 8.488 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 8.488 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.488 * [taylor]: Taking taylor expansion of k in k 8.488 * [backup-simplify]: Simplify 0 into 0 8.488 * [backup-simplify]: Simplify 1 into 1 8.489 * [backup-simplify]: Simplify (/ 1 1) into 1 8.489 * [taylor]: Taking taylor expansion of 1.0 in k 8.489 * [backup-simplify]: Simplify 1.0 into 1.0 8.489 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 8.490 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 8.491 * [backup-simplify]: Simplify (+ 1 0) into 1 8.492 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) 1) into (- (log (* -2.0 PI)) (log n)) 8.493 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 8.494 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 8.495 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 8.495 * [taylor]: Taking taylor expansion of (/ -1 k) in k 8.495 * [taylor]: Taking taylor expansion of -1 in k 8.495 * [backup-simplify]: Simplify -1 into -1 8.495 * [taylor]: Taking taylor expansion of k in k 8.495 * [backup-simplify]: Simplify 0 into 0 8.495 * [backup-simplify]: Simplify 1 into 1 8.495 * [backup-simplify]: Simplify (/ -1 1) into -1 8.496 * [backup-simplify]: Simplify (sqrt 0) into 0 8.497 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 8.498 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) 8.500 * [backup-simplify]: Simplify (* 1.0 (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) 8.501 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) 8.502 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.503 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 8.505 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 8.505 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 8.506 * [backup-simplify]: Simplify (+ 0 0) into 0 8.507 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 8.508 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.510 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 8.512 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 8.513 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0 8.521 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))))) into 0 8.521 * [taylor]: Taking taylor expansion of 0 in k 8.521 * [backup-simplify]: Simplify 0 into 0 8.522 * [backup-simplify]: Simplify 0 into 0 8.522 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 8.526 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 8.528 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) 8.530 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) 8.532 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) 8.533 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.534 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.538 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 8.538 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.538 * [backup-simplify]: Simplify (+ 0 0) into 0 8.539 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 8.541 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.543 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 8.546 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 8.547 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.547 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 8.549 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0 8.551 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k)))))) into 0 8.551 * [taylor]: Taking taylor expansion of 0 in k 8.551 * [backup-simplify]: Simplify 0 into 0 8.551 * [backup-simplify]: Simplify 0 into 0 8.552 * [backup-simplify]: Simplify 0 into 0 8.553 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.557 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 8.559 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) 8.562 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) 8.562 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) 8.565 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0))))))) into (- (+ (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2)))))))) 8.565 * * * [progress]: simplifying candidates 8.568 * [simplify]: Simplifying: (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (- (log 1.0) (log (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt 1)) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt 1)) (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 1) (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt 1)) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 1) (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (+ (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (- (log 1.0) (log (sqrt k)))) (+ (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (log (/ 1.0 (sqrt k)))) (+ (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (- (log 1.0) (log (sqrt k)))) (+ (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (log (/ 1.0 (sqrt k)))) (+ (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (- (log 1.0) (log (sqrt k)))) (+ (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (log (/ 1.0 (sqrt k)))) (+ (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (- (log 1.0) (log (sqrt k)))) (+ (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (log (/ 1.0 (sqrt k)))) (+ (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (- (log 1.0) (log (sqrt k)))) (+ (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log (/ 1.0 (sqrt k)))) (log (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (exp (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (* (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k)))) (* (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k)))) (* (cbrt (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (cbrt (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))))) (cbrt (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (* (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (sqrt (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (sqrt (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (* (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) 1.0) (* (pow (* (* 2.0 PI) n) (/ k 2.0)) (sqrt k)) (* (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (/ 1.0 (sqrt k)))) (* (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (/ 1.0 (sqrt k)))) (* (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (sqrt (/ 1.0 (sqrt k)))) (* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (sqrt (/ 1.0 (sqrt k)))) (* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k))))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (/ 1.0 (sqrt k)))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k))))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ (* (cbrt 1.0) (cbrt 1.0)) 1)) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k))))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ (sqrt 1.0) (sqrt 1))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ (sqrt 1.0) 1)) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1 (sqrt (* (cbrt k) (cbrt k))))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1 (sqrt (sqrt k)))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1 (sqrt 1))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1 (sqrt (sqrt k)))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1 1)) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (* (pow n (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (/ 1.0 (sqrt k))) (* (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (/ 1.0 (sqrt k))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))) (* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (/ 1.0 (sqrt k))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (* (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (/ 1.0 (sqrt k))) (- (+ (* 0.25 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2))))) (+ (* 0.125 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* 0.125 (* (pow (log (* 2.0 PI)) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))))))) (+ (* 0.5 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k))) (* 0.5 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k))))) (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (- (+ (* +nan.0 (pow k 2)) (- (+ +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))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k))))))))))))))))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 3)))))))) (- (+ (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2)))))))) 8.571 * * [simplify]: iteration 0: 335 enodes 8.677 * * [simplify]: iteration 1: 920 enodes 9.147 * * [simplify]: iteration 2: 3042 enodes 10.085 * * [simplify]: iteration complete: 5001 enodes 10.085 * * [simplify]: Extracting #0: cost 119 inf + 0 10.086 * * [simplify]: Extracting #1: cost 574 inf + 43 10.089 * * [simplify]: Extracting #2: cost 1046 inf + 2320 10.105 * * [simplify]: Extracting #3: cost 1288 inf + 29823 10.146 * * [simplify]: Extracting #4: cost 830 inf + 173088 10.233 * * [simplify]: Extracting #5: cost 357 inf + 386454 10.324 * * [simplify]: Extracting #6: cost 222 inf + 478076 10.450 * * [simplify]: Extracting #7: cost 61 inf + 551857 10.627 * * [simplify]: Extracting #8: cost 3 inf + 591222 10.812 * * [simplify]: Extracting #9: cost 0 inf + 592634 10.990 * * [simplify]: Extracting #10: cost 0 inf + 592194 11.112 * * [simplify]: Extracting #11: cost 0 inf + 592114 11.270 * [simplify]: Simplified to: (* (/ (- 1.0 k) 2.0) (log (* n (* PI 2.0)))) (* (/ (- 1.0 k) 2.0) (log (* n (* PI 2.0)))) (* (/ (- 1.0 k) 2.0) (log (* n (* PI 2.0)))) (* (/ (- 1.0 k) 2.0) (log (* n (* PI 2.0)))) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (pow (* n (* PI 2.0)) (/ 1.0 2.0)) (pow (* n (* PI 2.0)) (/ k 2.0)) (pow (* n (* PI 2.0)) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* n (* PI 2.0)) (sqrt (/ (- 1.0 k) 2.0))) (pow (* n (* PI 2.0)) (* (/ (cbrt (- 1.0 k)) (cbrt 2.0)) (/ (cbrt (- 1.0 k)) (cbrt 2.0)))) (pow (* n (* PI 2.0)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* n (* PI 2.0)) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* n (* PI 2.0)) (/ (/ (sqrt (- 1.0 k)) (cbrt 2.0)) (cbrt 2.0))) (pow (* n (* PI 2.0)) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* n (* PI 2.0)) (sqrt (- 1.0 k))) (pow (* n (* PI 2.0)) (/ (/ 1 (cbrt 2.0)) (cbrt 2.0))) (pow (* n (* PI 2.0)) (/ 1 (sqrt 2.0))) (* n (* PI 2.0)) (pow (* n (* PI 2.0)) (/ (/ (+ (sqrt k) (sqrt 1.0)) (cbrt 2.0)) (cbrt 2.0))) (pow (* n (* PI 2.0)) (/ (+ (sqrt k) (sqrt 1.0)) (sqrt 2.0))) (pow (* n (* PI 2.0)) (+ (sqrt k) (sqrt 1.0))) (pow (* n (* PI 2.0)) (/ (/ 1 (cbrt 2.0)) (cbrt 2.0))) (pow (* n (* PI 2.0)) (/ 1 (sqrt 2.0))) (* n (* PI 2.0)) (* n (* PI 2.0)) (pow (* n (* PI 2.0)) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (* (/ (- 1.0 k) 2.0) (log (* n (* PI 2.0)))) (exp (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))) (cbrt (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))) (* (* (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))) (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))) (sqrt (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))) (sqrt (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))) (pow (* n (* PI 2.0)) (/ (/ (- 1.0 k) 2) 2.0)) (pow (* n (* PI 2.0)) (/ (/ (- 1.0 k) 2) 2.0)) (* n (* PI 2.0)) (* n (* PI 2.0)) (log (* n (* PI 2.0))) (log (* n (* PI 2.0))) (log (* n (* PI 2.0))) (exp (* n (* PI 2.0))) (* (* n (* PI 2.0)) (* (* n (* PI 2.0)) (* n (* PI 2.0)))) (* (* n (* PI 2.0)) (* (* n (* PI 2.0)) (* n (* PI 2.0)))) (* (cbrt (* n (* PI 2.0))) (cbrt (* n (* PI 2.0)))) (cbrt (* n (* PI 2.0))) (* (* n (* PI 2.0)) (* (* n (* PI 2.0)) (* n (* PI 2.0)))) (sqrt (* n (* PI 2.0))) (sqrt (* n (* PI 2.0))) (* (* 2.0 (* PI (cbrt n))) (cbrt n)) (* (sqrt n) (* 2.0 PI)) (* 2.0 PI) (* PI n) (log (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (* (/ 1.0 (sqrt k)) (/ (* 1.0 1.0) k)) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (* (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (cbrt 1.0) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (fabs (cbrt k))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (fabs (cbrt k))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ (/ 1.0 (cbrt (sqrt k))) (cbrt (sqrt k))) (/ 1.0 (fabs (cbrt k))) (/ 1.0 (sqrt (sqrt k))) 1.0 (/ 1.0 (sqrt (sqrt k))) 1.0 (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (+ (log (/ 1.0 (sqrt k))) (* (/ (- 1.0 k) 2.0) (log (* n (* PI 2.0))))) (+ (log (/ 1.0 (sqrt k))) (* (/ (- 1.0 k) 2.0) (log (* n (* PI 2.0))))) (+ (log (/ 1.0 (sqrt k))) (* (/ (- 1.0 k) 2.0) (log (* n (* PI 2.0))))) (+ (log (/ 1.0 (sqrt k))) (* (/ (- 1.0 k) 2.0) (log (* n (* PI 2.0))))) (+ (log (/ 1.0 (sqrt k))) (* (/ (- 1.0 k) 2.0) (log (* n (* PI 2.0))))) (+ (log (/ 1.0 (sqrt k))) (* (/ (- 1.0 k) 2.0) (log (* n (* PI 2.0))))) (+ (log (/ 1.0 (sqrt k))) (* (/ (- 1.0 k) 2.0) (log (* n (* PI 2.0))))) (+ (log (/ 1.0 (sqrt k))) (* (/ (- 1.0 k) 2.0) (log (* n (* PI 2.0))))) (+ (log (/ 1.0 (sqrt k))) (* (/ (- 1.0 k) 2.0) (log (* n (* PI 2.0))))) (+ (log (/ 1.0 (sqrt k))) (* (/ (- 1.0 k) 2.0) (log (* n (* PI 2.0))))) (+ (log (/ 1.0 (sqrt k))) (* (/ (- 1.0 k) 2.0) (log (* n (* PI 2.0))))) (exp (/ (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))) (* (* (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (* (/ 1.0 (sqrt k)) (/ (* 1.0 1.0) k))) (* (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)))) (* (* (* (* (/ 1.0 (sqrt k)) (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)))) (/ 1.0 (sqrt k))) (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))) (* (cbrt (/ (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))) (cbrt (/ (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))) (cbrt (/ (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))) (* (* (* (* (/ 1.0 (sqrt k)) (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)))) (/ 1.0 (sqrt k))) (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))) (sqrt (/ (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))) (sqrt (/ (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))) (* (pow (* n (* PI 2.0)) (/ 1.0 2.0)) 1.0) (* (sqrt k) (pow (* n (* PI 2.0)) (/ k 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)))) (* (sqrt (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (sqrt (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (sqrt (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (sqrt (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (pow (* n (* PI 2.0)) (/ (/ (- 1.0 k) 2) 2.0)) (sqrt (/ 1.0 (sqrt k)))) (* (pow (* n (* PI 2.0)) (/ (/ (- 1.0 k) 2) 2.0)) (sqrt (/ 1.0 (sqrt k)))) (/ (pow (* n (* PI 2.0)) (/ (/ (- 1.0 k) 2) 2.0)) (/ (sqrt (sqrt k)) (sqrt 1.0))) (/ (pow (* n (* PI 2.0)) (/ (/ (- 1.0 k) 2) 2.0)) (/ (sqrt (sqrt k)) (sqrt 1.0))) (/ (pow (* n (* PI 2.0)) (/ (/ (- 1.0 k) 2) 2.0)) (/ (sqrt (sqrt k)) (sqrt 1.0))) (/ (pow (* n (* PI 2.0)) (/ (/ (- 1.0 k) 2) 2.0)) (/ (sqrt (sqrt k)) (sqrt 1.0))) (* (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k))))) (* (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (sqrt (/ 1.0 (sqrt k)))) (/ (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (* (/ (cbrt (sqrt k)) (cbrt 1.0)) (/ (cbrt (sqrt k)) (cbrt 1.0)))) (* (/ (* (cbrt 1.0) (cbrt 1.0)) (fabs (cbrt k))) (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))) (/ (* (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (cbrt 1.0)) (/ (sqrt (sqrt k)) (cbrt 1.0))) (* (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (* (cbrt 1.0) (cbrt 1.0))) (/ (* (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (cbrt 1.0)) (/ (sqrt (sqrt k)) (cbrt 1.0))) (* (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (* (cbrt 1.0) (cbrt 1.0))) (/ (* (/ (sqrt 1.0) (cbrt (sqrt k))) (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))) (cbrt (sqrt k))) (* (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (/ (sqrt 1.0) (fabs (cbrt k)))) (* (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (sqrt 1.0)) (* (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (sqrt 1.0)) (/ (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (fabs (cbrt k))) (/ (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k))) (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (/ (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k))) (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (* (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (* (/ 1.0 (sqrt k)) (pow n (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))) (/ 1.0 (sqrt k))) (/ (sqrt (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))) (/ (sqrt k) 1.0)) (/ (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)) (/ (pow (* n (* PI 2.0)) (/ (/ (- 1.0 k) 2) 2.0)) (/ (sqrt k) 1.0)) (* (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (/ (* (pow (* n (* PI 2.0)) (/ 1.0 2.0)) 1.0) (sqrt k)) (+ (+ (* (* (log (* 2.0 PI)) (log (* 2.0 PI))) (* (* (* k k) (exp (* 0.5 (log (* n (* PI 2.0)))))) 0.125)) (+ (* (exp (* 0.5 (log (* n (* PI 2.0))))) (* (* (* (log n) (* k k)) (log n)) 0.125)) (exp (* 0.5 (log (* n (* PI 2.0))))))) (- (* (* 0.25 (* (exp (* 0.5 (log (* n (* PI 2.0))))) (log (* 2.0 PI)))) (* (log n) (* k k))) (* (* k (+ (* (log n) (exp (* 0.5 (log (* n (* PI 2.0)))))) (* (exp (* 0.5 (log (* n (* PI 2.0))))) (log (* 2.0 PI))))) 0.5))) (exp (* (* 0.5 (- 1.0 k)) (log (* n (* PI 2.0))))) (exp (* (- (log (* PI -2.0)) (log (/ -1 n))) (* 0.5 (- 1.0 k)))) (* n (* PI 2.0)) (* n (* PI 2.0)) (* n (* PI 2.0)) (- (+ (- (* +nan.0 (* k k)) +nan.0) (* k +nan.0))) (- (+ (- (/ +nan.0 (* k k)) (/ +nan.0 k)) (/ +nan.0 (* (* k k) k)))) (+ (/ (- +nan.0) (* k k)) (- (/ +nan.0 k) +nan.0)) (+ (* (* (- (log (* 2.0 PI))) +nan.0) (* (* (* k k) (exp (* 0.5 (log (* n (* PI 2.0)))))) (log n))) (- (* (exp (* 0.5 (log (* n (* PI 2.0))))) +nan.0) (+ (- (* (* +nan.0 (* (log (* 2.0 PI)) (log (* 2.0 PI)))) (* (* k k) (exp (* 0.5 (log (* n (* PI 2.0))))))) (* (* (exp (* 0.5 (log (* n (* PI 2.0))))) +nan.0) (* k k))) (+ (- (* (* (exp (* 0.5 (log (* n (* PI 2.0))))) +nan.0) (* (* (log n) (* k k)) (log n))) (* +nan.0 (* (* (* k k) (exp (* 0.5 (log (* n (* PI 2.0)))))) (log n)))) (- (* (* (* k k) (exp (* 0.5 (log (* n (* PI 2.0)))))) (* +nan.0 (log (* 2.0 PI)))) (- (* (* (exp (* 0.5 (log (* n (* PI 2.0))))) +nan.0) (* k (log n))) (* (* (exp (* 0.5 (log (* n (* PI 2.0))))) k) (+ (* +nan.0 (log (* 2.0 PI))) (- +nan.0))))))))) (+ (* (- (/ +nan.0 k)) (/ (exp (* (* 0.5 (- 1.0 k)) (log (* n (* PI 2.0))))) k)) (- (* +nan.0 (/ (exp (* (* 0.5 (- 1.0 k)) (log (* n (* PI 2.0))))) k)) (* (/ (exp (* (* 0.5 (- 1.0 k)) (log (* n (* PI 2.0))))) k) (/ +nan.0 (* k k))))) (+ (- (* (exp (* (- (log (* PI -2.0)) (log (/ -1 n))) (* 0.5 (- 1.0 k)))) +nan.0)) (- (/ (* +nan.0 (exp (* (- (log (* PI -2.0)) (log (/ -1 n))) (* 0.5 (- 1.0 k))))) k) (/ (exp (* (- (log (* PI -2.0)) (log (/ -1 n))) (* 0.5 (- 1.0 k)))) (/ (* k k) +nan.0)))) 11.281 * * * [progress]: adding candidates to table 12.182 * * [progress]: iteration 3 / 4 12.182 * * * [progress]: picking best candidate 12.253 * * * * [pick]: Picked # 12.253 * * * [progress]: localizing error 12.281 * * * [progress]: generating rewritten candidates 12.281 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 12.313 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1) 12.339 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1) 12.348 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 12.420 * * * [progress]: generating series expansions 12.421 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 12.422 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 12.422 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 12.422 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 12.422 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 12.422 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 12.422 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 12.422 * [taylor]: Taking taylor expansion of 0.5 in k 12.422 * [backup-simplify]: Simplify 0.5 into 0.5 12.422 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 12.422 * [taylor]: Taking taylor expansion of 1.0 in k 12.422 * [backup-simplify]: Simplify 1.0 into 1.0 12.422 * [taylor]: Taking taylor expansion of k in k 12.422 * [backup-simplify]: Simplify 0 into 0 12.422 * [backup-simplify]: Simplify 1 into 1 12.422 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 12.422 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 12.422 * [taylor]: Taking taylor expansion of 2.0 in k 12.422 * [backup-simplify]: Simplify 2.0 into 2.0 12.422 * [taylor]: Taking taylor expansion of (* n PI) in k 12.422 * [taylor]: Taking taylor expansion of n in k 12.422 * [backup-simplify]: Simplify n into n 12.422 * [taylor]: Taking taylor expansion of PI in k 12.422 * [backup-simplify]: Simplify PI into PI 12.422 * [backup-simplify]: Simplify (* n PI) into (* n PI) 12.423 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 12.423 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 12.423 * [backup-simplify]: Simplify (- 0) into 0 12.424 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 12.424 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 12.424 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 12.424 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 12.424 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 12.424 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 12.425 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 12.425 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 12.425 * [taylor]: Taking taylor expansion of 0.5 in n 12.425 * [backup-simplify]: Simplify 0.5 into 0.5 12.425 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 12.425 * [taylor]: Taking taylor expansion of 1.0 in n 12.425 * [backup-simplify]: Simplify 1.0 into 1.0 12.425 * [taylor]: Taking taylor expansion of k in n 12.425 * [backup-simplify]: Simplify k into k 12.425 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 12.425 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 12.425 * [taylor]: Taking taylor expansion of 2.0 in n 12.425 * [backup-simplify]: Simplify 2.0 into 2.0 12.425 * [taylor]: Taking taylor expansion of (* n PI) in n 12.425 * [taylor]: Taking taylor expansion of n in n 12.425 * [backup-simplify]: Simplify 0 into 0 12.425 * [backup-simplify]: Simplify 1 into 1 12.425 * [taylor]: Taking taylor expansion of PI in n 12.425 * [backup-simplify]: Simplify PI into PI 12.426 * [backup-simplify]: Simplify (* 0 PI) into 0 12.426 * [backup-simplify]: Simplify (* 2.0 0) into 0 12.428 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.429 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 12.430 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.430 * [backup-simplify]: Simplify (- k) into (- k) 12.430 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 12.430 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 12.432 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.433 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 12.434 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 12.434 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 12.434 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 12.434 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 12.434 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 12.434 * [taylor]: Taking taylor expansion of 0.5 in n 12.434 * [backup-simplify]: Simplify 0.5 into 0.5 12.434 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 12.434 * [taylor]: Taking taylor expansion of 1.0 in n 12.434 * [backup-simplify]: Simplify 1.0 into 1.0 12.434 * [taylor]: Taking taylor expansion of k in n 12.434 * [backup-simplify]: Simplify k into k 12.434 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 12.434 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 12.434 * [taylor]: Taking taylor expansion of 2.0 in n 12.434 * [backup-simplify]: Simplify 2.0 into 2.0 12.434 * [taylor]: Taking taylor expansion of (* n PI) in n 12.434 * [taylor]: Taking taylor expansion of n in n 12.434 * [backup-simplify]: Simplify 0 into 0 12.434 * [backup-simplify]: Simplify 1 into 1 12.434 * [taylor]: Taking taylor expansion of PI in n 12.434 * [backup-simplify]: Simplify PI into PI 12.435 * [backup-simplify]: Simplify (* 0 PI) into 0 12.435 * [backup-simplify]: Simplify (* 2.0 0) into 0 12.436 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.437 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 12.438 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.438 * [backup-simplify]: Simplify (- k) into (- k) 12.438 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 12.438 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 12.439 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.440 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 12.441 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 12.441 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 12.441 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 12.441 * [taylor]: Taking taylor expansion of 0.5 in k 12.441 * [backup-simplify]: Simplify 0.5 into 0.5 12.441 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 12.441 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 12.441 * [taylor]: Taking taylor expansion of 1.0 in k 12.441 * [backup-simplify]: Simplify 1.0 into 1.0 12.441 * [taylor]: Taking taylor expansion of k in k 12.441 * [backup-simplify]: Simplify 0 into 0 12.441 * [backup-simplify]: Simplify 1 into 1 12.441 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 12.441 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 12.441 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 12.441 * [taylor]: Taking taylor expansion of 2.0 in k 12.441 * [backup-simplify]: Simplify 2.0 into 2.0 12.441 * [taylor]: Taking taylor expansion of PI in k 12.441 * [backup-simplify]: Simplify PI into PI 12.441 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.442 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.442 * [taylor]: Taking taylor expansion of (log n) in k 12.442 * [taylor]: Taking taylor expansion of n in k 12.442 * [backup-simplify]: Simplify n into n 12.442 * [backup-simplify]: Simplify (log n) into (log n) 12.442 * [backup-simplify]: Simplify (- 0) into 0 12.443 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 12.443 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 12.444 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 12.445 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 12.445 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 12.446 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 12.447 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 12.447 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 12.448 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 12.449 * [backup-simplify]: Simplify (- 0) into 0 12.449 * [backup-simplify]: Simplify (+ 0 0) into 0 12.449 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 12.450 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.451 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 12.452 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 12.452 * [taylor]: Taking taylor expansion of 0 in k 12.452 * [backup-simplify]: Simplify 0 into 0 12.452 * [backup-simplify]: Simplify 0 into 0 12.452 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 12.453 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 12.454 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 12.454 * [backup-simplify]: Simplify (+ 0 0) into 0 12.454 * [backup-simplify]: Simplify (- 1) into -1 12.455 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.456 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 12.457 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 12.459 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 12.461 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 12.462 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 12.463 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 12.467 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 12.467 * [backup-simplify]: Simplify (- 0) into 0 12.468 * [backup-simplify]: Simplify (+ 0 0) into 0 12.474 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 12.476 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.477 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 12.480 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 12.480 * [taylor]: Taking taylor expansion of 0 in k 12.480 * [backup-simplify]: Simplify 0 into 0 12.480 * [backup-simplify]: Simplify 0 into 0 12.480 * [backup-simplify]: Simplify 0 into 0 12.481 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 12.485 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 12.486 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 12.486 * [backup-simplify]: Simplify (+ 0 0) into 0 12.487 * [backup-simplify]: Simplify (- 0) into 0 12.487 * [backup-simplify]: Simplify (+ 0 0) into 0 12.488 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 12.490 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 12.492 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 12.496 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 12.502 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.25 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2))))) (+ (* 0.125 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* 0.125 (* (pow (log (* 2.0 PI)) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))))))) (+ (* 0.5 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k))) (* 0.5 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k))))) 12.503 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) 12.503 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 12.503 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 12.503 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 12.503 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 12.503 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 12.503 * [taylor]: Taking taylor expansion of 0.5 in k 12.503 * [backup-simplify]: Simplify 0.5 into 0.5 12.503 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 12.503 * [taylor]: Taking taylor expansion of 1.0 in k 12.503 * [backup-simplify]: Simplify 1.0 into 1.0 12.503 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.503 * [taylor]: Taking taylor expansion of k in k 12.503 * [backup-simplify]: Simplify 0 into 0 12.503 * [backup-simplify]: Simplify 1 into 1 12.503 * [backup-simplify]: Simplify (/ 1 1) into 1 12.503 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 12.503 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 12.503 * [taylor]: Taking taylor expansion of 2.0 in k 12.503 * [backup-simplify]: Simplify 2.0 into 2.0 12.503 * [taylor]: Taking taylor expansion of (/ PI n) in k 12.503 * [taylor]: Taking taylor expansion of PI in k 12.503 * [backup-simplify]: Simplify PI into PI 12.503 * [taylor]: Taking taylor expansion of n in k 12.503 * [backup-simplify]: Simplify n into n 12.503 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 12.503 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 12.503 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 12.504 * [backup-simplify]: Simplify (- 1) into -1 12.504 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.504 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 12.504 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 12.504 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) 12.504 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 12.504 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 12.504 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 12.504 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 12.505 * [taylor]: Taking taylor expansion of 0.5 in n 12.505 * [backup-simplify]: Simplify 0.5 into 0.5 12.505 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 12.505 * [taylor]: Taking taylor expansion of 1.0 in n 12.505 * [backup-simplify]: Simplify 1.0 into 1.0 12.505 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.505 * [taylor]: Taking taylor expansion of k in n 12.505 * [backup-simplify]: Simplify k into k 12.505 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.505 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 12.505 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 12.505 * [taylor]: Taking taylor expansion of 2.0 in n 12.505 * [backup-simplify]: Simplify 2.0 into 2.0 12.505 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.505 * [taylor]: Taking taylor expansion of PI in n 12.505 * [backup-simplify]: Simplify PI into PI 12.505 * [taylor]: Taking taylor expansion of n in n 12.505 * [backup-simplify]: Simplify 0 into 0 12.505 * [backup-simplify]: Simplify 1 into 1 12.505 * [backup-simplify]: Simplify (/ PI 1) into PI 12.505 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.506 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.506 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 12.506 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 12.506 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 12.507 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.508 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) 12.509 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 12.509 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 12.509 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 12.509 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 12.509 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 12.509 * [taylor]: Taking taylor expansion of 0.5 in n 12.509 * [backup-simplify]: Simplify 0.5 into 0.5 12.509 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 12.509 * [taylor]: Taking taylor expansion of 1.0 in n 12.509 * [backup-simplify]: Simplify 1.0 into 1.0 12.509 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.509 * [taylor]: Taking taylor expansion of k in n 12.509 * [backup-simplify]: Simplify k into k 12.509 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.509 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 12.509 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 12.509 * [taylor]: Taking taylor expansion of 2.0 in n 12.509 * [backup-simplify]: Simplify 2.0 into 2.0 12.509 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.509 * [taylor]: Taking taylor expansion of PI in n 12.509 * [backup-simplify]: Simplify PI into PI 12.509 * [taylor]: Taking taylor expansion of n in n 12.509 * [backup-simplify]: Simplify 0 into 0 12.509 * [backup-simplify]: Simplify 1 into 1 12.509 * [backup-simplify]: Simplify (/ PI 1) into PI 12.510 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.510 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.510 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 12.510 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 12.510 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 12.511 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.512 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) 12.513 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 12.513 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) in k 12.513 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) in k 12.513 * [taylor]: Taking taylor expansion of 0.5 in k 12.513 * [backup-simplify]: Simplify 0.5 into 0.5 12.513 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) in k 12.513 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 12.513 * [taylor]: Taking taylor expansion of 1.0 in k 12.513 * [backup-simplify]: Simplify 1.0 into 1.0 12.513 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.513 * [taylor]: Taking taylor expansion of k in k 12.513 * [backup-simplify]: Simplify 0 into 0 12.513 * [backup-simplify]: Simplify 1 into 1 12.513 * [backup-simplify]: Simplify (/ 1 1) into 1 12.513 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 12.513 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 12.513 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 12.513 * [taylor]: Taking taylor expansion of 2.0 in k 12.513 * [backup-simplify]: Simplify 2.0 into 2.0 12.513 * [taylor]: Taking taylor expansion of PI in k 12.513 * [backup-simplify]: Simplify PI into PI 12.514 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.514 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.514 * [taylor]: Taking taylor expansion of (log n) in k 12.514 * [taylor]: Taking taylor expansion of n in k 12.514 * [backup-simplify]: Simplify n into n 12.515 * [backup-simplify]: Simplify (log n) into (log n) 12.515 * [backup-simplify]: Simplify (- 1) into -1 12.515 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.515 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 12.516 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 12.516 * [backup-simplify]: Simplify (* -1 (- (log (* 2.0 PI)) (log n))) into (* -1 (- (log (* 2.0 PI)) (log n))) 12.517 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 12.518 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 12.519 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 12.519 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.520 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 12.521 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 12.521 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 12.521 * [backup-simplify]: Simplify (- 0) into 0 12.521 * [backup-simplify]: Simplify (+ 0 0) into 0 12.521 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 12.522 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.523 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 12.524 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 12.524 * [taylor]: Taking taylor expansion of 0 in k 12.524 * [backup-simplify]: Simplify 0 into 0 12.524 * [backup-simplify]: Simplify 0 into 0 12.524 * [backup-simplify]: Simplify 0 into 0 12.525 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.526 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 12.530 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 12.530 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.530 * [backup-simplify]: Simplify (- 0) into 0 12.531 * [backup-simplify]: Simplify (+ 0 0) into 0 12.532 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 12.533 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.535 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 12.537 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 12.538 * [taylor]: Taking taylor expansion of 0 in k 12.538 * [backup-simplify]: Simplify 0 into 0 12.538 * [backup-simplify]: Simplify 0 into 0 12.538 * [backup-simplify]: Simplify 0 into 0 12.538 * [backup-simplify]: Simplify 0 into 0 12.539 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.541 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 12.547 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 12.547 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.547 * [backup-simplify]: Simplify (- 0) into 0 12.548 * [backup-simplify]: Simplify (+ 0 0) into 0 12.549 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 12.551 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.553 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 12.555 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 12.556 * [taylor]: Taking taylor expansion of 0 in k 12.556 * [backup-simplify]: Simplify 0 into 0 12.556 * [backup-simplify]: Simplify 0 into 0 12.557 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) 12.558 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) 12.558 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 12.558 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 12.558 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 12.558 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 12.558 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 12.558 * [taylor]: Taking taylor expansion of 0.5 in k 12.558 * [backup-simplify]: Simplify 0.5 into 0.5 12.558 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 12.558 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.558 * [taylor]: Taking taylor expansion of k in k 12.558 * [backup-simplify]: Simplify 0 into 0 12.558 * [backup-simplify]: Simplify 1 into 1 12.559 * [backup-simplify]: Simplify (/ 1 1) into 1 12.559 * [taylor]: Taking taylor expansion of 1.0 in k 12.559 * [backup-simplify]: Simplify 1.0 into 1.0 12.559 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 12.559 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 12.559 * [taylor]: Taking taylor expansion of -2.0 in k 12.559 * [backup-simplify]: Simplify -2.0 into -2.0 12.559 * [taylor]: Taking taylor expansion of (/ PI n) in k 12.559 * [taylor]: Taking taylor expansion of PI in k 12.559 * [backup-simplify]: Simplify PI into PI 12.559 * [taylor]: Taking taylor expansion of n in k 12.559 * [backup-simplify]: Simplify n into n 12.559 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 12.559 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 12.559 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 12.560 * [backup-simplify]: Simplify (+ 1 0) into 1 12.560 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 12.560 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 12.560 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) 12.560 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 12.560 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 12.560 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 12.560 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 12.561 * [taylor]: Taking taylor expansion of 0.5 in n 12.561 * [backup-simplify]: Simplify 0.5 into 0.5 12.561 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 12.561 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.561 * [taylor]: Taking taylor expansion of k in n 12.561 * [backup-simplify]: Simplify k into k 12.561 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.561 * [taylor]: Taking taylor expansion of 1.0 in n 12.561 * [backup-simplify]: Simplify 1.0 into 1.0 12.561 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 12.561 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 12.561 * [taylor]: Taking taylor expansion of -2.0 in n 12.561 * [backup-simplify]: Simplify -2.0 into -2.0 12.561 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.561 * [taylor]: Taking taylor expansion of PI in n 12.561 * [backup-simplify]: Simplify PI into PI 12.561 * [taylor]: Taking taylor expansion of n in n 12.561 * [backup-simplify]: Simplify 0 into 0 12.561 * [backup-simplify]: Simplify 1 into 1 12.562 * [backup-simplify]: Simplify (/ PI 1) into PI 12.562 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 12.563 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 12.563 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 12.563 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 12.565 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.567 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) 12.568 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 12.568 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 12.568 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 12.568 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 12.568 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 12.568 * [taylor]: Taking taylor expansion of 0.5 in n 12.568 * [backup-simplify]: Simplify 0.5 into 0.5 12.568 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 12.568 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.568 * [taylor]: Taking taylor expansion of k in n 12.568 * [backup-simplify]: Simplify k into k 12.568 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.568 * [taylor]: Taking taylor expansion of 1.0 in n 12.568 * [backup-simplify]: Simplify 1.0 into 1.0 12.568 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 12.568 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 12.568 * [taylor]: Taking taylor expansion of -2.0 in n 12.568 * [backup-simplify]: Simplify -2.0 into -2.0 12.568 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.568 * [taylor]: Taking taylor expansion of PI in n 12.568 * [backup-simplify]: Simplify PI into PI 12.568 * [taylor]: Taking taylor expansion of n in n 12.569 * [backup-simplify]: Simplify 0 into 0 12.569 * [backup-simplify]: Simplify 1 into 1 12.569 * [backup-simplify]: Simplify (/ PI 1) into PI 12.570 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 12.571 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 12.571 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 12.571 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 12.572 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.574 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) 12.575 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 12.575 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) in k 12.575 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) in k 12.576 * [taylor]: Taking taylor expansion of 0.5 in k 12.576 * [backup-simplify]: Simplify 0.5 into 0.5 12.576 * [taylor]: Taking taylor expansion of (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) in k 12.576 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 12.576 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 12.576 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 12.576 * [taylor]: Taking taylor expansion of -2.0 in k 12.576 * [backup-simplify]: Simplify -2.0 into -2.0 12.576 * [taylor]: Taking taylor expansion of PI in k 12.576 * [backup-simplify]: Simplify PI into PI 12.576 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 12.578 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 12.578 * [taylor]: Taking taylor expansion of (log n) in k 12.578 * [taylor]: Taking taylor expansion of n in k 12.578 * [backup-simplify]: Simplify n into n 12.578 * [backup-simplify]: Simplify (log n) into (log n) 12.578 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 12.578 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.578 * [taylor]: Taking taylor expansion of k in k 12.578 * [backup-simplify]: Simplify 0 into 0 12.578 * [backup-simplify]: Simplify 1 into 1 12.578 * [backup-simplify]: Simplify (/ 1 1) into 1 12.578 * [taylor]: Taking taylor expansion of 1.0 in k 12.578 * [backup-simplify]: Simplify 1.0 into 1.0 12.579 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 12.580 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 12.580 * [backup-simplify]: Simplify (+ 1 0) into 1 12.582 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) 1) into (- (log (* -2.0 PI)) (log n)) 12.583 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 12.584 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 12.585 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 12.586 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.587 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 12.589 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 12.589 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 12.589 * [backup-simplify]: Simplify (+ 0 0) into 0 12.590 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 12.591 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.592 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 12.594 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 12.594 * [taylor]: Taking taylor expansion of 0 in k 12.594 * [backup-simplify]: Simplify 0 into 0 12.594 * [backup-simplify]: Simplify 0 into 0 12.594 * [backup-simplify]: Simplify 0 into 0 12.595 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.597 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 12.607 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 12.607 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.607 * [backup-simplify]: Simplify (+ 0 0) into 0 12.608 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 12.610 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.611 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 12.614 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 12.614 * [taylor]: Taking taylor expansion of 0 in k 12.614 * [backup-simplify]: Simplify 0 into 0 12.614 * [backup-simplify]: Simplify 0 into 0 12.614 * [backup-simplify]: Simplify 0 into 0 12.614 * [backup-simplify]: Simplify 0 into 0 12.615 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.616 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 12.620 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 12.620 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.620 * [backup-simplify]: Simplify (+ 0 0) into 0 12.621 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 12.623 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.624 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 12.625 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 12.625 * [taylor]: Taking taylor expansion of 0 in k 12.625 * [backup-simplify]: Simplify 0 into 0 12.625 * [backup-simplify]: Simplify 0 into 0 12.626 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 12.626 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1) 12.627 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 12.627 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 12.627 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 12.627 * [taylor]: Taking taylor expansion of 2.0 in n 12.627 * [backup-simplify]: Simplify 2.0 into 2.0 12.627 * [taylor]: Taking taylor expansion of (* n PI) in n 12.627 * [taylor]: Taking taylor expansion of n in n 12.627 * [backup-simplify]: Simplify 0 into 0 12.627 * [backup-simplify]: Simplify 1 into 1 12.627 * [taylor]: Taking taylor expansion of PI in n 12.627 * [backup-simplify]: Simplify PI into PI 12.627 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 12.627 * [taylor]: Taking taylor expansion of 2.0 in n 12.627 * [backup-simplify]: Simplify 2.0 into 2.0 12.627 * [taylor]: Taking taylor expansion of (* n PI) in n 12.627 * [taylor]: Taking taylor expansion of n in n 12.627 * [backup-simplify]: Simplify 0 into 0 12.627 * [backup-simplify]: Simplify 1 into 1 12.627 * [taylor]: Taking taylor expansion of PI in n 12.627 * [backup-simplify]: Simplify PI into PI 12.627 * [backup-simplify]: Simplify (* 0 PI) into 0 12.627 * [backup-simplify]: Simplify (* 2.0 0) into 0 12.628 * [backup-simplify]: Simplify 0 into 0 12.628 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.629 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 12.630 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.630 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 12.631 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 12.631 * [backup-simplify]: Simplify 0 into 0 12.632 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 12.632 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 12.632 * [backup-simplify]: Simplify 0 into 0 12.633 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 12.634 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 12.634 * [backup-simplify]: Simplify 0 into 0 12.635 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 12.635 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 12.635 * [backup-simplify]: Simplify 0 into 0 12.636 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 12.637 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 12.637 * [backup-simplify]: Simplify 0 into 0 12.638 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 12.639 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 12.639 * [backup-simplify]: Simplify 0 into 0 12.640 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 12.640 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 12.640 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 12.640 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 12.640 * [taylor]: Taking taylor expansion of 2.0 in n 12.640 * [backup-simplify]: Simplify 2.0 into 2.0 12.640 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.640 * [taylor]: Taking taylor expansion of PI in n 12.640 * [backup-simplify]: Simplify PI into PI 12.640 * [taylor]: Taking taylor expansion of n in n 12.640 * [backup-simplify]: Simplify 0 into 0 12.640 * [backup-simplify]: Simplify 1 into 1 12.640 * [backup-simplify]: Simplify (/ PI 1) into PI 12.641 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 12.641 * [taylor]: Taking taylor expansion of 2.0 in n 12.641 * [backup-simplify]: Simplify 2.0 into 2.0 12.641 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.641 * [taylor]: Taking taylor expansion of PI in n 12.641 * [backup-simplify]: Simplify PI into PI 12.641 * [taylor]: Taking taylor expansion of n in n 12.641 * [backup-simplify]: Simplify 0 into 0 12.641 * [backup-simplify]: Simplify 1 into 1 12.641 * [backup-simplify]: Simplify (/ PI 1) into PI 12.641 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.642 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.642 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.643 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 12.643 * [backup-simplify]: Simplify 0 into 0 12.643 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.644 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 12.644 * [backup-simplify]: Simplify 0 into 0 12.644 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.645 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 12.645 * [backup-simplify]: Simplify 0 into 0 12.646 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.647 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 12.647 * [backup-simplify]: Simplify 0 into 0 12.648 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.650 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 12.650 * [backup-simplify]: Simplify 0 into 0 12.651 * [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 12.653 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 12.653 * [backup-simplify]: Simplify 0 into 0 12.653 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 12.654 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 12.654 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 12.654 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 12.654 * [taylor]: Taking taylor expansion of -2.0 in n 12.654 * [backup-simplify]: Simplify -2.0 into -2.0 12.654 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.654 * [taylor]: Taking taylor expansion of PI in n 12.654 * [backup-simplify]: Simplify PI into PI 12.654 * [taylor]: Taking taylor expansion of n in n 12.654 * [backup-simplify]: Simplify 0 into 0 12.654 * [backup-simplify]: Simplify 1 into 1 12.655 * [backup-simplify]: Simplify (/ PI 1) into PI 12.655 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 12.655 * [taylor]: Taking taylor expansion of -2.0 in n 12.655 * [backup-simplify]: Simplify -2.0 into -2.0 12.655 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.655 * [taylor]: Taking taylor expansion of PI in n 12.655 * [backup-simplify]: Simplify PI into PI 12.655 * [taylor]: Taking taylor expansion of n in n 12.655 * [backup-simplify]: Simplify 0 into 0 12.655 * [backup-simplify]: Simplify 1 into 1 12.655 * [backup-simplify]: Simplify (/ PI 1) into PI 12.656 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 12.656 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 12.657 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.658 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 12.658 * [backup-simplify]: Simplify 0 into 0 12.660 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.661 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 12.661 * [backup-simplify]: Simplify 0 into 0 12.662 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.662 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 12.662 * [backup-simplify]: Simplify 0 into 0 12.663 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.664 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 12.664 * [backup-simplify]: Simplify 0 into 0 12.664 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.665 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 12.665 * [backup-simplify]: Simplify 0 into 0 12.666 * [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 12.667 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 12.667 * [backup-simplify]: Simplify 0 into 0 12.667 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 12.667 * * * * [progress]: [ 3 / 4 ] generating series at (2 1) 12.667 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 12.667 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 12.667 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 12.667 * [taylor]: Taking taylor expansion of 1.0 in k 12.667 * [backup-simplify]: Simplify 1.0 into 1.0 12.667 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 12.668 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.668 * [taylor]: Taking taylor expansion of k