53.421 * [progress]: [Phase 1 of 3] Setting up. 0.002 * * * [progress]: [1/2] Preparing points 0.174 * * * [progress]: [2/2] Setting up program. 0.183 * [progress]: [Phase 2 of 3] Improving. 0.183 * [simplify]: Simplifying: (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 0.184 * * [simplify]: iteration 0: 13 enodes 0.189 * * [simplify]: iteration 1: 29 enodes 0.200 * * [simplify]: iteration 2: 58 enodes 0.222 * * [simplify]: iteration 3: 114 enodes 0.272 * * [simplify]: iteration 4: 285 enodes 0.415 * * [simplify]: iteration 5: 806 enodes 1.398 * * [simplify]: iteration 6: 2693 enodes 2.316 * * [simplify]: iteration complete: 5001 enodes 2.316 * * [simplify]: Extracting #0: cost 1 inf + 0 2.317 * * [simplify]: Extracting #1: cost 108 inf + 0 2.320 * * [simplify]: Extracting #2: cost 443 inf + 1 2.325 * * [simplify]: Extracting #3: cost 1003 inf + 8 2.337 * * [simplify]: Extracting #4: cost 1325 inf + 10758 2.357 * * [simplify]: Extracting #5: cost 713 inf + 95758 2.445 * * [simplify]: Extracting #6: cost 212 inf + 355864 2.570 * * [simplify]: Extracting #7: cost 1 inf + 567087 2.730 * * [simplify]: Extracting #8: cost 0 inf + 554854 2.865 * [simplify]: Simplified to: (/ (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)) 2.865 * * [progress]: iteration 1 / 4 2.865 * * * [progress]: picking best candidate 2.870 * * * * [pick]: Picked # 2.870 * * * [progress]: localizing error 2.907 * * * [progress]: generating rewritten candidates 2.907 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 2.940 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1) 2.961 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1) 2.966 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 3.022 * * * [progress]: generating series expansions 3.022 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 3.023 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 3.024 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 3.024 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 3.024 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 3.024 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 3.024 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 3.024 * [taylor]: Taking taylor expansion of 0.5 in k 3.024 * [backup-simplify]: Simplify 0.5 into 0.5 3.024 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 3.024 * [taylor]: Taking taylor expansion of 1.0 in k 3.024 * [backup-simplify]: Simplify 1.0 into 1.0 3.024 * [taylor]: Taking taylor expansion of k in k 3.024 * [backup-simplify]: Simplify 0 into 0 3.024 * [backup-simplify]: Simplify 1 into 1 3.024 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 3.024 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 3.024 * [taylor]: Taking taylor expansion of 2.0 in k 3.024 * [backup-simplify]: Simplify 2.0 into 2.0 3.024 * [taylor]: Taking taylor expansion of (* n PI) in k 3.024 * [taylor]: Taking taylor expansion of n in k 3.024 * [backup-simplify]: Simplify n into n 3.024 * [taylor]: Taking taylor expansion of PI in k 3.024 * [backup-simplify]: Simplify PI into PI 3.024 * [backup-simplify]: Simplify (* n PI) into (* n PI) 3.024 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 3.024 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 3.025 * [backup-simplify]: Simplify (- 0) into 0 3.025 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 3.026 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 3.026 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 3.026 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 3.026 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 3.026 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 3.026 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 3.026 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 3.026 * [taylor]: Taking taylor expansion of 0.5 in n 3.026 * [backup-simplify]: Simplify 0.5 into 0.5 3.026 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 3.026 * [taylor]: Taking taylor expansion of 1.0 in n 3.026 * [backup-simplify]: Simplify 1.0 into 1.0 3.027 * [taylor]: Taking taylor expansion of k in n 3.027 * [backup-simplify]: Simplify k into k 3.027 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.027 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.027 * [taylor]: Taking taylor expansion of 2.0 in n 3.027 * [backup-simplify]: Simplify 2.0 into 2.0 3.027 * [taylor]: Taking taylor expansion of (* n PI) in n 3.027 * [taylor]: Taking taylor expansion of n in n 3.027 * [backup-simplify]: Simplify 0 into 0 3.027 * [backup-simplify]: Simplify 1 into 1 3.027 * [taylor]: Taking taylor expansion of PI in n 3.027 * [backup-simplify]: Simplify PI into PI 3.027 * [backup-simplify]: Simplify (* 0 PI) into 0 3.028 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.030 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.031 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.032 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.032 * [backup-simplify]: Simplify (- k) into (- k) 3.032 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 3.033 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 3.034 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.035 * [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)))) 3.036 * [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))))) 3.037 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 3.037 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 3.037 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 3.037 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 3.037 * [taylor]: Taking taylor expansion of 0.5 in n 3.037 * [backup-simplify]: Simplify 0.5 into 0.5 3.037 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 3.037 * [taylor]: Taking taylor expansion of 1.0 in n 3.037 * [backup-simplify]: Simplify 1.0 into 1.0 3.037 * [taylor]: Taking taylor expansion of k in n 3.037 * [backup-simplify]: Simplify k into k 3.037 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.037 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.037 * [taylor]: Taking taylor expansion of 2.0 in n 3.037 * [backup-simplify]: Simplify 2.0 into 2.0 3.037 * [taylor]: Taking taylor expansion of (* n PI) in n 3.037 * [taylor]: Taking taylor expansion of n in n 3.037 * [backup-simplify]: Simplify 0 into 0 3.037 * [backup-simplify]: Simplify 1 into 1 3.037 * [taylor]: Taking taylor expansion of PI in n 3.037 * [backup-simplify]: Simplify PI into PI 3.038 * [backup-simplify]: Simplify (* 0 PI) into 0 3.038 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.040 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.041 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.042 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.042 * [backup-simplify]: Simplify (- k) into (- k) 3.042 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 3.043 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 3.044 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.045 * [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)))) 3.046 * [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))))) 3.047 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 3.047 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 3.047 * [taylor]: Taking taylor expansion of 0.5 in k 3.047 * [backup-simplify]: Simplify 0.5 into 0.5 3.047 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 3.047 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 3.047 * [taylor]: Taking taylor expansion of 1.0 in k 3.047 * [backup-simplify]: Simplify 1.0 into 1.0 3.047 * [taylor]: Taking taylor expansion of k in k 3.047 * [backup-simplify]: Simplify 0 into 0 3.047 * [backup-simplify]: Simplify 1 into 1 3.047 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 3.047 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 3.047 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 3.047 * [taylor]: Taking taylor expansion of 2.0 in k 3.047 * [backup-simplify]: Simplify 2.0 into 2.0 3.047 * [taylor]: Taking taylor expansion of PI in k 3.047 * [backup-simplify]: Simplify PI into PI 3.048 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.049 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.049 * [taylor]: Taking taylor expansion of (log n) in k 3.049 * [taylor]: Taking taylor expansion of n in k 3.049 * [backup-simplify]: Simplify n into n 3.049 * [backup-simplify]: Simplify (log n) into (log n) 3.049 * [backup-simplify]: Simplify (- 0) into 0 3.050 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 3.051 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 3.052 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 3.053 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 3.054 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 3.056 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 3.057 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 3.058 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 3.059 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 3.060 * [backup-simplify]: Simplify (- 0) into 0 3.060 * [backup-simplify]: Simplify (+ 0 0) into 0 3.061 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 3.062 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.064 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 3.066 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 3.066 * [taylor]: Taking taylor expansion of 0 in k 3.066 * [backup-simplify]: Simplify 0 into 0 3.066 * [backup-simplify]: Simplify 0 into 0 3.067 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 3.068 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 3.069 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 3.070 * [backup-simplify]: Simplify (+ 0 0) into 0 3.070 * [backup-simplify]: Simplify (- 1) into -1 3.070 * [backup-simplify]: Simplify (+ 0 -1) into -1 3.072 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 3.074 * [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)))) 3.078 * [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)))))) 3.081 * [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)))))) 3.082 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 3.083 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 3.087 * [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 3.087 * [backup-simplify]: Simplify (- 0) into 0 3.088 * [backup-simplify]: Simplify (+ 0 0) into 0 3.089 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 3.090 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.097 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 3.099 * [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 3.099 * [taylor]: Taking taylor expansion of 0 in k 3.099 * [backup-simplify]: Simplify 0 into 0 3.099 * [backup-simplify]: Simplify 0 into 0 3.099 * [backup-simplify]: Simplify 0 into 0 3.100 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 3.104 * [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 3.106 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 3.106 * [backup-simplify]: Simplify (+ 0 0) into 0 3.106 * [backup-simplify]: Simplify (- 0) into 0 3.106 * [backup-simplify]: Simplify (+ 0 0) into 0 3.107 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 3.109 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 3.111 * [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)))))) 3.115 * [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)))))) 3.121 * [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))))) 3.121 * [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)))) 3.121 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 3.122 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 3.122 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 3.122 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 3.122 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 3.122 * [taylor]: Taking taylor expansion of 0.5 in k 3.122 * [backup-simplify]: Simplify 0.5 into 0.5 3.122 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 3.122 * [taylor]: Taking taylor expansion of 1.0 in k 3.122 * [backup-simplify]: Simplify 1.0 into 1.0 3.122 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.122 * [taylor]: Taking taylor expansion of k in k 3.122 * [backup-simplify]: Simplify 0 into 0 3.122 * [backup-simplify]: Simplify 1 into 1 3.122 * [backup-simplify]: Simplify (/ 1 1) into 1 3.122 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 3.122 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 3.122 * [taylor]: Taking taylor expansion of 2.0 in k 3.122 * [backup-simplify]: Simplify 2.0 into 2.0 3.122 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.122 * [taylor]: Taking taylor expansion of PI in k 3.122 * [backup-simplify]: Simplify PI into PI 3.122 * [taylor]: Taking taylor expansion of n in k 3.122 * [backup-simplify]: Simplify n into n 3.122 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 3.122 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 3.122 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 3.122 * [backup-simplify]: Simplify (- 1) into -1 3.123 * [backup-simplify]: Simplify (+ 0 -1) into -1 3.123 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 3.123 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 3.123 * [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)))))) 3.123 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 3.123 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 3.123 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 3.123 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 3.123 * [taylor]: Taking taylor expansion of 0.5 in n 3.123 * [backup-simplify]: Simplify 0.5 into 0.5 3.123 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.123 * [taylor]: Taking taylor expansion of 1.0 in n 3.123 * [backup-simplify]: Simplify 1.0 into 1.0 3.123 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.123 * [taylor]: Taking taylor expansion of k in n 3.123 * [backup-simplify]: Simplify k into k 3.124 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.124 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.124 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.124 * [taylor]: Taking taylor expansion of 2.0 in n 3.124 * [backup-simplify]: Simplify 2.0 into 2.0 3.124 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.124 * [taylor]: Taking taylor expansion of PI in n 3.124 * [backup-simplify]: Simplify PI into PI 3.124 * [taylor]: Taking taylor expansion of n in n 3.124 * [backup-simplify]: Simplify 0 into 0 3.124 * [backup-simplify]: Simplify 1 into 1 3.124 * [backup-simplify]: Simplify (/ PI 1) into PI 3.124 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.125 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.125 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 3.125 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 3.125 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 3.126 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.127 * [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)))) 3.128 * [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))))) 3.128 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 3.128 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 3.128 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 3.128 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 3.128 * [taylor]: Taking taylor expansion of 0.5 in n 3.128 * [backup-simplify]: Simplify 0.5 into 0.5 3.128 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.128 * [taylor]: Taking taylor expansion of 1.0 in n 3.128 * [backup-simplify]: Simplify 1.0 into 1.0 3.128 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.128 * [taylor]: Taking taylor expansion of k in n 3.128 * [backup-simplify]: Simplify k into k 3.128 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.128 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.128 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.128 * [taylor]: Taking taylor expansion of 2.0 in n 3.128 * [backup-simplify]: Simplify 2.0 into 2.0 3.128 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.128 * [taylor]: Taking taylor expansion of PI in n 3.128 * [backup-simplify]: Simplify PI into PI 3.128 * [taylor]: Taking taylor expansion of n in n 3.128 * [backup-simplify]: Simplify 0 into 0 3.128 * [backup-simplify]: Simplify 1 into 1 3.128 * [backup-simplify]: Simplify (/ PI 1) into PI 3.129 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.129 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.129 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 3.130 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 3.130 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 3.131 * [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))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) 3.132 * [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))))) 3.132 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) in k 3.132 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) in k 3.132 * [taylor]: Taking taylor expansion of 0.5 in k 3.132 * [backup-simplify]: Simplify 0.5 into 0.5 3.132 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) in k 3.132 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 3.132 * [taylor]: Taking taylor expansion of 1.0 in k 3.132 * [backup-simplify]: Simplify 1.0 into 1.0 3.132 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.132 * [taylor]: Taking taylor expansion of k in k 3.132 * [backup-simplify]: Simplify 0 into 0 3.132 * [backup-simplify]: Simplify 1 into 1 3.133 * [backup-simplify]: Simplify (/ 1 1) into 1 3.133 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 3.133 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 3.133 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 3.133 * [taylor]: Taking taylor expansion of 2.0 in k 3.133 * [backup-simplify]: Simplify 2.0 into 2.0 3.133 * [taylor]: Taking taylor expansion of PI in k 3.133 * [backup-simplify]: Simplify PI into PI 3.133 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.134 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.134 * [taylor]: Taking taylor expansion of (log n) in k 3.134 * [taylor]: Taking taylor expansion of n in k 3.134 * [backup-simplify]: Simplify n into n 3.134 * [backup-simplify]: Simplify (log n) into (log n) 3.134 * [backup-simplify]: Simplify (- 1) into -1 3.134 * [backup-simplify]: Simplify (+ 0 -1) into -1 3.134 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 3.135 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 3.136 * [backup-simplify]: Simplify (* -1 (- (log (* 2.0 PI)) (log n))) into (* -1 (- (log (* 2.0 PI)) (log n))) 3.136 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 3.137 * [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))))) 3.139 * [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))))) 3.140 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 3.140 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 3.142 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 3.142 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 3.143 * [backup-simplify]: Simplify (- 0) into 0 3.143 * [backup-simplify]: Simplify (+ 0 0) into 0 3.144 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 3.145 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.146 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 3.148 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 3.148 * [taylor]: Taking taylor expansion of 0 in k 3.148 * [backup-simplify]: Simplify 0 into 0 3.148 * [backup-simplify]: Simplify 0 into 0 3.149 * [backup-simplify]: Simplify 0 into 0 3.150 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.151 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 3.154 * [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 3.155 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 3.155 * [backup-simplify]: Simplify (- 0) into 0 3.156 * [backup-simplify]: Simplify (+ 0 0) into 0 3.156 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 3.158 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.160 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 3.162 * [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 3.162 * [taylor]: Taking taylor expansion of 0 in k 3.162 * [backup-simplify]: Simplify 0 into 0 3.163 * [backup-simplify]: Simplify 0 into 0 3.163 * [backup-simplify]: Simplify 0 into 0 3.163 * [backup-simplify]: Simplify 0 into 0 3.164 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.165 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 3.169 * [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 3.169 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 3.169 * [backup-simplify]: Simplify (- 0) into 0 3.169 * [backup-simplify]: Simplify (+ 0 0) into 0 3.170 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 3.171 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.172 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 3.174 * [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 3.174 * [taylor]: Taking taylor expansion of 0 in k 3.174 * [backup-simplify]: Simplify 0 into 0 3.174 * [backup-simplify]: Simplify 0 into 0 3.175 * [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)))))) 3.175 * [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))) 3.175 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 3.175 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 3.175 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 3.175 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 3.175 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 3.175 * [taylor]: Taking taylor expansion of 0.5 in k 3.175 * [backup-simplify]: Simplify 0.5 into 0.5 3.175 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 3.175 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.175 * [taylor]: Taking taylor expansion of k in k 3.175 * [backup-simplify]: Simplify 0 into 0 3.175 * [backup-simplify]: Simplify 1 into 1 3.176 * [backup-simplify]: Simplify (/ 1 1) into 1 3.176 * [taylor]: Taking taylor expansion of 1.0 in k 3.176 * [backup-simplify]: Simplify 1.0 into 1.0 3.176 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 3.176 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 3.176 * [taylor]: Taking taylor expansion of -2.0 in k 3.176 * [backup-simplify]: Simplify -2.0 into -2.0 3.176 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.176 * [taylor]: Taking taylor expansion of PI in k 3.176 * [backup-simplify]: Simplify PI into PI 3.176 * [taylor]: Taking taylor expansion of n in k 3.176 * [backup-simplify]: Simplify n into n 3.176 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 3.176 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 3.176 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 3.176 * [backup-simplify]: Simplify (+ 1 0) into 1 3.176 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 3.177 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 3.177 * [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)))) 3.177 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 3.177 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 3.177 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 3.177 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 3.177 * [taylor]: Taking taylor expansion of 0.5 in n 3.177 * [backup-simplify]: Simplify 0.5 into 0.5 3.177 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.177 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.177 * [taylor]: Taking taylor expansion of k in n 3.177 * [backup-simplify]: Simplify k into k 3.177 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.177 * [taylor]: Taking taylor expansion of 1.0 in n 3.177 * [backup-simplify]: Simplify 1.0 into 1.0 3.177 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 3.177 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.177 * [taylor]: Taking taylor expansion of -2.0 in n 3.177 * [backup-simplify]: Simplify -2.0 into -2.0 3.177 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.177 * [taylor]: Taking taylor expansion of PI in n 3.177 * [backup-simplify]: Simplify PI into PI 3.177 * [taylor]: Taking taylor expansion of n in n 3.177 * [backup-simplify]: Simplify 0 into 0 3.177 * [backup-simplify]: Simplify 1 into 1 3.177 * [backup-simplify]: Simplify (/ PI 1) into PI 3.178 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.178 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 3.178 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 3.179 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 3.179 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.180 * [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))) 3.181 * [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)))) 3.181 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 3.181 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 3.181 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 3.181 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 3.181 * [taylor]: Taking taylor expansion of 0.5 in n 3.181 * [backup-simplify]: Simplify 0.5 into 0.5 3.181 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.181 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.181 * [taylor]: Taking taylor expansion of k in n 3.181 * [backup-simplify]: Simplify k into k 3.181 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.181 * [taylor]: Taking taylor expansion of 1.0 in n 3.181 * [backup-simplify]: Simplify 1.0 into 1.0 3.181 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 3.181 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.181 * [taylor]: Taking taylor expansion of -2.0 in n 3.181 * [backup-simplify]: Simplify -2.0 into -2.0 3.181 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.181 * [taylor]: Taking taylor expansion of PI in n 3.181 * [backup-simplify]: Simplify PI into PI 3.181 * [taylor]: Taking taylor expansion of n in n 3.181 * [backup-simplify]: Simplify 0 into 0 3.181 * [backup-simplify]: Simplify 1 into 1 3.182 * [backup-simplify]: Simplify (/ PI 1) into PI 3.182 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.183 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 3.183 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 3.183 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 3.184 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.184 * [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))) 3.185 * [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)))) 3.185 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) in k 3.185 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) in k 3.185 * [taylor]: Taking taylor expansion of 0.5 in k 3.185 * [backup-simplify]: Simplify 0.5 into 0.5 3.185 * [taylor]: Taking taylor expansion of (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) in k 3.185 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 3.185 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 3.185 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 3.185 * [taylor]: Taking taylor expansion of -2.0 in k 3.185 * [backup-simplify]: Simplify -2.0 into -2.0 3.185 * [taylor]: Taking taylor expansion of PI in k 3.185 * [backup-simplify]: Simplify PI into PI 3.186 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.186 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 3.186 * [taylor]: Taking taylor expansion of (log n) in k 3.186 * [taylor]: Taking taylor expansion of n in k 3.187 * [backup-simplify]: Simplify n into n 3.187 * [backup-simplify]: Simplify (log n) into (log n) 3.187 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 3.187 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.187 * [taylor]: Taking taylor expansion of k in k 3.187 * [backup-simplify]: Simplify 0 into 0 3.187 * [backup-simplify]: Simplify 1 into 1 3.187 * [backup-simplify]: Simplify (/ 1 1) into 1 3.187 * [taylor]: Taking taylor expansion of 1.0 in k 3.187 * [backup-simplify]: Simplify 1.0 into 1.0 3.187 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 3.188 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 3.188 * [backup-simplify]: Simplify (+ 1 0) into 1 3.189 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) 1) into (- (log (* -2.0 PI)) (log n)) 3.189 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 3.190 * [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)))) 3.191 * [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)))) 3.191 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 3.192 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 3.193 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 3.193 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 3.193 * [backup-simplify]: Simplify (+ 0 0) into 0 3.194 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 3.194 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.195 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 3.196 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 3.196 * [taylor]: Taking taylor expansion of 0 in k 3.196 * [backup-simplify]: Simplify 0 into 0 3.196 * [backup-simplify]: Simplify 0 into 0 3.196 * [backup-simplify]: Simplify 0 into 0 3.197 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.198 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 3.204 * [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 3.204 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 3.204 * [backup-simplify]: Simplify (+ 0 0) into 0 3.205 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 3.206 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.207 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 3.208 * [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 3.208 * [taylor]: Taking taylor expansion of 0 in k 3.208 * [backup-simplify]: Simplify 0 into 0 3.208 * [backup-simplify]: Simplify 0 into 0 3.208 * [backup-simplify]: Simplify 0 into 0 3.208 * [backup-simplify]: Simplify 0 into 0 3.209 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.210 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 3.217 * [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 3.217 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 3.217 * [backup-simplify]: Simplify (+ 0 0) into 0 3.219 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 3.220 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.222 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 3.225 * [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 3.225 * [taylor]: Taking taylor expansion of 0 in k 3.225 * [backup-simplify]: Simplify 0 into 0 3.225 * [backup-simplify]: Simplify 0 into 0 3.227 * [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)))))) 3.227 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1) 3.227 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 3.227 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 3.227 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.227 * [taylor]: Taking taylor expansion of 2.0 in n 3.228 * [backup-simplify]: Simplify 2.0 into 2.0 3.228 * [taylor]: Taking taylor expansion of (* n PI) in n 3.228 * [taylor]: Taking taylor expansion of n in n 3.228 * [backup-simplify]: Simplify 0 into 0 3.228 * [backup-simplify]: Simplify 1 into 1 3.228 * [taylor]: Taking taylor expansion of PI in n 3.228 * [backup-simplify]: Simplify PI into PI 3.228 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.228 * [taylor]: Taking taylor expansion of 2.0 in n 3.228 * [backup-simplify]: Simplify 2.0 into 2.0 3.228 * [taylor]: Taking taylor expansion of (* n PI) in n 3.228 * [taylor]: Taking taylor expansion of n in n 3.228 * [backup-simplify]: Simplify 0 into 0 3.228 * [backup-simplify]: Simplify 1 into 1 3.228 * [taylor]: Taking taylor expansion of PI in n 3.228 * [backup-simplify]: Simplify PI into PI 3.229 * [backup-simplify]: Simplify (* 0 PI) into 0 3.229 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.229 * [backup-simplify]: Simplify 0 into 0 3.231 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.232 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.233 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.234 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 3.235 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 3.235 * [backup-simplify]: Simplify 0 into 0 3.237 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 3.238 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 3.238 * [backup-simplify]: Simplify 0 into 0 3.239 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 3.241 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 3.241 * [backup-simplify]: Simplify 0 into 0 3.242 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 3.244 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 3.244 * [backup-simplify]: Simplify 0 into 0 3.246 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 3.248 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 3.248 * [backup-simplify]: Simplify 0 into 0 3.250 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 3.252 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 3.252 * [backup-simplify]: Simplify 0 into 0 3.253 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 3.254 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 3.254 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 3.254 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.254 * [taylor]: Taking taylor expansion of 2.0 in n 3.254 * [backup-simplify]: Simplify 2.0 into 2.0 3.254 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.254 * [taylor]: Taking taylor expansion of PI in n 3.254 * [backup-simplify]: Simplify PI into PI 3.254 * [taylor]: Taking taylor expansion of n in n 3.254 * [backup-simplify]: Simplify 0 into 0 3.254 * [backup-simplify]: Simplify 1 into 1 3.254 * [backup-simplify]: Simplify (/ PI 1) into PI 3.254 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.254 * [taylor]: Taking taylor expansion of 2.0 in n 3.254 * [backup-simplify]: Simplify 2.0 into 2.0 3.254 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.255 * [taylor]: Taking taylor expansion of PI in n 3.255 * [backup-simplify]: Simplify PI into PI 3.255 * [taylor]: Taking taylor expansion of n in n 3.255 * [backup-simplify]: Simplify 0 into 0 3.255 * [backup-simplify]: Simplify 1 into 1 3.255 * [backup-simplify]: Simplify (/ PI 1) into PI 3.256 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.256 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.257 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 3.258 * [backup-simplify]: Simplify (+ (* 2.0 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)))) into 0 3.260 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 3.260 * [backup-simplify]: Simplify 0 into 0 3.261 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.263 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 3.263 * [backup-simplify]: Simplify 0 into 0 3.264 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.265 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 3.265 * [backup-simplify]: Simplify 0 into 0 3.267 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.268 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 3.268 * [backup-simplify]: Simplify 0 into 0 3.269 * [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 3.271 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 3.271 * [backup-simplify]: Simplify 0 into 0 3.272 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 3.273 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 3.273 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 3.273 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.273 * [taylor]: Taking taylor expansion of -2.0 in n 3.273 * [backup-simplify]: Simplify -2.0 into -2.0 3.273 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.273 * [taylor]: Taking taylor expansion of PI in n 3.273 * [backup-simplify]: Simplify PI into PI 3.273 * [taylor]: Taking taylor expansion of n in n 3.273 * [backup-simplify]: Simplify 0 into 0 3.273 * [backup-simplify]: Simplify 1 into 1 3.273 * [backup-simplify]: Simplify (/ PI 1) into PI 3.273 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.273 * [taylor]: Taking taylor expansion of -2.0 in n 3.273 * [backup-simplify]: Simplify -2.0 into -2.0 3.274 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.274 * [taylor]: Taking taylor expansion of PI in n 3.274 * [backup-simplify]: Simplify PI into PI 3.274 * [taylor]: Taking taylor expansion of n in n 3.274 * [backup-simplify]: Simplify 0 into 0 3.274 * [backup-simplify]: Simplify 1 into 1 3.274 * [backup-simplify]: Simplify (/ PI 1) into PI 3.275 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.275 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.276 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 3.277 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 3.277 * [backup-simplify]: Simplify 0 into 0 3.278 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.279 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 3.279 * [backup-simplify]: Simplify 0 into 0 3.280 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.282 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 3.282 * [backup-simplify]: Simplify 0 into 0 3.283 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.284 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 3.284 * [backup-simplify]: Simplify 0 into 0 3.285 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.287 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 3.287 * [backup-simplify]: Simplify 0 into 0 3.288 * [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 3.290 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 3.290 * [backup-simplify]: Simplify 0 into 0 3.291 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 3.291 * * * * [progress]: [ 3 / 4 ] generating series at (2 1) 3.291 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 3.291 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 3.291 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 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 (/ 1 k)) in k 3.292 * [taylor]: Taking taylor expansion of (/ 1 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 (/ 1 1) into 1 3.293 * [backup-simplify]: Simplify (sqrt 0) into 0 3.294 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.294 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 3.294 * [taylor]: Taking taylor expansion of 1.0 in k 3.294 * [backup-simplify]: Simplify 1.0 into 1.0 3.294 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 3.294 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.294 * [taylor]: Taking taylor expansion of k in k 3.294 * [backup-simplify]: Simplify 0 into 0 3.294 * [backup-simplify]: Simplify 1 into 1 3.295 * [backup-simplify]: Simplify (/ 1 1) into 1 3.295 * [backup-simplify]: Simplify (sqrt 0) into 0 3.296 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.297 * [backup-simplify]: Simplify (* 1.0 0) into 0 3.297 * [backup-simplify]: Simplify 0 into 0 3.298 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 3.299 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.300 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 3.302 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 3.304 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 3.305 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.305 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.309 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 3.312 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 3.312 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.313 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) 3.314 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 3.314 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 3.314 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 3.314 * [taylor]: Taking taylor expansion of 1.0 in k 3.314 * [backup-simplify]: Simplify 1.0 into 1.0 3.314 * [taylor]: Taking taylor expansion of (sqrt k) in k 3.314 * [taylor]: Taking taylor expansion of k in k 3.314 * [backup-simplify]: Simplify 0 into 0 3.314 * [backup-simplify]: Simplify 1 into 1 3.314 * [backup-simplify]: Simplify (sqrt 0) into 0 3.315 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.315 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 3.315 * [taylor]: Taking taylor expansion of 1.0 in k 3.315 * [backup-simplify]: Simplify 1.0 into 1.0 3.315 * [taylor]: Taking taylor expansion of (sqrt k) in k 3.315 * [taylor]: Taking taylor expansion of k in k 3.316 * [backup-simplify]: Simplify 0 into 0 3.316 * [backup-simplify]: Simplify 1 into 1 3.316 * [backup-simplify]: Simplify (sqrt 0) into 0 3.317 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.317 * [backup-simplify]: Simplify (* 1.0 0) into 0 3.317 * [backup-simplify]: Simplify 0 into 0 3.318 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 3.319 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.320 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 3.322 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 3.322 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.324 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 3.326 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 3.326 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.327 * [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)))))))) 3.327 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 3.327 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 3.327 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 3.327 * [taylor]: Taking taylor expansion of 1.0 in k 3.327 * [backup-simplify]: Simplify 1.0 into 1.0 3.327 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 3.327 * [taylor]: Taking taylor expansion of (/ -1 k) in k 3.327 * [taylor]: Taking taylor expansion of -1 in k 3.327 * [backup-simplify]: Simplify -1 into -1 3.327 * [taylor]: Taking taylor expansion of k in k 3.327 * [backup-simplify]: Simplify 0 into 0 3.327 * [backup-simplify]: Simplify 1 into 1 3.327 * [backup-simplify]: Simplify (/ -1 1) into -1 3.328 * [backup-simplify]: Simplify (sqrt 0) into 0 3.328 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 3.329 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 3.329 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 3.329 * [taylor]: Taking taylor expansion of 1.0 in k 3.329 * [backup-simplify]: Simplify 1.0 into 1.0 3.329 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 3.329 * [taylor]: Taking taylor expansion of (/ -1 k) in k 3.329 * [taylor]: Taking taylor expansion of -1 in k 3.329 * [backup-simplify]: Simplify -1 into -1 3.329 * [taylor]: Taking taylor expansion of k in k 3.329 * [backup-simplify]: Simplify 0 into 0 3.329 * [backup-simplify]: Simplify 1 into 1 3.329 * [backup-simplify]: Simplify (/ -1 1) into -1 3.329 * [backup-simplify]: Simplify (sqrt 0) into 0 3.330 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 3.330 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 3.330 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.331 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 3.333 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 3.340 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 3.340 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.341 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.344 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 3.346 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 3.346 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.347 * [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))))) 3.347 * * * * [progress]: [ 4 / 4 ] generating series at (2) 3.348 * [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)))) 3.348 * [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 3.348 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in n 3.348 * [taylor]: Taking taylor expansion of 1.0 in n 3.348 * [backup-simplify]: Simplify 1.0 into 1.0 3.348 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in n 3.348 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 3.348 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 3.348 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 3.348 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 3.348 * [taylor]: Taking taylor expansion of 0.5 in n 3.348 * [backup-simplify]: Simplify 0.5 into 0.5 3.348 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 3.348 * [taylor]: Taking taylor expansion of 1.0 in n 3.348 * [backup-simplify]: Simplify 1.0 into 1.0 3.348 * [taylor]: Taking taylor expansion of k in n 3.348 * [backup-simplify]: Simplify k into k 3.348 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.348 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.348 * [taylor]: Taking taylor expansion of 2.0 in n 3.348 * [backup-simplify]: Simplify 2.0 into 2.0 3.348 * [taylor]: Taking taylor expansion of (* n PI) in n 3.348 * [taylor]: Taking taylor expansion of n in n 3.348 * [backup-simplify]: Simplify 0 into 0 3.348 * [backup-simplify]: Simplify 1 into 1 3.348 * [taylor]: Taking taylor expansion of PI in n 3.348 * [backup-simplify]: Simplify PI into PI 3.348 * [backup-simplify]: Simplify (* 0 PI) into 0 3.349 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.350 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.351 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.352 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.352 * [backup-simplify]: Simplify (- k) into (- k) 3.352 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 3.353 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 3.354 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.355 * [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)))) 3.356 * [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))))) 3.356 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 3.356 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.356 * [taylor]: Taking taylor expansion of k in n 3.356 * [backup-simplify]: Simplify k into k 3.356 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.356 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 3.357 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 3.357 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 3.357 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in k 3.357 * [taylor]: Taking taylor expansion of 1.0 in k 3.357 * [backup-simplify]: Simplify 1.0 into 1.0 3.357 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in k 3.357 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 3.357 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 3.357 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 3.357 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 3.357 * [taylor]: Taking taylor expansion of 0.5 in k 3.357 * [backup-simplify]: Simplify 0.5 into 0.5 3.357 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 3.357 * [taylor]: Taking taylor expansion of 1.0 in k 3.357 * [backup-simplify]: Simplify 1.0 into 1.0 3.357 * [taylor]: Taking taylor expansion of k in k 3.357 * [backup-simplify]: Simplify 0 into 0 3.357 * [backup-simplify]: Simplify 1 into 1 3.357 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 3.357 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 3.357 * [taylor]: Taking taylor expansion of 2.0 in k 3.357 * [backup-simplify]: Simplify 2.0 into 2.0 3.357 * [taylor]: Taking taylor expansion of (* n PI) in k 3.357 * [taylor]: Taking taylor expansion of n in k 3.357 * [backup-simplify]: Simplify n into n 3.357 * [taylor]: Taking taylor expansion of PI in k 3.357 * [backup-simplify]: Simplify PI into PI 3.357 * [backup-simplify]: Simplify (* n PI) into (* n PI) 3.357 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 3.358 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 3.358 * [backup-simplify]: Simplify (- 0) into 0 3.358 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 3.359 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 3.359 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 3.359 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 3.359 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 3.359 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.359 * [taylor]: Taking taylor expansion of k in k 3.359 * [backup-simplify]: Simplify 0 into 0 3.359 * [backup-simplify]: Simplify 1 into 1 3.360 * [backup-simplify]: Simplify (/ 1 1) into 1 3.360 * [backup-simplify]: Simplify (sqrt 0) into 0 3.361 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.361 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in k 3.361 * [taylor]: Taking taylor expansion of 1.0 in k 3.361 * [backup-simplify]: Simplify 1.0 into 1.0 3.361 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in k 3.361 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 3.361 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 3.361 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 3.361 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 3.361 * [taylor]: Taking taylor expansion of 0.5 in k 3.362 * [backup-simplify]: Simplify 0.5 into 0.5 3.362 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 3.362 * [taylor]: Taking taylor expansion of 1.0 in k 3.362 * [backup-simplify]: Simplify 1.0 into 1.0 3.362 * [taylor]: Taking taylor expansion of k in k 3.362 * [backup-simplify]: Simplify 0 into 0 3.362 * [backup-simplify]: Simplify 1 into 1 3.362 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 3.362 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 3.362 * [taylor]: Taking taylor expansion of 2.0 in k 3.362 * [backup-simplify]: Simplify 2.0 into 2.0 3.362 * [taylor]: Taking taylor expansion of (* n PI) in k 3.362 * [taylor]: Taking taylor expansion of n in k 3.362 * [backup-simplify]: Simplify n into n 3.362 * [taylor]: Taking taylor expansion of PI in k 3.362 * [backup-simplify]: Simplify PI into PI 3.362 * [backup-simplify]: Simplify (* n PI) into (* n PI) 3.362 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 3.362 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 3.362 * [backup-simplify]: Simplify (- 0) into 0 3.363 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 3.363 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 3.363 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 3.364 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 3.364 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 3.364 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.364 * [taylor]: Taking taylor expansion of k in k 3.364 * [backup-simplify]: Simplify 0 into 0 3.364 * [backup-simplify]: Simplify 1 into 1 3.364 * [backup-simplify]: Simplify (/ 1 1) into 1 3.364 * [backup-simplify]: Simplify (sqrt 0) into 0 3.366 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.366 * [backup-simplify]: Simplify (* (pow (* 2.0 (* n PI)) 0.5) 0) into 0 3.367 * [backup-simplify]: Simplify (* 1.0 0) into 0 3.367 * [taylor]: Taking taylor expansion of 0 in n 3.367 * [backup-simplify]: Simplify 0 into 0 3.367 * [backup-simplify]: Simplify 0 into 0 3.367 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 3.368 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* n PI))) into 0 3.369 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 1) into 0 3.369 * [backup-simplify]: Simplify (- 1) into -1 3.369 * [backup-simplify]: Simplify (+ 0 -1) into -1 3.371 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5) 3.372 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 (* n PI))))) into (- (* 0.5 (log (* 2.0 (* n PI))))) 3.372 * [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))))) 3.374 * [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))) 3.376 * [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))) 3.376 * [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 3.376 * [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 3.376 * [taylor]: Taking taylor expansion of +nan.0 in n 3.376 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.376 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 3.376 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 3.376 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 3.376 * [taylor]: Taking taylor expansion of 0.5 in n 3.376 * [backup-simplify]: Simplify 0.5 into 0.5 3.376 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 3.376 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 3.376 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 3.376 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 3.376 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 3.376 * [taylor]: Taking taylor expansion of 1.0 in n 3.376 * [backup-simplify]: Simplify 1.0 into 1.0 3.376 * [taylor]: Taking taylor expansion of (log PI) in n 3.376 * [taylor]: Taking taylor expansion of PI in n 3.376 * [backup-simplify]: Simplify PI into PI 3.377 * [backup-simplify]: Simplify (log PI) into (log PI) 3.378 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 3.379 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 3.379 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 3.379 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 3.379 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 3.379 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 3.379 * [taylor]: Taking taylor expansion of 1.0 in n 3.380 * [backup-simplify]: Simplify 1.0 into 1.0 3.380 * [taylor]: Taking taylor expansion of (log n) in n 3.380 * [taylor]: Taking taylor expansion of n in n 3.380 * [backup-simplify]: Simplify 0 into 0 3.380 * [backup-simplify]: Simplify 1 into 1 3.380 * [backup-simplify]: Simplify (log 1) into 0 3.380 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 3.380 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 3.381 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 3.381 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 3.381 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 3.381 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 3.381 * [taylor]: Taking taylor expansion of 1.0 in n 3.381 * [backup-simplify]: Simplify 1.0 into 1.0 3.381 * [taylor]: Taking taylor expansion of (log 2.0) in n 3.381 * [taylor]: Taking taylor expansion of 2.0 in n 3.381 * [backup-simplify]: Simplify 2.0 into 2.0 3.381 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 3.382 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 3.384 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 3.384 * [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) 3.386 * [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) 3.387 * [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)) 3.388 * [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))) 3.389 * [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) 3.391 * [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)) 3.392 * [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))) 3.394 * [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))) 3.394 * [backup-simplify]: Simplify 0 into 0 3.395 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 3.398 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 3.398 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 3.399 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 3.401 * [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 3.402 * [backup-simplify]: Simplify (- 0) into 0 3.402 * [backup-simplify]: Simplify (+ 0 0) into 0 3.403 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0 3.404 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 (* n PI)))))) into 0 3.405 * [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))) 3.409 * [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))))) 3.414 * [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))))) 3.414 * [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 3.414 * [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 3.414 * [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 3.414 * [taylor]: Taking taylor expansion of +nan.0 in n 3.414 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.414 * [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 3.414 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 3.414 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 3.414 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 3.414 * [taylor]: Taking taylor expansion of 0.5 in n 3.414 * [backup-simplify]: Simplify 0.5 into 0.5 3.414 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 3.414 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 3.414 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 3.414 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 3.414 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 3.414 * [taylor]: Taking taylor expansion of 1.0 in n 3.414 * [backup-simplify]: Simplify 1.0 into 1.0 3.415 * [taylor]: Taking taylor expansion of (log PI) in n 3.415 * [taylor]: Taking taylor expansion of PI in n 3.415 * [backup-simplify]: Simplify PI into PI 3.415 * [backup-simplify]: Simplify (log PI) into (log PI) 3.416 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 3.418 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 3.418 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 3.418 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 3.418 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 3.418 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 3.418 * [taylor]: Taking taylor expansion of 1.0 in n 3.418 * [backup-simplify]: Simplify 1.0 into 1.0 3.418 * [taylor]: Taking taylor expansion of (log n) in n 3.418 * [taylor]: Taking taylor expansion of n in n 3.418 * [backup-simplify]: Simplify 0 into 0 3.418 * [backup-simplify]: Simplify 1 into 1 3.418 * [backup-simplify]: Simplify (log 1) into 0 3.419 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 3.419 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 3.419 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 3.419 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 3.419 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 3.419 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 3.419 * [taylor]: Taking taylor expansion of 1.0 in n 3.419 * [backup-simplify]: Simplify 1.0 into 1.0 3.419 * [taylor]: Taking taylor expansion of (log 2.0) in n 3.419 * [taylor]: Taking taylor expansion of 2.0 in n 3.419 * [backup-simplify]: Simplify 2.0 into 2.0 3.419 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 3.420 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 3.422 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 3.422 * [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) 3.424 * [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) 3.425 * [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)) 3.426 * [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))) 3.428 * [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) 3.428 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.428 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.428 * [taylor]: Taking taylor expansion of 2.0 in n 3.428 * [backup-simplify]: Simplify 2.0 into 2.0 3.428 * [taylor]: Taking taylor expansion of (* n PI) in n 3.428 * [taylor]: Taking taylor expansion of n in n 3.428 * [backup-simplify]: Simplify 0 into 0 3.428 * [backup-simplify]: Simplify 1 into 1 3.428 * [taylor]: Taking taylor expansion of PI in n 3.428 * [backup-simplify]: Simplify PI into PI 3.428 * [backup-simplify]: Simplify (* 0 PI) into 0 3.429 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.430 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.432 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.433 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.433 * [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 3.433 * [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 3.433 * [taylor]: Taking taylor expansion of +nan.0 in n 3.433 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.433 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 3.433 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 3.433 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 3.433 * [taylor]: Taking taylor expansion of 0.5 in n 3.433 * [backup-simplify]: Simplify 0.5 into 0.5 3.433 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 3.433 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 3.433 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 3.433 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 3.433 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) 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 PI) in n 3.433 * [taylor]: Taking taylor expansion of PI in n 3.434 * [backup-simplify]: Simplify PI into PI 3.434 * [backup-simplify]: Simplify (log PI) into (log PI) 3.435 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 3.436 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 3.437 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 3.437 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 3.437 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 3.437 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 3.437 * [taylor]: Taking taylor expansion of 1.0 in n 3.437 * [backup-simplify]: Simplify 1.0 into 1.0 3.437 * [taylor]: Taking taylor expansion of (log n) in n 3.437 * [taylor]: Taking taylor expansion of n in n 3.437 * [backup-simplify]: Simplify 0 into 0 3.437 * [backup-simplify]: Simplify 1 into 1 3.437 * [backup-simplify]: Simplify (log 1) into 0 3.438 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 3.438 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 3.438 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 3.438 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 3.438 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 3.438 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 3.438 * [taylor]: Taking taylor expansion of 1.0 in n 3.438 * [backup-simplify]: Simplify 1.0 into 1.0 3.438 * [taylor]: Taking taylor expansion of (log 2.0) in n 3.438 * [taylor]: Taking taylor expansion of 2.0 in n 3.438 * [backup-simplify]: Simplify 2.0 into 2.0 3.439 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 3.439 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 3.441 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 3.442 * [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) 3.443 * [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) 3.445 * [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)) 3.446 * [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))) 3.448 * [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) 3.449 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.452 * [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))) 3.455 * [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)))) 3.456 * [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)) 3.458 * [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))) 3.462 * [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))))))) 3.468 * [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))))))))) 3.474 * [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))))))) 3.476 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0 3.477 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log 2.0))) into 0 3.478 * [backup-simplify]: Simplify (* (exp (* 1.0 (log 2.0))) (+ (* (/ (pow 0 1) 1)))) into 0 3.480 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 3.480 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 3.481 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log n))) into 0 3.487 * [backup-simplify]: Simplify (* (exp (* 1.0 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 3.488 * [backup-simplify]: Simplify (+ (* (pow n 1.0) 0) (* 0 (pow 2.0 1.0))) into 0 3.490 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 3.491 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log PI))) into 0 3.493 * [backup-simplify]: Simplify (* (exp (* 1.0 (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 3.494 * [backup-simplify]: Simplify (+ (* (pow PI 1.0) 0) (* 0 (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0))) into 0 3.497 * [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 3.498 * [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 3.501 * [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 3.503 * [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 3.503 * [backup-simplify]: Simplify (- 0) into 0 3.503 * [backup-simplify]: Simplify 0 into 0 3.503 * [backup-simplify]: Simplify 0 into 0 3.504 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.508 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 3.509 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 