in k 12.668 * [backup-simplify]: Simplify 0 into 0 12.668 * [backup-simplify]: Simplify 1 into 1 12.668 * [backup-simplify]: Simplify (/ 1 1) into 1 12.668 * [backup-simplify]: Simplify (sqrt 0) into 0 12.669 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 12.669 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 12.669 * [taylor]: Taking taylor expansion of 1.0 in k 12.669 * [backup-simplify]: Simplify 1.0 into 1.0 12.669 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 12.669 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.669 * [taylor]: Taking taylor expansion of k in k 12.669 * [backup-simplify]: Simplify 0 into 0 12.669 * [backup-simplify]: Simplify 1 into 1 12.669 * [backup-simplify]: Simplify (/ 1 1) into 1 12.670 * [backup-simplify]: Simplify (sqrt 0) into 0 12.670 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 12.671 * [backup-simplify]: Simplify (* 1.0 0) into 0 12.671 * [backup-simplify]: Simplify 0 into 0 12.672 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 12.672 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 12.672 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 12.674 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 12.675 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 12.675 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 12.676 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.678 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 12.679 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 12.679 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 12.680 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) 12.680 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 12.680 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 12.680 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 12.680 * [taylor]: Taking taylor expansion of 1.0 in k 12.681 * [backup-simplify]: Simplify 1.0 into 1.0 12.681 * [taylor]: Taking taylor expansion of (sqrt k) in k 12.681 * [taylor]: Taking taylor expansion of k in k 12.681 * [backup-simplify]: Simplify 0 into 0 12.681 * [backup-simplify]: Simplify 1 into 1 12.681 * [backup-simplify]: Simplify (sqrt 0) into 0 12.682 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 12.682 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 12.682 * [taylor]: Taking taylor expansion of 1.0 in k 12.682 * [backup-simplify]: Simplify 1.0 into 1.0 12.682 * [taylor]: Taking taylor expansion of (sqrt k) in k 12.682 * [taylor]: Taking taylor expansion of k in k 12.682 * [backup-simplify]: Simplify 0 into 0 12.682 * [backup-simplify]: Simplify 1 into 1 12.682 * [backup-simplify]: Simplify (sqrt 0) into 0 12.683 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 12.683 * [backup-simplify]: Simplify (* 1.0 0) into 0 12.683 * [backup-simplify]: Simplify 0 into 0 12.684 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 12.684 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 12.686 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 12.687 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 12.687 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 12.690 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 12.692 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 12.692 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 12.694 * [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)))))))) 12.694 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 12.694 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 12.694 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 12.694 * [taylor]: Taking taylor expansion of 1.0 in k 12.694 * [backup-simplify]: Simplify 1.0 into 1.0 12.694 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 12.694 * [taylor]: Taking taylor expansion of (/ -1 k) in k 12.694 * [taylor]: Taking taylor expansion of -1 in k 12.694 * [backup-simplify]: Simplify -1 into -1 12.694 * [taylor]: Taking taylor expansion of k in k 12.694 * [backup-simplify]: Simplify 0 into 0 12.694 * [backup-simplify]: Simplify 1 into 1 12.695 * [backup-simplify]: Simplify (/ -1 1) into -1 12.695 * [backup-simplify]: Simplify (sqrt 0) into 0 12.696 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 12.697 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 12.697 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 12.697 * [taylor]: Taking taylor expansion of 1.0 in k 12.697 * [backup-simplify]: Simplify 1.0 into 1.0 12.697 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 12.697 * [taylor]: Taking taylor expansion of (/ -1 k) in k 12.697 * [taylor]: Taking taylor expansion of -1 in k 12.697 * [backup-simplify]: Simplify -1 into -1 12.697 * [taylor]: Taking taylor expansion of k in k 12.697 * [backup-simplify]: Simplify 0 into 0 12.697 * [backup-simplify]: Simplify 1 into 1 12.697 * [backup-simplify]: Simplify (/ -1 1) into -1 12.698 * [backup-simplify]: Simplify (sqrt 0) into 0 12.699 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 12.699 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 12.699 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.700 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 12.703 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 12.706 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 12.706 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 12.707 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.718 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 12.722 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 12.722 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 12.724 * [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))))) 12.724 * * * * [progress]: [ 4 / 4 ] generating series at (2) 12.724 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) into (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) 12.724 * [approximate]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in (k n) around 0 12.725 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in n 12.725 * [taylor]: Taking taylor expansion of 1.0 in n 12.725 * [backup-simplify]: Simplify 1.0 into 1.0 12.725 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in n 12.725 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 12.725 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 12.725 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 12.725 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 12.725 * [taylor]: Taking taylor expansion of 0.5 in n 12.725 * [backup-simplify]: Simplify 0.5 into 0.5 12.725 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 12.725 * [taylor]: Taking taylor expansion of 1.0 in n 12.725 * [backup-simplify]: Simplify 1.0 into 1.0 12.725 * [taylor]: Taking taylor expansion of k in n 12.725 * [backup-simplify]: Simplify k into k 12.725 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 12.725 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 12.725 * [taylor]: Taking taylor expansion of 2.0 in n 12.725 * [backup-simplify]: Simplify 2.0 into 2.0 12.725 * [taylor]: Taking taylor expansion of (* n PI) in n 12.725 * [taylor]: Taking taylor expansion of n in n 12.725 * [backup-simplify]: Simplify 0 into 0 12.725 * [backup-simplify]: Simplify 1 into 1 12.725 * [taylor]: Taking taylor expansion of PI in n 12.725 * [backup-simplify]: Simplify PI into PI 12.726 * [backup-simplify]: Simplify (* 0 PI) into 0 12.726 * [backup-simplify]: Simplify (* 2.0 0) into 0 12.728 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.729 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 12.730 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.730 * [backup-simplify]: Simplify (- k) into (- k) 12.730 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 12.730 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 12.731 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.732 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 12.732 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 12.733 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 12.733 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.733 * [taylor]: Taking taylor expansion of k in n 12.733 * [backup-simplify]: Simplify k into k 12.733 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.733 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 12.733 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 12.733 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 12.733 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in k 12.733 * [taylor]: Taking taylor expansion of 1.0 in k 12.733 * [backup-simplify]: Simplify 1.0 into 1.0 12.733 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in k 12.733 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 12.733 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 12.733 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 12.733 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 12.733 * [taylor]: Taking taylor expansion of 0.5 in k 12.733 * [backup-simplify]: Simplify 0.5 into 0.5 12.733 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 12.733 * [taylor]: Taking taylor expansion of 1.0 in k 12.733 * [backup-simplify]: Simplify 1.0 into 1.0 12.733 * [taylor]: Taking taylor expansion of k in k 12.733 * [backup-simplify]: Simplify 0 into 0 12.733 * [backup-simplify]: Simplify 1 into 1 12.733 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 12.733 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 12.733 * [taylor]: Taking taylor expansion of 2.0 in k 12.733 * [backup-simplify]: Simplify 2.0 into 2.0 12.733 * [taylor]: Taking taylor expansion of (* n PI) in k 12.733 * [taylor]: Taking taylor expansion of n in k 12.733 * [backup-simplify]: Simplify n into n 12.733 * [taylor]: Taking taylor expansion of PI in k 12.733 * [backup-simplify]: Simplify PI into PI 12.733 * [backup-simplify]: Simplify (* n PI) into (* n PI) 12.733 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 12.734 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 12.734 * [backup-simplify]: Simplify (- 0) into 0 12.734 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 12.734 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 12.734 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 12.735 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 12.735 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 12.735 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.735 * [taylor]: Taking taylor expansion of k in k 12.735 * [backup-simplify]: Simplify 0 into 0 12.735 * [backup-simplify]: Simplify 1 into 1 12.735 * [backup-simplify]: Simplify (/ 1 1) into 1 12.735 * [backup-simplify]: Simplify (sqrt 0) into 0 12.736 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 12.736 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in k 12.736 * [taylor]: Taking taylor expansion of 1.0 in k 12.736 * [backup-simplify]: Simplify 1.0 into 1.0 12.736 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in k 12.736 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 12.736 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 12.736 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 12.736 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 12.736 * [taylor]: Taking taylor expansion of 0.5 in k 12.736 * [backup-simplify]: Simplify 0.5 into 0.5 12.736 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 12.736 * [taylor]: Taking taylor expansion of 1.0 in k 12.736 * [backup-simplify]: Simplify 1.0 into 1.0 12.736 * [taylor]: Taking taylor expansion of k in k 12.736 * [backup-simplify]: Simplify 0 into 0 12.736 * [backup-simplify]: Simplify 1 into 1 12.736 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 12.736 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 12.736 * [taylor]: Taking taylor expansion of 2.0 in k 12.736 * [backup-simplify]: Simplify 2.0 into 2.0 12.736 * [taylor]: Taking taylor expansion of (* n PI) in k 12.736 * [taylor]: Taking taylor expansion of n in k 12.736 * [backup-simplify]: Simplify n into n 12.736 * [taylor]: Taking taylor expansion of PI in k 12.736 * [backup-simplify]: Simplify PI into PI 12.736 * [backup-simplify]: Simplify (* n PI) into (* n PI) 12.736 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 12.736 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 12.737 * [backup-simplify]: Simplify (- 0) into 0 12.737 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 12.737 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 12.737 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 12.737 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 12.737 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 12.737 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.737 * [taylor]: Taking taylor expansion of k in k 12.737 * [backup-simplify]: Simplify 0 into 0 12.738 * [backup-simplify]: Simplify 1 into 1 12.738 * [backup-simplify]: Simplify (/ 1 1) into 1 12.738 * [backup-simplify]: Simplify (sqrt 0) into 0 12.739 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 12.739 * [backup-simplify]: Simplify (* (pow (* 2.0 (* n PI)) 0.5) 0) into 0 12.739 * [backup-simplify]: Simplify (* 1.0 0) into 0 12.739 * [taylor]: Taking taylor expansion of 0 in n 12.739 * [backup-simplify]: Simplify 0 into 0 12.739 * [backup-simplify]: Simplify 0 into 0 12.740 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 12.740 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* n PI))) into 0 12.740 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 1) into 0 12.741 * [backup-simplify]: Simplify (- 1) into -1 12.741 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.742 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5) 12.742 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 (* n PI))))) into (- (* 0.5 (log (* 2.0 (* n PI))))) 12.743 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 1) 1)))) into (* -0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) 12.744 * [backup-simplify]: Simplify (+ (* (pow (* 2.0 (* n PI)) 0.5) +nan.0) (* (* -0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) 0)) into (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) 12.745 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) (* 0 0)) into (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 12.745 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) in n 12.745 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) in n 12.745 * [taylor]: Taking taylor expansion of +nan.0 in n 12.745 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.745 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 12.745 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 12.745 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 12.745 * [taylor]: Taking taylor expansion of 0.5 in n 12.745 * [backup-simplify]: Simplify 0.5 into 0.5 12.745 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 12.745 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 12.745 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 12.745 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 12.745 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 12.745 * [taylor]: Taking taylor expansion of 1.0 in n 12.745 * [backup-simplify]: Simplify 1.0 into 1.0 12.745 * [taylor]: Taking taylor expansion of (log PI) in n 12.745 * [taylor]: Taking taylor expansion of PI in n 12.745 * [backup-simplify]: Simplify PI into PI 12.746 * [backup-simplify]: Simplify (log PI) into (log PI) 12.746 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 12.747 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 12.747 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 12.747 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 12.747 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 12.747 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 12.747 * [taylor]: Taking taylor expansion of 1.0 in n 12.747 * [backup-simplify]: Simplify 1.0 into 1.0 12.747 * [taylor]: Taking taylor expansion of (log n) in n 12.747 * [taylor]: Taking taylor expansion of n in n 12.747 * [backup-simplify]: Simplify 0 into 0 12.747 * [backup-simplify]: Simplify 1 into 1 12.748 * [backup-simplify]: Simplify (log 1) into 0 12.748 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 12.748 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 12.748 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 12.748 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 12.748 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 12.748 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 12.748 * [taylor]: Taking taylor expansion of 1.0 in n 12.748 * [backup-simplify]: Simplify 1.0 into 1.0 12.748 * [taylor]: Taking taylor expansion of (log 2.0) in n 12.748 * [taylor]: Taking taylor expansion of 2.0 in n 12.748 * [backup-simplify]: Simplify 2.0 into 2.0 12.748 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 12.749 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 12.750 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 12.750 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0) 12.751 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 12.752 * [backup-simplify]: Simplify (log (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)) 12.752 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0))) 12.753 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 12.754 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) 12.755 * [backup-simplify]: Simplify (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) into (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) 12.756 * [backup-simplify]: Simplify (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 12.756 * [backup-simplify]: Simplify 0 into 0 12.756 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 12.758 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 12.759 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 12.760 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 12.762 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 (* n PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 2) into 0 12.762 * [backup-simplify]: Simplify (- 0) into 0 12.763 * [backup-simplify]: Simplify (+ 0 0) into 0 12.763 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0 12.764 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 (* n PI)))))) into 0 12.766 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) 12.769 * [backup-simplify]: Simplify (+ (* (pow (* 2.0 (* n PI)) 0.5) +nan.0) (+ (* (* -0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) +nan.0) (* (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) 0))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))) 12.773 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))) (+ (* 0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) (* 0 0))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))) 12.774 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))) in n 12.774 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) in n 12.774 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) in n 12.774 * [taylor]: Taking taylor expansion of +nan.0 in n 12.774 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.774 * [taylor]: Taking taylor expansion of (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI)))) in n 12.774 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 12.774 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 12.774 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 12.774 * [taylor]: Taking taylor expansion of 0.5 in n 12.774 * [backup-simplify]: Simplify 0.5 into 0.5 12.774 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 12.774 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 12.774 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 12.774 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 12.774 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 12.774 * [taylor]: Taking taylor expansion of 1.0 in n 12.774 * [backup-simplify]: Simplify 1.0 into 1.0 12.774 * [taylor]: Taking taylor expansion of (log PI) in n 12.774 * [taylor]: Taking taylor expansion of PI in n 12.774 * [backup-simplify]: Simplify PI into PI 12.774 * [backup-simplify]: Simplify (log PI) into (log PI) 12.775 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 12.777 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 12.777 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 12.777 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 12.777 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 12.777 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 12.777 * [taylor]: Taking taylor expansion of 1.0 in n 12.777 * [backup-simplify]: Simplify 1.0 into 1.0 12.777 * [taylor]: Taking taylor expansion of (log n) in n 12.777 * [taylor]: Taking taylor expansion of n in n 12.777 * [backup-simplify]: Simplify 0 into 0 12.777 * [backup-simplify]: Simplify 1 into 1 12.777 * [backup-simplify]: Simplify (log 1) into 0 12.778 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 12.778 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 12.778 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 12.778 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 12.778 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 12.778 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 12.778 * [taylor]: Taking taylor expansion of 1.0 in n 12.778 * [backup-simplify]: Simplify 1.0 into 1.0 12.778 * [taylor]: Taking taylor expansion of (log 2.0) in n 12.778 * [taylor]: Taking taylor expansion of 2.0 in n 12.778 * [backup-simplify]: Simplify 2.0 into 2.0 12.778 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 12.779 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 12.780 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 12.781 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0) 12.782 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 12.783 * [backup-simplify]: Simplify (log (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)) 12.785 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0))) 12.786 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 12.786 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 12.786 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 12.786 * [taylor]: Taking taylor expansion of 2.0 in n 12.786 * [backup-simplify]: Simplify 2.0 into 2.0 12.786 * [taylor]: Taking taylor expansion of (* n PI) in n 12.786 * [taylor]: Taking taylor expansion of n in n 12.786 * [backup-simplify]: Simplify 0 into 0 12.786 * [backup-simplify]: Simplify 1 into 1 12.786 * [taylor]: Taking taylor expansion of PI in n 12.786 * [backup-simplify]: Simplify PI into PI 12.787 * [backup-simplify]: Simplify (* 0 PI) into 0 12.787 * [backup-simplify]: Simplify (* 2.0 0) into 0 12.788 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.790 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 12.791 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.791 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) in n 12.791 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) in n 12.791 * [taylor]: Taking taylor expansion of +nan.0 in n 12.791 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.791 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 12.791 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 12.791 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 12.791 * [taylor]: Taking taylor expansion of 0.5 in n 12.791 * [backup-simplify]: Simplify 0.5 into 0.5 12.791 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 12.791 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 12.791 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 12.791 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 12.791 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 12.791 * [taylor]: Taking taylor expansion of 1.0 in n 12.791 * [backup-simplify]: Simplify 1.0 into 1.0 12.791 * [taylor]: Taking taylor expansion of (log PI) in n 12.791 * [taylor]: Taking taylor expansion of PI in n 12.791 * [backup-simplify]: Simplify PI into PI 12.792 * [backup-simplify]: Simplify (log PI) into (log PI) 12.792 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 12.794 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 12.794 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 12.794 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 12.794 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 12.794 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 12.794 * [taylor]: Taking taylor expansion of 1.0 in n 12.794 * [backup-simplify]: Simplify 1.0 into 1.0 12.794 * [taylor]: Taking taylor expansion of (log n) in n 12.794 * [taylor]: Taking taylor expansion of n in n 12.794 * [backup-simplify]: Simplify 0 into 0 12.794 * [backup-simplify]: Simplify 1 into 1 12.794 * [backup-simplify]: Simplify (log 1) into 0 12.795 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 12.795 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 12.795 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 12.795 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 12.795 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 12.795 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 12.795 * [taylor]: Taking taylor expansion of 1.0 in n 12.795 * [backup-simplify]: Simplify 1.0 into 1.0 12.795 * [taylor]: Taking taylor expansion of (log 2.0) in n 12.795 * [taylor]: Taking taylor expansion of 2.0 in n 12.795 * [backup-simplify]: Simplify 2.0 into 2.0 12.796 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 12.797 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 12.798 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 12.799 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0) 12.800 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 12.802 * [backup-simplify]: Simplify (log (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)) 12.803 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0))) 12.805 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 12.806 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.809 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) (+ (log (* 2.0 PI)) (log n))) into (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n))) 12.811 * [backup-simplify]: Simplify (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n)))) into (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n)))) 12.813 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) 12.814 * [backup-simplify]: Simplify (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) into (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) 12.818 * [backup-simplify]: Simplify (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n)))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))))) 12.824 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))) into (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log (* 2.0 PI))))))))) 12.831 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log (* 2.0 PI))))))))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))))) 12.832 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0 12.833 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log 2.0))) into 0 12.835 * [backup-simplify]: Simplify (* (exp (* 1.0 (log 2.0))) (+ (* (/ (pow 0 1) 1)))) into 0 12.836 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 12.837 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 12.837 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log n))) into 0 12.838 * [backup-simplify]: Simplify (* (exp (* 1.0 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 12.839 * [backup-simplify]: Simplify (+ (* (pow n 1.0) 0) (* 0 (pow 2.0 1.0))) into 0 12.841 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 12.841 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log PI))) into 0 12.849 * [backup-simplify]: Simplify (* (exp (* 1.0 (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 12.850 * [backup-simplify]: Simplify (+ (* (pow PI 1.0) 0) (* 0 (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0))) into 0 12.853 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1)))) 1) into 0 12.855 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)))) into 0 12.857 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 12.860 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5))) into 