3.510 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 3.512 * [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 3.512 * [backup-simplify]: Simplify (- 0) into 0 3.512 * [backup-simplify]: Simplify (+ 0 0) into 0 3.513 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1.0)))) into 0 3.514 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (+ (* 0 0) (* 0 (log (* 2.0 (* n PI))))))) into 0 3.515 * [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))) 3.518 * [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)))))))) 3.525 * [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)))))))) 3.525 * [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 3.525 * [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 3.525 * [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 3.525 * [taylor]: Taking taylor expansion of +nan.0 in n 3.525 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.525 * [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 3.525 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 3.525 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 3.525 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 3.525 * [taylor]: Taking taylor expansion of 0.5 in n 3.525 * [backup-simplify]: Simplify 0.5 into 0.5 3.525 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 3.525 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 3.525 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 3.525 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 3.525 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 3.525 * [taylor]: Taking taylor expansion of 1.0 in n 3.525 * [backup-simplify]: Simplify 1.0 into 1.0 3.525 * [taylor]: Taking taylor expansion of (log PI) in n 3.525 * [taylor]: Taking taylor expansion of PI in n 3.525 * [backup-simplify]: Simplify PI into PI 3.525 * [backup-simplify]: Simplify (log PI) into (log PI) 3.526 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 3.527 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 3.527 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 3.527 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 3.527 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 3.527 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 3.527 * [taylor]: Taking taylor expansion of 1.0 in n 3.527 * [backup-simplify]: Simplify 1.0 into 1.0 3.527 * [taylor]: Taking taylor expansion of (log n) in n 3.527 * [taylor]: Taking taylor expansion of n in n 3.527 * [backup-simplify]: Simplify 0 into 0 3.527 * [backup-simplify]: Simplify 1 into 1 3.527 * [backup-simplify]: Simplify (log 1) into 0 3.528 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 3.528 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 3.528 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 3.528 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 3.528 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 3.528 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 3.528 * [taylor]: Taking taylor expansion of 1.0 in n 3.528 * [backup-simplify]: Simplify 1.0 into 1.0 3.528 * [taylor]: Taking taylor expansion of (log 2.0) in n 3.528 * [taylor]: Taking taylor expansion of 2.0 in n 3.528 * [backup-simplify]: Simplify 2.0 into 2.0 3.528 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 3.529 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 3.529 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 3.530 * [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) 3.531 * [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) 3.532 * [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)) 3.532 * [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))) 3.534 * [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) 3.534 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.534 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.534 * [taylor]: Taking taylor expansion of 2.0 in n 3.534 * [backup-simplify]: Simplify 2.0 into 2.0 3.534 * [taylor]: Taking taylor expansion of (* n PI) in n 3.534 * [taylor]: Taking taylor expansion of n in n 3.534 * [backup-simplify]: Simplify 0 into 0 3.534 * [backup-simplify]: Simplify 1 into 1 3.534 * [taylor]: Taking taylor expansion of PI in n 3.534 * [backup-simplify]: Simplify PI into PI 3.534 * [backup-simplify]: Simplify (* 0 PI) into 0 3.535 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.536 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.537 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.537 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.537 * [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 3.537 * [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 3.537 * [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 3.537 * [taylor]: Taking taylor expansion of +nan.0 in n 3.537 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.537 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n 3.537 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n 3.537 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n 3.537 * [taylor]: Taking taylor expansion of 0.5 in n 3.537 * [backup-simplify]: Simplify 0.5 into 0.5 3.537 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n 3.537 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n 3.537 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 3.537 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 3.537 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 3.538 * [taylor]: Taking taylor expansion of 1.0 in n 3.538 * [backup-simplify]: Simplify 1.0 into 1.0 3.538 * [taylor]: Taking taylor expansion of (log 2.0) in n 3.538 * [taylor]: Taking taylor expansion of 2.0 in n 3.538 * [backup-simplify]: Simplify 2.0 into 2.0 3.538 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 3.538 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 3.539 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 3.539 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n 3.539 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 3.539 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 3.539 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) 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 n) in n 3.539 * [taylor]: Taking taylor expansion of n in n 3.539 * [backup-simplify]: Simplify 0 into 0 3.539 * [backup-simplify]: Simplify 1 into 1 3.540 * [backup-simplify]: Simplify (log 1) into 0 3.540 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 3.540 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 3.540 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 3.540 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 3.540 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 3.540 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 3.540 * [taylor]: Taking taylor expansion of 1.0 in n 3.540 * [backup-simplify]: Simplify 1.0 into 1.0 3.540 * [taylor]: Taking taylor expansion of (log PI) in n 3.540 * [taylor]: Taking taylor expansion of PI in n 3.540 * [backup-simplify]: Simplify PI into PI 3.540 * [backup-simplify]: Simplify (log PI) into (log PI) 3.541 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 3.543 * [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) 3.545 * [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) 3.546 * [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))) 3.549 * [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) 3.549 * [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 3.549 * [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 3.549 * [taylor]: Taking taylor expansion of +nan.0 in n 3.549 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.549 * [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 3.549 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 3.549 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 3.549 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 3.549 * [taylor]: Taking taylor expansion of 0.5 in n 3.549 * [backup-simplify]: Simplify 0.5 into 0.5 3.549 * [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) 3.553 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 3.553 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 3.553 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 3.553 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 3.553 * [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 3.554 * [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) 3.557 * [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) 3.558 * [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))) 3.562 * [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) 3.562 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n 3.562 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.562 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.562 * [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 3.563 * [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)) 3.570 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.572 * [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))) 3.573 * [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)))) 3.575 * [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)) 3.576 * [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)) 3.578 * [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))) 3.583 * [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)))))))))) 3.610 * [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))))))))))))) 3.620 * [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))))))))))))) 3.629 * [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))))))))))))))) 3.644 * [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))))))))))))))))))))))) 3.645 * [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))) 3.645 * [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 3.645 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in n 3.645 * [taylor]: Taking taylor expansion of 1.0 in n 3.645 * [backup-simplify]: Simplify 1.0 into 1.0 3.645 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in n 3.645 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 3.645 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 3.645 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 3.645 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 3.645 * [taylor]: Taking taylor expansion of 0.5 in n 3.645 * [backup-simplify]: Simplify 0.5 into 0.5 3.645 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.645 * [taylor]: Taking taylor expansion of 1.0 in n 3.645 * [backup-simplify]: Simplify 1.0 into 1.0 3.645 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.645 * [taylor]: Taking taylor expansion of k in n 3.645 * [backup-simplify]: Simplify k into k 3.646 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.646 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.646 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.646 * [taylor]: Taking taylor expansion of 2.0 in n 3.646 * [backup-simplify]: Simplify 2.0 into 2.0 3.646 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.646 * [taylor]: Taking taylor expansion of PI in n 3.646 * [backup-simplify]: Simplify PI into PI 3.646 * [taylor]: Taking taylor expansion of n in n 3.646 * [backup-simplify]: Simplify 0 into 0 3.646 * [backup-simplify]: Simplify 1 into 1 3.646 * [backup-simplify]: Simplify (/ PI 1) into PI 3.646 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.647 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.647 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 3.647 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 3.647 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 3.648 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.649 * [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)))) 3.649 * [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))))) 3.649 * [taylor]: Taking taylor expansion of (sqrt k) in n 3.649 * [taylor]: Taking taylor expansion of k in n 3.650 * [backup-simplify]: Simplify k into k 3.650 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 3.650 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 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)))))) 3.651 * [taylor]: Taking taylor expansion of (sqrt k) in k 3.651 * [taylor]: Taking taylor expansion of k in k 3.651 * [backup-simplify]: Simplify 0 into 0 3.651 * [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 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in k 3.653 * [taylor]: Taking taylor expansion of 1.0 in k 3.653 * [backup-simplify]: Simplify 1.0 into 1.0 3.653 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in k 3.653 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 3.653 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 3.653 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 3.653 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 3.653 * [taylor]: Taking taylor expansion of 0.5 in k 3.653 * [backup-simplify]: Simplify 0.5 into 0.5 3.653 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 3.653 * [taylor]: Taking taylor expansion of 1.0 in k 3.653 * [backup-simplify]: Simplify 1.0 into 1.0 3.653 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.653 * [taylor]: Taking taylor expansion of k in k 3.653 * [backup-simplify]: Simplify 0 into 0 3.653 * [backup-simplify]: Simplify 1 into 1 3.653 * [backup-simplify]: Simplify (/ 1 1) into 1 3.653 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 3.653 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 3.653 * [taylor]: Taking taylor expansion of 2.0 in k 3.653 * [backup-simplify]: Simplify 2.0 into 2.0 3.653 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.653 * [taylor]: Taking taylor expansion of PI in k 3.653 * [backup-simplify]: Simplify PI into PI 3.653 * [taylor]: Taking taylor expansion of n in k 3.653 * [backup-simplify]: Simplify n into n 3.653 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 3.653 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 3.653 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 3.654 * [backup-simplify]: Simplify (- 1) into -1 3.654 * [backup-simplify]: Simplify (+ 0 -1) into -1 3.654 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 3.654 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 3.654 * [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)))))) 3.654 * [taylor]: Taking taylor expansion of (sqrt k) in k 3.654 * [taylor]: Taking taylor expansion of k in k 3.654 * [backup-simplify]: Simplify 0 into 0 3.654 * [backup-simplify]: Simplify 1 into 1 3.655 * [backup-simplify]: Simplify (sqrt 0) into 0 3.655 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.656 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) 0) into 0 3.656 * [backup-simplify]: Simplify (* 1.0 0) into 0 3.656 * [taylor]: Taking taylor expansion of 0 in n 3.656 * [backup-simplify]: Simplify 0 into 0 3.656 * [backup-simplify]: Simplify 0 into 0 3.656 * [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)))))))) 3.657 * [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)))))))) 3.657 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) in n 3.657 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))) in n 3.657 * [taylor]: Taking taylor expansion of +nan.0 in n 3.657 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.657 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) in n 3.657 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))) in n 3.657 * [taylor]: Taking taylor expansion of 0.5 in n 3.657 * [backup-simplify]: Simplify 0.5 into 0.5 3.657 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))) in n 3.657 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.657 * [taylor]: Taking taylor expansion of 1.0 in n 3.657 * [backup-simplify]: Simplify 1.0 into 1.0 3.657 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.657 * [taylor]: Taking taylor expansion of k in n 3.657 * [backup-simplify]: Simplify k into k 3.657 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.657 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.657 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.657 * [taylor]: Taking taylor expansion of 2.0 in n 3.657 * [backup-simplify]: Simplify 2.0 into 2.0 3.657 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.657 * [taylor]: Taking taylor expansion of PI in n 3.657 * [backup-simplify]: Simplify PI into PI 3.657 * [taylor]: Taking taylor expansion of n in n 3.657 * [backup-simplify]: Simplify 0 into 0 3.657 * [backup-simplify]: Simplify 1 into 1 3.658 * [backup-simplify]: Simplify (/ PI 1) into PI 3.658 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.659 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.659 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 3.659 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 3.660 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.660 * [backup-simplify]: Simplify (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) into (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) 3.661 * [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)))) 3.662 * [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))))) 3.663 * [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)))))) 3.664 * [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))))))) 3.664 * [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))))))) 3.664 * [backup-simplify]: Simplify 0 into 0 3.666 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 3.667 * [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)))))))) 3.667 * [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)))))))) 3.667 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) in n 3.667 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))) in n 3.667 * [taylor]: Taking taylor expansion of +nan.0 in n 3.667 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.667 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) in n 3.667 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))) in n 3.668 * [taylor]: Taking taylor expansion of 0.5 in n 3.668 * [backup-simplify]: Simplify 0.5 into 0.5 3.668 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))) in n 3.668 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.668 * [taylor]: Taking taylor expansion of 1.0 in n 3.668 * [backup-simplify]: Simplify 1.0 into 1.0 3.668 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.668 * [taylor]: Taking taylor expansion of k in n 3.668 * [backup-simplify]: Simplify k into k 3.668 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.668 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.668 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.668 * [taylor]: Taking taylor expansion of 2.0 in n 3.668 * [backup-simplify]: Simplify 2.0 into 2.0 3.668 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.668 * [taylor]: Taking taylor expansion of PI in n 3.668 * [backup-simplify]: Simplify PI into PI 3.668 * [taylor]: Taking taylor expansion of n in n 3.668 * [backup-simplify]: Simplify 0 into 0 3.668 * [backup-simplify]: Simplify 1 into 1 3.668 * [backup-simplify]: Simplify (/ PI 1) into PI 3.668 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.669 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.669 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 3.669 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 3.670 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.671 * [backup-simplify]: Simplify (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) into (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) 3.672 * [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)))) 3.672 * [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))))) 3.673 * [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)))))) 3.674 * [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))))))) 3.675 * [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))))))) 3.675 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 3.676 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 3.677 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 3.677 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 3.677 * [backup-simplify]: Simplify (- 0) into 0 3.677 * [backup-simplify]: Simplify (+ 0 0) into 0 3.678 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.679 * [backup-simplify]: Simplify (+ (* (- 1.0 (/ 1 k)) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 3.680 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into 0 3.681 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 3.682 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into 0 3.683 * [backup-simplify]: Simplify (- 0) into 0 3.683 * [backup-simplify]: Simplify 0 into 0 3.683 * [backup-simplify]: Simplify 0 into 0 3.685 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 3.686 * [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)))))))) 3.687 * [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)))))))) 3.687 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) in n 3.687 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))) in n 3.687 * [taylor]: Taking taylor expansion of +nan.0 in n 3.687 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.687 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) in n 3.687 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))) in n 3.687 * [taylor]: Taking taylor expansion of 0.5 in n 3.687 * [backup-simplify]: Simplify 0.5 into 0.5 3.687 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))) in n 3.687 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.687 * [taylor]: Taking taylor expansion of 1.0 in n 3.687 * [backup-simplify]: Simplify 1.0 into 1.0 3.687 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.687 * [taylor]: Taking taylor expansion of k in n 3.687 * [backup-simplify]: Simplify k into k 3.687 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.687 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.687 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.687 * [taylor]: Taking taylor expansion of 2.0 in n 3.687 * [backup-simplify]: Simplify 2.0 into 2.0 3.687 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.687 * [taylor]: Taking taylor expansion of PI in n 3.687 * [backup-simplify]: Simplify PI into PI 3.687 * [taylor]: Taking taylor expansion of n in n 3.687 * [backup-simplify]: Simplify 0 into 0 3.687 * [backup-simplify]: Simplify 1 into 1 3.687 * [backup-simplify]: Simplify (/ PI 1) into PI 3.688 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.688 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.688 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 3.688 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 3.689 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.694 * [backup-simplify]: Simplify (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) into (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) 3.695 * [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)))) 3.696 * [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))))) 3.696 * [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)))))) 3.697 * [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))))))) 3.698 * [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))))))) 3.701 * [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)))))))) 3.701 * [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)))) 3.701 * [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 3.701 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n 3.701 * [taylor]: Taking taylor expansion of 1.0 in n 3.701 * [backup-simplify]: Simplify 1.0 into 1.0 3.701 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n 3.701 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 3.701 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 3.701 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 3.702 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 3.702 * [taylor]: Taking taylor expansion of 0.5 in n 3.702 * [backup-simplify]: Simplify 0.5 into 0.5 3.702 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.702 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.702 * [taylor]: Taking taylor expansion of k in n 3.702 * [backup-simplify]: Simplify k into k 3.702 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.702 * [taylor]: Taking taylor expansion of 1.0 in n 3.702 * [backup-simplify]: Simplify 1.0 into 1.0 3.702 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 3.702 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.702 * [taylor]: Taking taylor expansion of -2.0 in n 3.702 * [backup-simplify]: Simplify -2.0 into -2.0 3.702 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.702 * [taylor]: Taking taylor expansion of PI in n 3.702 * [backup-simplify]: Simplify PI into PI 3.702 * [taylor]: Taking taylor expansion of n in n 3.702 * [backup-simplify]: Simplify 0 into 0 3.702 * [backup-simplify]: Simplify 1 into 1 3.702 * [backup-simplify]: Simplify (/ PI 1) into PI 3.702 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.703 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 3.703 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 3.703 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 3.704 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.705 * [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))) 3.706 * [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)))) 3.706 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 3.706 * [taylor]: Taking taylor expansion of (/ -1 k) in n 3.706 * [taylor]: Taking taylor expansion of -1 in n 3.706 * [backup-simplify]: Simplify -1 into -1 3.706 * [taylor]: Taking taylor expansion of k in n 3.706 * [backup-simplify]: Simplify k into k 3.706 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 3.706 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 3.706 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 3.706 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 3.707 * [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))) 3.707 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 3.707 * [taylor]: Taking taylor expansion of 1.0 in k 3.707 * [backup-simplify]: Simplify 1.0 into 1.0 3.707 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 3.707 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 3.707 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 3.707 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 3.707 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 3.707 * [taylor]: Taking taylor expansion of 0.5 in k 3.707 * [backup-simplify]: Simplify 0.5 into 0.5 3.707 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 3.707 * [taylor]: Taking taylor expansion of (/ 1 k) in k 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 3.707 * [backup-simplify]: Simplify (/ 1 1) into 1 3.707 * [taylor]: Taking taylor expansion of 1.0 in k 3.707 * [backup-simplify]: Simplify 1.0 into 1.0 3.707 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 3.707 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 3.707 * [taylor]: Taking taylor expansion of -2.0 in k 3.707 * [backup-simplify]: Simplify -2.0 into -2.0 3.707 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.707 * [taylor]: Taking taylor expansion of PI in k 3.707 * [backup-simplify]: Simplify PI into PI 3.707 * [taylor]: Taking taylor expansion of n in k 3.707 * [backup-simplify]: Simplify n into n 3.707 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 3.707 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 3.707 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 3.708 * [backup-simplify]: Simplify (+ 1 0) into 1 3.708 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 3.708 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 3.708 * [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)))) 3.708 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 3.708 * [taylor]: Taking taylor expansion of (/ -1 k) in k 3.708 * [taylor]: Taking taylor expansion of -1 in k 3.708 * [backup-simplify]: Simplify -1 into -1 3.708 * [taylor]: Taking taylor expansion of k in k 3.708 * [backup-simplify]: Simplify 0 into 0 3.708 * [backup-simplify]: Simplify 1 into 1 3.709 * [backup-simplify]: Simplify (/ -1 1) into -1 3.709 * [backup-simplify]: Simplify (sqrt 0) into 0 3.710 * [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 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 3.710 * [taylor]: Taking taylor expansion of 1.0 in k 3.710 * [backup-simplify]: Simplify 1.0 into 1.0 3.710 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 3.710 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 3.710 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 3.710 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 3.710 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 3.710 * [taylor]: Taking taylor expansion of 0.5 in k 3.710 * [backup-simplify]: Simplify 0.5 into 0.5 3.710 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 3.710 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.710 * [taylor]: Taking taylor expansion of k in k 3.710 * [backup-simplify]: Simplify 0 into 0 3.710 * [backup-simplify]: Simplify 1 into 1 3.710 * [backup-simplify]: Simplify (/ 1 1) into 1 3.710 * [taylor]: Taking taylor expansion of 1.0 in k 3.710 * [backup-simplify]: Simplify 1.0 into 1.0 3.710 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 3.710 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 3.710 * [taylor]: Taking taylor expansion of -2.0 in k 3.710 * [backup-simplify]: Simplify -2.0 into -2.0 3.710 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.710 * [taylor]: Taking taylor expansion of PI in k 3.710 * [backup-simplify]: Simplify PI into PI 3.710 * [taylor]: Taking taylor expansion of n in k 3.710 * [backup-simplify]: Simplify n into n 3.711 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 3.711 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 3.711 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 3.711 * [backup-simplify]: Simplify (+ 1 0) into 1 3.711 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 3.711 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 3.711 * [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)))) 3.711 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 3.711 * [taylor]: Taking taylor expansion of (/ -1 k) in k 3.711 * [taylor]: Taking taylor expansion of -1 in k 3.711 * [backup-simplify]: Simplify -1 into -1 3.711 * [taylor]: Taking taylor expansion of k in k 3.711 * [backup-simplify]: Simplify 0 into 0 3.711 * [backup-simplify]: Simplify 1 into 1 3.712 * [backup-simplify]: Simplify (/ -1 1) into -1 3.712 * [backup-simplify]: Simplify (sqrt 0) into 0 3.713 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 3.713 * [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))))) 3.713 * [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))))) 3.713 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) in n 3.713 * [taylor]: Taking taylor expansion of +nan.0 in n 3.713 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.713 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) in n 3.713 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))) in n 3.714 * [taylor]: Taking taylor expansion of 0.5 in n 3.714 * [backup-simplify]: Simplify 0.5 into 0.5 3.714 * [taylor]: Taking taylor expansion of (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)) in n 3.714 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 3.714 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.714 * [taylor]: Taking taylor expansion of -2.0 in n 3.714 * [backup-simplify]: Simplify -2.0 into -2.0 3.714 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.714 * [taylor]: Taking taylor expansion of PI in n 3.714 * [backup-simplify]: Simplify PI into PI 3.714 * [taylor]: Taking taylor expansion of n in n 3.714 * [backup-simplify]: Simplify 0 into 0 3.714 * [backup-simplify]: Simplify 1 into 1 3.714 * [backup-simplify]: Simplify (/ PI 1) into PI 3.714 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.715 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 3.715 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.715 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.715 * [taylor]: Taking taylor expansion