0 12.860 * [backup-simplify]: Simplify (- 0) into 0 12.860 * [backup-simplify]: Simplify 0 into 0 12.860 * [backup-simplify]: Simplify 0 into 0 12.861 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.865 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 12.866 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 12.867 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 12.868 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 (* n PI)) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 (* n PI)) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 6) into 0 12.869 * [backup-simplify]: Simplify (- 0) into 0 12.869 * [backup-simplify]: Simplify (+ 0 0) into 0 12.870 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1.0)))) into 0 12.871 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (+ (* 0 0) (* 0 (log (* 2.0 (* n PI))))))) into 0 12.872 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 3) 6)) (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -0.020833333333333332 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 3))) 12.876 * [backup-simplify]: Simplify (+ (* (pow (* 2.0 (* n PI)) 0.5) +nan.0) (+ (* (* -0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) +nan.0) (+ (* (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) +nan.0) (* (* -0.020833333333333332 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 3))) 0)))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))))) 12.882 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))))))) (+ (* 0 (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))) (+ (* 0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) (* 0 0)))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))))) 12.882 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))))) in n 12.882 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))))) in n 12.882 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) in n 12.882 * [taylor]: Taking taylor expansion of +nan.0 in n 12.882 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.882 * [taylor]: Taking taylor expansion of (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI)))) in n 12.882 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 12.882 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 12.882 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 12.882 * [taylor]: Taking taylor expansion of 0.5 in n 12.882 * [backup-simplify]: Simplify 0.5 into 0.5 12.882 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 12.882 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 12.882 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 12.882 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 12.882 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 12.882 * [taylor]: Taking taylor expansion of 1.0 in n 12.882 * [backup-simplify]: Simplify 1.0 into 1.0 12.882 * [taylor]: Taking taylor expansion of (log PI) in n 12.882 * [taylor]: Taking taylor expansion of PI in n 12.882 * [backup-simplify]: Simplify PI into PI 12.882 * [backup-simplify]: Simplify (log PI) into (log PI) 12.883 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 12.884 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 12.884 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 12.884 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 12.884 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 12.884 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 12.884 * [taylor]: Taking taylor expansion of 1.0 in n 12.884 * [backup-simplify]: Simplify 1.0 into 1.0 12.884 * [taylor]: Taking taylor expansion of (log n) in n 12.884 * [taylor]: Taking taylor expansion of n in n 12.884 * [backup-simplify]: Simplify 0 into 0 12.884 * [backup-simplify]: Simplify 1 into 1 12.884 * [backup-simplify]: Simplify (log 1) into 0 12.885 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 12.885 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 12.885 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 12.885 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 12.885 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 12.885 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 12.885 * [taylor]: Taking taylor expansion of 1.0 in n 12.885 * [backup-simplify]: Simplify 1.0 into 1.0 12.885 * [taylor]: Taking taylor expansion of (log 2.0) in n 12.885 * [taylor]: Taking taylor expansion of 2.0 in n 12.885 * [backup-simplify]: Simplify 2.0 into 2.0 12.885 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 12.886 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 12.887 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 12.887 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0) 12.888 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 12.889 * [backup-simplify]: Simplify (log (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)) 12.889 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0))) 12.890 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 12.890 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 12.890 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 12.890 * [taylor]: Taking taylor expansion of 2.0 in n 12.890 * [backup-simplify]: Simplify 2.0 into 2.0 12.890 * [taylor]: Taking taylor expansion of (* n PI) in n 12.890 * [taylor]: Taking taylor expansion of n in n 12.890 * [backup-simplify]: Simplify 0 into 0 12.890 * [backup-simplify]: Simplify 1 into 1 12.890 * [taylor]: Taking taylor expansion of PI in n 12.890 * [backup-simplify]: Simplify PI into PI 12.891 * [backup-simplify]: Simplify (* 0 PI) into 0 12.891 * [backup-simplify]: Simplify (* 2.0 0) into 0 12.892 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.893 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 12.894 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.894 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))) in n 12.894 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))) in n 12.894 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) in n 12.894 * [taylor]: Taking taylor expansion of +nan.0 in n 12.894 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.894 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n 12.894 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n 12.894 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n 12.894 * [taylor]: Taking taylor expansion of 0.5 in n 12.894 * [backup-simplify]: Simplify 0.5 into 0.5 12.894 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n 12.894 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n 12.894 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 12.894 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 12.894 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 12.894 * [taylor]: Taking taylor expansion of 1.0 in n 12.894 * [backup-simplify]: Simplify 1.0 into 1.0 12.894 * [taylor]: Taking taylor expansion of (log 2.0) in n 12.894 * [taylor]: Taking taylor expansion of 2.0 in n 12.894 * [backup-simplify]: Simplify 2.0 into 2.0 12.895 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 12.895 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 12.897 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 12.897 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n 12.897 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 12.897 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 12.897 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 12.897 * [taylor]: Taking taylor expansion of 1.0 in n 12.897 * [backup-simplify]: Simplify 1.0 into 1.0 12.897 * [taylor]: Taking taylor expansion of (log n) in n 12.897 * [taylor]: Taking taylor expansion of n in n 12.897 * [backup-simplify]: Simplify 0 into 0 12.897 * [backup-simplify]: Simplify 1 into 1 12.898 * [backup-simplify]: Simplify (log 1) into 0 12.898 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 12.898 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 12.898 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 12.898 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 12.898 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 12.898 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 12.898 * [taylor]: Taking taylor expansion of 1.0 in n 12.898 * [backup-simplify]: Simplify 1.0 into 1.0 12.898 * [taylor]: Taking taylor expansion of (log PI) in n 12.898 * [taylor]: Taking taylor expansion of PI in n 12.898 * [backup-simplify]: Simplify PI into PI 12.899 * [backup-simplify]: Simplify (log PI) into (log PI) 12.900 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 12.901 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 12.902 * [backup-simplify]: Simplify (* (pow n 1.0) (pow PI 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 12.903 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 12.904 * [backup-simplify]: Simplify (log (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0)) 12.906 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0))) 12.907 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 12.907 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))) in n 12.907 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) in n 12.907 * [taylor]: Taking taylor expansion of +nan.0 in n 12.907 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.907 * [taylor]: Taking taylor expansion of (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)) in n 12.907 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 12.907 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 12.907 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 12.907 * [taylor]: Taking taylor expansion of 0.5 in n 12.907 * [backup-simplify]: Simplify 0.5 into 0.5 12.907 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 12.907 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 12.908 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 12.908 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 12.908 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 12.908 * [taylor]: Taking taylor expansion of 1.0 in n 12.908 * [backup-simplify]: Simplify 1.0 into 1.0 12.908 * [taylor]: Taking taylor expansion of (log PI) in n 12.908 * [taylor]: Taking taylor expansion of PI in n 12.908 * [backup-simplify]: Simplify PI into PI 12.908 * [backup-simplify]: Simplify (log PI) into (log PI) 12.909 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 12.911 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 12.911 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 12.911 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 12.911 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 12.911 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 12.911 * [taylor]: Taking taylor expansion of 1.0 in n 12.911 * [backup-simplify]: Simplify 1.0 into 1.0 12.911 * [taylor]: Taking taylor expansion of (log n) in n 12.911 * [taylor]: Taking taylor expansion of n in n 12.911 * [backup-simplify]: Simplify 0 into 0 12.911 * [backup-simplify]: Simplify 1 into 1 12.911 * [backup-simplify]: Simplify (log 1) into 0 12.912 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 12.912 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 12.912 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 12.912 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 12.912 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 12.912 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 12.912 * [taylor]: Taking taylor expansion of 1.0 in n 12.912 * [backup-simplify]: Simplify 1.0 into 1.0 12.912 * [taylor]: Taking taylor expansion of (log 2.0) in n 12.912 * [taylor]: Taking taylor expansion of 2.0 in n 12.912 * [backup-simplify]: Simplify 2.0 into 2.0 12.913 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 12.913 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 12.915 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 12.916 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0) 12.917 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 12.918 * [backup-simplify]: Simplify (log (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)) 12.919 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0))) 12.921 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 12.921 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n 12.921 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 12.921 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 12.921 * [taylor]: Taking taylor expansion of 2.0 in n 12.921 * [backup-simplify]: Simplify 2.0 into 2.0 12.921 * [taylor]: Taking taylor expansion of (* n PI) in n 12.921 * [taylor]: Taking taylor expansion of n in n 12.921 * [backup-simplify]: Simplify 0 into 0 12.921 * [backup-simplify]: Simplify 1 into 1 12.921 * [taylor]: Taking taylor expansion of PI in n 12.921 * [backup-simplify]: Simplify PI into PI 12.922 * [backup-simplify]: Simplify (* 0 PI) into 0 12.922 * [backup-simplify]: Simplify (* 2.0 0) into 0 12.924 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.925 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 12.926 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.928 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.929 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.932 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) (+ (log (* 2.0 PI)) (log n))) into (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n))) 12.934 * [backup-simplify]: Simplify (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n)))) into (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n)))) 12.936 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) 12.937 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.939 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.941 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (+ (log (* 2.0 PI)) (log n))) into (pow (+ (log (* 2.0 PI)) (log n)) 2) 12.944 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) (pow (+ (log (* 2.0 PI)) (log n)) 2)) into (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (+ (log (* 2.0 PI)) (log n)) 2)) 12.946 * [backup-simplify]: Simplify (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (+ (log (* 2.0 PI)) (log n)) 2))) into (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (+ (log (* 2.0 PI)) (log n)) 2))) 12.949 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (+ (log (* 2.0 PI)) (log n)) 2)))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log n) 2)))))))) 12.959 * [backup-simplify]: Simplify (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log n) 2))))))))) into (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log n) 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))) 12.970 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log n) 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log n) 2)))))))))) 12.984 * [backup-simplify]: Simplify (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log n) 2))))))))))) into (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log n) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))))))))))) 12.993 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log n) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))))))))) into (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log n) 2))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))))))))))) 13.004 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log n) 2))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))))))))))) into (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log n) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (log n))))))))))))))) 13.033 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log n) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (log n))))))))))))))) (pow (* 1 k) 2)) (+ (* (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))))) (* 1 k)) (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))) into (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) k)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow k 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (pow (log (* 2.0 PI)) 2) (pow k 2)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) k))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log n) k))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (pow k 2)))) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (pow (log n) 2) (pow k 2))))))))))))))))))))))) 13.035 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt (/ 1 k))) (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0))) into (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) 13.035 * [approximate]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in (k n) around 0 13.035 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in n 13.035 * [taylor]: Taking taylor expansion of 1.0 in n 13.035 * [backup-simplify]: Simplify 1.0 into 1.0 13.035 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in n 13.035 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 13.035 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 13.035 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 13.035 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 13.035 * [taylor]: Taking taylor expansion of 0.5 in n 13.035 * [backup-simplify]: Simplify 0.5 into 0.5 13.035 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 13.035 * [taylor]: Taking taylor expansion of 1.0 in n 13.035 * [backup-simplify]: Simplify 1.0 into 1.0 13.035 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.035 * [taylor]: Taking taylor expansion of k in n 13.035 * [backup-simplify]: Simplify k into k 13.035 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.035 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 13.035 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 13.036 * [taylor]: Taking taylor expansion of 2.0 in n 13.036 * [backup-simplify]: Simplify 2.0 into 2.0 13.036 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.036 * [taylor]: Taking taylor expansion of PI in n 13.036 * [backup-simplify]: Simplify PI into PI 13.036 * [taylor]: Taking taylor expansion of n in n 13.036 * [backup-simplify]: Simplify 0 into 0 13.036 * [backup-simplify]: Simplify 1 into 1 13.037 * [backup-simplify]: Simplify (/ PI 1) into PI 13.037 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 13.038 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 13.038 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 13.038 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 13.038 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 13.040 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 13.041 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) 13.043 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 13.043 * [taylor]: Taking taylor expansion of (sqrt k) in n 13.043 * [taylor]: Taking taylor expansion of k in n 13.043 * [backup-simplify]: Simplify k into k 13.043 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 13.043 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 13.043 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in k 13.043 * [taylor]: Taking taylor expansion of 1.0 in k 13.043 * [backup-simplify]: Simplify 1.0 into 1.0 13.043 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in k 13.043 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 13.043 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 13.043 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 13.043 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 13.043 * [taylor]: Taking taylor expansion of 0.5 in k 13.043 * [backup-simplify]: Simplify 0.5 into 0.5 13.043 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 13.043 * [taylor]: Taking taylor expansion of 1.0 in k 13.043 * [backup-simplify]: Simplify 1.0 into 1.0 13.043 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.043 * [taylor]: Taking taylor expansion of k in k 13.043 * [backup-simplify]: Simplify 0 into 0 13.043 * [backup-simplify]: Simplify 1 into 1 13.044 * [backup-simplify]: Simplify (/ 1 1) into 1 13.044 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 13.044 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 13.044 * [taylor]: Taking taylor expansion of 2.0 in k 13.044 * [backup-simplify]: Simplify 2.0 into 2.0 13.044 * [taylor]: Taking taylor expansion of (/ PI n) in k 13.044 * [taylor]: Taking taylor expansion of PI in k 13.044 * [backup-simplify]: Simplify PI into PI 13.044 * [taylor]: Taking taylor expansion of n in k 13.044 * [backup-simplify]: Simplify n into n 13.044 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 13.044 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 13.044 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 13.045 * [backup-simplify]: Simplify (- 1) into -1 13.045 * [backup-simplify]: Simplify (+ 0 -1) into -1 13.046 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 13.046 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 13.046 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) 13.046 * [taylor]: Taking taylor expansion of (sqrt k) in k 13.046 * [taylor]: Taking taylor expansion of k in k 13.046 * [backup-simplify]: Simplify 0 into 0 13.046 * [backup-simplify]: Simplify 1 into 1 13.047 * [backup-simplify]: Simplify (sqrt 0) into 0 13.048 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 13.048 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in k 13.048 * [taylor]: Taking taylor expansion of 1.0 in k 13.048 * [backup-simplify]: Simplify 1.0 into 1.0 13.048 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in k 13.048 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 13.048 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 13.048 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 13.048 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 13.048 * [taylor]: Taking taylor expansion of 0.5 in k 13.048 * [backup-simplify]: Simplify 0.5 into 0.5 13.048 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 13.048 * [taylor]: Taking taylor expansion of 1.0 in k 13.048 * [backup-simplify]: Simplify 1.0 into 1.0 13.048 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.048 * [taylor]: Taking taylor expansion of k in k 13.048 * [backup-simplify]: Simplify 0 into 0 13.048 * [backup-simplify]: Simplify 1 into 1 13.049 * [backup-simplify]: Simplify (/ 1 1) into 1 13.049 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 13.049 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 13.049 * [taylor]: Taking taylor expansion of 2.0 in k 13.049 * [backup-simplify]: Simplify 2.0 into 2.0 13.049 * [taylor]: Taking taylor expansion of (/ PI n) in k 13.049 * [taylor]: Taking taylor expansion of PI in k 13.049 * [backup-simplify]: Simplify PI into PI 13.049 * [taylor]: Taking taylor expansion of n in k 13.049 * [backup-simplify]: Simplify n into n 13.049 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 13.049 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 13.049 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 13.050 * [backup-simplify]: Simplify (- 1) into -1 13.050 * [backup-simplify]: Simplify (+ 0 -1) into -1 13.050 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 13.051 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 13.051 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) 13.051 * [taylor]: Taking taylor expansion of (sqrt k) in k 13.051 * [taylor]: Taking taylor expansion of k in k 13.051 * [backup-simplify]: Simplify 0 into 0 13.051 * [backup-simplify]: Simplify 1 into 1 13.051 * [backup-simplify]: Simplify (sqrt 0) into 0 13.052 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 13.053 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) 0) into 0 13.053 * [backup-simplify]: Simplify (* 1.0 0) into 0 13.053 * [taylor]: Taking taylor expansion of 0 in n 13.053 * [backup-simplify]: Simplify 0 into 0 13.053 * [backup-simplify]: Simplify 0 into 0 13.054 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) 13.055 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) 13.055 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) in n 13.055 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))) in n 13.055 * [taylor]: Taking taylor expansion of +nan.0 in n 13.055 * [backup-simplify]: Simplify +nan.0 into +nan.0 13.055 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) in n 13.055 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))) in n 13.055 * [taylor]: Taking taylor expansion of 0.5 in n 13.055 * [backup-simplify]: Simplify 0.5 into 0.5 13.055 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))) in n 13.055 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 13.055 * [taylor]: Taking taylor expansion of 1.0 in n 13.055 * [backup-simplify]: Simplify 1.0 into 1.0 13.055 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.055 * [taylor]: Taking taylor expansion of k in n 13.055 * [backup-simplify]: Simplify k into k 13.055 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.055 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 13.055 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 13.055 * [taylor]: Taking taylor expansion of 2.0 in n 13.055 * [backup-simplify]: Simplify 2.0 into 2.0 13.056 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.056 * [taylor]: Taking taylor expansion of PI in n 13.056 * [backup-simplify]: Simplify PI into PI 13.056 * [taylor]: Taking taylor expansion of n in n 13.056 * [backup-simplify]: Simplify 0 into 0 13.056 * [backup-simplify]: Simplify 1 into 1 13.056 * [backup-simplify]: Simplify (/ PI 1) into PI 13.057 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 13.058 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 13.058 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 13.058 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 13.059 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 13.061 * [backup-simplify]: Simplify (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) into (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) 13.062 * [backup-simplify]: Simplify (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) 13.063 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 13.064 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) 13.066 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) 13.067 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) 13.067 * [backup-simplify]: Simplify 0 into 0 13.070 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 13.071 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) 13.072 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))) (* 0 0))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) 13.072 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) in n 13.072 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))) in n 13.072 * [taylor]: Taking taylor expansion of +nan.0 in n 13.072 * [backup-simplify]: Simplify +nan.0 into +nan.0 13.072 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) in n 13.072 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))) in n 13.072 * [taylor]: Taking taylor expansion of 0.5 in n 13.072 * [backup-simplify]: Simplify 0.5 into 0.5 13.072 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))) in n 13.072 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 13.072 * [taylor]: Taking taylor expansion of 1.0 in n 13.072 * [backup-simplify]: Simplify 1.0 into 1.0 13.072 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.072 * [taylor]: Taking taylor expansion of k in n 13.072 * [backup-simplify]: Simplify k into k 13.073 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.073 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 13.073 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 13.073 * [taylor]: Taking taylor expansion of 2.0 in n 13.073 * [backup-simplify]: Simplify 2.0 into 2.0 13.073 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.073 * [taylor]: Taking taylor expansion of PI in n 13.073 * [backup-simplify]: Simplify PI into PI 13.073 * [taylor]: Taking taylor expansion of n in n 13.073 * [backup-simplify]: Simplify 0 into 0 13.073 * [backup-simplify]: Simplify 1 into 1 13.073 * [backup-simplify]: Simplify (/ PI 1) into PI 13.074 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 13.075 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 13.075 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 13.075 