of k in n 3.715 * [backup-simplify]: Simplify k into k 3.715 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.715 * [taylor]: Taking taylor expansion of 1.0 in n 3.715 * [backup-simplify]: Simplify 1.0 into 1.0 3.716 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.716 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 3.717 * [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))) 3.718 * [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)))) 3.719 * [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))))) 3.720 * [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))))) 3.720 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 3.722 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 3.723 * [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)))))) 3.723 * [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)))))) 3.723 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) in n 3.723 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) in n 3.723 * [taylor]: Taking taylor expansion of +nan.0 in n 3.723 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.723 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) in n 3.723 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))) in n 3.723 * [taylor]: Taking taylor expansion of 0.5 in n 3.723 * [backup-simplify]: Simplify 0.5 into 0.5 3.723 * [taylor]: Taking taylor expansion of (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)) in n 3.723 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 3.723 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.723 * [taylor]: Taking taylor expansion of -2.0 in n 3.723 * [backup-simplify]: Simplify -2.0 into -2.0 3.723 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.723 * [taylor]: Taking taylor expansion of PI in n 3.723 * [backup-simplify]: Simplify PI into PI 3.723 * [taylor]: Taking taylor expansion of n in n 3.724 * [backup-simplify]: Simplify 0 into 0 3.724 * [backup-simplify]: Simplify 1 into 1 3.724 * [backup-simplify]: Simplify (/ PI 1) into PI 3.724 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.725 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 3.725 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.725 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.725 * [taylor]: Taking taylor expansion of k in n 3.725 * [backup-simplify]: Simplify k into k 3.725 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.725 * [taylor]: Taking taylor expansion of 1.0 in n 3.725 * [backup-simplify]: Simplify 1.0 into 1.0 3.726 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.726 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 3.727 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) into (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) 3.727 * [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))) 3.728 * [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)))) 3.729 * [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))))) 3.730 * [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)))))) 3.731 * [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)))))) 3.732 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.732 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 3.732 * [backup-simplify]: Simplify (+ 0 0) into 0 3.733 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 3.733 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 3.734 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 3.735 * [backup-simplify]: Simplify (+ (* (- (log (* -2.0 PI)) (log n)) 0) (* 0 (+ (/ 1 k) 1.0))) into 0 3.736 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into 0 3.737 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 3.738 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into 0 3.738 * [backup-simplify]: Simplify 0 into 0 3.739 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.741 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 3.742 * [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)))))) 3.742 * [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)))))) 3.742 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) in n 3.743 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) in n 3.743 * [taylor]: Taking taylor expansion of +nan.0 in n 3.743 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.743 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) in n 3.743 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))) in n 3.743 * [taylor]: Taking taylor expansion of 0.5 in n 3.743 * [backup-simplify]: Simplify 0.5 into 0.5 3.743 * [taylor]: Taking taylor expansion of (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)) in n 3.743 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 3.743 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.743 * [taylor]: Taking taylor expansion of -2.0 in n 3.743 * [backup-simplify]: Simplify -2.0 into -2.0 3.743 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.743 * [taylor]: Taking taylor expansion of PI in n 3.743 * [backup-simplify]: Simplify PI into PI 3.743 * [taylor]: Taking taylor expansion of n in n 3.743 * [backup-simplify]: Simplify 0 into 0 3.743 * [backup-simplify]: Simplify 1 into 1 3.743 * [backup-simplify]: Simplify (/ PI 1) into PI 3.743 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.744 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 3.744 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.744 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.744 * [taylor]: Taking taylor expansion of k in n 3.744 * [backup-simplify]: Simplify k into k 3.744 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.744 * [taylor]: Taking taylor expansion of 1.0 in n 3.744 * [backup-simplify]: Simplify 1.0 into 1.0 3.745 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.745 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 3.746 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) into (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) 3.747 * [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))) 3.747 * [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)))) 3.748 * [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))))) 3.749 * [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)))))) 3.750 * [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)))))) 3.752 * [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)))))))) 3.752 * * * [progress]: simplifying candidates 3.756 * [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)))))))) 3.762 * * [simplify]: iteration 0: 353 enodes 3.900 * * [simplify]: iteration 1: 975 enodes 4.439 * * [simplify]: iteration 2: 3261 enodes 5.475 * * [simplify]: iteration complete: 5001 enodes 5.475 * * [simplify]: Extracting #0: cost 117 inf + 0 5.476 * * [simplify]: Extracting #1: cost 590 inf + 2 5.479 * * [simplify]: Extracting #2: cost 1034 inf + 2722 5.487 * * [simplify]: Extracting #3: cost 1271 inf + 29363 5.512 * * [simplify]: Extracting #4: cost 841 inf + 157190 5.594 * * [simplify]: Extracting #5: cost 492 inf + 353948 5.687 * * [simplify]: Extracting #6: cost 429 inf + 453894 5.817 * * [simplify]: Extracting #7: cost 178 inf + 668763 5.978 * * [simplify]: Extracting #8: cost 60 inf + 770866 6.156 * * [simplify]: Extracting #9: cost 5 inf + 834102 6.326 * * [simplify]: Extracting #10: cost 0 inf + 842935 6.497 * * [simplify]: Extracting #11: cost 0 inf + 842895 6.702 * [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))))))))) 6.716 * * * [progress]: adding candidates to table 7.593 * * [progress]: iteration 2 / 4 7.593 * * * [progress]: picking best candidate 7.650 * * * * [pick]: Picked # 7.650 * * * [progress]: localizing error 7.680 * * * [progress]: generating rewritten candidates 7.680 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 7.694 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1 2) 7.703 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1) 7.712 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 7.758 * * * [progress]: generating series expansions 7.758 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 7.758 * [backup-simplify]: Simplify (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 7.759 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 7.759 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 7.759 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 7.759 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 7.759 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 7.759 * [taylor]: Taking taylor expansion of 0.5 in k 7.759 * [backup-simplify]: Simplify 0.5 into 0.5 7.759 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 7.759 * [taylor]: Taking taylor expansion of 1.0 in k 7.759 * [backup-simplify]: Simplify 1.0 into 1.0 7.759 * [taylor]: Taking taylor expansion of k in k 7.759 * [backup-simplify]: Simplify 0 into 0 7.759 * [backup-simplify]: Simplify 1 into 1 7.759 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 7.759 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 7.759 * [taylor]: Taking taylor expansion of 2.0 in k 7.759 * [backup-simplify]: Simplify 2.0 into 2.0 7.759 * [taylor]: Taking taylor expansion of (* n PI) in k 7.759 * [taylor]: Taking taylor expansion of n in k 7.759 * [backup-simplify]: Simplify n into n 7.759 * [taylor]: Taking taylor expansion of PI in k 7.759 * [backup-simplify]: Simplify PI into PI 7.759 * [backup-simplify]: Simplify (* n PI) into (* n PI) 7.759 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 7.759 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 7.759 * [backup-simplify]: Simplify (- 0) into 0 7.760 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 7.760 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 7.760 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 7.760 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 7.760 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 7.760 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 7.760 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 7.760 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 7.760 * [taylor]: Taking taylor expansion of 0.5 in n 7.760 * [backup-simplify]: Simplify 0.5 into 0.5 7.760 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 7.760 * [taylor]: Taking taylor expansion of 1.0 in n 7.760 * [backup-simplify]: Simplify 1.0 into 1.0 7.760 * [taylor]: Taking taylor expansion of k in n 7.760 * [backup-simplify]: Simplify k into k 7.760 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 7.760 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 7.760 * [taylor]: Taking taylor expansion of 2.0 in n 7.760 * [backup-simplify]: Simplify 2.0 into 2.0 7.760 * [taylor]: Taking taylor expansion of (* n PI) in n 7.760 * [taylor]: Taking taylor expansion of n in n 7.760 * [backup-simplify]: Simplify 0 into 0 7.761 * [backup-simplify]: Simplify 1 into 1 7.761 * [taylor]: Taking taylor expansion of PI in n 7.761 * [backup-simplify]: Simplify PI into PI 7.761 * [backup-simplify]: Simplify (* 0 PI) into 0 7.761 * [backup-simplify]: Simplify (* 2.0 0) into 0 7.762 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 7.763 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 7.764 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 7.764 * [backup-simplify]: Simplify (- k) into (- k) 7.764 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 7.764 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 7.765 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 7.765 * [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)))) 7.766 * [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))))) 7.767 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 7.767 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 7.767 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 7.767 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 7.767 * [taylor]: Taking taylor expansion of 0.5 in n 7.767 * [backup-simplify]: Simplify 0.5 into 0.5 7.767 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 7.767 * [taylor]: Taking taylor expansion of 1.0 in n 7.767 * [backup-simplify]: Simplify 1.0 into 1.0 7.767 * [taylor]: Taking taylor expansion of k in n 7.767 * [backup-simplify]: Simplify k into k 7.767 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 7.767 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 7.767 * [taylor]: Taking taylor expansion of 2.0 in n 7.767 * [backup-simplify]: Simplify 2.0 into 2.0 7.767 * [taylor]: Taking taylor expansion of (* n PI) in n 7.767 * [taylor]: Taking taylor expansion of n in n 7.767 * [backup-simplify]: Simplify 0 into 0 7.767 * [backup-simplify]: Simplify 1 into 1 7.767 * [taylor]: Taking taylor expansion of PI in n 7.767 * [backup-simplify]: Simplify PI into PI 7.767 * [backup-simplify]: Simplify (* 0 PI) into 0 7.767 * [backup-simplify]: Simplify (* 2.0 0) into 0 7.768 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 7.769 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 7.770 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 7.770 * [backup-simplify]: Simplify (- k) into (- k) 7.770 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 7.770 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 7.771 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 7.772 * [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)))) 7.773 * [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))))) 7.773 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 7.773 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 7.773 * [taylor]: Taking taylor expansion of 0.5 in k 7.773 * [backup-simplify]: Simplify 0.5 into 0.5 7.773 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 7.773 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 7.773 * [taylor]: Taking taylor expansion of 1.0 in k 7.773 * [backup-simplify]: Simplify 1.0 into 1.0 7.773 * [taylor]: Taking taylor expansion of k in k 7.773 * [backup-simplify]: Simplify 0 into 0 7.773 * [backup-simplify]: Simplify 1 into 1 7.773 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 7.773 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 7.773 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 7.773 * [taylor]: Taking taylor expansion of 2.0 in k 7.773 * [backup-simplify]: Simplify 2.0 into 2.0 7.773 * [taylor]: Taking taylor expansion of PI in k 7.773 * [backup-simplify]: Simplify PI into PI 7.773 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 7.774 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 7.774 * [taylor]: Taking taylor expansion of (log n) in k 7.774 * [taylor]: Taking taylor expansion of n in k 7.774 * [backup-simplify]: Simplify n into n 7.774 * [backup-simplify]: Simplify (log n) into (log n) 7.774 * [backup-simplify]: Simplify (- 0) into 0 7.775 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 7.775 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 7.776 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 7.777 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 7.777 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 7.778 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 7.779 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 7.779 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 7.780 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 7.781 * [backup-simplify]: Simplify (- 0) into 0 7.781 * [backup-simplify]: Simplify (+ 0 0) into 0 7.781 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 7.782 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 7.783 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 7.784 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 7.784 * [taylor]: Taking taylor expansion of 0 in k 7.784 * [backup-simplify]: Simplify 0 into 0 7.784 * [backup-simplify]: Simplify 0 into 0 7.784 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 7.785 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 7.786 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 7.786 * [backup-simplify]: Simplify (+ 0 0) into 0 7.786 * [backup-simplify]: Simplify (- 1) into -1 7.787 * [backup-simplify]: Simplify (+ 0 -1) into -1 7.788 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 7.789 * [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)))) 7.793 * [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)))))) 7.796 * [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)))))) 7.797 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 7.798 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 7.802 * [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 7.802 * [backup-simplify]: Simplify (- 0) into 0 7.803 * [backup-simplify]: Simplify (+ 0 0) into 0 7.804 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 7.806 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 7.807 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 7.810 * [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 7.810 * [taylor]: Taking taylor expansion of 0 in k 7.810 * [backup-simplify]: Simplify 0 into 0 7.810 * [backup-simplify]: Simplify 0 into 0 7.810 * [backup-simplify]: Simplify 0 into 0 7.811 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 7.815 * [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 7.817 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 7.817 * [backup-simplify]: Simplify (+ 0 0) into 0 7.818 * [backup-simplify]: Simplify (- 0) into 0 7.818 * [backup-simplify]: Simplify (+ 0 0) into 0 7.820 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 7.823 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 7.827 * [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)))))) 7.839 * [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)))))) 7.849 * [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))))) 7.850 * [backup-simplify]: Simplify (pow (* 2.0 (* (/ 1 n) PI)) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) 7.850 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 7.850 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 7.850 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 7.850 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 7.850 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 7.850 * [taylor]: Taking taylor expansion of 0.5 in k 7.850 * [backup-simplify]: Simplify 0.5 into 0.5 7.850 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 7.850 * [taylor]: Taking taylor expansion of 1.0 in k 7.850 * [backup-simplify]: Simplify 1.0 into 1.0 7.850 * [taylor]: Taking taylor expansion of (/ 1 k) in k 7.850 * [taylor]: Taking taylor expansion of k in k 7.850 * [backup-simplify]: Simplify 0 into 0 7.850 * [backup-simplify]: Simplify 1 into 1 7.851 * [backup-simplify]: Simplify (/ 1 1) into 1 7.851 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 7.851 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 7.851 * [taylor]: Taking taylor expansion of 2.0 in k 7.851 * [backup-simplify]: Simplify 2.0 into 2.0 7.851 * [taylor]: Taking taylor expansion of (/ PI n) in k 7.851 * [taylor]: Taking taylor expansion of PI in k 7.851 * [backup-simplify]: Simplify PI into PI 7.851 * [taylor]: Taking taylor expansion of n in k 7.851 * [backup-simplify]: Simplify n into n 7.851 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 7.851 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 7.851 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 7.852 * [backup-simplify]: Simplify (- 1) into -1 7.852 * [backup-simplify]: Simplify (+ 0 -1) into -1 7.853 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 7.853 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 7.853 * [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)))))) 7.853 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 7.853 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 7.853 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 7.853 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 7.853 * [taylor]: Taking taylor expansion of 0.5 in n 7.853 * [backup-simplify]: Simplify 0.5 into 0.5 7.853 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 7.853 * [taylor]: Taking taylor expansion of 1.0 in n 7.853 * [backup-simplify]: Simplify 1.0 into 1.0 7.853 * [taylor]: Taking taylor expansion of (/ 1 k) in n 7.853 * [taylor]: Taking taylor expansion of k in n 7.853 * [backup-simplify]: Simplify k into k 7.854 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 7.854 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 7.854 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 7.854 * [taylor]: Taking taylor expansion of 2.0 in n 7.854 * [backup-simplify]: Simplify 2.0 into 2.0 7.854 * [taylor]: Taking taylor expansion of (/ PI n) in n 7.854 * [taylor]: Taking taylor expansion of PI in n 7.854 * [backup-simplify]: Simplify PI into PI 7.854 * [taylor]: Taking taylor expansion of n in n 7.854 * [backup-simplify]: Simplify 0 into 0 7.854 * [backup-simplify]: Simplify 1 into 1 7.854 * [backup-simplify]: Simplify (/ PI 1) into PI 7.855 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 7.856 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 7.856 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 7.856 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 7.856 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 7.858 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 7.859 * [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)))) 7.860 * [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))))) 7.860 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 7.860 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 7.860 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 7.860 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 7.861 * [taylor]: Taking taylor expansion of 0.5 in n 7.861 * [backup-simplify]: Simplify 0.5 into 0.5 7.861 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 7.861 * [taylor]: Taking taylor expansion of 1.0 in n 7.861 * [backup-simplify]: Simplify 1.0 into 1.0 7.861 * [taylor]: Taking taylor expansion of (/ 1 k) in n 7.861 * [taylor]: Taking taylor expansion of k in n 7.861 * [backup-simplify]: Simplify k into k 7.861 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 7.861 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 7.861 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 7.861 * [taylor]: Taking taylor expansion of 2.0 in n 7.861 * [backup-simplify]: Simplify 2.0 into 2.0 7.861 * [taylor]: Taking taylor expansion of (/ PI n) in n 7.861 * [taylor]: Taking taylor expansion of PI in n 7.861 * [backup-simplify]: Simplify PI into PI 7.861 * [taylor]: Taking taylor expansion of n in n 7.861 * [backup-simplify]: Simplify 0 into 0 7.861 * [backup-simplify]: Simplify 1 into 1 7.862 * [backup-simplify]: Simplify (/ PI 1) into PI 7.862 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 7.863 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 7.863 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 7.863 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 7.864 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 7.865 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 7.866 * [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)))) 7.867 * [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))))) 7.867 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) in k 7.867 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) in k 7.867 * [taylor]: Taking taylor expansion of 0.5 in k 7.867 * [backup-simplify]: Simplify 0.5 into 0.5 7.867 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) in k 7.867 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 7.867 * [taylor]: Taking taylor expansion of 1.0 in k 7.867 * [backup-simplify]: Simplify 1.0 into 1.0 7.867 * [taylor]: Taking taylor expansion of (/ 1 k) in k 7.867 * [taylor]: Taking taylor expansion of k in k 7.867 * [backup-simplify]: Simplify 0 into 0 7.867 * [backup-simplify]: Simplify 1 into 1 7.867 * [backup-simplify]: Simplify (/ 1 1) into 1 7.867 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 7.867 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 7.867 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 7.867 * [taylor]: Taking taylor expansion of 2.0 in k 7.867 * [backup-simplify]: Simplify 2.0 into 2.0 7.867 * [taylor]: Taking taylor expansion of PI in k 7.867 * [backup-simplify]: Simplify PI into PI 7.868 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 7.868 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 7.868 * [taylor]: Taking taylor expansion of (log n) in k 7.868 * [taylor]: Taking taylor expansion of n in k 7.868 * [backup-simplify]: Simplify n into n 7.869 * [backup-simplify]: Simplify (log n) into (log n) 7.869 * [backup-simplify]: Simplify (- 1) into -1 7.869 * [backup-simplify]: Simplify (+ 0 -1) into -1 7.869 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 7.870 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 7.870 * [backup-simplify]: Simplify (* -1 (- (log (* 2.0 PI)) (log n))) into (* -1 (- (log (* 2.0 PI)) (log n))) 7.871 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 7.872 * [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))))) 7.873 * [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))))) 7.873 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 7.874 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 7.875 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 7.875 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 7.875 * [backup-simplify]: Simplify (- 0) into 0 7.875 * [backup-simplify]: Simplify (+ 0 0) into 0 7.876 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 7.877 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 7.877 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 7.878 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 7.879 * [taylor]: Taking taylor expansion of 0 in k 7.879 * [backup-simplify]: Simplify 0 into 0 7.879 * [backup-simplify]: Simplify 0 into 0 7.879 * [backup-simplify]: Simplify 0 into 0 7.879 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 7.880 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 7.882 * [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 7.882 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 7.882 * [backup-simplify]: Simplify (- 0) into 0 7.883 * [backup-simplify]: Simplify (+ 0 0) into 0 7.883 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 7.884 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 7.885 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 7.887 * [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 7.887 * [taylor]: Taking taylor expansion of 0 in k 7.887 * [backup-simplify]: Simplify 0 into 0 7.887 * [backup-simplify]: Simplify 0 into 0 7.887 * [backup-simplify]: Simplify 0 into 0 7.887 * [backup-simplify]: Simplify 0 into 0 7.887 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 7.888 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 7.891 * [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 7.891 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 7.892 * [backup-simplify]: Simplify (- 0) into 0 7.892 * [backup-simplify]: Simplify (+ 0 0) into 0 7.893 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 7.894 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 7.896 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 7.899 * [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 7.899 * [taylor]: Taking taylor expansion of 0 in k 7.899 * [backup-simplify]: Simplify 0 into 0 7.899 * [backup-simplify]: Simplify 0 into 0 7.901 * [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)))))) 7.901 * [backup-simplify]: Simplify (pow (* 2.0 (* (/ 1 (- n)) PI)) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) 7.901 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 7.901 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 7.901 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 7.901 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 7.901 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 7.901 * [taylor]: Taking taylor expansion of 0.5 in k 7.901 * [backup-simplify]: Simplify 0.5 into 0.5 7.901 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 7.901 * [taylor]: Taking taylor expansion of (/ 1 k) in k 7.901 * [taylor]: Taking taylor expansion of k in k 7.901 * [backup-simplify]: Simplify 0 into 0 7.901 * [backup-simplify]: Simplify 1 into 1 7.902 * [backup-simplify]: Simplify (/ 1 1) into 1 7.902 * [taylor]: Taking taylor expansion of 1.0 in k 7.902 * [backup-simplify]: Simplify 1.0 into 1.0 7.902 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 7.902 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 7.902 * [taylor]: Taking taylor expansion of -2.0 in k 7.902 * [backup-simplify]: Simplify -2.0 into -2.0 7.902 * [taylor]: Taking taylor expansion of (/ PI n) in k 7.902 * [taylor]: Taking taylor expansion of PI in k 7.902 * [backup-simplify]: Simplify PI into PI 7.902 * [taylor]: Taking taylor expansion of n in k 7.902 * [backup-simplify]: Simplify n into n 7.902 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 7.902 * [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 0) 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 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) 7.904 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 7.904 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 7.904 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 7.904 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) 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 k) 1.0) in n 7.905 * [taylor]: Taking taylor expansion of (/ 1 k) in n 7.905 * [taylor]: Taking taylor expansion of k in n 7.905 * [backup-simplify]: Simplify k into k 7.905 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 7.905 * [taylor]: Taking taylor expansion of 1.0 in n 7.905 * [backup-simplify]: Simplify 1.0 into 1.0 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 7.906 * [backup-simplify]: Simplify (/ PI 1) into PI 7.906 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 7.907 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 7.907 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 7.907 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 7.909 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 7.910 * [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))) 7.911 * [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)))) 7.912 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 7.912 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 7.912 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 7.912 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 7.912 * [taylor]: Taking taylor expansion of 0.5 in n 7.912 * [backup-simplify]: Simplify 0.5 into 0.5 7.912 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 7.912 * [taylor]: Taking taylor expansion of (/ 1 k) in n 7.912 * [taylor]: Taking taylor expansion of k in n 7.912 * [backup-simplify]: Simplify k into k 7.912 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 7.912 * [taylor]: Taking taylor expansion of 1.0 in n 7.912 * [backup-simplify]: Simplify 1.0 into 1.0 7.912 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 7.912 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 7.912 * [taylor]: Taking taylor expansion of -2.0 in n 7.912 * [backup-simplify]: Simplify -2.0 into -2.0 7.912 * [taylor]: Taking taylor expansion of (/ PI n) in n 7.912 * [taylor]: Taking taylor expansion of PI in n 7.912 * [backup-simplify]: Simplify PI into PI 7.912 * [taylor]: Taking taylor expansion of n in n 7.912 * [backup-simplify]: Simplify 0 into 0 7.912 * [backup-simplify]: Simplify 1 into 1 7.913 * [backup-simplify]: Simplify (/ PI 1) into PI 7.913 * [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) 1.0) into (+ (/ 1 k) 1.0) 7.915 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 7.916 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 7.918 * [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))) 7.919 * [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)))) 7.919 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) in k 7.919 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) 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 