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 13.076 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 13.078 * [backup-simplify]: Simplify (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) into (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) 13.079 * [backup-simplify]: Simplify (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) 13.080 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 13.081 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) 13.083 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) 13.084 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) 13.085 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 13.086 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 13.087 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 13.087 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 13.087 * [backup-simplify]: Simplify (- 0) into 0 13.087 * [backup-simplify]: Simplify (+ 0 0) into 0 13.088 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 13.089 * [backup-simplify]: Simplify (+ (* (- 1.0 (/ 1 k)) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 13.090 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into 0 13.091 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 13.093 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into 0 13.093 * [backup-simplify]: Simplify (- 0) into 0 13.093 * [backup-simplify]: Simplify 0 into 0 13.093 * [backup-simplify]: Simplify 0 into 0 13.095 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 13.096 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) 13.097 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))) (* 0 0)))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) 13.097 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) in n 13.097 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))) in n 13.097 * [taylor]: Taking taylor expansion of +nan.0 in n 13.097 * [backup-simplify]: Simplify +nan.0 into +nan.0 13.097 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) in n 13.097 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))) in n 13.097 * [taylor]: Taking taylor expansion of 0.5 in n 13.097 * [backup-simplify]: Simplify 0.5 into 0.5 13.097 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))) in n 13.097 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 13.097 * [taylor]: Taking taylor expansion of 1.0 in n 13.097 * [backup-simplify]: Simplify 1.0 into 1.0 13.097 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.097 * [taylor]: Taking taylor expansion of k in n 13.097 * [backup-simplify]: Simplify k into k 13.097 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.097 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 13.097 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 13.097 * [taylor]: Taking taylor expansion of 2.0 in n 13.097 * [backup-simplify]: Simplify 2.0 into 2.0 13.097 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.097 * [taylor]: Taking taylor expansion of PI in n 13.097 * [backup-simplify]: Simplify PI into PI 13.097 * [taylor]: Taking taylor expansion of n in n 13.097 * [backup-simplify]: Simplify 0 into 0 13.097 * [backup-simplify]: Simplify 1 into 1 13.097 * [backup-simplify]: Simplify (/ PI 1) into PI 13.098 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 13.098 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 13.098 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 13.098 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 13.099 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 13.100 * [backup-simplify]: Simplify (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) into (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) 13.101 * [backup-simplify]: Simplify (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) 13.101 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 13.102 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) 13.107 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) 13.108 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) 13.111 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 3)))))))) 13.111 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt (/ 1 (- k)))) (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0))) into (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) 13.112 * [approximate]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in (k n) around 0 13.112 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n 13.112 * [taylor]: Taking taylor expansion of 1.0 in n 13.112 * [backup-simplify]: Simplify 1.0 into 1.0 13.112 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n 13.112 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 13.112 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 13.112 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 13.112 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 13.112 * [taylor]: Taking taylor expansion of 0.5 in n 13.112 * [backup-simplify]: Simplify 0.5 into 0.5 13.112 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 13.112 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.112 * [taylor]: Taking taylor expansion of k in n 13.112 * [backup-simplify]: Simplify k into k 13.112 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.112 * [taylor]: Taking taylor expansion of 1.0 in n 13.112 * [backup-simplify]: Simplify 1.0 into 1.0 13.112 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 13.112 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 13.112 * [taylor]: Taking taylor expansion of -2.0 in n 13.112 * [backup-simplify]: Simplify -2.0 into -2.0 13.112 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.112 * [taylor]: Taking taylor expansion of PI in n 13.112 * [backup-simplify]: Simplify PI into PI 13.112 * [taylor]: Taking taylor expansion of n in n 13.112 * [backup-simplify]: Simplify 0 into 0 13.112 * [backup-simplify]: Simplify 1 into 1 13.112 * [backup-simplify]: Simplify (/ PI 1) into PI 13.113 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 13.113 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 13.113 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 13.113 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 13.114 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 13.115 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) 13.116 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 13.116 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 13.116 * [taylor]: Taking taylor expansion of (/ -1 k) in n 13.116 * [taylor]: Taking taylor expansion of -1 in n 13.116 * [backup-simplify]: Simplify -1 into -1 13.116 * [taylor]: Taking taylor expansion of k in n 13.116 * [backup-simplify]: Simplify k into k 13.116 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 13.116 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 13.116 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 13.116 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 13.117 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) into (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) 13.117 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 13.117 * [taylor]: Taking taylor expansion of 1.0 in k 13.117 * [backup-simplify]: Simplify 1.0 into 1.0 13.117 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 13.117 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 13.117 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 13.117 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 13.117 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 13.117 * [taylor]: Taking taylor expansion of 0.5 in k 13.117 * [backup-simplify]: Simplify 0.5 into 0.5 13.117 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 13.117 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.117 * [taylor]: Taking taylor expansion of k in k 13.117 * [backup-simplify]: Simplify 0 into 0 13.117 * [backup-simplify]: Simplify 1 into 1 13.118 * [backup-simplify]: Simplify (/ 1 1) into 1 13.118 * [taylor]: Taking taylor expansion of 1.0 in k 13.118 * [backup-simplify]: Simplify 1.0 into 1.0 13.118 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 13.118 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 13.118 * [taylor]: Taking taylor expansion of -2.0 in k 13.118 * [backup-simplify]: Simplify -2.0 into -2.0 13.118 * [taylor]: Taking taylor expansion of (/ PI n) in k 13.118 * [taylor]: Taking taylor expansion of PI in k 13.118 * [backup-simplify]: Simplify PI into PI 13.118 * [taylor]: Taking taylor expansion of n in k 13.118 * [backup-simplify]: Simplify n into n 13.118 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 13.118 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 13.118 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 13.119 * [backup-simplify]: Simplify (+ 1 0) into 1 13.119 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 13.119 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 13.120 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) 13.120 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 13.120 * [taylor]: Taking taylor expansion of (/ -1 k) in k 13.120 * [taylor]: Taking taylor expansion of -1 in k 13.120 * [backup-simplify]: Simplify -1 into -1 13.120 * [taylor]: Taking taylor expansion of k in k 13.120 * [backup-simplify]: Simplify 0 into 0 13.120 * [backup-simplify]: Simplify 1 into 1 13.120 * [backup-simplify]: Simplify (/ -1 1) into -1 13.121 * [backup-simplify]: Simplify (sqrt 0) into 0 13.122 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 13.122 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) 13.122 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 13.122 * [taylor]: Taking taylor expansion of 1.0 in k 13.122 * [backup-simplify]: Simplify 1.0 into 1.0 13.123 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 13.123 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 13.123 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 13.123 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 13.123 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 13.123 * [taylor]: Taking taylor expansion of 0.5 in k 13.123 * [backup-simplify]: Simplify 0.5 into 0.5 13.123 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 13.123 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.123 * [taylor]: Taking taylor expansion of k in k 13.123 * [backup-simplify]: Simplify 0 into 0 13.123 * [backup-simplify]: Simplify 1 into 1 13.123 * [backup-simplify]: Simplify (/ 1 1) into 1 13.123 * [taylor]: Taking taylor expansion of 1.0 in k 13.123 * [backup-simplify]: Simplify 1.0 into 1.0 13.123 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 13.123 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 13.123 * [taylor]: Taking taylor expansion of -2.0 in k 13.123 * [backup-simplify]: Simplify -2.0 into -2.0 13.123 * [taylor]: Taking taylor expansion of (/ PI n) in k 13.123 * [taylor]: Taking taylor expansion of PI in k 13.123 * [backup-simplify]: Simplify PI into PI 13.123 * [taylor]: Taking taylor expansion of n in k 13.124 * [backup-simplify]: Simplify n into n 13.124 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 13.124 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 13.124 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 13.124 * [backup-simplify]: Simplify (+ 1 0) into 1 13.125 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 13.125 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 13.125 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) 13.125 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 13.125 * [taylor]: Taking taylor expansion of (/ -1 k) in k 13.125 * [taylor]: Taking taylor expansion of -1 in k 13.125 * [backup-simplify]: Simplify -1 into -1 13.125 * [taylor]: Taking taylor expansion of k in k 13.125 * [backup-simplify]: Simplify 0 into 0 13.125 * [backup-simplify]: Simplify 1 into 1 13.126 * [backup-simplify]: Simplify (/ -1 1) into -1 13.126 * [backup-simplify]: Simplify (sqrt 0) into 0 13.127 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 13.128 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) 13.128 * [backup-simplify]: Simplify (* 1.0 (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) into (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) 13.128 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) in n 13.128 * [taylor]: Taking taylor expansion of +nan.0 in n 13.128 * [backup-simplify]: Simplify +nan.0 into +nan.0 13.128 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) in n 13.128 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))) in n 13.128 * [taylor]: Taking taylor expansion of 0.5 in n 13.128 * [backup-simplify]: Simplify 0.5 into 0.5 13.128 * [taylor]: Taking taylor expansion of (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)) in n 13.128 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 13.128 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 13.128 * [taylor]: Taking taylor expansion of -2.0 in n 13.128 * [backup-simplify]: Simplify -2.0 into -2.0 13.128 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.128 * [taylor]: Taking taylor expansion of PI in n 13.128 * [backup-simplify]: Simplify PI into PI 13.129 * [taylor]: Taking taylor expansion of n in n 13.129 * [backup-simplify]: Simplify 0 into 0 13.129 * [backup-simplify]: Simplify 1 into 1 13.129 * [backup-simplify]: Simplify (/ PI 1) into PI 13.130 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 13.131 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 13.131 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 13.131 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.131 * [taylor]: Taking taylor expansion of k in n 13.131 * [backup-simplify]: Simplify k into k 13.131 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.131 * [taylor]: Taking taylor expansion of 1.0 in n 13.131 * [backup-simplify]: Simplify 1.0 into 1.0 13.133 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 13.133 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 13.134 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) into (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) 13.135 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) 13.136 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 13.138 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) 13.139 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) 13.140 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 13.143 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 13.144 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) 13.145 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) 13.145 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) in n 13.145 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) in n 13.145 * [taylor]: Taking taylor expansion of +nan.0 in n 13.145 * [backup-simplify]: Simplify +nan.0 into +nan.0 13.145 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) in n 13.145 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))) in n 13.145 * [taylor]: Taking taylor expansion of 0.5 in n 13.145 * [backup-simplify]: Simplify 0.5 into 0.5 13.145 * [taylor]: Taking taylor expansion of (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)) in n 13.145 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 13.145 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 13.145 * [taylor]: Taking taylor expansion of -2.0 in n 13.145 * [backup-simplify]: Simplify -2.0 into -2.0 13.145 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.145 * [taylor]: Taking taylor expansion of PI in n 13.145 * [backup-simplify]: Simplify PI into PI 13.145 * [taylor]: Taking taylor expansion of n in n 13.145 * [backup-simplify]: Simplify 0 into 0 13.145 * [backup-simplify]: Simplify 1 into 1 13.146 * [backup-simplify]: Simplify (/ PI 1) into PI 13.146 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 13.147 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 13.148 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 13.148 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.148 * [taylor]: Taking taylor expansion of k in n 13.148 * [backup-simplify]: Simplify k into k 13.148 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.148 * [taylor]: Taking taylor expansion of 1.0 in n 13.148 * [backup-simplify]: Simplify 1.0 into 1.0 13.149 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 13.149 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 13.151 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) into (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) 13.152 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) 13.153 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 13.155 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) 13.156 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) 13.157 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) 13.159 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 13.159 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 13.159 * [backup-simplify]: Simplify (+ 0 0) into 0 13.160 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 13.161 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 13.163 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 13.164 * [backup-simplify]: Simplify (+ (* (- (log (* -2.0 PI)) (log n)) 0) (* 0 (+ (/ 1 k) 1.0))) into 0 13.166 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into 0 13.168 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 13.170 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into 0 13.170 * [backup-simplify]: Simplify 0 into 0 13.171 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.175 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 13.177 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) 13.178 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) 13.178 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) in n 13.178 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) in n 13.178 * [taylor]: Taking taylor expansion of +nan.0 in n 13.178 * [backup-simplify]: Simplify +nan.0 into +nan.0 13.178 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) in n 13.178 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))) in n 13.178 * [taylor]: Taking taylor expansion of 0.5 in n 13.178 * [backup-simplify]: Simplify 0.5 into 0.5 13.178 * [taylor]: Taking taylor expansion of (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)) in n 13.178 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 13.178 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 13.178 * [taylor]: Taking taylor expansion of -2.0 in n 13.178 * [backup-simplify]: Simplify -2.0 into -2.0 13.178 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.178 * [taylor]: Taking taylor expansion of PI in n 13.179 * [backup-simplify]: Simplify PI into PI 13.179 * [taylor]: Taking taylor expansion of n in n 13.179 * [backup-simplify]: Simplify 0 into 0 13.179 * [backup-simplify]: Simplify 1 into 1 13.179 * [backup-simplify]: Simplify (/ PI 1) into PI 13.180 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 13.181 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 13.181 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 13.181 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.181 * [taylor]: Taking taylor expansion of k in n 13.181 * [backup-simplify]: Simplify k into k 13.181 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.181 * [taylor]: Taking taylor expansion of 1.0 in n 13.181 * [backup-simplify]: Simplify 1.0 into 1.0 13.183 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 13.183 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 13.184 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) into (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) 13.185 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) 13.187 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 13.188 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) 13.190 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) 13.191 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) 13.196 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))))) (* 1 (/ 1 (- k)))) (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0))))))) into (- (+ (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2)))))))) 13.196 * * * [progress]: simplifying candidates 13.201 * [simplify]: Simplifying: (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (- (log 1.0) (log (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt 1)) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt 1)) (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 1) (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt 1)) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 1) (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (+ (- (log 1.0) (log (sqrt k))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (+ (log (/ 1.0 (sqrt k))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (exp (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (* (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (* (/ 1.0 (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) 1) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (- (+ (* 0.25 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2))))) (+ (* 0.125 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* 0.125 (* (pow (log (* 2.0 PI)) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))))))) (+ (* 0.5 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k))) (* 0.5 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k))))) (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (- (+ (* +nan.0 (pow k 2)) (- (+ +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))))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) k)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow k 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (pow (log (* 2.0 PI)) 2) (pow k 2)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) k))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log n) k))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (pow k 2)))) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (pow (log n) 2) (pow k 2))))))))))))))))))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 3)))))))) (- (+ (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2)))))))) 13.208 * * [simplify]: iteration 0: 353 enodes 13.309 * * [simplify]: iteration 1: 975 enodes 13.788 * * [simplify]: iteration 2: 3261 enodes 14.878 * * [simplify]: iteration complete: 5001 enodes 14.878 * * [simplify]: Extracting #0: cost 117 inf + 0 14.881 * * [simplify]: Extracting #1: cost 590 inf + 2 14.886 * * [simplify]: Extracting #2: cost 1034 inf + 2722 14.900 * * [simplify]: Extracting #3: cost 1271 inf + 29363 14.940 * * [simplify]: Extracting #4: cost 841 inf + 157190 15.009 * * [simplify]: Extracting #5: cost 492 inf + 353948 15.116 * * [simplify]: Extracting #6: cost 429 inf + 453894 15.241 * * [simplify]: Extracting #7: cost 178 inf + 668763 15.402 * * [simplify]: Extracting #8: cost 60 inf + 770866 15.579 * * [simplify]: Extracting #9: cost 5 inf + 834102 15.738 * * [simplify]: Extracting #10: cost 0 inf + 842935 15.916 * * [simplify]: Extracting #11: cost 0 inf + 842895 16.099 * [simplify]: Simplified to: (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (* (/ (cbrt (- 1.0 k)) (cbrt 2.0)) (/ (cbrt (- 1.0 k)) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (* (/ (cbrt (- 1.0 k)) (sqrt 2.0)) (cbrt (- 1.0 k)))) (pow (* (* 2.0 PI) n) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (cbrt 2.0)) (cbrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (sqrt (- 1.0 k))) (pow (* (* 2.0 PI) n) (/ (/ 1 (cbrt 2.0)) (cbrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (* (* 2.0 PI) n) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt k) (sqrt 1.0)) (cbrt 2.0)) (cbrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt k) (sqrt 1.0)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (+ (sqrt k) (sqrt 1.0))) (pow (* (* 2.0 PI) n) (/ (/ 1 (cbrt 2.0)) (cbrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2) 2.0)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2) 2.0)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (log (* (* 2.0 PI) n)) (log (* (* 2.0 PI) n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* 2.0 PI) n) (* (* (* 2.0 PI) n) (* (* 2.0 PI) n))) (* (* (* 2.0 PI) n) (* (* (* 2.0 PI) n) (* (* 2.0 PI) n))) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* 2.0 PI) n) (* (* (* 2.0 PI) n) (* (* 2.0 PI) n))) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* 2.0 (* (sqrt n) PI)) (* 2.0 PI) (* PI n) (log (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (* (/ 1.0 (sqrt k)) (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k)))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (/ 1.0 (sqrt k)) (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k)))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (* (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (cbrt 1.0) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (fabs (cbrt k))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (fabs (cbrt k))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (fabs (cbrt k))) (/ 1.0 (sqrt (sqrt k))) 1.0 (/ 1.0 (sqrt (sqrt k))) 1.0 (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (+ (log (/ 1.0 (sqrt k))) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n)))) (+ (log (/ 1.0 (sqrt k))) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n)))) (+ (log (/ 1.0 (sqrt k))) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n)))) (+ (log (/ 1.0 (sqrt k))) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n)))) (+ (log (/ 1.0 (sqrt k))) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n)))) (+ (log (/ 1.0 (sqrt k))) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n)))) (+ (log (/ 1.0 (sqrt k))) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n)))) (+ (log (/ 1.0 (sqrt k))) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n)))) (+ (log (/ 1.0 (sqrt k))) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n)))) (+ (log (/ 1.0 (sqrt k))) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n)))) (+ (log (/ 1.0 (sqrt k))) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n)))) (exp (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))))) (* (cbrt (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (cbrt (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))))) (cbrt (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))))) (sqrt (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (sqrt (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2) 2.0)) (sqrt (/ 1.0 (sqrt k)))) (* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2) 2.0)) (sqrt (/ 1.0 (sqrt k)))) (* (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2) 2.0))) (* (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2) 2.0))) (* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))) (* (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (/ 1.0 (sqrt k))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (/ (* 1.0 (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt k)) (/ 1.0 (sqrt k)) (* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2) 2.0)) (/ 1.0 (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (/ 1.0 (sqrt k)))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ (cbrt 1.0) (cbrt (sqrt k)))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ (cbrt 1.0) (sqrt (cbrt k)))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ (cbrt 1.0) (sqrt k))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ (cbrt 1.0) (sqrt k))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ (sqrt 1.0) (cbrt (sqrt k)))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ (sqrt 1.0) (sqrt (cbrt k)))) (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt 1.0)) (sqrt (sqrt k))) (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt 1.0)) (sqrt k)) (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt 1.0)) (sqrt (sqrt k))) (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt 1.0)) (sqrt k)) (/ 1.0 (/ (cbrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt (cbrt k)))) (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt (sqrt k))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))) (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt (sqrt k))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))) (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k)) (/ (* (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) 1.0) (sqrt k)) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (+ (+ (+ (* (* (* (log n) (log n)) (* (* k k) (exp (* (log (* (* 2.0 PI) n)) 0.5)))) 0.125) (exp (* (log (* (* 2.0 PI) n)) 0.5))) (* (* (log (* 2.0 PI)) (log (* 2.0 PI))) (* (* (* k k) (exp (* (log (* (* 2.0 PI) n)) 0.5))) 0.125))) (- (* (* (* 0.25 (log (* 2.0 PI))) (exp (* (log (* (* 2.0 PI) n)) 0.5))) (* (log n) (* k k))) (* (* k (+ (* (exp (* (log (* (* 2.0 PI) n)) 0.5)) (log n)) (* (log (* 2.0 PI)) (exp (* (log (* (* 2.0 PI) n)) 0.5))))) 0.5))) (exp (* 0.5 (* (- 1.0 k) (log (* (* 2.0 PI) n))))) (exp (* (* (- 1.0 k) 0.5) (- (log (* PI -2.0)) (log (/ -1 n))))) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (* (- +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 k)) +nan.0)) (- (+ (- (* k (* (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5) +nan.0)) (* (* k k) (* (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5) +nan.0))) (- (* (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5) (* +nan.0 (* (log n) (* k k)))) (- (* +nan.0 (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5)) (+ (- (* (* (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5) (* (* k (log (* 2.0 PI))) (* k (log (* 2.0 PI))))) +nan.0) (* +nan.0 (* (* (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5) (log (* 2.0 PI))) (* (log n) (* k k))))) (+ (- (* +nan.0 (* (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5) (* (log (* 2.0 PI)) k))) (* (* (* +nan.0 (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5)) (log n)) k)) (- (* (* +nan.0 (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5)) (* (* k k) (log (* 2.0 PI)))) (* +nan.0 (* (* (* k (log n)) (* k (log n))) (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5)))))))))) (- (* (/ (- +nan.0) k) (/ (exp (* 0.5 (* (- 1.0 k) (log (* (* 2.0 PI) n))))) k)) (+ (* (- +nan.0) (/ (exp (* 0.5 (* (- 1.0 k) (log (* (* 2.0 PI) n))))) k)) (* (/ +nan.0 (* k k)) (/ (exp (* 0.5 (* (- 1.0 k) (log (* (* 2.0 PI) n))))) k)))) (- (+ (- (* (exp (* (* (- 1.0 k) 0.5) (- (log (* PI -2.0)) (log (/ -1 n))))) +nan.0) (/ (* (exp (* (* (- 1.0 k) 0.5) (- (log (* PI -2.0)) (log (/ -1 n))))) +nan.0) k)) (/ +nan.0 (/ (* k k) (exp (* (* (- 1.0 k) 0.5) (- (log (* PI -2.0)) (log (/ -1 n))))))))) 16.117 * * * [progress]: adding candidates to table 16.980 * * [progress]: iteration 4 / 4 16.980 * * * [progress]: picking best candidate 17.016 * * * * [pick]: Picked # 17.016 * * * [progress]: localizing error 17.052 * * * [progress]: generating rewritten candidates 17.052 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 1 2) 17.072 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1 2) 17.092 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1 2 1) 17.118 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1 2 1) 17.142 * * * [progress]: generating series expansions 17.142 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 1 2) 17.143 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 17.143 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 17.143 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 17.143 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 17.143 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 17.143 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 17.143 * [taylor]: Taking taylor expansion of 0.5 in k 17.143 * [backup-simplify]: Simplify 0.5 into 0.5 17.143 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 17.143 * [taylor]: Taking taylor expansion of 1.0 in k 17.143 * [backup-simplify]: Simplify 1.0 into 1.0 17.143 * [taylor]: Taking taylor expansion of k in k 17.143 * [backup-simplify]: Simplify 0 into 0 17.143 * [backup-simplify]: Simplify 1 into 1 17.143 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 17.143 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 17.143 * [taylor]: Taking taylor expansion of 2.0 in k 17.143 * [backup-simplify]: Simplify 2.0 into 2.0 17.143 * [taylor]: Taking taylor expansion of (* n PI) in k 17.143 * [taylor]: Taking taylor expansion of n in k 17.143 * [backup-simplify]: Simplify n into n 17.143 * [taylor]: Taking taylor expansion of PI in k 17.143 * [backup-simplify]: Simplify PI into PI 17.144 * [backup-simplify]: Simplify (* n PI) into (* n PI) 17.144 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 17.144 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 17.144 * [backup-simplify]: Simplify (- 0) into 0 17.144 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 17.144 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 17.145 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 17.145 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 17.145 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 17.145 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 17.145 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 17.145 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 17.145 * [taylor]: Taking taylor expansion of 0.5 in n 17.145 * [backup-simplify]: Simplify 0.5 into 0.5 17.145 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 17.145 * [taylor]: Taking taylor expansion of 1.0 in n 17.145 * [backup-simplify]: Simplify 1.0 into 1.0 17.145 * [taylor]: Taking taylor expansion of k in n 17.145 * [backup-simplify]: Simplify k into k 17.145 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 17.145 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 17.145 * [taylor]: Taking taylor expansion of 2.0 in n 17.145 * [backup-simplify]: Simplify 2.0 into 2.0 17.145 * [taylor]: Taking taylor expansion of (* n PI) in n 17.145 * [taylor]: Taking taylor expansion of n in n 17.145 * [backup-simplify]: Simplify 0 into 0 17.145 * [backup-simplify]: Simplify 1 into 1 17.145 * [taylor]: Taking taylor expansion of PI in n 17.145 * [backup-simplify]: Simplify PI into PI 17.145 * [backup-simplify]: Simplify (* 0 PI) into 0 17.146 * [backup-simplify]: Simplify (* 2.0 0) into 0 17.147 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 17.147 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 17.148 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 17.148 * [backup-simplify]: Simplify (- k) into (- k) 17.148 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 17.148 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 17.149 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 17.153 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 17.154 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 17.154 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 17.154 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 17.154 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 17.154 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 17.154 * [taylor]: Taking taylor expansion of 0.5 in n 17.154 * [backup-simplify]: Simplify 0.5 into 0.5 17.154 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 17.154 * [taylor]: Taking taylor expansion of 1.0 in n 17.154 * [backup-simplify]: Simplify 1.0 into 1.0 17.154 * [taylor]: Taking taylor expansion of k in n 17.154 * [backup-simplify]: Simplify k into k 17.154 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 17.154 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 17.154 * [taylor]: Taking taylor expansion of 2.0 in n 17.154 * [backup-simplify]: Simplify 2.0 into 2.0 17.154 * [taylor]: Taking taylor expansion of (* n PI) in n 17.154 * [taylor]: Taking taylor expansion of n in n 17.154 * [backup-simplify]: Simplify 0 into 0 17.154 * [backup-simplify]: Simplify 1 into 1 17.154 * [taylor]: Taking taylor expansion of PI in n 17.154 * [backup-simplify]: Simplify PI into PI 17.154 * [backup-simplify]: Simplify (* 0 PI) into 0 17.155 * [backup-simplify]: Simplify (* 2.0 0) into 0 17.156 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 17.157 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 17.157 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 17.157 * [backup-simplify]: Simplify (- k) into (- k) 17.157 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 17.157 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 17.158 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 17.159 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 17.160 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 17.160 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 17.160 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 17.160 * [taylor]: Taking taylor expansion of 0.5 in k 17.160 * [backup-simplify]: Simplify 0.5 into 0.5 17.160 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 17.160 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 17.160 * [taylor]: Taking taylor expansion of 1.0 in k 17.160 * [backup-simplify]: Simplify 1.0 into 1.0 17.160 * [taylor]: Taking taylor expansion of k in k 17.160 * [backup-simplify]: Simplify 0 into 0 17.160 * [backup-simplify]: Simplify 1 into 1 17.160 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 17.160 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 17.160 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 17.160 * [taylor]: Taking taylor expansion of 2.0 in k 17.160 * [backup-simplify]: Simplify 2.0 into 2.0 17.160 * [taylor]: Taking taylor expansion of PI in k 17.160 * [backup-simplify]: Simplify PI into PI 17.160 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 17.161 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 17.161 * [taylor]: Taking taylor expansion of (log n) in k 17.161 * [taylor]: Taking taylor expansion of n in k 17.161 * [backup-simplify]: Simplify n into n 17.161 * [backup-simplify]: Simplify (log n) into (log n) 17.161 * [backup-simplify]: Simplify (- 0) into 0 17.162 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 17.163 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 17.164 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 17.165 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 17.167 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 17.168 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 17.169 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 17.170 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 17.172 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 17.172 * [backup-simplify]: Simplify (- 0) into 0 17.173 * [backup-simplify]: Simplify (+ 0 0) into 0 17.173 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 17.175 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 17.176 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 17.178 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 17.178 * [taylor]: Taking taylor expansion of 0 in k 17.178 * [backup-simplify]: Simplify 0 into 0 17.178 * [backup-simplify]: Simplify 0 into 0 17.178 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 17.179 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 17.180 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 17.180 * [backup-simplify]: Simplify (+ 0 0) into 0 17.180 * [backup-simplify]: Simplify (- 1) into -1 17.181 * [backup-simplify]: Simplify (+ 0 -1) into -1 17.182 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 17.183 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 17.185 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 17.187 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 17.187 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 17.188 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 17.190 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 17.190 * [backup-simplify]: Simplify (- 0) into 0 17.191 * [backup-simplify]: Simplify (+ 0 0) into 0 17.191 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 17.192 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 17.193 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 17.195 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 17.195 * [taylor]: Taking taylor expansion of 0 in k 17.195 * [backup-simplify]: Simplify 0 into 0 17.195 * [backup-simplify]: Simplify 0 into 0 17.195 * [backup-simplify]: Simplify 0 into 0 17.196 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 17.198 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 17.199 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 17.199 * [backup-simplify]: Simplify (+ 0 0) into 0 17.199 * [backup-simplify]: Simplify (- 0) into 0 17.200 * [backup-simplify]: Simplify (+ 0 0) into 0 17.201 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 17.202 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 17.205 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 17.209 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 17.218 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.25 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2))))) (+ (* 0.125 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* 0.125 (* (pow (log (* 2.0 PI)) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))))))) (+ (* 0.5 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k))) (* 0.5 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k))))) 17.219 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) 17.219 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 17.219 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 17.219 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 17.219 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 17.219 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 17.219 * [taylor]: Taking taylor expansion of 0.5 in k 17.219 * [backup-simplify]: Simplify 0.5 into 0.5 17.219 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 17.219 * [taylor]: Taking taylor expansion of 1.0 in k 17.219 * [backup-simplify]: Simplify 1.0 into 1.0 17.219 * [taylor]: Taking taylor expansion of (/ 1 k) in k 17.219 * [taylor]: Taking taylor expansion of k in k 17.219 * [backup-simplify]: Simplify 0 into 0 17.219 * [backup-simplify]: Simplify 1 into 1 17.219 * [backup-simplify]: Simplify (/ 1 1) into 1 17.219 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 17.219 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 17.219 * [taylor]: Taking taylor expansion of 2.0 in k 17.219 * [backup-simplify]: Simplify 2.0 into 2.0 17.220 * [taylor]: Taking taylor expansion of (/ PI n) in k 17.220 * [taylor]: Taking taylor expansion of PI in k 17.220 * [backup-simplify]: Simplify PI into PI 17.220 * [taylor]: Taking taylor expansion of n in k 17.220 * [backup-simplify]: Simplify n into n 17.220 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 17.220 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 17.220 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 17.220 * [backup-simplify]: Simplify (- 1) into -1 17.221 * [backup-simplify]: Simplify (+ 0 -1) into -1 17.221 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 17.221 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 17.221 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) 17.221 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 17.221 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 17.221 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 17.221 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 17.221 * [taylor]: Taking taylor expansion of 0.5 in n 17.222 * [backup-simplify]: Simplify 0.5 into 0.5 17.222 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 17.222 * [taylor]: Taking taylor expansion of 1.0 in n 17.222 * [backup-simplify]: Simplify 1.0 into 1.0 17.222 * [taylor]: Taking taylor expansion of (/ 1 k) in n 17.222 * [taylor]: Taking taylor expansion of k in n 17.222 * [backup-simplify]: Simplify k into k 17.222 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 17.222 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 17.222 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 17.222 * [taylor]: Taking taylor expansion of 2.0 in n 17.222 * [backup-simplify]: Simplify 2.0 into 2.0 17.222 * [taylor]: Taking taylor expansion of (/ PI n) in n 17.222 * [taylor]: Taking taylor expansion of PI in n 17.222 * [backup-simplify]: Simplify PI into PI 17.222 * [taylor]: Taking taylor expansion of n in n 17.222 * [backup-simplify]: Simplify 0 into 0 17.222 * [backup-simplify]: Simplify 1 into 1 17.222 * [backup-simplify]: Simplify (/ PI 1) into PI 17.223 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 17.224 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 17.224 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 17.224 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 17.224 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 17.225 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 17.227 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) 17.228 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 17.228 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 17.228 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 17.228 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 17.228 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 17.228 * [taylor]: Taking taylor expansion of 0.5 in n 17.228 * [backup-simplify]: Simplify 0.5 into 0.5 17.228 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 17.228 * [taylor]: Taking taylor expansion of 1.0 in n 17.228 * [backup-simplify]: Simplify 1.0 into 1.0 17.228 * [taylor]: Taking taylor expansion of (/ 1 k) in n 17.228 * [taylor]: Taking taylor expansion of k in n 17.228 * [backup-simplify]: Simplify k into k 17.228 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 17.228 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 17.228 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 17.228 * [taylor]: Taking taylor expansion of 2.0 in n 17.228 * [backup-simplify]: Simplify 2.0 into 2.0 17.228 * [taylor]: Taking taylor expansion of (/ PI n) in n 17.228 * [taylor]: Taking taylor expansion of PI in n 17.228 * [backup-simplify]: Simplify PI into PI 17.228 * [taylor]: Taking taylor expansion of n in n 17.228 * [backup-simplify]: Simplify 0 into 0 17.228 * [backup-simplify]: Simplify 1 into 1 17.229 * [backup-simplify]: Simplify (/ PI 1) into PI 17.229 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 17.230 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 17.231 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 17.231 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 17.231 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 17.232 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 17.234 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) 17.235 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 17.236 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) in k 17.236 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) in k 17.236 * [taylor]: Taking taylor expansion of 0.5 in k 17.236 * [backup-simplify]: Simplify 0.5 into 0.5 17.236 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) in k 17.236 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 17.236 * [taylor]: Taking taylor expansion of 1.0 in k 17.236 * [backup-simplify]: Simplify 1.0 into 1.0 17.236 * [taylor]: Taking taylor expansion of (/ 1 k) in k 17.236 * [taylor]: Taking taylor expansion of k in k 17.236 * [backup-simplify]: Simplify 0 into 0 17.236 * [backup-simplify]: Simplify 1 into 1 17.236 * [backup-simplify]: Simplify (/ 1 1) into 1 17.236 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 17.236 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 17.236 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 17.236 * [taylor]: Taking taylor expansion of 2.0 in k 17.236 * [backup-simplify]: Simplify 2.0 into 2.0 17.236 * [taylor]: Taking taylor expansion of PI in k 17.236 * [backup-simplify]: Simplify PI into PI 17.237 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 17.238 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 17.238 * [taylor]: Taking taylor expansion of (log n) in k 17.238 * [taylor]: Taking taylor expansion of n in k 17.238 * [backup-simplify]: Simplify n into n 17.238 * [backup-simplify]: Simplify (log n) into (log n) 17.239 * [backup-simplify]: Simplify (- 1) into -1 17.239 * [backup-simplify]: Simplify (+ 0 -1) into -1 17.239 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 17.240 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 17.241 * [backup-simplify]: Simplify (* -1 (- (log (* 2.0 PI)) (log n))) into (* -1 (- (log (* 2.0 PI)) (log n))) 17.243 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 17.244 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 17.245 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 17.246 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 17.246 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 17.247 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 17.248 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 17.248 * [backup-simplify]: Simplify (- 0) into 0 17.248 * [backup-simplify]: Simplify (+ 0 0) into 0 17.248 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 17.249 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 17.250 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 17.251 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 17.251 * [taylor]: Taking taylor expansion of 0 in k 17.251 * [backup-simplify]: Simplify 0 into 0 17.251 * [backup-simplify]: Simplify 0 into 0 17.251 * [backup-simplify]: Simplify 0 into 0 17.252 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.252 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 17.254 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 17.254 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 17.255 * [backup-simplify]: Simplify (- 0) into 0 17.255 * [backup-simplify]: Simplify (+ 0 0) into 0 17.255 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 17.256 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 17.257 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 17.259 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 17.259 * [taylor]: Taking taylor expansion of 0 in k 17.259 * [backup-simplify]: Simplify 0 into 0 17.259 * [backup-simplify]: Simplify 0 into 0 17.259 * [backup-simplify]: Simplify 0 into 0 17.259 * [backup-simplify]: Simplify 0 into 0 17.259 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.264 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 17.268 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 17.268 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 17.268 * [backup-simplify]: Simplify (- 0) into 0 17.269 * [backup-simplify]: Simplify (+ 0 0) into 0 17.269 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 17.270 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 17.271 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 17.273 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 17.273 * [taylor]: Taking taylor expansion of 0 in k 17.273 * [backup-simplify]: Simplify 0 into 0 17.273 * [backup-simplify]: Simplify 0 into 0 17.274 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) 17.275 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) 17.275 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 17.275 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 17.275 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 17.275 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 17.275 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 17.275 * [taylor]: Taking taylor expansion of 0.5 in k 17.275 * [backup-simplify]: Simplify 0.5 into 0.5 17.275 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 17.275 * [taylor]: Taking taylor expansion of (/ 1 k) in k 17.275 * [taylor]: Taking taylor expansion of k in k 17.275 * [backup-simplify]: Simplify 0 into 0 17.275 * [backup-simplify]: Simplify 1 into 1 17.275 * [backup-simplify]: Simplify (/ 1 1) into 1 17.275 * [taylor]: Taking taylor expansion of 1.0 in k 17.275 * [backup-simplify]: Simplify 1.0 into 1.0 17.275 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 17.275 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 17.275 * [taylor]: Taking taylor expansion of -2.0 in k 17.276 * [backup-simplify]: Simplify -2.0 into -2.0 17.276 * [taylor]: Taking taylor expansion of (/ PI n) in k 17.276 * [taylor]: Taking taylor expansion of PI in k 17.276 * [backup-simplify]: Simplify PI into PI 17.276 * [taylor]: Taking taylor expansion of n in k 17.276 * [backup-simplify]: Simplify n into n 17.276 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 17.276 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 17.276 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 17.276 * [backup-simplify]: Simplify (+ 1 0) into 1 17.277 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 17.277 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 17.277 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) 17.277 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 17.277 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 17.277 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 17.277 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 17.277 * [taylor]: Taking taylor expansion of 0.5 in n 17.278 * [backup-simplify]: Simplify 0.5 into 0.5 17.278 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 17.278 * [taylor]: Taking taylor expansion of (/ 1 k) in n 17.278 * [taylor]: Taking taylor expansion of k in n 17.278 * [backup-simplify]: Simplify k into k 17.278 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 17.278 * [taylor]: Taking taylor expansion of 1.0 in n 17.278 * [backup-simplify]: Simplify 1.0 into 1.0 17.278 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 17.278 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 17.278 * [taylor]: Taking taylor expansion of -2.0 in n 17.278 * [backup-simplify]: Simplify -2.0 into -2.0 17.278 * [taylor]: Taking taylor expansion of (/ PI n) in n 17.278 * [taylor]: Taking taylor expansion of PI in n 17.278 * [backup-simplify]: Simplify PI into PI 17.278 * [taylor]: Taking taylor expansion of n in n 17.278 * [backup-simplify]: Simplify 0 into 0 17.278 * [backup-simplify]: Simplify 1 into 1 17.279 * [backup-simplify]: Simplify (/ PI 1) into PI 17.279 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 17.280 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 17.280 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 17.281 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 17.282 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 17.283 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) 17.284 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 17.285 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 17.285 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 17.285 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 17.285 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 17.285 * [taylor]: Taking taylor expansion of 0.5 in n 17.285 * [backup-simplify]: Simplify 0.5 into 0.5 17.285 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 17.285 * [taylor]: Taking taylor expansion of (/ 1 k) in n 17.285 * [taylor]: Taking taylor expansion of k in n 17.285 * [backup-simplify]: Simplify k into k 17.285 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 17.285 * [taylor]: Taking taylor expansion of 1.0 in n 17.285 * [backup-simplify]: Simplify 1.0 into 1.0 17.285 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 17.285 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 17.285 * [taylor]: Taking taylor expansion of -2.0 in n 17.285 * [backup-simplify]: Simplify -2.0 into -2.0 17.285 * [taylor]: Taking taylor expansion of (/ PI n) in n 17.285 * [taylor]: Taking taylor expansion of PI in n 17.285 * [backup-simplify]: Simplify PI into PI 17.285 * [taylor]: Taking taylor expansion of n in n 17.285 * [backup-simplify]: Simplify 0 into 0 17.285 * [backup-simplify]: Simplify 1 into 1 17.286 * [backup-simplify]: Simplify (/ PI 1) into PI 17.286 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 17.287 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 17.287 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 17.288 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 17.289 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 