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) in k 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 7.919 * [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) 7.921 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 7.921 * [taylor]: Taking taylor expansion of (/ 1 k) in k 7.921 * [taylor]: Taking taylor expansion of k in k 7.921 * [backup-simplify]: Simplify 0 into 0 7.921 * [backup-simplify]: Simplify 1 into 1 7.922 * [backup-simplify]: Simplify (/ 1 1) into 1 7.922 * [taylor]: Taking taylor expansion of 1.0 in k 7.922 * [backup-simplify]: Simplify 1.0 into 1.0 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 0) into 1 7.925 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) 1) into (- (log (* -2.0 PI)) (log n)) 7.926 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 7.927 * [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)))) 7.929 * [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)))) 7.930 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 7.931 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 7.933 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 7.933 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 7.933 * [backup-simplify]: Simplify (+ 0 0) into 0 7.934 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 7.935 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 7.937 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 7.939 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 7.939 * [taylor]: Taking taylor expansion of 0 in k 7.939 * [backup-simplify]: Simplify 0 into 0 7.939 * [backup-simplify]: Simplify 0 into 0 7.939 * [backup-simplify]: Simplify 0 into 0 7.940 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 7.941 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 7.945 * [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 7.945 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 7.946 * [backup-simplify]: Simplify (+ 0 0) into 0 7.947 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 7.948 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 7.950 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 7.952 * [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 7.953 * [taylor]: Taking taylor expansion of 0 in k 7.953 * [backup-simplify]: Simplify 0 into 0 7.953 * [backup-simplify]: Simplify 0 into 0 7.953 * [backup-simplify]: Simplify 0 into 0 7.953 * [backup-simplify]: Simplify 0 into 0 7.954 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 7.955 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 7.961 * [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 7.962 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 7.962 * [backup-simplify]: Simplify (+ 0 0) into 0 7.963 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 7.965 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 7.973 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 7.976 * [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 7.976 * [taylor]: Taking taylor expansion of 0 in k 7.976 * [backup-simplify]: Simplify 0 into 0 7.976 * [backup-simplify]: Simplify 0 into 0 7.978 * [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)))))) 7.978 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1 2) 7.978 * [backup-simplify]: Simplify (* n PI) into (* n PI) 7.978 * [approximate]: Taking taylor expansion of (* n PI) in (n) around 0 7.978 * [taylor]: Taking taylor expansion of (* n PI) in n 7.978 * [taylor]: Taking taylor expansion of n in n 7.978 * [backup-simplify]: Simplify 0 into 0 7.978 * [backup-simplify]: Simplify 1 into 1 7.978 * [taylor]: Taking taylor expansion of PI in n 7.978 * [backup-simplify]: Simplify PI into PI 7.978 * [taylor]: Taking taylor expansion of (* n PI) in n 7.978 * [taylor]: Taking taylor expansion of n in n 7.978 * [backup-simplify]: Simplify 0 into 0 7.978 * [backup-simplify]: Simplify 1 into 1 7.978 * [taylor]: Taking taylor expansion of PI in n 7.978 * [backup-simplify]: Simplify PI into PI 7.979 * [backup-simplify]: Simplify (* 0 PI) into 0 7.979 * [backup-simplify]: Simplify 0 into 0 7.981 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 7.981 * [backup-simplify]: Simplify PI into PI 7.982 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 7.982 * [backup-simplify]: Simplify 0 into 0 7.983 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 7.983 * [backup-simplify]: Simplify 0 into 0 7.984 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 7.984 * [backup-simplify]: Simplify 0 into 0 7.986 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 7.986 * [backup-simplify]: Simplify 0 into 0 7.988 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 7.988 * [backup-simplify]: Simplify 0 into 0 7.990 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 7.990 * [backup-simplify]: Simplify 0 into 0 7.990 * [backup-simplify]: Simplify (* PI n) into (* n PI) 7.990 * [backup-simplify]: Simplify (* (/ 1 n) PI) into (/ PI n) 7.990 * [approximate]: Taking taylor expansion of (/ PI n) in (n) around 0 7.990 * [taylor]: Taking taylor expansion of (/ PI n) in n 7.990 * [taylor]: Taking taylor expansion of PI in n 7.990 * [backup-simplify]: Simplify PI into PI 7.990 * [taylor]: Taking taylor expansion of n in n 7.990 * [backup-simplify]: Simplify 0 into 0 7.990 * [backup-simplify]: Simplify 1 into 1 7.991 * [backup-simplify]: Simplify (/ PI 1) into PI 7.991 * [taylor]: Taking taylor expansion of (/ PI n) in n 7.991 * [taylor]: Taking taylor expansion of PI in n 7.991 * [backup-simplify]: Simplify PI into PI 7.991 * [taylor]: Taking taylor expansion of n in n 7.991 * [backup-simplify]: Simplify 0 into 0 7.991 * [backup-simplify]: Simplify 1 into 1 7.992 * [backup-simplify]: Simplify (/ PI 1) into PI 7.992 * [backup-simplify]: Simplify PI into PI 7.993 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 7.993 * [backup-simplify]: Simplify 0 into 0 7.994 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 7.994 * [backup-simplify]: Simplify 0 into 0 7.995 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 7.995 * [backup-simplify]: Simplify 0 into 0 7.996 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 7.996 * [backup-simplify]: Simplify 0 into 0 7.997 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 7.997 * [backup-simplify]: Simplify 0 into 0 7.998 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 7.998 * [backup-simplify]: Simplify 0 into 0 7.999 * [backup-simplify]: Simplify (* PI (/ 1 (/ 1 n))) into (* n PI) 7.999 * [backup-simplify]: Simplify (* (/ 1 (- n)) PI) into (* -1 (/ PI n)) 7.999 * [approximate]: Taking taylor expansion of (* -1 (/ PI n)) in (n) around 0 7.999 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n 7.999 * [taylor]: Taking taylor expansion of -1 in n 7.999 * [backup-simplify]: Simplify -1 into -1 7.999 * [taylor]: Taking taylor expansion of (/ PI n) in n 7.999 * [taylor]: Taking taylor expansion of PI in n 7.999 * [backup-simplify]: Simplify PI into PI 7.999 * [taylor]: Taking taylor expansion of n in n 7.999 * [backup-simplify]: Simplify 0 into 0 7.999 * [backup-simplify]: Simplify 1 into 1 8.000 * [backup-simplify]: Simplify (/ PI 1) into PI 8.000 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n 8.000 * [taylor]: Taking taylor expansion of -1 in n 8.000 * [backup-simplify]: Simplify -1 into -1 8.000 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.000 * [taylor]: Taking taylor expansion of PI in n 8.000 * [backup-simplify]: Simplify PI into PI 8.000 * [taylor]: Taking taylor expansion of n in n 8.000 * [backup-simplify]: Simplify 0 into 0 8.000 * [backup-simplify]: Simplify 1 into 1 8.000 * [backup-simplify]: Simplify (/ PI 1) into PI 8.001 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI) 8.001 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI) 8.002 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.003 * [backup-simplify]: Simplify (+ (* -1 0) (* 0 PI)) into 0 8.003 * [backup-simplify]: Simplify 0 into 0 8.004 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.005 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 PI))) into 0 8.005 * [backup-simplify]: Simplify 0 into 0 8.006 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.008 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 8.008 * [backup-simplify]: Simplify 0 into 0 8.009 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.010 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 8.010 * [backup-simplify]: Simplify 0 into 0 8.011 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.013 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 8.013 * [backup-simplify]: Simplify 0 into 0 8.014 * [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 8.016 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 8.016 * [backup-simplify]: Simplify 0 into 0 8.017 * [backup-simplify]: Simplify (* (* -1 PI) (/ 1 (/ 1 (- n)))) into (* n PI) 8.017 * * * * [progress]: [ 3 / 4 ] generating series at (2 1) 8.017 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 8.017 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 8.017 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 8.017 * [taylor]: Taking taylor expansion of 1.0 in k 8.017 * [backup-simplify]: Simplify 1.0 into 1.0 8.017 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 8.017 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.017 * [taylor]: Taking taylor expansion of k in k 8.017 * [backup-simplify]: Simplify 0 into 0 8.017 * [backup-simplify]: Simplify 1 into 1 8.017 * [backup-simplify]: Simplify (/ 1 1) into 1 8.018 * [backup-simplify]: Simplify (sqrt 0) into 0 8.019 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.019 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 8.019 * [taylor]: Taking taylor expansion of 1.0 in k 8.019 * [backup-simplify]: Simplify 1.0 into 1.0 8.019 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 8.019 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.019 * [taylor]: Taking taylor expansion of k in k 8.019 * [backup-simplify]: Simplify 0 into 0 8.019 * [backup-simplify]: Simplify 1 into 1 8.020 * [backup-simplify]: Simplify (/ 1 1) into 1 8.020 * [backup-simplify]: Simplify (sqrt 0) into 0 8.021 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.022 * [backup-simplify]: Simplify (* 1.0 0) into 0 8.022 * [backup-simplify]: Simplify 0 into 0 8.024 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 8.024 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.025 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 8.028 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 8.030 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 8.030 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.031 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.036 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 8.038 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 8.039 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.040 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) 8.040 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 8.040 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 8.040 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 8.040 * [taylor]: Taking taylor expansion of 1.0 in k 8.040 * [backup-simplify]: Simplify 1.0 into 1.0 8.040 * [taylor]: Taking taylor expansion of (sqrt k) in k 8.040 * [taylor]: Taking taylor expansion of k in k 8.040 * [backup-simplify]: Simplify 0 into 0 8.040 * [backup-simplify]: Simplify 1 into 1 8.041 * [backup-simplify]: Simplify (sqrt 0) into 0 8.042 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.042 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 8.042 * [taylor]: Taking taylor expansion of 1.0 in k 8.042 * [backup-simplify]: Simplify 1.0 into 1.0 8.042 * [taylor]: Taking taylor expansion of (sqrt k) in k 8.042 * [taylor]: Taking taylor expansion of k in k 8.042 * [backup-simplify]: Simplify 0 into 0 8.042 * [backup-simplify]: Simplify 1 into 1 8.043 * [backup-simplify]: Simplify (sqrt 0) into 0 8.044 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.045 * [backup-simplify]: Simplify (* 1.0 0) into 0 8.045 * [backup-simplify]: Simplify 0 into 0 8.046 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 8.047 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.050 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 8.052 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 8.052 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.055 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 8.056 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 8.056 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.057 * [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)))))))) 8.057 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 8.057 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 8.057 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 8.057 * [taylor]: Taking taylor expansion of 1.0 in k 8.057 * [backup-simplify]: Simplify 1.0 into 1.0 8.057 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 8.057 * [taylor]: Taking taylor expansion of (/ -1 k) in k 8.058 * [taylor]: Taking taylor expansion of -1 in k 8.058 * [backup-simplify]: Simplify -1 into -1 8.058 * [taylor]: Taking taylor expansion of k in k 8.058 * [backup-simplify]: Simplify 0 into 0 8.058 * [backup-simplify]: Simplify 1 into 1 8.058 * [backup-simplify]: Simplify (/ -1 1) into -1 8.058 * [backup-simplify]: Simplify (sqrt 0) into 0 8.059 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 8.059 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 8.059 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 8.059 * [taylor]: Taking taylor expansion of 1.0 in k 8.059 * [backup-simplify]: Simplify 1.0 into 1.0 8.059 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 8.059 * [taylor]: Taking taylor expansion of (/ -1 k) in k 8.059 * [taylor]: Taking taylor expansion of -1 in k 8.059 * [backup-simplify]: Simplify -1 into -1 8.059 * [taylor]: Taking taylor expansion of k in k 8.059 * [backup-simplify]: Simplify 0 into 0 8.059 * [backup-simplify]: Simplify 1 into 1 8.060 * [backup-simplify]: Simplify (/ -1 1) into -1 8.060 * [backup-simplify]: Simplify (sqrt 0) into 0 8.060 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 8.061 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 8.061 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.061 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 8.063 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 8.065 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 8.065 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.066 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.068 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 8.071 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 8.071 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.072 * [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))))) 8.072 * * * * [progress]: [ 4 / 4 ] generating series at (2) 8.072 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) into (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) 8.072 * [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 8.072 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in n 8.072 * [taylor]: Taking taylor expansion of 1.0 in n 8.072 * [backup-simplify]: Simplify 1.0 into 1.0 8.072 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in n 8.072 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 8.072 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 8.072 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 8.072 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 8.072 * [taylor]: Taking taylor expansion of 0.5 in n 8.072 * [backup-simplify]: Simplify 0.5 into 0.5 8.072 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 8.072 * [taylor]: Taking taylor expansion of 1.0 in n 8.072 * [backup-simplify]: Simplify 1.0 into 1.0 8.072 * [taylor]: Taking taylor expansion of k in n 8.072 * [backup-simplify]: Simplify k into k 8.072 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 8.072 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 8.072 * [taylor]: Taking taylor expansion of 2.0 in n 8.072 * [backup-simplify]: Simplify 2.0 into 2.0 8.072 * [taylor]: Taking taylor expansion of (* n PI) in n 8.072 * [taylor]: Taking taylor expansion of n in n 8.072 * [backup-simplify]: Simplify 0 into 0 8.072 * [backup-simplify]: Simplify 1 into 1 8.072 * [taylor]: Taking taylor expansion of PI in n 8.072 * [backup-simplify]: Simplify PI into PI 8.072 * [backup-simplify]: Simplify (* 0 PI) into 0 8.073 * [backup-simplify]: Simplify (* 2.0 0) into 0 8.074 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.075 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 8.076 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.076 * [backup-simplify]: Simplify (- k) into (- k) 8.076 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 8.076 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 8.077 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.078 * [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)))) 8.079 * [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))))) 8.079 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 8.079 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.079 * [taylor]: Taking taylor expansion of k in n 8.079 * [backup-simplify]: Simplify k into k 8.079 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.079 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 8.079 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 8.079 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 8.079 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in k 8.079 * [taylor]: Taking taylor expansion of 1.0 in k 8.079 * [backup-simplify]: Simplify 1.0 into 1.0 8.079 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in k 8.079 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 8.079 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 8.079 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 8.079 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 8.079 * [taylor]: Taking taylor expansion of 0.5 in k 8.079 * [backup-simplify]: Simplify 0.5 into 0.5 8.079 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 8.079 * [taylor]: Taking taylor expansion of 1.0 in k 8.079 * [backup-simplify]: Simplify 1.0 into 1.0 8.079 * [taylor]: Taking taylor expansion of k in k 8.079 * [backup-simplify]: Simplify 0 into 0 8.079 * [backup-simplify]: Simplify 1 into 1 8.079 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 8.079 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 8.079 * [taylor]: Taking taylor expansion of 2.0 in k 8.079 * [backup-simplify]: Simplify 2.0 into 2.0 8.079 * [taylor]: Taking taylor expansion of (* n PI) in k 8.079 * [taylor]: Taking taylor expansion of n in k 8.079 * [backup-simplify]: Simplify n into n 8.079 * [taylor]: Taking taylor expansion of PI in k 8.079 * [backup-simplify]: Simplify PI into PI 8.079 * [backup-simplify]: Simplify (* n PI) into (* n PI) 8.079 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 8.079 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 8.080 * [backup-simplify]: Simplify (- 0) into 0 8.080 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 8.080 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 8.080 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 8.080 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 8.080 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 8.080 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.080 * [taylor]: Taking taylor expansion of k in k 8.080 * [backup-simplify]: Simplify 0 into 0 8.080 * [backup-simplify]: Simplify 1 into 1 8.081 * [backup-simplify]: Simplify (/ 1 1) into 1 8.081 * [backup-simplify]: Simplify (sqrt 0) into 0 8.082 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.082 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in k 8.082 * [taylor]: Taking taylor expansion of 1.0 in k 8.082 * [backup-simplify]: Simplify 1.0 into 1.0 8.082 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in k 8.082 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 8.082 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 8.082 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 8.082 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 8.082 * [taylor]: Taking taylor expansion of 0.5 in k 8.082 * [backup-simplify]: Simplify 0.5 into 0.5 8.082 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 8.082 * [taylor]: Taking taylor expansion of 1.0 in k 8.082 * [backup-simplify]: Simplify 1.0 into 1.0 8.082 * [taylor]: Taking taylor expansion of k in k 8.082 * [backup-simplify]: Simplify 0 into 0 8.082 * [backup-simplify]: Simplify 1 into 1 8.082 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 8.082 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 8.082 * [taylor]: Taking taylor expansion of 2.0 in k 8.082 * [backup-simplify]: Simplify 2.0 into 2.0 8.082 * [taylor]: Taking taylor expansion of (* n PI) in k 8.082 * [taylor]: Taking taylor expansion of n in k 8.082 * [backup-simplify]: Simplify n into n 8.082 * [taylor]: Taking taylor expansion of PI in k 8.082 * [backup-simplify]: Simplify PI into PI 8.082 * [backup-simplify]: Simplify (* n PI) into (* n PI) 8.082 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 8.083 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 8.083 * [backup-simplify]: Simplify (- 0) into 0 8.083 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 8.083 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 8.083 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 8.083 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 8.084 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 8.084 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.084 * [taylor]: Taking taylor expansion of k in k 8.084 * [backup-simplify]: Simplify 0 into 0 8.084 * [backup-simplify]: Simplify 1 into 1 8.084 * [backup-simplify]: Simplify (/ 1 1) into 1 8.084 * [backup-simplify]: Simplify (sqrt 0) into 0 8.085 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.085 * [backup-simplify]: Simplify (* (pow (* 2.0 (* n PI)) 0.5) 0) into 0 8.085 * [backup-simplify]: Simplify (* 1.0 0) into 0 8.085 * [taylor]: Taking taylor expansion of 0 in n 8.085 * [backup-simplify]: Simplify 0 into 0 8.085 * [backup-simplify]: Simplify 0 into 0 8.086 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 8.086 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* n PI))) into 0 8.087 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 1) into 0 8.087 * [backup-simplify]: Simplify (- 1) into -1 8.087 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.088 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5) 8.089 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 (* n PI))))) into (- (* 0.5 (log (* 2.0 (* n PI))))) 8.089 * [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))))) 8.091 * [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))) 8.092 * [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))) 8.093 * [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 8.093 * [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 8.093 * [taylor]: Taking taylor expansion of +nan.0 in n 8.093 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.093 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 8.093 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 8.093 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 8.093 * [taylor]: Taking taylor expansion of 0.5 in n 8.093 * [backup-simplify]: Simplify 0.5 into 0.5 8.093 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 8.093 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 8.093 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 8.093 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 8.093 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 8.093 * [taylor]: Taking taylor expansion of 1.0 in n 8.093 * [backup-simplify]: Simplify 1.0 into 1.0 8.093 * [taylor]: Taking taylor expansion of (log PI) in n 8.093 * [taylor]: Taking taylor expansion of PI in n 8.093 * [backup-simplify]: Simplify PI into PI 8.094 * [backup-simplify]: Simplify (log PI) into (log PI) 8.095 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 8.096 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 8.096 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 8.096 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 8.096 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 8.096 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 8.096 * [taylor]: Taking taylor expansion of 1.0 in n 8.096 * [backup-simplify]: Simplify 1.0 into 1.0 8.096 * [taylor]: Taking taylor expansion of (log n) in n 8.097 * [taylor]: Taking taylor expansion of n in n 8.097 * [backup-simplify]: Simplify 0 into 0 8.097 * [backup-simplify]: Simplify 1 into 1 8.097 * [backup-simplify]: Simplify (log 1) into 0 8.104 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 8.105 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 8.105 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 8.105 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 8.105 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 8.105 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 8.105 * [taylor]: Taking taylor expansion of 1.0 in n 8.105 * [backup-simplify]: Simplify 1.0 into 1.0 8.105 * [taylor]: Taking taylor expansion of (log 2.0) in n 8.105 * [taylor]: Taking taylor expansion of 2.0 in n 8.105 * [backup-simplify]: Simplify 2.0 into 2.0 8.106 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 8.107 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 8.108 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 8.109 * [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) 8.110 * [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) 8.111 * [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)) 8.113 * [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))) 8.114 * [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) 8.116 * [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)) 8.117 * [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))) 8.118 * [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))) 8.119 * [backup-simplify]: Simplify 0 into 0 8.119 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 8.122 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 8.123 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 8.124 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 8.126 * [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 8.126 * [backup-simplify]: Simplify (- 0) into 0 8.127 * [backup-simplify]: Simplify (+ 0 0) into 0 8.128 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0 8.129 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 (* n PI)))))) into 0 8.130 * [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))) 8.135 * [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))))) 8.140 * [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))))) 8.140 * [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 8.140 * [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 8.140 * [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 8.140 * [taylor]: Taking taylor expansion of +nan.0 in n 8.140 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.140 * [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 8.140 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 8.141 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 8.141 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 8.141 * [taylor]: Taking taylor expansion of 0.5 in n 8.141 * [backup-simplify]: Simplify 0.5 into 0.5 8.141 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 8.141 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 8.141 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 8.141 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 8.141 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 8.141 * [taylor]: Taking taylor expansion of 1.0 in n 8.141 * [backup-simplify]: Simplify 1.0 into 1.0 8.141 * [taylor]: Taking taylor expansion of (log PI) in n 8.141 * [taylor]: Taking taylor expansion of PI in n 8.141 * [backup-simplify]: Simplify PI into PI 8.142 * [backup-simplify]: Simplify (log PI) into (log PI) 8.143 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 8.144 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 8.144 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 8.144 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 8.144 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 8.144 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 8.144 * [taylor]: Taking taylor expansion of 1.0 in n 8.145 * [backup-simplify]: Simplify 1.0 into 1.0 8.145 * [taylor]: Taking taylor expansion of (log n) in n 8.145 * [taylor]: Taking taylor expansion of n in n 8.145 * [backup-simplify]: Simplify 0 into 0 8.145 * [backup-simplify]: Simplify 1 into 1 8.145 * [backup-simplify]: Simplify (log 1) into 0 8.145 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 8.146 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 8.146 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 8.146 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 8.146 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 8.146 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 8.146 * [taylor]: Taking taylor expansion of 1.0 in n 8.146 * [backup-simplify]: Simplify 1.0 into 1.0 8.146 * [taylor]: Taking taylor expansion of (log 2.0) in n 8.146 * [taylor]: Taking taylor expansion of 2.0 in n 8.146 * [backup-simplify]: Simplify 2.0 into 2.0 8.146 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 8.147 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 8.149 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 8.149 * [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) 8.151 * [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) 8.152 * [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)) 8.153 * [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))) 8.155 * [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) 8.155 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 8.155 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 8.155 * [taylor]: Taking taylor expansion of 2.0 in n 8.155 * [backup-simplify]: Simplify 2.0 into 2.0 8.155 * [taylor]: Taking taylor expansion of (* n PI) in n 8.155 * [taylor]: Taking taylor expansion of n in n 8.155 * [backup-simplify]: Simplify 0 into 0 8.155 * [backup-simplify]: Simplify 1 into 1 8.155 * [taylor]: Taking taylor expansion of PI in n 8.155 * [backup-simplify]: Simplify PI into PI 8.156 * [backup-simplify]: Simplify (* 0 PI) into 0 8.156 * [backup-simplify]: Simplify (* 2.0 0) into 0 8.158 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.159 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 8.160 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.160 * [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 8.160 * [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 8.160 * [taylor]: Taking taylor expansion of +nan.0 in n 8.160 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.160 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 8.160 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 8.161 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 8.161 * [taylor]: Taking taylor expansion of 0.5 in n 8.161 * [backup-simplify]: Simplify 0.5 into 0.5 8.161 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 8.161 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 8.161 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 8.161 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 8.161 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 8.161 * [taylor]: Taking taylor expansion of 1.0 in n 8.161 * [backup-simplify]: Simplify 1.0 into 1.0 8.161 * [taylor]: Taking taylor expansion of (log PI) in n 8.161 * [taylor]: Taking taylor expansion of PI in n 8.161 * [backup-simplify]: Simplify PI into PI 8.161 * [backup-simplify]: Simplify (log PI) into (log PI) 8.162 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 8.164 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 8.164 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 8.164 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 8.164 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 8.164 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 8.164 * [taylor]: Taking taylor expansion of 1.0 in n 8.164 * [backup-simplify]: Simplify 1.0 into 1.0 8.164 * [taylor]: Taking taylor expansion of (log n) in n 8.164 * [taylor]: Taking taylor expansion of n in n 8.164 * [backup-simplify]: Simplify 0 into 0 8.164 * [backup-simplify]: Simplify 1 into 1 8.165 * [backup-simplify]: Simplify (log 1) into 0 8.165 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 8.165 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 8.165 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 8.165 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 8.165 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 8.165 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 8.165 * [taylor]: Taking taylor expansion of 1.0 in n 8.165 * [backup-simplify]: Simplify 1.0 into 1.0 8.166 * [taylor]: Taking taylor expansion of (log 2.0) in n 8.166 * [taylor]: Taking taylor expansion of 2.0 in n 8.166 * [backup-simplify]: Simplify 2.0 into 2.0 8.166 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 8.167 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 8.168 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 8.169 * [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) 8.170 * [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) 8.172 * [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)) 8.173 * [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))) 8.174 * [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) 8.176 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.179 * [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))) 8.181 * [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)))) 8.183 * [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)) 8.184 * [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))) 8.188 * [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))))))) 8.195 * [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))))))))) 8.201 * [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))))))) 8.203 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0 8.204 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log 2.0))) into 0 8.205 * [backup-simplify]: Simplify (* (exp (* 1.0 (log 2.0))) (+ (* (/ (pow 0 1) 1)))) into 0 8.206 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 8.207 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 8.207 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log n))) into 0 8.208 * [backup-simplify]: Simplify (* (exp (* 1.0 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 8.209 * [backup-simplify]: Simplify (+ (* (pow n 1.0) 0) (* 0 (pow 2.0 1.0))) into 0 8.210 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 8.211 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log PI))) into 0 8.213 * [backup-simplify]: Simplify (* (exp (* 1.0 (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 8.214 * [backup-simplify]: Simplify (+ (* (pow PI 1.0) 0) (* 0 (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0))) into 0 8.217 * [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 8.218 * [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 8.221 * [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 8.223 * [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 8.223 * [backup-simplify]: Simplify (- 0) into 0 8.223 * [backup-simplify]: Simplify 0 into 0 8.223 * [backup-simplify]: Simplify 0 into 0 8.224 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.228 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 8.229 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 8.230 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 8.233 * [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 8.233 * [backup-simplify]: Simplify (- 0) into 0 8.234 * [backup-simplify]: Simplify (+ 0 0) into 0 8.235 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1.0)))) into 0 8.236 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (+ (* 0 0) (* 0 (log (* 2.0 (* n PI))))))) into 0 8.238 * [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))) 8.244 * [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)))))))) 8.262 * [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)))))))) 8.262 * [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 8.262 * [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 8.262 * [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 8.262 * [taylor]: Taking taylor expansion of +nan.0 in n 8.262 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.262 * [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 8.262 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 8.262 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 8.262 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 8.263 * [taylor]: Taking taylor expansion of 0.5 in n 8.263 * [backup-simplify]: Simplify 0.5 into 0.5 8.263 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 8.263 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 8.263 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 8.263 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 8.263 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 8.263 * [taylor]: Taking taylor expansion of 1.0 in n 8.263 * [backup-simplify]: Simplify 1.0 into 1.0 8.263 * [taylor]: Taking taylor expansion of (log PI) in n 8.263 * [taylor]: Taking taylor expansion of PI in n 8.263 * [backup-simplify]: Simplify PI into PI 8.263 * [backup-simplify]: Simplify (log PI) into (log PI) 8.264 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 8.266 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 8.266 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 8.266 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 8.266 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 8.266 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 8.266 * [taylor]: Taking taylor expansion of 1.0 in n 8.266 * [backup-simplify]: Simplify 1.0 into 1.0 8.266 * [taylor]: Taking taylor expansion of (log n) in n 8.266 * [taylor]: Taking taylor expansion of n in n 8.266 * [backup-simplify]: Simplify 0 into 0 8.266 * [backup-simplify]: Simplify 1 into 1 8.267 * [backup-simplify]: Simplify (log 1) into 0 8.267 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 8.267 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 8.267 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 8.267 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 8.267 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 8.267 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 8.267 * [taylor]: Taking taylor expansion of 1.0 in n 8.267 * [backup-simplify]: Simplify 1.0 into 1.0 8.267 * [taylor]: Taking taylor expansion of (log 2.0) in n 8.267 * [taylor]: Taking taylor expansion of 2.0 in n 8.267 * [backup-simplify]: Simplify 2.0 into 2.0 8.268 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 8.269 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 8.270 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 8.270 * [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) 8.271 * [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) 8.272 * [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)) 8.273 * [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))) 8.273 * [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) 8.273 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 8.273 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 8.273 * [taylor]: Taking taylor expansion of 2.0 in n 8.274 * [backup-simplify]: Simplify 2.0 into 2.0 8.274 * [taylor]: Taking taylor expansion of (* n PI) in n 8.274 * [taylor]: Taking taylor expansion of n in n 8.274 * [backup-simplify]: Simplify 0 into 0 8.274 * [backup-simplify]: Simplify 1 into 1 8.274 * [taylor]: Taking taylor expansion of PI in n 8.274 * [backup-simplify]: Simplify PI into PI 8.274 * [backup-simplify]: Simplify (* 0 PI) into 0 8.274 * [backup-simplify]: Simplify (* 2.0 0) into 0 8.275 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.276 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 8.277 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.277 * [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 8.277 * [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 8.277 * [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 8.277 * [taylor]: Taking taylor expansion of +nan.0 in n 8.277 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.277 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n 8.277 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n 8.277 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n 8.277 * [taylor]: Taking taylor expansion of 0.5 in n 8.277 * [backup-simplify]: Simplify 0.5 into 0.5 8.277 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n 8.277 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n 8.277 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 8.277 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 8.277 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 8.277 * [taylor]: Taking taylor expansion of 1.0 in n 8.277 * [backup-simplify]: Simplify 1.0 into 1.0 8.277 * [taylor]: Taking taylor expansion of (log 2.0) in n 8.277 * [taylor]: Taking taylor expansion of 2.0 in n 8.277 * [backup-simplify]: Simplify 2.0 into 2.0 8.277 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 8.278 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 8.279 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 8.279 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n 8.279 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 8.279 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 8.279 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 8.279 * [taylor]: Taking taylor expansion of 1.0 in n 8.279 * [backup-simplify]: Simplify 1.0 into 1.0 8.279 * [taylor]: Taking taylor expansion of (log n) in n 8.279 * [taylor]: Taking taylor expansion of n in n 8.279 * [backup-simplify]: Simplify 0 into 0 8.279 * [backup-simplify]: Simplify 1 into 1 8.279 * [backup-simplify]: Simplify (log 1) into 0 8.279 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 8.279 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 8.279 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 8.279 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 8.279 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 8.280 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 8.280 * [taylor]: Taking taylor expansion of 1.0 in n 8.280 * [backup-simplify]: Simplify 1.0 into 1.0 8.280 * [taylor]: Taking taylor expansion of (log PI) in n 8.280 * [taylor]: Taking taylor expansion of PI in n 8.280 * [backup-simplify]: Simplify PI into PI 8.280 * [backup-simplify]: Simplify (log PI) into (log PI) 8.280 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 8.281 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 8.282 * [backup-simplify]: Simplify (* (pow n 1.0) (pow PI 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 8.283 * [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) 8.283 * [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)) 8.284 * [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))) 8.285 * [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) 8.285 * [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 8.285 * [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 8.285 * [taylor]: Taking taylor expansion of +nan.0 in n 8.285 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.285 * [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 8.285 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 8.285 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 8.285 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 8.285 * [taylor]: Taking taylor expansion of 0.5 in n 8.285 * [backup-simplify]: Simplify 0.5 into 0.5 8.285 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 8.285 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 8.285 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 8.285 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 8.285 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 8.285 * [taylor]: Taking taylor expansion of 1.0 in n 8.285 * [backup-simplify]: Simplify 1.0 into 1.0 8.285 * [taylor]: Taking taylor expansion of (log PI) in n 8.285 * [taylor]: Taking taylor expansion of PI in n 8.285 * [backup-simplify]: Simplify PI into PI 8.286 * [backup-simplify]: Simplify (log PI) into (log PI) 8.286 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 8.287 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 8.287 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 8.287 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 8.287 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 8.287 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 8.287 * [taylor]: Taking taylor expansion of 1.0 in n 8.287 * [backup-simplify]: Simplify 1.0 into 1.0 8.287 * [taylor]: Taking taylor expansion of (log n) in n 8.287 * [taylor]: Taking taylor expansion of n in n 8.287 * [backup-simplify]: Simplify 0 into 0 8.287 * [backup-simplify]: Simplify 1 into 1 8.288 * [backup-simplify]: Simplify (log 1) into 0 8.288 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 8.288 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 8.288 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 8.288 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 8.288 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 8.288 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 8.288 * [taylor]: Taking taylor expansion of 1.0 in n 8.288 * [backup-simplify]: Simplify 1.0 into 1.0 8.288 * [taylor]: Taking taylor expansion of (log 2.0) in n 8.288 * [taylor]: Taking taylor expansion of 2.0 in n 8.288 * [backup-simplify]: Simplify 2.0 into 2.0 8.288 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 8.289 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 8.290 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 8.290 * [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) 8.291 * [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) 8.292 * [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)) 8.293 * [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))) 8.294 * [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) 8.294 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n 8.294 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 8.294 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 8.294 * [taylor]: Taking taylor expansion of 2.0 in n 8.294 * [backup-simplify]: Simplify 2.0 into 2.0 8.294 * [taylor]: Taking taylor expansion of (* n PI) in n 8.294 * [taylor]: Taking taylor expansion of n in n 8.294 * [backup-simplify]: Simplify 0 into 0 8.294 * [backup-simplify]: Simplify 1 into 1 8.294 * [taylor]: Taking taylor expansion of PI in n 8.294 * [backup-simplify]: Simplify PI into PI 8.294 * [backup-simplify]: Simplify (* 0 PI) into 0 8.295 * [backup-simplify]: Simplify (* 2.0 0) into 0 8.295 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.296 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 8.297 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.298 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.299 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.301 * [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))) 8.302 * [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)))) 8.303 * [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)) 8.304 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.305 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.306 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (+ (log (* 2.0 PI)) (log n))) into (pow (+ (log (* 2.0 PI)) (log n)) 2) 8.308 * [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)) 8.309 * [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))) 8.311 * [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)))))))) 8.317 * [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))))))))) 8.323 * [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)))))))))) 8.331 * [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))))))))))))) 8.344 * [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))))))))))))) 8.361 * [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))))))))))))))) 8.394 * [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))))))))))))))))))))))) 8.394 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt (/ 1 k))) (pow (* 2.0 (* (/ 1 n) PI)) (/ (- 1.0 (/ 1 k)) 2.0))) into (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) 8.394 * [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 8.394 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in n 8.394 * [taylor]: Taking taylor expansion of 1.0 in n 8.395 * [backup-simplify]: Simplify 1.0 into 1.0 8.395 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in n 8.395 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 8.395 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 8.395 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 8.395 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 8.395 * [taylor]: Taking taylor expansion of 0.5 in n 8.395 * [backup-simplify]: Simplify 0.5 into 0.5 8.395 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 8.395 * [taylor]: Taking taylor expansion of 1.0 in n 8.395 * [backup-simplify]: Simplify 1.0 into 1.0 8.395 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.395 * [taylor]: Taking taylor expansion of k in n 8.395 * [backup-simplify]: Simplify k into k 8.395 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.395 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 8.395 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 8.395 * [taylor]: Taking taylor expansion of 2.0 in n 8.395 * [backup-simplify]: Simplify 2.0 into 2.0 8.395 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.395 * [taylor]: Taking taylor expansion of PI in n 8.395 * [backup-simplify]: Simplify PI into PI 8.395 * [taylor]: Taking taylor expansion of n in n 8.395 * [backup-simplify]: Simplify 0 into 0 8.395 * [backup-simplify]: Simplify 1 into 1 8.396 * [backup-simplify]: Simplify (/ PI 1) into PI 8.396 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.397 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.397 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 8.398 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 8.398 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 8.399 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.400 * [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)))) 8.401 * [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))))) 8.401 * [taylor]: Taking taylor expansion of (sqrt k) in n 8.401 * [taylor]: Taking taylor expansion of k in n 8.401 * [backup-simplify]: Simplify k into k 8.402 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 8.402 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 8.402 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in k 8.402 * [taylor]: Taking taylor expansion of 1.0 in k 8.402 * [backup-simplify]: Simplify 1.0 into 1.0 8.402 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in k 8.402 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 8.402 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 8.402 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 8.402 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 8.402 * [taylor]: Taking taylor expansion of 0.5 in k 8.402 * [backup-simplify]: Simplify 0.5 into 0.5 8.402 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 8.402 * [taylor]: Taking taylor expansion of 1.0 in k 8.402 * [backup-simplify]: Simplify 1.0 into 1.0 8.402 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.402 * [taylor]: Taking taylor expansion of k in k 8.402 * [backup-simplify]: Simplify 0 into 0 8.402 * [backup-simplify]: Simplify 1 into 1 8.402 * [backup-simplify]: Simplify (/ 1 1) into 1 8.402 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 8.402 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 8.403 * [taylor]: Taking taylor expansion of 2.0 in k 8.403 * [backup-simplify]: Simplify 2.0 into 2.0 8.403 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.403 * [taylor]: Taking taylor expansion of PI in k 8.403 * [backup-simplify]: Simplify PI into PI 8.403 * [taylor]: Taking taylor expansion of n in k 8.403 * [backup-simplify]: Simplify n into n 8.403 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 8.403 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 8.403 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 8.403 * [backup-simplify]: Simplify (- 1) into -1 8.404 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.404 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 8.404 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 8.404 * [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)))))) 8.405 * [taylor]: Taking taylor expansion of (sqrt k) in k 8.405 * [taylor]: Taking taylor expansion of k in k 8.405 * [backup-simplify]: Simplify 0 into 0 8.405 * [backup-simplify]: Simplify 1 into 1 8.405 * [backup-simplify]: Simplify (sqrt 0) into 0 8.406 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.406 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in k 8.406 * [taylor]: Taking taylor expansion of 1.0 in k 8.406 * [backup-simplify]: Simplify 1.0 into 1.0 8.406 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in k 8.406 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 8.407 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 8.407 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 8.407 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 8.407 * [taylor]: Taking taylor expansion of 0.5 in k 8.407 * [backup-simplify]: Simplify 0.5 into 0.5 8.407 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 8.407 * [taylor]: Taking taylor expansion of 1.0 in k 8.407 * [backup-simplify]: Simplify 1.0 into 1.0 8.407 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.407 * [taylor]: Taking taylor expansion of k in k 8.407 * [backup-simplify]: Simplify 0 into 0 8.407 * [backup-simplify]: Simplify 1 into 1 8.407 * [backup-simplify]: Simplify (/ 1 1) into 1 8.407 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 8.407 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 8.407 * [taylor]: Taking taylor expansion of 2.0 in k 8.407 * [backup-simplify]: Simplify 2.0 into 2.0 8.407 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.407 * [taylor]: Taking taylor expansion of PI in k 8.407 * [backup-simplify]: Simplify PI into PI 8.407 * [taylor]: Taking taylor expansion of n in k 8.407 * [backup-simplify]: Simplify n into n 8.407 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 8.408 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 8.408 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 8.408 * [backup-simplify]: Simplify (- 1) into -1 8.408 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.409 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 8.409 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 8.409 * [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)))))) 8.409 * [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 8.410 * [backup-simplify]: Simplify (sqrt 0) into 0 8.411 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.411 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) 0) into 0 8.412 * [backup-simplify]: Simplify (* 1.0 0) into 0 8.412 * [taylor]: Taking taylor expansion of 0 in n 8.412 * [backup-simplify]: Simplify 0 into 0 8.412 * [backup-simplify]: Simplify 0 into 0 8.412 * [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)))))))) 8.413 * [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)))))))) 8.413 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) in n 8.413 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))) in n 8.413 * [taylor]: Taking taylor expansion of +nan.0 in n 8.413 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.413 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) in n 8.413 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))) in n 8.413 * [taylor]: Taking taylor expansion of 0.5 in n 8.413 * [backup-simplify]: Simplify 0.5 into 0.5 8.413 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))) in n 8.413 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 8.413 * [taylor]: Taking taylor expansion of 1.0 in n 8.413 * [backup-simplify]: Simplify 1.0 into 1.0 8.414 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.414 * [taylor]: Taking taylor expansion of k in n 8.414 * [backup-simplify]: Simplify k into k 8.414 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.414 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 8.414 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 8.414 * [taylor]: Taking taylor expansion of 2.0 in n 8.414 * [backup-simplify]: Simplify 2.0 into 2.0 8.414 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.414 * [taylor]: Taking taylor expansion of PI in n 8.414 * [backup-simplify]: Simplify PI into PI 8.414 * [taylor]: Taking taylor expansion of n in n 8.414 * [backup-simplify]: Simplify 0 into 0 8.414 * [backup-simplify]: Simplify 1 into 1 8.414 * [backup-simplify]: Simplify (/ PI 1) into PI 8.415 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.416 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.416 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 8.416 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 8.417 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.419 * [backup-simplify]: Simplify (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) into (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) 8.420 * [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)))) 8.421 * [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))))) 8.422 * [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)))))) 8.424 * [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))))))) 8.425 * [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))))))) 8.425 * [backup-simplify]: Simplify 0 into 0 8.428 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 8.429 * [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)))))))) 8.430 * [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)))))))) 8.430 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) in n 8.430 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))) in n 8.430 * [taylor]: Taking taylor expansion of +nan.0 in n 8.430 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.431 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) in n 8.431 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))) in n 8.431 * [taylor]: Taking taylor expansion of 0.5 in n 8.431 * [backup-simplify]: Simplify 0.5 into 0.5 8.431 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))) in n 8.431 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 8.431 * [taylor]: Taking taylor expansion of 1.0 in n 8.431 * [backup-simplify]: Simplify 1.0 into 1.0 8.431 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.431 * [taylor]: Taking taylor expansion of k in n 8.431 * [backup-simplify]: Simplify k into k 8.431 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.431 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 8.431 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 8.431 * [taylor]: Taking taylor expansion of 2.0 in n 8.431 * [backup-simplify]: Simplify 2.0 into 2.0 8.431 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.431 * [taylor]: Taking taylor expansion of PI in n 8.431 * [backup-simplify]: Simplify PI into PI 8.431 * [taylor]: Taking taylor expansion of n in n 8.431 * [backup-simplify]: Simplify 0 into 0 8.431 * [backup-simplify]: Simplify 1 into 1 8.432 * [backup-simplify]: Simplify (/ PI 1) into PI 8.432 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.433 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.433 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 8.434 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 8.435 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.436 * [backup-simplify]: Simplify (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) into (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) 8.438 * [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)))) 8.439 * [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))))) 8.440 * [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)))))) 8.442 * [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))))))) 8.443 * [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))))))) 8.445 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.445 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 8.447 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 8.447 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 8.448 * [backup-simplify]: Simplify (- 0) into 0 8.448 * [backup-simplify]: Simplify (+ 0 0) into 0 8.450 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.451 * [backup-simplify]: Simplify (+ (* (- 1.0 (/ 1 k)) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 8.453 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into 0 8.455 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 8.456 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into 0 8.457 * [backup-simplify]: Simplify (- 0) into 0 8.457 * [backup-simplify]: Simplify 0 into 0 8.457 * [backup-simplify]: Simplify 0 into 0 8.461 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 8.462 * [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)))))))) 8.463 * [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)))))))) 8.463 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) in n 8.463 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))) in n 8.463 * [taylor]: Taking taylor expansion of +nan.0 in n 8.463 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.463 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) in n 8.464 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))) in n 8.464 * [taylor]: Taking taylor expansion of 0.5 in n 8.464 * [backup-simplify]: Simplify 0.5 into 0.5 8.464 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))) in n 8.464 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 8.464 * [taylor]: Taking taylor expansion of 1.0 in n 8.464 * [backup-simplify]: Simplify 1.0 into 1.0 8.464 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.464 * [taylor]: Taking taylor expansion of k in n 8.464 * [backup-simplify]: Simplify k into k 8.464 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.464 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 8.464 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 8.464 * [taylor]: Taking taylor expansion of 2.0 in n 8.464 * [backup-simplify]: Simplify 2.0 into 2.0 8.464 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.464 * [taylor]: Taking taylor expansion of PI in n 8.464 * [backup-simplify]: Simplify PI into PI 8.464 * [taylor]: Taking taylor expansion of n in n 8.464 * [backup-simplify]: Simplify 0 into 0 8.464 * [backup-simplify]: Simplify 1 into 1 8.465 * [backup-simplify]: Simplify (/ PI 1) into PI 8.465 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.467 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.467 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 8.467 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 8.468 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.469 * [backup-simplify]: Simplify (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) into (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) 8.471 * [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)))) 8.472 * [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))))) 8.473 * [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)))))) 8.475 * [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))))))) 8.476 * [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))))))) 8.481 * [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)))))))) 