17.290 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) 17.291 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 17.291 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) in k 17.292 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) in k 17.292 * [taylor]: Taking taylor expansion of 0.5 in k 17.292 * [backup-simplify]: Simplify 0.5 into 0.5 17.292 * [taylor]: Taking taylor expansion of (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) in k 17.292 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 17.292 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 17.292 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 17.292 * [taylor]: Taking taylor expansion of -2.0 in k 17.292 * [backup-simplify]: Simplify -2.0 into -2.0 17.292 * [taylor]: Taking taylor expansion of PI in k 17.292 * [backup-simplify]: Simplify PI into PI 17.292 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 17.293 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 17.293 * [taylor]: Taking taylor expansion of (log n) in k 17.294 * [taylor]: Taking taylor expansion of n in k 17.294 * [backup-simplify]: Simplify n into n 17.294 * [backup-simplify]: Simplify (log n) into (log n) 17.294 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 17.294 * [taylor]: Taking taylor expansion of (/ 1 k) in k 17.294 * [taylor]: Taking taylor expansion of k in k 17.294 * [backup-simplify]: Simplify 0 into 0 17.294 * [backup-simplify]: Simplify 1 into 1 17.294 * [backup-simplify]: Simplify (/ 1 1) into 1 17.294 * [taylor]: Taking taylor expansion of 1.0 in k 17.294 * [backup-simplify]: Simplify 1.0 into 1.0 17.294 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 17.295 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 17.296 * [backup-simplify]: Simplify (+ 1 0) into 1 17.297 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) 1) into (- (log (* -2.0 PI)) (log n)) 17.298 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 17.299 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 17.301 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 17.302 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 17.302 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 17.304 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 17.304 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 17.305 * [backup-simplify]: Simplify (+ 0 0) into 0 17.305 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 17.306 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 17.307 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 17.308 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 17.308 * [taylor]: Taking taylor expansion of 0 in k 17.308 * [backup-simplify]: Simplify 0 into 0 17.308 * [backup-simplify]: Simplify 0 into 0 17.308 * [backup-simplify]: Simplify 0 into 0 17.309 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.309 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 17.311 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 17.311 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 17.312 * [backup-simplify]: Simplify (+ 0 0) into 0 17.312 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 17.313 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 17.314 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 17.316 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 17.316 * [taylor]: Taking taylor expansion of 0 in k 17.316 * [backup-simplify]: Simplify 0 into 0 17.316 * [backup-simplify]: Simplify 0 into 0 17.316 * [backup-simplify]: Simplify 0 into 0 17.316 * [backup-simplify]: Simplify 0 into 0 17.316 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.317 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 17.320 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 17.320 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 17.321 * [backup-simplify]: Simplify (+ 0 0) into 0 17.321 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 17.322 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 17.323 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 17.325 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 17.325 * [taylor]: Taking taylor expansion of 0 in k 17.325 * [backup-simplify]: Simplify 0 into 0 17.325 * [backup-simplify]: Simplify 0 into 0 17.326 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 17.326 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1 2) 17.326 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 17.326 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 17.326 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 17.326 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 17.326 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 17.326 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 17.326 * [taylor]: Taking taylor expansion of 0.5 in k 17.326 * [backup-simplify]: Simplify 0.5 into 0.5 17.326 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 17.327 * [taylor]: Taking taylor expansion of 1.0 in k 17.327 * [backup-simplify]: Simplify 1.0 into 1.0 17.327 * [taylor]: Taking taylor expansion of k in k 17.327 * [backup-simplify]: Simplify 0 into 0 17.327 * [backup-simplify]: Simplify 1 into 1 17.327 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 17.327 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 17.327 * [taylor]: Taking taylor expansion of 2.0 in k 17.327 * [backup-simplify]: Simplify 2.0 into 2.0 17.327 * [taylor]: Taking taylor expansion of (* n PI) in k 17.327 * [taylor]: Taking taylor expansion of n in k 17.327 * [backup-simplify]: Simplify n into n 17.327 * [taylor]: Taking taylor expansion of PI in k 17.327 * [backup-simplify]: Simplify PI into PI 17.327 * [backup-simplify]: Simplify (* n PI) into (* n PI) 17.327 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 17.327 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 17.327 * [backup-simplify]: Simplify (- 0) into 0 17.327 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 17.328 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 17.328 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 17.328 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 17.328 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 17.328 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 17.328 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 17.328 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 17.328 * [taylor]: Taking taylor expansion of 0.5 in n 17.328 * [backup-simplify]: Simplify 0.5 into 0.5 17.328 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 17.328 * [taylor]: Taking taylor expansion of 1.0 in n 17.328 * [backup-simplify]: Simplify 1.0 into 1.0 17.328 * [taylor]: Taking taylor expansion of k in n 17.328 * [backup-simplify]: Simplify k into k 17.328 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 17.328 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 17.328 * [taylor]: Taking taylor expansion of 2.0 in n 17.328 * [backup-simplify]: Simplify 2.0 into 2.0 17.328 * [taylor]: Taking taylor expansion of (* n PI) in n 17.328 * [taylor]: Taking taylor expansion of n in n 17.328 * [backup-simplify]: Simplify 0 into 0 17.328 * [backup-simplify]: Simplify 1 into 1 17.328 * [taylor]: Taking taylor expansion of PI in n 17.328 * [backup-simplify]: Simplify PI into PI 17.329 * [backup-simplify]: Simplify (* 0 PI) into 0 17.329 * [backup-simplify]: Simplify (* 2.0 0) into 0 17.330 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 17.331 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 17.331 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 17.331 * [backup-simplify]: Simplify (- k) into (- k) 17.331 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 17.332 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 17.332 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 17.333 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 17.334 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 17.334 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 17.334 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 17.334 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 17.334 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 17.334 * [taylor]: Taking taylor expansion of 0.5 in n 17.334 * [backup-simplify]: Simplify 0.5 into 0.5 17.334 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 17.334 * [taylor]: Taking taylor expansion of 1.0 in n 17.334 * [backup-simplify]: Simplify 1.0 into 1.0 17.334 * [taylor]: Taking taylor expansion of k in n 17.334 * [backup-simplify]: Simplify k into k 17.334 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 17.334 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 17.334 * [taylor]: Taking taylor expansion of 2.0 in n 17.334 * [backup-simplify]: Simplify 2.0 into 2.0 17.334 * [taylor]: Taking taylor expansion of (* n PI) in n 17.334 * [taylor]: Taking taylor expansion of n in n 17.334 * [backup-simplify]: Simplify 0 into 0 17.334 * [backup-simplify]: Simplify 1 into 1 17.334 * [taylor]: Taking taylor expansion of PI in n 17.334 * [backup-simplify]: Simplify PI into PI 17.334 * [backup-simplify]: Simplify (* 0 PI) into 0 17.335 * [backup-simplify]: Simplify (* 2.0 0) into 0 17.336 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 17.337 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 17.337 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 17.337 * [backup-simplify]: Simplify (- k) into (- k) 17.337 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 17.337 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 17.338 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 17.339 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 17.340 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 17.340 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 17.340 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 17.340 * [taylor]: Taking taylor expansion of 0.5 in k 17.340 * [backup-simplify]: Simplify 0.5 into 0.5 17.340 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 17.340 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 17.340 * [taylor]: Taking taylor expansion of 1.0 in k 17.340 * [backup-simplify]: Simplify 1.0 into 1.0 17.340 * [taylor]: Taking taylor expansion of k in k 17.340 * [backup-simplify]: Simplify 0 into 0 17.340 * [backup-simplify]: Simplify 1 into 1 17.340 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 17.340 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 17.340 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 17.340 * [taylor]: Taking taylor expansion of 2.0 in k 17.340 * [backup-simplify]: Simplify 2.0 into 2.0 17.340 * [taylor]: Taking taylor expansion of PI in k 17.340 * [backup-simplify]: Simplify PI into PI 17.340 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 17.341 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 17.341 * [taylor]: Taking taylor expansion of (log n) in k 17.341 * [taylor]: Taking taylor expansion of n in k 17.341 * [backup-simplify]: Simplify n into n 17.341 * [backup-simplify]: Simplify (log n) into (log n) 17.341 * [backup-simplify]: Simplify (- 0) into 0 17.341 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 17.342 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 17.343 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 17.343 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 17.344 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 17.345 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 17.345 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 17.346 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 17.347 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 17.347 * [backup-simplify]: Simplify (- 0) into 0 17.347 * [backup-simplify]: Simplify (+ 0 0) into 0 17.348 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 17.349 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 17.349 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 17.350 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 17.350 * [taylor]: Taking taylor expansion of 0 in k 17.351 * [backup-simplify]: Simplify 0 into 0 17.351 * [backup-simplify]: Simplify 0 into 0 17.351 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 17.352 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 17.352 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 17.353 * [backup-simplify]: Simplify (+ 0 0) into 0 17.353 * [backup-simplify]: Simplify (- 1) into -1 17.353 * [backup-simplify]: Simplify (+ 0 -1) into -1 17.354 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 17.356 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 17.358 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 17.359 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 17.360 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 17.361 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 17.367 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 17.368 * [backup-simplify]: Simplify (- 0) into 0 17.368 * [backup-simplify]: Simplify (+ 0 0) into 0 17.368 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 17.369 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 17.370 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 17.372 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 17.372 * [taylor]: Taking taylor expansion of 0 in k 17.372 * [backup-simplify]: Simplify 0 into 0 17.373 * [backup-simplify]: Simplify 0 into 0 17.373 * [backup-simplify]: Simplify 0 into 0 17.373 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 17.375 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 17.376 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 17.376 * [backup-simplify]: Simplify (+ 0 0) into 0 17.377 * [backup-simplify]: Simplify (- 0) into 0 17.377 * [backup-simplify]: Simplify (+ 0 0) into 0 17.378 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 17.380 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 17.383 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 17.386 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 17.392 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.25 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2))))) (+ (* 0.125 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* 0.125 (* (pow (log (* 2.0 PI)) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))))))) (+ (* 0.5 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k))) (* 0.5 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k))))) 17.393 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) 17.393 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 17.393 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 17.393 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 17.393 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 17.393 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 17.393 * [taylor]: Taking taylor expansion of 0.5 in k 17.393 * [backup-simplify]: Simplify 0.5 into 0.5 17.393 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 17.393 * [taylor]: Taking taylor expansion of 1.0 in k 17.393 * [backup-simplify]: Simplify 1.0 into 1.0 17.393 * [taylor]: Taking taylor expansion of (/ 1 k) in k 17.393 * [taylor]: Taking taylor expansion of k in k 17.393 * [backup-simplify]: Simplify 0 into 0 17.393 * [backup-simplify]: Simplify 1 into 1 17.393 * [backup-simplify]: Simplify (/ 1 1) into 1 17.393 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 17.393 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 17.393 * [taylor]: Taking taylor expansion of 2.0 in k 17.393 * [backup-simplify]: Simplify 2.0 into 2.0 17.393 * [taylor]: Taking taylor expansion of (/ PI n) in k 17.393 * [taylor]: Taking taylor expansion of PI in k 17.393 * [backup-simplify]: Simplify PI into PI 17.393 * [taylor]: Taking taylor expansion of n in k 17.393 * [backup-simplify]: Simplify n into n 17.393 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 17.393 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 17.394 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 17.394 * [backup-simplify]: Simplify (- 1) into -1 17.394 * [backup-simplify]: Simplify (+ 0 -1) into -1 17.394 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 17.394 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 17.395 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) 17.395 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 17.395 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 17.395 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 17.395 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 17.395 * [taylor]: Taking taylor expansion of 0.5 in n 17.395 * [backup-simplify]: Simplify 0.5 into 0.5 17.395 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 17.395 * [taylor]: Taking taylor expansion of 1.0 in n 17.395 * [backup-simplify]: Simplify 1.0 into 1.0 17.395 * [taylor]: Taking taylor expansion of (/ 1 k) in n 17.395 * [taylor]: Taking taylor expansion of k in n 17.395 * [backup-simplify]: Simplify k into k 17.395 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 17.395 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 17.395 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 17.395 * [taylor]: Taking taylor expansion of 2.0 in n 17.395 * [backup-simplify]: Simplify 2.0 into 2.0 17.395 * [taylor]: Taking taylor expansion of (/ PI n) in n 17.395 * [taylor]: Taking taylor expansion of PI in n 17.395 * [backup-simplify]: Simplify PI into PI 17.395 * [taylor]: Taking taylor expansion of n in n 17.395 * [backup-simplify]: Simplify 0 into 0 17.395 * [backup-simplify]: Simplify 1 into 1 17.395 * [backup-simplify]: Simplify (/ PI 1) into PI 17.396 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 17.396 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 17.396 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 17.396 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 17.396 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 17.397 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 17.398 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) 17.399 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 17.399 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 17.399 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 17.399 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 17.399 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 17.399 * [taylor]: Taking taylor expansion of 0.5 in n 17.399 * [backup-simplify]: Simplify 0.5 into 0.5 17.399 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 17.399 * [taylor]: Taking taylor expansion of 1.0 in n 17.399 * [backup-simplify]: Simplify 1.0 into 1.0 17.399 * [taylor]: Taking taylor expansion of (/ 1 k) in n 17.399 * [taylor]: Taking taylor expansion of k in n 17.399 * [backup-simplify]: Simplify k into k 17.399 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 17.399 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 17.399 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 17.399 * [taylor]: Taking taylor expansion of 2.0 in n 17.399 * [backup-simplify]: Simplify 2.0 into 2.0 17.399 * [taylor]: Taking taylor expansion of (/ PI n) in n 17.399 * [taylor]: Taking taylor expansion of PI in n 17.399 * [backup-simplify]: Simplify PI into PI 17.399 * [taylor]: Taking taylor expansion of n in n 17.399 * [backup-simplify]: Simplify 0 into 0 17.399 * [backup-simplify]: Simplify 1 into 1 17.400 * [backup-simplify]: Simplify (/ PI 1) into PI 17.400 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 17.400 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 17.401 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 17.401 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 17.401 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 17.402 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 17.402 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) 17.403 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 17.403 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) in k 17.403 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) in k 17.403 * [taylor]: Taking taylor expansion of 0.5 in k 17.403 * [backup-simplify]: Simplify 0.5 into 0.5 17.403 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) in k 17.403 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 17.403 * [taylor]: Taking taylor expansion of 1.0 in k 17.403 * [backup-simplify]: Simplify 1.0 into 1.0 17.403 * [taylor]: Taking taylor expansion of (/ 1 k) in k 17.403 * [taylor]: Taking taylor expansion of k in k 17.403 * [backup-simplify]: Simplify 0 into 0 17.403 * [backup-simplify]: Simplify 1 into 1 17.404 * [backup-simplify]: Simplify (/ 1 1) into 1 17.404 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 17.404 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 17.404 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 17.404 * [taylor]: Taking taylor expansion of 2.0 in k 17.404 * [backup-simplify]: Simplify 2.0 into 2.0 17.404 * [taylor]: Taking taylor expansion of PI in k 17.404 * [backup-simplify]: Simplify PI into PI 17.404 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 17.405 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 17.405 * [taylor]: Taking taylor expansion of (log n) in k 17.405 * [taylor]: Taking taylor expansion of n in k 17.405 * [backup-simplify]: Simplify n into n 17.405 * [backup-simplify]: Simplify (log n) into (log n) 17.405 * [backup-simplify]: Simplify (- 1) into -1 17.405 * [backup-simplify]: Simplify (+ 0 -1) into -1 17.405 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 17.406 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 17.407 * [backup-simplify]: Simplify (* -1 (- (log (* 2.0 PI)) (log n))) into (* -1 (- (log (* 2.0 PI)) (log n))) 17.407 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 17.408 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 17.409 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 17.409 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 17.410 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 17.411 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 17.411 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 17.411 * [backup-simplify]: Simplify (- 0) into 0 17.411 * [backup-simplify]: Simplify (+ 0 0) into 0 17.412 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 17.413 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 17.413 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 17.415 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 17.415 * [taylor]: Taking taylor expansion of 0 in k 17.415 * [backup-simplify]: Simplify 0 into 0 17.415 * [backup-simplify]: Simplify 0 into 0 17.415 * [backup-simplify]: Simplify 0 into 0 17.415 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.416 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 17.418 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 17.419 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 17.419 * [backup-simplify]: Simplify (- 0) into 0 17.419 * [backup-simplify]: Simplify (+ 0 0) into 0 17.420 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 17.421 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 17.421 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 17.423 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 17.423 * [taylor]: Taking taylor expansion of 0 in k 17.423 * [backup-simplify]: Simplify 0 into 0 17.423 * [backup-simplify]: Simplify 0 into 0 17.423 * [backup-simplify]: Simplify 0 into 0 17.423 * [backup-simplify]: Simplify 0 into 0 17.424 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.424 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 17.428 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 17.428 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 17.428 * [backup-simplify]: Simplify (- 0) into 0 17.428 * [backup-simplify]: Simplify (+ 0 0) into 0 17.429 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 17.430 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 17.431 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 17.433 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 17.433 * [taylor]: Taking taylor expansion of 0 in k 17.433 * [backup-simplify]: Simplify 0 into 0 17.433 * [backup-simplify]: Simplify 0 into 0 17.434 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) 17.434 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) 17.434 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 17.434 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 17.434 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 17.434 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 17.434 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 17.434 * [taylor]: Taking taylor expansion of 0.5 in k 17.434 * [backup-simplify]: Simplify 0.5 into 0.5 17.434 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 17.434 * [taylor]: Taking taylor expansion of (/ 1 k) in k 17.434 * [taylor]: Taking taylor expansion of k in k 17.434 * [backup-simplify]: Simplify 0 into 0 17.434 * [backup-simplify]: Simplify 1 into 1 17.435 * [backup-simplify]: Simplify (/ 1 1) into 1 17.435 * [taylor]: Taking taylor expansion of 1.0 in k 17.435 * [backup-simplify]: Simplify 1.0 into 1.0 17.435 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 17.435 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 17.435 * [taylor]: Taking taylor expansion of -2.0 in k 17.435 * [backup-simplify]: Simplify -2.0 into -2.0 17.435 * [taylor]: Taking taylor expansion of (/ PI n) in k 17.435 * [taylor]: Taking taylor expansion of PI in k 17.435 * [backup-simplify]: Simplify PI into PI 17.435 * [taylor]: Taking taylor expansion of n in k 17.435 * [backup-simplify]: Simplify n into n 17.435 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 17.435 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 17.435 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 17.435 * [backup-simplify]: Simplify (+ 1 0) into 1 17.436 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 17.436 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 17.436 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) 17.436 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 17.436 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 17.436 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 17.436 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 17.436 * [taylor]: Taking taylor expansion of 0.5 in n 17.436 * [backup-simplify]: Simplify 0.5 into 0.5 17.436 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 17.436 * [taylor]: Taking taylor expansion of (/ 1 k) in n 17.436 * [taylor]: Taking taylor expansion of k in n 17.436 * [backup-simplify]: Simplify k into k 17.436 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 17.436 * [taylor]: Taking taylor expansion of 1.0 in n 17.436 * [backup-simplify]: Simplify 1.0 into 1.0 17.436 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 17.436 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 17.436 * [taylor]: Taking taylor expansion of -2.0 in n 17.436 * [backup-simplify]: Simplify -2.0 into -2.0 17.436 * [taylor]: Taking taylor expansion of (/ PI n) in n 17.436 * [taylor]: Taking taylor expansion of PI in n 17.436 * [backup-simplify]: Simplify PI into PI 17.436 * [taylor]: Taking taylor expansion of n in n 17.436 * [backup-simplify]: Simplify 0 into 0 17.436 * [backup-simplify]: Simplify 1 into 1 17.437 * [backup-simplify]: Simplify (/ PI 1) into PI 17.437 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 17.438 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 17.438 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 17.438 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 17.439 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 17.439 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) 17.440 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 17.440 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 17.440 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 17.440 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 17.440 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 17.440 * [taylor]: Taking taylor expansion of 0.5 in n 17.440 * [backup-simplify]: Simplify 0.5 into 0.5 17.440 