8.482 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt (/ 1 (- k)))) (pow (* 2.0 (* (/ 1 (- n)) PI)) (/ (- 1.0 (/ 1 (- k))) 2.0))) into (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) 8.482 * [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 8.482 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n 8.482 * [taylor]: Taking taylor expansion of 1.0 in n 8.482 * [backup-simplify]: Simplify 1.0 into 1.0 8.482 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n 8.482 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 8.482 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 8.482 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 8.482 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 8.482 * [taylor]: Taking taylor expansion of 0.5 in n 8.482 * [backup-simplify]: Simplify 0.5 into 0.5 8.482 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 8.482 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.482 * [taylor]: Taking taylor expansion of k in n 8.482 * [backup-simplify]: Simplify k into k 8.482 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.482 * [taylor]: Taking taylor expansion of 1.0 in n 8.482 * [backup-simplify]: Simplify 1.0 into 1.0 8.482 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 8.482 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 8.482 * [taylor]: Taking taylor expansion of -2.0 in n 8.482 * [backup-simplify]: Simplify -2.0 into -2.0 8.482 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.482 * [taylor]: Taking taylor expansion of PI in n 8.482 * [backup-simplify]: Simplify PI into PI 8.482 * [taylor]: Taking taylor expansion of n in n 8.482 * [backup-simplify]: Simplify 0 into 0 8.482 * [backup-simplify]: Simplify 1 into 1 8.483 * [backup-simplify]: Simplify (/ PI 1) into PI 8.484 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.485 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 8.485 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 8.485 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 8.486 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.488 * [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))) 8.489 * [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)))) 8.489 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 8.489 * [taylor]: Taking taylor expansion of (/ -1 k) in n 8.489 * [taylor]: Taking taylor expansion of -1 in n 8.489 * [backup-simplify]: Simplify -1 into -1 8.489 * [taylor]: Taking taylor expansion of k in n 8.489 * [backup-simplify]: Simplify k into k 8.489 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 8.489 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 8.489 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 8.489 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 8.491 * [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))) 8.491 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 8.491 * [taylor]: Taking taylor expansion of 1.0 in k 8.491 * [backup-simplify]: Simplify 1.0 into 1.0 8.491 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 8.491 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 8.491 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 8.491 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 8.491 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 8.491 * [taylor]: Taking taylor expansion of 0.5 in k 8.491 * [backup-simplify]: Simplify 0.5 into 0.5 8.491 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 8.491 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.491 * [taylor]: Taking taylor expansion of k in k 8.491 * [backup-simplify]: Simplify 0 into 0 8.491 * [backup-simplify]: Simplify 1 into 1 8.492 * [backup-simplify]: Simplify (/ 1 1) into 1 8.492 * [taylor]: Taking taylor expansion of 1.0 in k 8.492 * [backup-simplify]: Simplify 1.0 into 1.0 8.492 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 8.492 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 8.492 * [taylor]: Taking taylor expansion of -2.0 in k 8.492 * [backup-simplify]: Simplify -2.0 into -2.0 8.492 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.492 * [taylor]: Taking taylor expansion of PI in k 8.492 * [backup-simplify]: Simplify PI into PI 8.492 * [taylor]: Taking taylor expansion of n in k 8.492 * [backup-simplify]: Simplify n into n 8.492 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 8.492 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 8.492 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 8.493 * [backup-simplify]: Simplify (+ 1 0) into 1 8.493 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 8.493 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 8.494 * [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)))) 8.494 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 8.494 * [taylor]: Taking taylor expansion of (/ -1 k) in k 8.494 * [taylor]: Taking taylor expansion of -1 in k 8.494 * [backup-simplify]: Simplify -1 into -1 8.494 * [taylor]: Taking taylor expansion of k in k 8.494 * [backup-simplify]: Simplify 0 into 0 8.494 * [backup-simplify]: Simplify 1 into 1 8.495 * [backup-simplify]: Simplify (/ -1 1) into -1 8.495 * [backup-simplify]: Simplify (sqrt 0) into 0 8.496 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 8.497 * [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))))) 8.497 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 8.497 * [taylor]: Taking taylor expansion of 1.0 in k 8.497 * [backup-simplify]: Simplify 1.0 into 1.0 8.497 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 8.497 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 8.497 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 8.497 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 8.497 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 8.497 * [taylor]: Taking taylor expansion of 0.5 in k 8.497 * [backup-simplify]: Simplify 0.5 into 0.5 8.497 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 8.497 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.497 * [taylor]: Taking taylor expansion of k in k 8.497 * [backup-simplify]: Simplify 0 into 0 8.497 * [backup-simplify]: Simplify 1 into 1 8.498 * [backup-simplify]: Simplify (/ 1 1) into 1 8.498 * [taylor]: Taking taylor expansion of 1.0 in k 8.498 * [backup-simplify]: Simplify 1.0 into 1.0 8.498 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 8.498 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 8.498 * [taylor]: Taking taylor expansion of -2.0 in k 8.498 * [backup-simplify]: Simplify -2.0 into -2.0 8.498 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.498 * [taylor]: Taking taylor expansion of PI in k 8.498 * [backup-simplify]: Simplify PI into PI 8.498 * [taylor]: Taking taylor expansion of n in k 8.498 * [backup-simplify]: Simplify n into n 8.498 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 8.498 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 8.498 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 8.499 * [backup-simplify]: Simplify (+ 1 0) into 1 8.499 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 8.499 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 8.500 * [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)))) 8.500 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 8.500 * [taylor]: Taking taylor expansion of (/ -1 k) in k 8.500 * [taylor]: Taking taylor expansion of -1 in k 8.500 * [backup-simplify]: Simplify -1 into -1 8.500 * [taylor]: Taking taylor expansion of k in k 8.500 * [backup-simplify]: Simplify 0 into 0 8.500 * [backup-simplify]: Simplify 1 into 1 8.500 * [backup-simplify]: Simplify (/ -1 1) into -1 8.501 * [backup-simplify]: Simplify (sqrt 0) into 0 8.502 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 8.502 * [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))))) 8.503 * [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))))) 8.503 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) in n 8.503 * [taylor]: Taking taylor expansion of +nan.0 in n 8.503 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.503 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) in n 8.503 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))) in n 8.503 * [taylor]: Taking taylor expansion of 0.5 in n 8.503 * [backup-simplify]: Simplify 0.5 into 0.5 8.503 * [taylor]: Taking taylor expansion of (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)) in n 8.503 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 8.503 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 8.503 * [taylor]: Taking taylor expansion of -2.0 in n 8.503 * [backup-simplify]: Simplify -2.0 into -2.0 8.503 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.503 * [taylor]: Taking taylor expansion of PI in n 8.503 * [backup-simplify]: Simplify PI into PI 8.503 * [taylor]: Taking taylor expansion of n in n 8.503 * [backup-simplify]: Simplify 0 into 0 8.503 * [backup-simplify]: Simplify 1 into 1 8.504 * [backup-simplify]: Simplify (/ PI 1) into PI 8.504 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.505 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 8.505 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 8.505 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.505 * [taylor]: Taking taylor expansion of k in n 8.505 * [backup-simplify]: Simplify k into k 8.505 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.505 * [taylor]: Taking taylor expansion of 1.0 in n 8.505 * [backup-simplify]: Simplify 1.0 into 1.0 8.507 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.507 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 8.508 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) into (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) 8.509 * [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))) 8.511 * [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)))) 8.512 * [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))))) 8.513 * [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))))) 8.514 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 8.517 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 8.524 * [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)))))) 8.525 * [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)))))) 8.525 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) in n 8.525 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) in n 8.525 * [taylor]: Taking taylor expansion of +nan.0 in n 8.525 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.525 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) in n 8.525 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))) in n 8.525 * [taylor]: Taking taylor expansion of 0.5 in n 8.525 * [backup-simplify]: Simplify 0.5 into 0.5 8.525 * [taylor]: Taking taylor expansion of (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)) in n 8.525 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 8.525 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 8.525 * [taylor]: Taking taylor expansion of -2.0 in n 8.525 * [backup-simplify]: Simplify -2.0 into -2.0 8.525 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.525 * [taylor]: Taking taylor expansion of PI in n 8.525 * [backup-simplify]: Simplify PI into PI 8.525 * [taylor]: Taking taylor expansion of n in n 8.525 * [backup-simplify]: Simplify 0 into 0 8.525 * [backup-simplify]: Simplify 1 into 1 8.526 * [backup-simplify]: Simplify (/ PI 1) into PI 8.526 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.528 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 8.528 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 8.528 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.528 * [taylor]: Taking taylor expansion of k in n 8.528 * [backup-simplify]: Simplify k into k 8.528 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.528 * [taylor]: Taking taylor expansion of 1.0 in n 8.528 * [backup-simplify]: Simplify 1.0 into 1.0 8.529 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.529 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 8.531 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) into (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) 8.532 * [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))) 8.533 * [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)))) 8.534 * [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))))) 8.536 * [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)))))) 8.537 * [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)))))) 8.539 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.539 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 8.539 * [backup-simplify]: Simplify (+ 0 0) into 0 8.540 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.541 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 8.543 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 8.544 * [backup-simplify]: Simplify (+ (* (- (log (* -2.0 PI)) (log n)) 0) (* 0 (+ (/ 1 k) 1.0))) into 0 8.546 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into 0 8.548 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 8.550 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into 0 8.550 * [backup-simplify]: Simplify 0 into 0 8.551 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.555 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 8.557 * [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)))))) 8.559 * [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)))))) 8.559 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) in n 8.559 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) in n 8.559 * [taylor]: Taking taylor expansion of +nan.0 in n 8.559 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.559 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) in n 8.559 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))) in n 8.559 * [taylor]: Taking taylor expansion of 0.5 in n 8.559 * [backup-simplify]: Simplify 0.5 into 0.5 8.559 * [taylor]: Taking taylor expansion of (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)) in n 8.559 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 8.559 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 8.559 * [taylor]: Taking taylor expansion of -2.0 in n 8.559 * [backup-simplify]: Simplify -2.0 into -2.0 8.559 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.559 * [taylor]: Taking taylor expansion of PI in n 8.559 * [backup-simplify]: Simplify PI into PI 8.559 * [taylor]: Taking taylor expansion of n in n 8.559 * [backup-simplify]: Simplify 0 into 0 8.559 * [backup-simplify]: Simplify 1 into 1 8.560 * [backup-simplify]: Simplify (/ PI 1) into PI 8.561 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.562 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 8.562 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 8.562 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.562 * [taylor]: Taking taylor expansion of k in n 8.562 * [backup-simplify]: Simplify k into k 8.562 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.562 * [taylor]: Taking taylor expansion of 1.0 in n 8.562 * [backup-simplify]: Simplify 1.0 into 1.0 8.563 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.564 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 8.565 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) into (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) 8.566 * [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))) 8.567 * [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)))) 8.569 * [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))))) 8.570 * [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)))))) 8.571 * [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)))))) 8.576 * [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)))))))) 8.576 * * * [progress]: simplifying candidates 8.581 * [simplify]: Simplifying: (* (+ (log 2.0) (+ (log n) (log PI))) (/ (- 1.0 k) 2.0)) (* (+ (log 2.0) (log (* n PI))) (/ (- 1.0 k) 2.0)) (* (log (* 2.0 (* n PI))) (/ (- 1.0 k) 2.0)) (* (log (* 2.0 (* n PI))) (/ (- 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 (* n PI)) (/ 1.0 2.0)) (pow (* 2.0 (* n PI)) (/ k 2.0)) (pow (* 2.0 (* n PI)) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* 2.0 (* n PI)) (sqrt (/ (- 1.0 k) 2.0))) (pow (* 2.0 (* n PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* n PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* 2.0 (* n PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* 2.0 (* n PI)) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* n PI)) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* 2.0 (* n PI)) (/ (sqrt (- 1.0 k)) 1)) (pow (* 2.0 (* n PI)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* n PI)) (/ 1 (sqrt 2.0))) (pow (* 2.0 (* n PI)) (/ 1 1)) (pow (* 2.0 (* n PI)) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* n PI)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* 2.0 (* n PI)) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* 2.0 (* n PI)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* n PI)) (/ 1 (sqrt 2.0))) (pow (* 2.0 (* n PI)) (/ 1 1)) (pow (* 2.0 (* n PI)) 1) (pow (* 2.0 (* n PI)) (- 1.0 k)) (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0)) (log (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (exp (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (cbrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (pow (* 2.0 (* n PI)) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* 2.0 (* n PI)) (/ (/ (- 1.0 k) 2.0) 2)) (* n PI) (+ (log n) (log PI)) (log (* n PI)) (exp (* n PI)) (* (* (* n n) n) (* (* PI PI) PI)) (* (cbrt (* n PI)) (cbrt (* n PI))) (cbrt (* n PI)) (* (* (* n PI) (* n PI)) (* n PI)) (sqrt (* n PI)) (sqrt (* n PI)) (* (sqrt n) (sqrt PI)) (* (sqrt n) (sqrt PI)) (* n (* (cbrt PI) (cbrt PI))) (* n (sqrt PI)) (* n 1) (* (cbrt n) PI) (* (sqrt n) PI) (* n PI) (- (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 n) (log PI))) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (* (+ (log 2.0) (log (* n PI))) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (* (log (* 2.0 (* n PI))) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (* (log (* 2.0 (* n PI))) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (log (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))) (+ (log (/ 1.0 (sqrt k))) (* (+ (log 2.0) (+ (log n) (log PI))) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (* (+ (log 2.0) (log (* n PI))) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (* (log (* 2.0 (* n PI))) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (* (log (* 2.0 (* n PI))) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (log (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))) (exp (* (/ 1.0 (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))) (* (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))) (* (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (* (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))) (* (cbrt (* (/ 1.0 (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))) (* (* (* (/ 1.0 (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))) (* 1.0 (pow (* 2.0 (* n PI)) (/ 1.0 2.0))) (* (sqrt k) (pow (* 2.0 (* n PI)) (/ k 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* 2.0 (* n PI)) (/ (/ (- 1.0 k) 2.0) 2))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* 2.0 (* n PI)) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* 2.0 (* n PI)) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* 2.0 (* n PI)) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* 2.0 (* n PI)) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* 2.0 (* n PI)) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ 1.0 (sqrt k)) (pow 2.0 (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (* (cbrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (cbrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))))) (* (/ 1.0 (sqrt k)) (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) 1) (* (/ 1.0 (sqrt k)) (pow (* 2.0 (* n PI)) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (/ 1.0 (sqrt k))) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (cbrt (sqrt k))) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (cbrt k))) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (cbrt (sqrt k))) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (cbrt k))) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (cbrt (sqrt k))) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (cbrt k))) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* (/ 1 (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* 2.0 (* n PI)) (/ 1.0 2.0))) (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 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)))))) (* n PI) (* n PI) (* 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)))))))) 8.588 * * [simplify]: iteration 0: 352 enodes 8.702 * * [simplify]: iteration 1: 954 enodes 9.148 * * [simplify]: iteration 2: 3115 enodes 10.078 * * [simplify]: iteration complete: 5000 enodes 10.078 * * [simplify]: Extracting #0: cost 120 inf + 0 10.080 * * [simplify]: Extracting #1: cost 551 inf + 44 10.086 * * [simplify]: Extracting #2: cost 937 inf + 3570 10.100 * * [simplify]: Extracting #3: cost 1211 inf + 25997 10.155 * * [simplify]: Extracting #4: cost 819 inf + 184252 10.247 * * [simplify]: Extracting #5: cost 503 inf + 353323 10.355 * * [simplify]: Extracting #6: cost 295 inf + 581759 10.470 * * [simplify]: Extracting #7: cost 129 inf + 728440 10.653 * * [simplify]: Extracting #8: cost 32 inf + 820382 10.830 * * [simplify]: Extracting #9: cost 2 inf + 849747 11.016 * * [simplify]: Extracting #10: cost 0 inf + 851900 11.186 * [simplify]: Simplified to: (* (log (* (* PI 2.0) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* PI 2.0) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* PI 2.0) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* PI 2.0) n)) (/ (- 1.0 k) 2.0)) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (pow (* (* PI 2.0) n) (/ 1.0 2.0)) (pow (* (* PI 2.0) n) (/ k 2.0)) (pow (* (* PI 2.0) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* PI 2.0) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* PI 2.0) n) (* (/ (cbrt (- 1.0 k)) (cbrt 2.0)) (/ (cbrt (- 1.0 k)) (cbrt 2.0)))) (pow (* (* PI 2.0) n) (* (/ (cbrt (- 1.0 k)) (sqrt 2.0)) (cbrt (- 1.0 k)))) (pow (* (* PI 2.0) n) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* (* PI 2.0) n) (/ (/ (sqrt (- 1.0 k)) (cbrt 2.0)) (cbrt 2.0))) (pow (* (* PI 2.0) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* PI 2.0) n) (sqrt (- 1.0 k))) (pow (* (* PI 2.0) n) (/ (/ 1 (cbrt 2.0)) (cbrt 2.0))) (pow (* (* PI 2.0) n) (/ 1 (sqrt 2.0))) (* (* PI 2.0) n) (pow (* (* PI 2.0) n) (/ (/ (+ (sqrt k) (sqrt 1.0)) (cbrt 2.0)) (cbrt 2.0))) (pow (* (* PI 2.0) n) (/ (+ (sqrt k) (sqrt 1.0)) (sqrt 2.0))) (pow (* (* PI 2.0) n) (+ (sqrt k) (sqrt 1.0))) (pow (* (* PI 2.0) n) (/ (/ 1 (cbrt 2.0)) (cbrt 2.0))) (pow (* (* PI 2.0) n) (/ 1 (sqrt 2.0))) (* (* PI 2.0) n) (* (* PI 2.0) n) (pow (* (* PI 2.0) n) (- 1.0 k)) (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* PI n) (/ (- 1.0 k) 2.0)) (* (log (* (* PI 2.0) n)) (/ (- 1.0 k) 2.0)) (exp (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)))) (sqrt (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (pow (* (* PI 2.0) n) (/ (- 1.0 k) (* 2.0 2))) (pow (* (* PI 2.0) n) (/ (- 1.0 k) (* 2.0 2))) (* PI n) (log (* PI n)) (log (* PI n)) (exp (* PI n)) (* (* PI n) (* (* PI n) (* PI n))) (* (cbrt (* PI n)) (cbrt (* PI n))) (cbrt (* PI n)) (* (* PI n) (* (* PI n) (* PI n))) (sqrt (* PI n)) (sqrt (* PI n)) (* (sqrt n) (sqrt PI)) (* (sqrt n) (sqrt PI)) (* (* (cbrt PI) (cbrt PI)) n) (* n (sqrt PI)) n (* PI (cbrt n)) (* (sqrt n) PI) (* PI n) (log (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (/ (* 1.0 (* 1.0 1.0)) (sqrt k)) k) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (/ (/ (* 1.0 (* 1.0 1.0)) (sqrt k)) 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 (* (* PI 2.0) n)) (/ (- 1.0 k) 2.0)) (log (/ 1.0 (sqrt k)))) (+ (* (log (* (* PI 2.0) n)) (/ (- 1.0 k) 2.0)) (log (/ 1.0 (sqrt k)))) (+ (* (log (* (* PI 2.0) n)) (/ (- 1.0 k) 2.0)) (log (/ 1.0 (sqrt k)))) (+ (* (log (* (* PI 2.0) n)) (/ (- 1.0 k) 2.0)) (log (/ 1.0 (sqrt k)))) (+ (* (log (* (* PI 2.0) n)) (/ (- 1.0 k) 2.0)) (log (/ 1.0 (sqrt k)))) (+ (* (log (* (* PI 2.0) n)) (/ (- 1.0 k) 2.0)) (log (/ 1.0 (sqrt k)))) (+ (* (log (* (* PI 2.0) n)) (/ (- 1.0 k) 2.0)) (log (/ 1.0 (sqrt k)))) (+ (* (log (* (* PI 2.0) n)) (/ (- 1.0 k) 2.0)) (log (/ 1.0 (sqrt k)))) (+ (* (log (* (* PI 2.0) n)) (/ (- 1.0 k) 2.0)) (log (/ 1.0 (sqrt k)))) (+ (* (log (* (* PI 2.0) n)) (/ (- 1.0 k) 2.0)) (log (/ 1.0 (sqrt k)))) (+ (* (log (* (* PI 2.0) n)) (/ (- 1.0 k) 2.0)) (log (/ 1.0 (sqrt k)))) (exp (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (/ (* (* 1.0 (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (* 1.0 (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)))) (/ (* (sqrt k) k) 1.0))) (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (/ (* (* 1.0 (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (* 1.0 (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)))) (/ (* (sqrt k) k) 1.0))) (* (cbrt (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (cbrt (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))))) (cbrt (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (/ (* (* 1.0 (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (* 1.0 (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)))) (/ (* (sqrt k) k) 1.0))) (sqrt (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (sqrt (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (* (pow (* (* PI 2.0) n) (/ 1.0 2.0)) 1.0) (* (sqrt k) (pow (* (* PI 2.0) n) (/ k 2.0))) (* (sqrt (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (sqrt (/ 1.0 (sqrt k)))) (* (sqrt (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (sqrt (/ 1.0 (sqrt k)))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* PI 2.0) n) (/ (- 1.0 k) (* 2.0 2)))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* PI 2.0) n) (/ (- 1.0 k) (* 2.0 2)))) (/ (* (sqrt (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (sqrt 1.0)) (sqrt (sqrt k))) (/ (* (sqrt (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (sqrt 1.0)) (sqrt (sqrt k))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* PI 2.0) n) (/ (- 1.0 k) (* 2.0 2)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* PI 2.0) n) (/ (- 1.0 k) (* 2.0 2)))) (/ (* (sqrt (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (sqrt 1.0)) (sqrt (sqrt k))) (/ (* (sqrt (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (sqrt 1.0)) (sqrt (sqrt k))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* PI 2.0) n) (/ (- 1.0 k) (* 2.0 2)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* PI 2.0) n) (/ (- 1.0 k) (* 2.0 2)))) (* (/ 1.0 (sqrt k)) (pow 2.0 (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (* (cbrt (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))))) (* (sqrt (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k)) (/ 1.0 (/ (sqrt k) (pow (* (* PI 2.0) n) (/ (- 1.0 k) (* 2.0 2))))) (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (cbrt (/ 1.0 (sqrt k)))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (cbrt (sqrt k))) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (/ (cbrt 1.0) (sqrt (cbrt k)))) (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (/ (cbrt 1.0) (sqrt (sqrt k)))) (/ (cbrt 1.0) (/ (sqrt k) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)))) (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (/ (cbrt 1.0) (sqrt (sqrt k)))) (/ (cbrt 1.0) (/ (sqrt k) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)))) (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (/ (sqrt 1.0) (cbrt (sqrt k)))) (/ (* (sqrt 1.0) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (sqrt (cbrt k))) (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (/ (sqrt 1.0) (sqrt (sqrt k)))) (/ (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (sqrt 1.0)) (sqrt k)) (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (/ (sqrt 1.0) (sqrt (sqrt k)))) (/ (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (sqrt 1.0)) (sqrt k)) (/ (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) 1.0) (cbrt (sqrt k))) (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt (cbrt k)))) (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt (sqrt k)))) (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))) (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt (sqrt k)))) (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))) (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))) (/ (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (sqrt k)) (* (pow (* (* PI 2.0) n) (/ 1.0 2.0)) (/ 1.0 (sqrt k))) (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) 1.0) (- (+ (+ (* (* 0.125 (* (* (log n) (log n)) (* k k))) (exp (* (log (* (* PI 2.0) n)) 0.5))) (exp (* (log (* (* PI 2.0) n)) 0.5))) (+ (* (* (* 0.125 (* (log (* PI 2.0)) (log (* PI 2.0)))) (* k k)) (exp (* (log (* (* PI 2.0) n)) 0.5))) (* (* (* (log (* PI 2.0)) 0.25) (exp (* (log (* (* PI 2.0) n)) 0.5))) (* (log n) (* k k))))) (* (* k (+ (* (exp (* (log (* (* PI 2.0) n)) 0.5)) (log n)) (* (exp (* (log (* (* PI 2.0) n)) 0.5)) (log (* PI 2.0))))) 0.5)) (exp (* (log (* (* PI 2.0) n)) (* (- 1.0 k) 0.5))) (exp (* (* 0.5 (- (log (* PI -2.0)) (log (/ -1 n)))) (- 1.0 k))) (* PI n) (* PI n) (* PI n) (+ (- (* (* k k) +nan.0)) (- +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))) (- (+ (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5) k)) (* (* k k) (* (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5) +nan.0))) (+ (- (* (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5) (* (* (log n) (* k k)) +nan.0)) (* +nan.0 (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (+ (- (* (* (* +nan.0 (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5)) (* k k)) (* (log (* PI 2.0)) (log (* PI 2.0)))) (* (* +nan.0 (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5)) (* (* (log n) (* k k)) (log (* PI 2.0))))) (+ (- (* (* +nan.0 (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5)) (* k (log (* PI 2.0)))) (* (* +nan.0 (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5)) (* (log n) k))) (- (* (* (* +nan.0 (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5)) (log (* PI 2.0))) (* k k)) (* (* +nan.0 (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5)) (* (* k (log n)) (* k (log n)))))))))) (- (+ (- (/ (* +nan.0 (exp (* (log (* (* PI 2.0) n)) (* (- 1.0 k) 0.5)))) (* k k)) (/ (* +nan.0 (exp (* (log (* (* PI 2.0) n)) (* (- 1.0 k) 0.5)))) k)) (/ (* +nan.0 (exp (* (log (* (* PI 2.0) n)) (* (- 1.0 k) 0.5)))) (* k (* k k))))) (- (+ (- (* +nan.0 (exp (* (* 0.5 (- (log (* PI -2.0)) (log (/ -1 n)))) (- 1.0 k)))) (/ (* +nan.0 (exp (* (* 0.5 (- (log (* PI -2.0)) (log (/ -1 n)))) (- 1.0 k)))) k)) (/ (* +nan.0 (exp (* (* 0.5 (- (log (* PI -2.0)) (log (/ -1 n)))) (- 1.0 k)))) (* k k)))) 11.197 * * * [progress]: adding candidates to table 12.067 * * [progress]: iteration 3 / 4 12.067 * * * [progress]: picking best candidate 12.110 * * * * [pick]: Picked # 12.110 * * * [progress]: localizing error 12.144 * * * [progress]: generating rewritten candidates 12.144 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2) 12.157 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 2 1) 12.167 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1) 12.177 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2) 12.205 * * * [progress]: generating series expansions 12.205 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2) 12.205 * [backup-simplify]: Simplify (pow (* n PI) (/ (- 1.0 k) 2.0)) into (pow (* n PI) (* 0.5 (- 1.0 k))) 12.205 * [approximate]: Taking taylor expansion of (pow (* n PI) (* 0.5 (- 1.0 k))) in (n k) around 0 12.205 * [taylor]: Taking taylor expansion of (pow (* n PI) (* 0.5 (- 1.0 k))) in k 12.205 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* n PI)))) in k 12.205 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* n PI))) in k 12.205 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 12.205 * [taylor]: Taking taylor expansion of 0.5 in k 12.205 * [backup-simplify]: Simplify 0.5 into 0.5 12.205 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 