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 17.440 * [taylor]: Taking taylor expansion of (/ 1 k) in n 17.440 * [taylor]: Taking taylor expansion of k in n 17.440 * [backup-simplify]: Simplify k into k 17.440 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 17.440 * [taylor]: Taking taylor expansion of 1.0 in n 17.440 * [backup-simplify]: Simplify 1.0 into 1.0 17.440 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 17.440 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 17.440 * [taylor]: Taking taylor expansion of -2.0 in n 17.440 * [backup-simplify]: Simplify -2.0 into -2.0 17.440 * [taylor]: Taking taylor expansion of (/ PI n) in n 17.440 * [taylor]: Taking taylor expansion of PI in n 17.440 * [backup-simplify]: Simplify PI into PI 17.440 * [taylor]: Taking taylor expansion of n in n 17.440 * [backup-simplify]: Simplify 0 into 0 17.440 * [backup-simplify]: Simplify 1 into 1 17.441 * [backup-simplify]: Simplify (/ PI 1) into PI 17.441 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 17.442 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 17.442 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 17.442 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 17.443 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 17.443 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) 17.444 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 17.444 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) in k 17.444 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) in k 17.444 * [taylor]: Taking taylor expansion of 0.5 in k 17.444 * [backup-simplify]: Simplify 0.5 into 0.5 17.444 * [taylor]: Taking taylor expansion of (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) in k 17.444 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 17.444 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 17.444 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 17.444 * [taylor]: Taking taylor expansion of -2.0 in k 17.444 * [backup-simplify]: Simplify -2.0 into -2.0 17.444 * [taylor]: Taking taylor expansion of PI in k 17.444 * [backup-simplify]: Simplify PI into PI 17.445 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 17.445 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 17.445 * [taylor]: Taking taylor expansion of (log n) in k 17.445 * [taylor]: Taking taylor expansion of n in k 17.445 * [backup-simplify]: Simplify n into n 17.445 * [backup-simplify]: Simplify (log n) into (log n) 17.446 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 17.446 * [taylor]: Taking taylor expansion of (/ 1 k) in k 17.446 * [taylor]: Taking taylor expansion of k in k 17.446 * [backup-simplify]: Simplify 0 into 0 17.446 * [backup-simplify]: Simplify 1 into 1 17.446 * [backup-simplify]: Simplify (/ 1 1) into 1 17.446 * [taylor]: Taking taylor expansion of 1.0 in k 17.446 * [backup-simplify]: Simplify 1.0 into 1.0 17.446 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 17.447 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 17.447 * [backup-simplify]: Simplify (+ 1 0) into 1 17.447 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) 1) into (- (log (* -2.0 PI)) (log n)) 17.448 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 17.449 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 17.450 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 17.450 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 17.451 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 17.452 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 17.452 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 17.452 * [backup-simplify]: Simplify (+ 0 0) into 0 17.452 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 17.453 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 17.454 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 17.455 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 17.455 * [taylor]: Taking taylor expansion of 0 in k 17.455 * [backup-simplify]: Simplify 0 into 0 17.455 * [backup-simplify]: Simplify 0 into 0 17.455 * [backup-simplify]: Simplify 0 into 0 17.460 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.461 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 17.463 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 17.463 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 17.463 * [backup-simplify]: Simplify (+ 0 0) into 0 17.464 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 17.465 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 17.466 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 17.468 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 17.468 * [taylor]: Taking taylor expansion of 0 in k 17.468 * [backup-simplify]: Simplify 0 into 0 17.468 * [backup-simplify]: Simplify 0 into 0 17.469 * [backup-simplify]: Simplify 0 into 0 17.469 * [backup-simplify]: Simplify 0 into 0 17.470 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.471 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 17.477 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 17.478 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 17.478 * [backup-simplify]: Simplify (+ 0 0) into 0 17.480 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 17.481 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 17.483 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 17.486 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 17.486 * [taylor]: Taking taylor expansion of 0 in k 17.486 * [backup-simplify]: Simplify 0 into 0 17.486 * [backup-simplify]: Simplify 0 into 0 17.487 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 17.487 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1 2 1) 17.488 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 17.488 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 17.488 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 17.488 * [taylor]: Taking taylor expansion of 2.0 in n 17.488 * [backup-simplify]: Simplify 2.0 into 2.0 17.488 * [taylor]: Taking taylor expansion of (* n PI) in n 17.488 * [taylor]: Taking taylor expansion of n in n 17.488 * [backup-simplify]: Simplify 0 into 0 17.488 * [backup-simplify]: Simplify 1 into 1 17.488 * [taylor]: Taking taylor expansion of PI in n 17.488 * [backup-simplify]: Simplify PI into PI 17.488 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 17.488 * [taylor]: Taking taylor expansion of 2.0 in n 17.488 * [backup-simplify]: Simplify 2.0 into 2.0 17.488 * [taylor]: Taking taylor expansion of (* n PI) in n 17.488 * [taylor]: Taking taylor expansion of n in n 17.488 * [backup-simplify]: Simplify 0 into 0 17.488 * [backup-simplify]: Simplify 1 into 1 17.488 * [taylor]: Taking taylor expansion of PI in n 17.488 * [backup-simplify]: Simplify PI into PI 17.489 * [backup-simplify]: Simplify (* 0 PI) into 0 17.489 * [backup-simplify]: Simplify (* 2.0 0) into 0 17.489 * [backup-simplify]: Simplify 0 into 0 17.490 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 17.491 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 17.492 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 17.492 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 17.493 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 17.493 * [backup-simplify]: Simplify 0 into 0 17.493 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 17.494 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 17.494 * [backup-simplify]: Simplify 0 into 0 17.495 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 17.496 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 17.496 * [backup-simplify]: Simplify 0 into 0 17.496 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 17.497 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 17.497 * [backup-simplify]: Simplify 0 into 0 17.498 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 17.499 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 17.499 * [backup-simplify]: Simplify 0 into 0 17.500 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 17.501 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 17.501 * [backup-simplify]: Simplify 0 into 0 17.502 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 17.502 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 17.502 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 17.502 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 17.502 * [taylor]: Taking taylor expansion of 2.0 in n 17.502 * [backup-simplify]: Simplify 2.0 into 2.0 17.502 * [taylor]: Taking taylor expansion of (/ PI n) in n 17.502 * [taylor]: Taking taylor expansion of PI in n 17.502 * [backup-simplify]: Simplify PI into PI 17.502 * [taylor]: Taking taylor expansion of n in n 17.502 * [backup-simplify]: Simplify 0 into 0 17.502 * [backup-simplify]: Simplify 1 into 1 17.502 * [backup-simplify]: Simplify (/ PI 1) into PI 17.502 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 17.502 * [taylor]: Taking taylor expansion of 2.0 in n 17.503 * [backup-simplify]: Simplify 2.0 into 2.0 17.503 * [taylor]: Taking taylor expansion of (/ PI n) in n 17.503 * [taylor]: Taking taylor expansion of PI in n 17.503 * [backup-simplify]: Simplify PI into PI 17.503 * [taylor]: Taking taylor expansion of n in n 17.503 * [backup-simplify]: Simplify 0 into 0 17.503 * [backup-simplify]: Simplify 1 into 1 17.503 * [backup-simplify]: Simplify (/ PI 1) into PI 17.503 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 17.504 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 17.504 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 17.504 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 17.505 * [backup-simplify]: Simplify 0 into 0 17.505 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.506 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 17.506 * [backup-simplify]: Simplify 0 into 0 17.506 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.507 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 17.507 * [backup-simplify]: Simplify 0 into 0 17.508 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.508 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 17.508 * [backup-simplify]: Simplify 0 into 0 17.509 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.510 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 17.510 * [backup-simplify]: Simplify 0 into 0 17.511 * [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 17.511 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 17.511 * [backup-simplify]: Simplify 0 into 0 17.512 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 17.512 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 17.512 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 17.512 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 17.512 * [taylor]: Taking taylor expansion of -2.0 in n 17.512 * [backup-simplify]: Simplify -2.0 into -2.0 17.512 * [taylor]: Taking taylor expansion of (/ PI n) in n 17.512 * [taylor]: Taking taylor expansion of PI in n 17.512 * [backup-simplify]: Simplify PI into PI 17.512 * [taylor]: Taking taylor expansion of n in n 17.512 * [backup-simplify]: Simplify 0 into 0 17.512 * [backup-simplify]: Simplify 1 into 1 17.513 * [backup-simplify]: Simplify (/ PI 1) into PI 17.513 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 17.513 * [taylor]: Taking taylor expansion of -2.0 in n 17.513 * [backup-simplify]: Simplify -2.0 into -2.0 17.513 * [taylor]: Taking taylor expansion of (/ PI n) in n 17.513 * [taylor]: Taking taylor expansion of PI in n 17.513 * [backup-simplify]: Simplify PI into PI 17.513 * [taylor]: Taking taylor expansion of n in n 17.513 * [backup-simplify]: Simplify 0 into 0 17.513 * [backup-simplify]: Simplify 1 into 1 17.513 * [backup-simplify]: Simplify (/ PI 1) into PI 17.513 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 17.514 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 17.514 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 17.515 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 17.515 * [backup-simplify]: Simplify 0 into 0 17.515 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.516 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 17.516 * [backup-simplify]: Simplify 0 into 0 17.517 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.517 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 17.517 * [backup-simplify]: Simplify 0 into 0 17.518 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.519 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 17.519 * [backup-simplify]: Simplify 0 into 0 17.519 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.520 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 17.520 * [backup-simplify]: Simplify 0 into 0 17.521 * [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 17.522 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 17.522 * [backup-simplify]: Simplify 0 into 0 17.522 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 17.522 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1 2 1) 17.523 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 17.523 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 17.523 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 17.523 * [taylor]: Taking taylor expansion of 2.0 in n 17.523 * [backup-simplify]: Simplify 2.0 into 2.0 17.523 * [taylor]: Taking taylor expansion of (* n PI) in n 17.523 * [taylor]: Taking taylor expansion of n in n 17.523 * [backup-simplify]: Simplify 0 into 0 17.523 * [backup-simplify]: Simplify 1 into 1 17.523 * [taylor]: Taking taylor expansion of PI in n 17.523 * [backup-simplify]: Simplify PI into PI 17.523 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 17.523 * [taylor]: Taking taylor expansion of 2.0 in n 17.523 * [backup-simplify]: Simplify 2.0 into 2.0 17.523 * [taylor]: Taking taylor expansion of (* n PI) in n 17.523 * [taylor]: Taking taylor expansion of n in n 17.523 * [backup-simplify]: Simplify 0 into 0 17.523 * [backup-simplify]: Simplify 1 into 1 17.523 * [taylor]: Taking taylor expansion of PI in n 17.523 * [backup-simplify]: Simplify PI into PI 17.523 * [backup-simplify]: Simplify (* 0 PI) into 0 17.524 * [backup-simplify]: Simplify (* 2.0 0) into 0 17.524 * [backup-simplify]: Simplify 0 into 0 17.525 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 17.525 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 17.526 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 17.526 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 17.527 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 17.527 * [backup-simplify]: Simplify 0 into 0 17.528 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 17.528 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 17.528 * [backup-simplify]: Simplify 0 into 0 17.529 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 17.530 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 17.530 * [backup-simplify]: Simplify 0 into 0 17.531 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 17.532 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 17.532 * [backup-simplify]: Simplify 0 into 0 17.533 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 17.534 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 17.534 * [backup-simplify]: Simplify 0 into 0 17.535 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 17.536 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 17.536 * [backup-simplify]: Simplify 0 into 0 17.536 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 17.536 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 17.536 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 17.536 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 17.537 * [taylor]: Taking taylor expansion of 2.0 in n 17.537 * [backup-simplify]: Simplify 2.0 into 2.0 17.537 * [taylor]: Taking taylor expansion of (/ PI n) in n 17.537 * [taylor]: Taking taylor expansion of PI in n 17.537 * [backup-simplify]: Simplify PI into PI 17.537 * [taylor]: Taking taylor expansion of n in n 17.537 * [backup-simplify]: Simplify 0 into 0 17.537 * [backup-simplify]: Simplify 1 into 1 17.537 * [backup-simplify]: Simplify (/ PI 1) into PI 17.537 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 17.537 * [taylor]: Taking taylor expansion of 2.0 in n 17.537 * [backup-simplify]: Simplify 2.0 into 2.0 17.537 * [taylor]: Taking taylor expansion of (/ PI n) in n 17.537 * [taylor]: Taking taylor expansion of PI in n 17.537 * [backup-simplify]: Simplify PI into PI 17.537 * [taylor]: Taking taylor expansion of n in n 17.537 * [backup-simplify]: Simplify 0 into 0 17.537 * [backup-simplify]: Simplify 1 into 1 17.537 * [backup-simplify]: Simplify (/ PI 1) into PI 17.538 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 17.538 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 17.539 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 17.539 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 17.539 * [backup-simplify]: Simplify 0 into 0 17.540 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.540 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 17.540 * [backup-simplify]: Simplify 0 into 0 17.541 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.542 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 17.542 * [backup-simplify]: Simplify 0 into 0 17.543 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.545 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 17.545 * [backup-simplify]: Simplify 0 into 0 17.546 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.547 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 17.547 * [backup-simplify]: Simplify 0 into 0 17.549 * [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 17.550 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 17.550 * [backup-simplify]: Simplify 0 into 0 17.551 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 17.552 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 17.552 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 17.552 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 17.552 * [taylor]: Taking taylor expansion of -2.0 in n 17.552 * [backup-simplify]: Simplify -2.0 into -2.0 17.552 * [taylor]: Taking taylor expansion of (/ PI n) in n 17.552 * [taylor]: Taking taylor expansion of PI in n 17.552 * [backup-simplify]: Simplify PI into PI 17.552 * [taylor]: Taking taylor expansion of n in n 17.552 * [backup-simplify]: Simplify 0 into 0 17.552 * [backup-simplify]: Simplify 1 into 1 17.552 * [backup-simplify]: Simplify (/ PI 1) into PI 17.552 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 17.553 * [taylor]: Taking taylor expansion of -2.0 in n 17.553 * [backup-simplify]: Simplify -2.0 into -2.0 17.553 * [taylor]: Taking taylor expansion of (/ PI n) in n 17.553 * [taylor]: Taking taylor expansion of PI in n 17.553 * [backup-simplify]: Simplify PI into PI 17.553 * [taylor]: Taking taylor expansion of n in n 17.553 * [backup-simplify]: Simplify 0 into 0 17.553 * [backup-simplify]: Simplify 1 into 1 17.553 * [backup-simplify]: Simplify (/ PI 1) into PI 17.554 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 17.554 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 17.555 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 17.556 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 17.556 * [backup-simplify]: Simplify 0 into 0 17.557 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.558 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 17.558 * [backup-simplify]: Simplify 0 into 0 17.559 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.560 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 17.561 * [backup-simplify]: Simplify 0 into 0 17.562 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.563 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 17.563 * [backup-simplify]: Simplify 0 into 0 17.564 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.572 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 17.572 * [backup-simplify]: Simplify 0 into 0 17.574 * [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 17.576 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 17.576 * [backup-simplify]: Simplify 0 into 0 17.576 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 17.577 * * * [progress]: simplifying candidates 17.580 * [simplify]: Simplifying: (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (- (+ (* 0.25 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2))))) (+ (* 0.125 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* 0.125 (* (pow (log (* 2.0 PI)) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))))))) (+ (* 0.5 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k))) (* 0.5 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k))))) (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* 0.25 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2))))) (+ (* 0.125 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* 0.125 (* (pow (log (* 2.0 PI)) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))))))) (+ (* 0.5 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k))) (* 0.5 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k))))) (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) 17.584 * * [simplify]: iteration 0: 150 enodes 17.644 * * [simplify]: iteration 1: 425 enodes 17.885 * * [simplify]: iteration 2: 1406 enodes 18.506 * * [simplify]: iteration complete: 5001 enodes 18.506 * * [simplify]: Extracting #0: cost 40 inf + 0 18.508 * * [simplify]: Extracting #1: cost 530 inf + 0 18.516 * * [simplify]: Extracting #2: cost 1501 inf + 683 18.529 * * [simplify]: Extracting #3: cost 1620 inf + 41156 18.579 * * [simplify]: Extracting #4: cost 659 inf + 262405 19.028 * * [simplify]: Extracting #5: cost 224 inf + 453670 19.153 * * [simplify]: Extracting #6: cost 101 inf + 517429 19.284 * * [simplify]: Extracting #7: cost 11 inf + 539677 19.471 * * [simplify]: Extracting #8: cost 0 inf + 541908 19.630 * [simplify]: Simplified to: (* (/ (- 1.0 k) 2.0) (log (* n (* PI 2.0)))) (* (/ (- 1.0 k) 2.0) (log (* n (* PI 2.0)))) (* (/ (- 1.0 k) 2.0) (log (* n (* PI 2.0)))) (* (/ (- 1.0 k) 2.0) (log (* n (* PI 2.0)))) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (pow (* n (* PI 2.0)) (/ 1.0 2.0)) (pow (* n (* PI 2.0)) (/ k 2.0)) (pow (* n (* PI 2.0)) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* n (* PI 2.0)) (sqrt (/ (- 1.0 k) 2.0))) (pow (* n (* PI 2.0)) (* (/ (cbrt (- 1.0 k)) (cbrt 2.0)) (/ (cbrt (- 1.0 k)) (cbrt 2.0)))) (pow (* n (* PI 2.0)) (* (/ (cbrt (- 1.0 k)) (sqrt 2.0)) (cbrt (- 1.0 k)))) (pow (* n (* PI 2.0)) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* n (* PI 2.0)) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* n (* PI 2.0)) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* n (* PI 2.0)) (sqrt (- 1.0 k))) (pow (* n (* PI 2.0)) (/ (/ 1 (cbrt 2.0)) (cbrt 2.0))) (pow (* n (* PI 2.0)) (/ 1 (sqrt 2.0))) (* n (* PI 2.0)) (pow (* n (* PI 2.0)) (/ (/ (+ (sqrt 1.0) (sqrt k)) (cbrt 2.0)) (cbrt 2.0))) (pow (* n (* PI 2.0)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* n (* PI 2.0)) (+ (sqrt 1.0) (sqrt k))) (pow (* n (* PI 2.0)) (/ (/ 1 (cbrt 2.0)) (cbrt 2.0))) (pow (* n (* PI 2.0)) (/ 1 (sqrt 2.0))) (* n (* PI 2.0)) (* n (* PI 2.0)) (pow (* n (* PI 2.0)) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (* (/ (- 1.0 k) 2.0) (log (* n (* PI 2.0)))) (exp (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))) (cbrt (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))) (pow (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) 3) (sqrt (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))) (sqrt (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))) (pow (* n (* PI 2.0)) (/ (- 1.0 k) (* 2.0 2))) (pow (* n (* PI 2.0)) (/ (- 1.0 k) (* 2.0 2))) (* (/ (- 1.0 k) 2.0) (log (* n (* PI 2.0)))) (* (/ (- 1.0 k) 2.0) (log (* n (* PI 2.0)))) (* (/ (- 1.0 k) 2.0) (log (* n (* PI 2.0)))) (* (/ (- 1.0 k) 2.0) (log (* n (* PI 2.0)))) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (pow (* n (* PI 2.0)) (/ 1.0 2.0)) (pow (* n (* PI 2.0)) (/ k 2.0)) (pow (* n (* PI 2.0)) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* n (* PI 2.0)) (sqrt (/ (- 1.0 k) 2.0))) (pow (* n (* PI 2.0)) (* (/ (cbrt (- 1.0 k)) (cbrt 2.0)) (/ (cbrt (- 1.0 k)) (cbrt 2.0)))) (pow (* n (* PI 2.0)) (* (/ (cbrt (- 1.0 k)) (sqrt 2.0)) (cbrt (- 1.0 k)))) (pow (* n (* PI 2.0)) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* n (* PI 2.0)) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* n (* PI 2.0)) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* n (* PI 2.0)) (sqrt (- 1.0 k))) (pow (* n (* PI 2.0)) (/ (/ 1 (cbrt 2.0)) (cbrt 2.0))) (pow (* n (* PI 2.0)) (/ 1 (sqrt 2.0))) (* n (* PI 2.0)) (pow (* n (* PI 2.0)) (/ (/ (+ (sqrt 1.0) (sqrt k)) (cbrt 2.0)) (cbrt 2.0))) (pow (* n (* PI 2.0)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* n (* PI 2.0)) (+ (sqrt 1.0) (sqrt k))) (pow (* n (* PI 2.0)) (/ (/ 1 (cbrt 2.0)) (cbrt 2.0))) (pow (* n (* PI 2.0)) (/ 1 (sqrt 2.0))) (* n (* PI 2.0)) (* n (* PI 2.0)) (pow (* n (* PI 2.0)) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (* (/ (- 1.0 k) 2.0) (log (* n (* PI 2.0)))) (exp (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))) (cbrt (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))) (pow (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) 3) (sqrt (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))) (sqrt (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))) (pow (* n (* PI 2.0)) (/ (- 1.0 k) (* 2.0 2))) (pow (* n (* PI 2.0)) (/ (- 1.0 k) (* 2.0 2))) (* n (* PI 2.0)) (* n (* PI 2.0)) (log (* n (* PI 2.0))) (log (* n (* PI 2.0))) (log (* n (* PI 2.0))) (exp (* n (* PI 2.0))) (* (* (* n (* 2.0 PI)) (* n (* 2.0 PI))) (* n (* 2.0 PI))) (* (* (* n (* 2.0 PI)) (* n (* 2.0 PI))) (* n (* 2.0 PI))) (* (cbrt (* n (* PI 2.0))) (cbrt (* n (* PI 2.0)))) (cbrt (* n (* PI 2.0))) (* (* (* n (* 2.0 PI)) (* n (* 2.0 PI))) (* n (* 2.0 PI))) (sqrt (* n (* PI 2.0))) (sqrt (* n (* PI 2.0))) (* (* (* (cbrt n) (cbrt n)) 2.0) PI) (* (* 2.0 PI) (sqrt n)) (* 2.0 PI) (* PI n) (* n (* PI 2.0)) (* n (* PI 2.0)) (log (* n (* PI 2.0))) (log (* n (* PI 2.0))) (log (* n (* PI 2.0))) (exp (* n (* PI 2.0))) (* (* (* n (* 2.0 PI)) (* n (* 2.0 PI))) (* n (* 2.0 PI))) (* (* (* n (* 2.0 PI)) (* n (* 2.0 PI))) (* n (* 2.0 PI))) (* (cbrt (* n (* PI 2.0))) (cbrt (* n (* PI 2.0)))) (cbrt (* n (* PI 2.0))) (* (* (* n (* 2.0 PI)) (* n (* 2.0 PI))) (* n (* 2.0 PI))) (sqrt (* n (* PI 2.0))) (sqrt (* n (* PI 2.0))) (* (* (* (cbrt n) (cbrt n)) 2.0) PI) (* (* 2.0 PI) (sqrt n)) (* 2.0 PI) (* PI n) (+ (* (* (* (* 0.25 (log (* 2.0 PI))) (exp (* 0.5 (log (* n (* PI 2.0)))))) (log n)) (* k k)) (- (+ (* (exp (* 0.5 (log (* n (* PI 2.0))))) (+ (* (* 0.125 (* k (log n))) (* k (log n))) (* 0.125 (* (* (log (* 2.0 PI)) k) (* (log (* 2.0 PI)) k))))) (exp (* 0.5 (log (* n (* PI 2.0)))))) (* (* (* k (exp (* 0.5 (log (* n (* PI 2.0)))))) (log (* n (* PI 2.0)))) 0.5))) (exp (* (- 1.0 k) (* 0.5 (log (* n (* PI 2.0)))))) (exp (* (* (- (log (* -2.0 PI)) (log (/ -1 n))) (- 1.0 k)) 0.5)) (+ (* (* (* (* 0.25 (log (* 2.0 PI))) (exp (* 0.5 (log (* n (* PI 2.0)))))) (log n)) (* k k)) (- (+ (* (exp (* 0.5 (log (* n (* PI 2.0))))) (+ (* (* 0.125 (* k (log n))) (* k (log n))) (* 0.125 (* (* (log (* 2.0 PI)) k) (* (log (* 2.0 PI)) k))))) (exp (* 0.5 (log (* n (* PI 2.0)))))) (* (* (* k (exp (* 0.5 (log (* n (* PI 2.0)))))) (log (* n (* PI 2.0)))) 0.5))) (exp (* (- 1.0 k) (* 0.5 (log (* n (* PI 2.0)))))) (exp (* (* (- (log (* -2.0 PI)) (log (/ -1 n))) (- 1.0 k)) 0.5)) (* n (* PI 2.0)) (* n (* PI 2.0)) (* n (* PI 2.0)) (* n (* PI 2.0)) (* n (* PI 2.0)) (* n (* PI 2.0)) 19.649 * * * [progress]: adding candidates to table 20.549 * [progress]: [Phase 3 of 3] Extracting. 20.549 * * [regime]: Finding splitpoints for: (# # # # # # # #) 20.550 * * * [regime-changes]: Trying 4 branch expressions: ((* (* 2.0 PI) n) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) n k) 20.550 * * * * [regimes]: Trying to branch on (* (* 2.0 PI) n) from (# # # # # # # #) 20.629 * * * * [regimes]: Trying to branch on (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) from (# # # # # # # #) 20.737 * * * * [regimes]: Trying to branch on n from (# # # # # # # #) 20.826 * * * * [regimes]: Trying to branch on k from (# # # # # # # #) 20.895 * * * [regime]: Found split indices: #