12.205 * [taylor]: Taking taylor expansion of 1.0 in k 12.205 * [backup-simplify]: Simplify 1.0 into 1.0 12.205 * [taylor]: Taking taylor expansion of k in k 12.205 * [backup-simplify]: Simplify 0 into 0 12.205 * [backup-simplify]: Simplify 1 into 1 12.205 * [taylor]: Taking taylor expansion of (log (* n PI)) in k 12.205 * [taylor]: Taking taylor expansion of (* n PI) in k 12.205 * [taylor]: Taking taylor expansion of n in k 12.205 * [backup-simplify]: Simplify n into n 12.205 * [taylor]: Taking taylor expansion of PI in k 12.205 * [backup-simplify]: Simplify PI into PI 12.205 * [backup-simplify]: Simplify (* n PI) into (* n PI) 12.205 * [backup-simplify]: Simplify (log (* n PI)) into (log (* n PI)) 12.206 * [backup-simplify]: Simplify (- 0) into 0 12.206 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 12.207 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 12.207 * [backup-simplify]: Simplify (* 0.5 (log (* n PI))) into (* 0.5 (log (* n PI))) 12.207 * [backup-simplify]: Simplify (exp (* 0.5 (log (* n PI)))) into (pow (* n PI) 0.5) 12.207 * [taylor]: Taking taylor expansion of (pow (* n PI) (* 0.5 (- 1.0 k))) in n 12.207 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* n PI)))) in n 12.207 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* n PI))) in n 12.207 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 12.207 * [taylor]: Taking taylor expansion of 0.5 in n 12.207 * [backup-simplify]: Simplify 0.5 into 0.5 12.207 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 12.207 * [taylor]: Taking taylor expansion of 1.0 in n 12.207 * [backup-simplify]: Simplify 1.0 into 1.0 12.207 * [taylor]: Taking taylor expansion of k in n 12.207 * [backup-simplify]: Simplify k into k 12.207 * [taylor]: Taking taylor expansion of (log (* n PI)) in n 12.207 * [taylor]: Taking taylor expansion of (* n PI) in n 12.207 * [taylor]: Taking taylor expansion of n in n 12.207 * [backup-simplify]: Simplify 0 into 0 12.207 * [backup-simplify]: Simplify 1 into 1 12.207 * [taylor]: Taking taylor expansion of PI in n 12.207 * [backup-simplify]: Simplify PI into PI 12.207 * [backup-simplify]: Simplify (* 0 PI) into 0 12.208 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.209 * [backup-simplify]: Simplify (log PI) into (log PI) 12.209 * [backup-simplify]: Simplify (- k) into (- k) 12.209 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 12.209 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 12.209 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n)) 12.210 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log PI) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log PI) (log n)))) 12.210 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log PI) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log PI) (log n))))) 12.210 * [taylor]: Taking taylor expansion of (pow (* n PI) (* 0.5 (- 1.0 k))) in n 12.210 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* n PI)))) in n 12.210 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* n PI))) in n 12.210 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 12.210 * [taylor]: Taking taylor expansion of 0.5 in n 12.210 * [backup-simplify]: Simplify 0.5 into 0.5 12.210 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 12.210 * [taylor]: Taking taylor expansion of 1.0 in n 12.210 * [backup-simplify]: Simplify 1.0 into 1.0 12.210 * [taylor]: Taking taylor expansion of k in n 12.210 * [backup-simplify]: Simplify k into k 12.210 * [taylor]: Taking taylor expansion of (log (* n PI)) in n 12.210 * [taylor]: Taking taylor expansion of (* n PI) in n 12.210 * [taylor]: Taking taylor expansion of n in n 12.210 * [backup-simplify]: Simplify 0 into 0 12.210 * [backup-simplify]: Simplify 1 into 1 12.210 * [taylor]: Taking taylor expansion of PI in n 12.210 * [backup-simplify]: Simplify PI into PI 12.211 * [backup-simplify]: Simplify (* 0 PI) into 0 12.212 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.212 * [backup-simplify]: Simplify (log PI) into (log PI) 12.212 * [backup-simplify]: Simplify (- k) into (- k) 12.212 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 12.212 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 12.213 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n)) 12.213 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log PI) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log PI) (log n)))) 12.213 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log PI) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log PI) (log n))))) 12.213 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log PI) (log n))))) in k 12.213 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log PI) (log n)))) in k 12.213 * [taylor]: Taking taylor expansion of 0.5 in k 12.213 * [backup-simplify]: Simplify 0.5 into 0.5 12.213 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log PI) (log n))) in k 12.213 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 12.213 * [taylor]: Taking taylor expansion of 1.0 in k 12.213 * [backup-simplify]: Simplify 1.0 into 1.0 12.213 * [taylor]: Taking taylor expansion of k in k 12.213 * [backup-simplify]: Simplify 0 into 0 12.213 * [backup-simplify]: Simplify 1 into 1 12.213 * [taylor]: Taking taylor expansion of (+ (log PI) (log n)) in k 12.214 * [taylor]: Taking taylor expansion of (log PI) in k 12.214 * [taylor]: Taking taylor expansion of PI in k 12.214 * [backup-simplify]: Simplify PI into PI 12.214 * [backup-simplify]: Simplify (log PI) into (log PI) 12.214 * [taylor]: Taking taylor expansion of (log n) in k 12.214 * [taylor]: Taking taylor expansion of n in k 12.214 * [backup-simplify]: Simplify n into n 12.214 * [backup-simplify]: Simplify (log n) into (log n) 12.214 * [backup-simplify]: Simplify (- 0) into 0 12.214 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 12.215 * [backup-simplify]: Simplify (+ (log PI) (log n)) into (+ (log PI) (log n)) 12.215 * [backup-simplify]: Simplify (* 1.0 (+ (log PI) (log n))) into (* 1.0 (+ (log PI) (log n))) 12.215 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log PI) (log n)))) into (* 0.5 (+ (log PI) (log n))) 12.216 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log PI) (log n)))) into (exp (* 0.5 (+ (log PI) (log n)))) 12.216 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log PI) (log n)))) into (exp (* 0.5 (+ (log PI) (log n)))) 12.217 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 12.218 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 12.218 * [backup-simplify]: Simplify (- 0) into 0 12.218 * [backup-simplify]: Simplify (+ 0 0) into 0 12.218 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 12.219 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n)) 12.219 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log PI) (log n)))) into 0 12.220 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log PI) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 12.220 * [taylor]: Taking taylor expansion of 0 in k 12.220 * [backup-simplify]: Simplify 0 into 0 12.220 * [backup-simplify]: Simplify 0 into 0 12.221 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 12.222 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 12.222 * [backup-simplify]: Simplify (+ 0 0) into 0 12.223 * [backup-simplify]: Simplify (- 1) into -1 12.223 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.224 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log PI) (log n)))) into (- (+ (log PI) (log n))) 12.225 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log PI) (log n)))) (* 0 (* 1.0 (+ (log PI) (log n))))) into (- (+ (* 0.5 (log PI)) (* 0.5 (log n)))) 12.227 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log PI) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log PI)) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log PI)) (* 0.5 (log n))) (exp (* 0.5 (+ (log PI) (log n)))))) 12.229 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.5 (log PI)) (* 0.5 (log n))) (exp (* 0.5 (+ (log PI) (log n)))))) into (* -1 (* (+ (* 0.5 (log PI)) (* 0.5 (log n))) (exp (* 0.5 (+ (log PI) (log n)))))) 12.230 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 12.238 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 12.238 * [backup-simplify]: Simplify (- 0) into 0 12.239 * [backup-simplify]: Simplify (+ 0 0) into 0 12.240 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 12.240 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n)) 12.241 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log PI) (log n))))) into 0 12.243 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log PI) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 12.243 * [taylor]: Taking taylor expansion of 0 in k 12.243 * [backup-simplify]: Simplify 0 into 0 12.243 * [backup-simplify]: Simplify 0 into 0 12.244 * [backup-simplify]: Simplify 0 into 0 12.247 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 12.249 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 12.250 * [backup-simplify]: Simplify (+ 0 0) into 0 12.250 * [backup-simplify]: Simplify (- 0) into 0 12.251 * [backup-simplify]: Simplify (+ 0 0) into 0 12.252 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log PI) (log n))))) into 0 12.254 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log PI) (log n)))) (* 0 (* 1.0 (+ (log PI) (log n)))))) into 0 12.256 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log PI) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log PI)) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log PI) 2)) (* 0.25 (* (log PI) (log n))))) (exp (* 0.5 (+ (log PI) (log n))))) 12.260 * [backup-simplify]: Simplify (* (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log PI) 2)) (* 0.25 (* (log PI) (log n))))) (exp (* 0.5 (+ (log PI) (log n))))) into (* (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log PI) 2)) (* 0.25 (* (log PI) (log n))))) (exp (* 0.5 (+ (log PI) (log n))))) 12.267 * [backup-simplify]: Simplify (+ (* (* (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log PI) 2)) (* 0.25 (* (log PI) (log n))))) (exp (* 0.5 (+ (log PI) (log n))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.5 (log PI)) (* 0.5 (log n))) (exp (* 0.5 (+ (log PI) (log n)))))) (* k 1)) (exp (* 0.5 (+ (log PI) (log n)))))) into (- (+ (exp (* 0.5 (+ (log PI) (log n)))) (+ (* 0.125 (* (exp (* 0.5 (+ (log PI) (log n)))) (* (pow (log PI) 2) (pow k 2)))) (+ (* 0.125 (* (exp (* 0.5 (+ (log PI) (log n)))) (* (pow (log n) 2) (pow k 2)))) (* 0.25 (* (exp (* 0.5 (+ (log PI) (log n)))) (* (log PI) (* (log n) (pow k 2)))))))) (+ (* 0.5 (* (exp (* 0.5 (+ (log PI) (log n)))) (* (log n) k))) (* 0.5 (* (exp (* 0.5 (+ (log PI) (log n)))) (* (log PI) k))))) 12.267 * [backup-simplify]: Simplify (pow (* (/ 1 n) PI) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (/ PI n) (* 0.5 (- 1.0 (/ 1 k)))) 12.267 * [approximate]: Taking taylor expansion of (pow (/ PI n) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 12.267 * [taylor]: Taking taylor expansion of (pow (/ PI n) (* 0.5 (- 1.0 (/ 1 k)))) in k 12.267 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ PI n)))) in k 12.267 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ PI n))) in k 12.267 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 12.267 * [taylor]: Taking taylor expansion of 0.5 in k 12.267 * [backup-simplify]: Simplify 0.5 into 0.5 12.267 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 12.267 * [taylor]: Taking taylor expansion of 1.0 in k 12.267 * [backup-simplify]: Simplify 1.0 into 1.0 12.267 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.267 * [taylor]: Taking taylor expansion of k in k 12.267 * [backup-simplify]: Simplify 0 into 0 12.267 * [backup-simplify]: Simplify 1 into 1 12.268 * [backup-simplify]: Simplify (/ 1 1) into 1 12.268 * [taylor]: Taking taylor expansion of (log (/ PI n)) in k 12.268 * [taylor]: Taking taylor expansion of (/ PI n) in k 12.268 * [taylor]: Taking taylor expansion of PI in k 12.268 * [backup-simplify]: Simplify PI into PI 12.268 * [taylor]: Taking taylor expansion of n in k 12.268 * [backup-simplify]: Simplify n into n 12.268 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 12.268 * [backup-simplify]: Simplify (log (/ PI n)) into (log (/ PI n)) 12.269 * [backup-simplify]: Simplify (- 1) into -1 12.269 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.271 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 12.271 * [backup-simplify]: Simplify (* -0.5 (log (/ PI n))) into (* -0.5 (log (/ PI n))) 12.271 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ PI n)))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (/ PI n))))) 12.271 * [taylor]: Taking taylor expansion of (pow (/ PI n) (* 0.5 (- 1.0 (/ 1 k)))) in n 12.271 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ PI n)))) in n 12.271 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ PI n))) in n 12.271 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 12.271 * [taylor]: Taking taylor expansion of 0.5 in n 12.271 * [backup-simplify]: Simplify 0.5 into 0.5 12.271 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 12.271 * [taylor]: Taking taylor expansion of 1.0 in n 12.271 * [backup-simplify]: Simplify 1.0 into 1.0 12.271 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.271 * [taylor]: Taking taylor expansion of k in n 12.271 * [backup-simplify]: Simplify k into k 12.271 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.272 * [taylor]: Taking taylor expansion of (log (/ PI n)) in n 12.272 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.272 * [taylor]: Taking taylor expansion of PI in n 12.272 * [backup-simplify]: Simplify PI into PI 12.272 * [taylor]: Taking taylor expansion of n in n 12.272 * [backup-simplify]: Simplify 0 into 0 12.272 * [backup-simplify]: Simplify 1 into 1 12.272 * [backup-simplify]: Simplify (/ PI 1) into PI 12.273 * [backup-simplify]: Simplify (log PI) into (log PI) 12.273 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 12.273 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 12.273 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 12.274 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 12.274 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log PI) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log PI) (log n)))) 12.275 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log PI) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log PI) (log n))))) 12.275 * [taylor]: Taking taylor expansion of (pow (/ PI n) (* 0.5 (- 1.0 (/ 1 k)))) in n 12.275 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ PI n)))) in n 12.275 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ PI n))) in n 12.275 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 12.275 * [taylor]: Taking taylor expansion of 0.5 in n 12.275 * [backup-simplify]: Simplify 0.5 into 0.5 12.275 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 12.275 * [taylor]: Taking taylor expansion of 1.0 in n 12.275 * [backup-simplify]: Simplify 1.0 into 1.0 12.275 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.275 * [taylor]: Taking taylor expansion of k in n 12.275 * [backup-simplify]: Simplify k into k 12.275 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.275 * [taylor]: Taking taylor expansion of (log (/ PI n)) in n 12.275 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.275 * [taylor]: Taking taylor expansion of PI in n 12.275 * [backup-simplify]: Simplify PI into PI 12.275 * [taylor]: Taking taylor expansion of n in n 12.275 * [backup-simplify]: Simplify 0 into 0 12.275 * [backup-simplify]: Simplify 1 into 1 12.275 * [backup-simplify]: Simplify (/ PI 1) into PI 12.276 * [backup-simplify]: Simplify (log PI) into (log PI) 12.276 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 12.276 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 12.276 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 12.276 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 12.277 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log PI) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log PI) (log n)))) 12.277 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log PI) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log PI) (log n))))) 12.277 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log PI) (log n))))) in k 12.277 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (- (log PI) (log n)))) in k 12.277 * [taylor]: Taking taylor expansion of 0.5 in k 12.277 * [backup-simplify]: Simplify 0.5 into 0.5 12.277 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (- (log PI) (log n))) in k 12.277 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 12.277 * [taylor]: Taking taylor expansion of 1.0 in k 12.277 * [backup-simplify]: Simplify 1.0 into 1.0 12.277 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.277 * [taylor]: Taking taylor expansion of k in k 12.277 * [backup-simplify]: Simplify 0 into 0 12.277 * [backup-simplify]: Simplify 1 into 1 12.278 * [backup-simplify]: Simplify (/ 1 1) into 1 12.278 * [taylor]: Taking taylor expansion of (- (log PI) (log n)) in k 12.278 * [taylor]: Taking taylor expansion of (log PI) in k 12.278 * [taylor]: Taking taylor expansion of PI in k 12.278 * [backup-simplify]: Simplify PI into PI 12.278 * [backup-simplify]: Simplify (log PI) into (log PI) 12.278 * [taylor]: Taking taylor expansion of (log n) in k 12.278 * [taylor]: Taking taylor expansion of n in k 12.278 * [backup-simplify]: Simplify n into n 12.278 * [backup-simplify]: Simplify (log n) into (log n) 12.278 * [backup-simplify]: Simplify (- 1) into -1 12.279 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.279 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 12.279 * [backup-simplify]: Simplify (+ (log PI) (- (log n))) into (- (log PI) (log n)) 12.279 * [backup-simplify]: Simplify (* -1 (- (log PI) (log n))) into (* -1 (- (log PI) (log n))) 12.280 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log PI) (log n)))) into (* -0.5 (- (log PI) (log n))) 12.280 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log PI) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log PI) (log n))))) 12.280 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log PI) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log PI) (log n))))) 12.281 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.282 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 12.282 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 12.282 * [backup-simplify]: Simplify (- 0) into 0 12.282 * [backup-simplify]: Simplify (+ 0 0) into 0 12.283 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 12.283 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 12.284 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log PI) (log n)))) into 0 12.284 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log PI) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 12.284 * [taylor]: Taking taylor expansion of 0 in k 12.284 * [backup-simplify]: Simplify 0 into 0 12.284 * [backup-simplify]: Simplify 0 into 0 12.285 * [backup-simplify]: Simplify 0 into 0 12.285 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.287 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 12.287 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.288 * [backup-simplify]: Simplify (- 0) into 0 12.288 * [backup-simplify]: Simplify (+ 0 0) into 0 12.288 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 12.289 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 12.290 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log PI) (log n))))) into 0 12.291 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log PI) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 12.291 * [taylor]: Taking taylor expansion of 0 in k 12.291 * [backup-simplify]: Simplify 0 into 0 12.291 * [backup-simplify]: Simplify 0 into 0 12.291 * [backup-simplify]: Simplify 0 into 0 12.291 * [backup-simplify]: Simplify 0 into 0 12.292 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.295 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0 12.295 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.295 * [backup-simplify]: Simplify (- 0) into 0 12.295 * [backup-simplify]: Simplify (+ 0 0) into 0 12.296 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 12.297 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 12.298 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log PI) (log n)))))) into 0 12.299 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log PI) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 12.299 * [taylor]: Taking taylor expansion of 0 in k 12.299 * [backup-simplify]: Simplify 0 into 0 12.299 * [backup-simplify]: Simplify 0 into 0 12.299 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log PI) (log (/ 1 n)))))) into (exp (* 0.5 (* (- 1.0 k) (- (log PI) (log (/ 1 n)))))) 12.300 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) PI) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -1 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) 12.300 * [approximate]: Taking taylor expansion of (pow (* -1 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 12.300 * [taylor]: Taking taylor expansion of (pow (* -1 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 12.300 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -1 (/ PI n))))) in k 12.300 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -1 (/ PI n)))) in k 12.300 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 12.300 * [taylor]: Taking taylor expansion of 0.5 in k 12.300 * [backup-simplify]: Simplify 0.5 into 0.5 12.300 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 12.300 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.300 * [taylor]: Taking taylor expansion of k in k 12.300 * [backup-simplify]: Simplify 0 into 0 12.300 * [backup-simplify]: Simplify 1 into 1 12.300 * [backup-simplify]: Simplify (/ 1 1) into 1 12.300 * [taylor]: Taking taylor expansion of 1.0 in k 12.300 * [backup-simplify]: Simplify 1.0 into 1.0 12.300 * [taylor]: Taking taylor expansion of (log (* -1 (/ PI n))) in k 12.300 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in k 12.300 * [taylor]: Taking taylor expansion of -1 in k 12.300 * [backup-simplify]: Simplify -1 into -1 12.300 * [taylor]: Taking taylor expansion of (/ PI n) in k 12.300 * [taylor]: Taking taylor expansion of PI in k 12.300 * [backup-simplify]: Simplify PI into PI 12.300 * [taylor]: Taking taylor expansion of n in k 12.300 * [backup-simplify]: Simplify n into n 12.300 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 12.300 * [backup-simplify]: Simplify (* -1 (/ PI n)) into (* -1 (/ PI n)) 12.300 * [backup-simplify]: Simplify (log (* -1 (/ PI n))) into (log (* -1 (/ PI n))) 12.301 * [backup-simplify]: Simplify (+ 1 0) into 1 12.301 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 12.301 * [backup-simplify]: Simplify (* 0.5 (log (* -1 (/ PI n)))) into (* 0.5 (log (* -1 (/ PI n)))) 12.301 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -1 (/ PI n))))) into (exp (* 0.5 (* (log (* -1 (/ PI n))) (+ (/ 1 k) 1.0)))) 12.301 * [taylor]: Taking taylor expansion of (pow (* -1 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 12.301 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -1 (/ PI n))))) in n 12.301 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -1 (/ PI n)))) in n 12.301 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 12.301 * [taylor]: Taking taylor expansion of 0.5 in n 12.301 * [backup-simplify]: Simplify 0.5 into 0.5 12.301 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 12.301 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.301 * [taylor]: Taking taylor expansion of k in n 12.301 * [backup-simplify]: Simplify k into k 12.301 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.301 * [taylor]: Taking taylor expansion of 1.0 in n 12.301 * [backup-simplify]: Simplify 1.0 into 1.0 12.301 * [taylor]: Taking taylor expansion of (log (* -1 (/ PI n))) in n 12.301 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n 12.301 * [taylor]: Taking taylor expansion of -1 in n 12.301 * [backup-simplify]: Simplify -1 into -1 12.301 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.301 * [taylor]: Taking taylor expansion of PI in n 12.301 * [backup-simplify]: Simplify PI into PI 12.302 * [taylor]: Taking taylor expansion of n in n 12.302 * [backup-simplify]: Simplify 0 into 0 12.302 * [backup-simplify]: Simplify 1 into 1 12.302 * [backup-simplify]: Simplify (/ PI 1) into PI 12.302 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI) 12.303 * [backup-simplify]: Simplify (log (* -1 PI)) into (log (* -1 PI)) 12.303 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 12.303 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 12.304 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 12.305 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -1 PI)) (log n))) into (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0))) 12.305 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) 12.305 * [taylor]: Taking taylor expansion of (pow (* -1 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 12.305 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -1 (/ PI n))))) in n 12.305 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -1 (/ PI n)))) in n 12.305 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 12.305 * [taylor]: Taking taylor expansion of 0.5 in n 12.305 * [backup-simplify]: Simplify 0.5 into 0.5 12.305 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 12.306 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.306 * [taylor]: Taking taylor expansion of k in n 12.306 * [backup-simplify]: Simplify k into k 12.306 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.306 * [taylor]: Taking taylor expansion of 1.0 in n 12.306 * [backup-simplify]: Simplify 1.0 into 1.0 12.306 * [taylor]: Taking taylor expansion of (log (* -1 (/ PI n))) in n 12.306 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n 12.306 * [taylor]: Taking taylor expansion of -1 in n 12.306 * [backup-simplify]: Simplify -1 into -1 12.306 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.306 * [taylor]: Taking taylor expansion of PI in n 12.306 * [backup-simplify]: Simplify PI into PI 12.306 * [taylor]: Taking taylor expansion of n in n 12.306 * [backup-simplify]: Simplify 0 into 0 12.306 * [backup-simplify]: Simplify 1 into 1 12.306 * [backup-simplify]: Simplify (/ PI 1) into PI 12.307 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI) 12.307 * [backup-simplify]: Simplify (log (* -1 PI)) into (log (* -1 PI)) 12.307 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 12.307 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 12.308 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 12.309 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -1 PI)) (log n))) into (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0))) 12.310 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) 12.310 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) in k 12.310 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0))) in k 12.310 * [taylor]: Taking taylor expansion of 0.5 in k 12.310 * [backup-simplify]: Simplify 0.5 into 0.5 12.310 * [taylor]: Taking taylor expansion of (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)) in k 12.310 * [taylor]: Taking taylor expansion of (- (log (* -1 PI)) (log n)) in k 12.310 * [taylor]: Taking taylor expansion of (log (* -1 PI)) in k 12.310 * [taylor]: Taking taylor expansion of (* -1 PI) in k 12.310 * [taylor]: Taking taylor expansion of -1 in k 12.310 * [backup-simplify]: Simplify -1 into -1 12.310 * [taylor]: Taking taylor expansion of PI in k 12.310 * [backup-simplify]: Simplify PI into PI 12.310 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI) 12.311 * [backup-simplify]: Simplify (log (* -1 PI)) into (log (* -1 PI)) 12.311 * [taylor]: Taking taylor expansion of (log n) in k 12.311 * [taylor]: Taking taylor expansion of n in k 12.311 * [backup-simplify]: Simplify n into n 12.311 * [backup-simplify]: Simplify (log n) into (log n) 12.311 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 12.311 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.311 * [taylor]: Taking taylor expansion of k in k 12.311 * [backup-simplify]: Simplify 0 into 0 12.311 * [backup-simplify]: Simplify 1 into 1 12.311 * [backup-simplify]: Simplify (/ 1 1) into 1 12.311 * [taylor]: Taking taylor expansion of 1.0 in k 12.311 * [backup-simplify]: Simplify 1.0 into 1.0 12.311 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 12.312 * [backup-simplify]: Simplify (+ (log (* -1 PI)) (- (log n))) into (- (log (* -1 PI)) (log n)) 12.312 * [backup-simplify]: Simplify (+ 1 0) into 1 12.313 * [backup-simplify]: Simplify (* (- (log (* -1 PI)) (log n)) 1) into (- (log (* -1 PI)) (log n)) 12.314 * [backup-simplify]: Simplify (* 0.5 (- (log (* -1 PI)) (log n))) into (* 0.5 (- (log (* -1 PI)) (log n))) 12.315 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) 12.315 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) 12.316 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.316 * [backup-simplify]: Simplify (+ (* -1 0) (* 0 PI)) into 0 12.318 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -1 PI) 1)))) 1) into 0 12.318 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 12.318 * [backup-simplify]: Simplify (+ 0 0) into 0 12.318 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 12.319 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 12.320 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -1 PI)) (log n)))) into 0 12.321 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 12.321 * [taylor]: Taking taylor expansion of 0 in k 12.321 * [backup-simplify]: Simplify 0 into 0 12.321 * [backup-simplify]: Simplify 0 into 0 12.321 * [backup-simplify]: Simplify 0 into 0 12.322 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.323 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 PI))) into 0 12.324 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -1 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -1 PI) 1)))) 2) into 0 12.325 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.325 * [backup-simplify]: Simplify (+ 0 0) into 0 12.325 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 12.326 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 12.327 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -1 PI)) (log n))))) into 0 12.329 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 12.329 * [taylor]: Taking taylor expansion of 0 in k 12.329 * [backup-simplify]: Simplify 0 into 0 12.329 * [backup-simplify]: Simplify 0 into 0 12.329 * [backup-simplify]: Simplify 0 into 0 12.329 * [backup-simplify]: Simplify 0 into 0 12.330 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.330 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 12.334 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -1 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -1 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -1 PI) 1)))) 6) into 0 12.334 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.334 * [backup-simplify]: Simplify (+ 0 0) into 0 12.335 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 12.336 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 12.337 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -1 PI)) (log n)))))) into 0 12.339 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -1 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 12.339 * [taylor]: Taking taylor expansion of 0 in k 12.339 * [backup-simplify]: Simplify 0 into 0 12.339 * [backup-simplify]: Simplify 0 into 0 12.340 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -1 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))) into (exp (* 0.5 (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1.0 k)))) 12.340 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 2 1) 12.340 * [backup-simplify]: Simplify (* n PI) into (* n PI) 12.340 * [approximate]: Taking taylor expansion of (* n PI) in (n) around 0 12.340 * [taylor]: Taking taylor expansion of (* n PI) in n 12.340 * [taylor]: Taking taylor expansion of n in n 12.340 * [backup-simplify]: Simplify 0 into 0 12.340 * [backup-simplify]: Simplify 1 into 1 12.340 * [taylor]: Taking taylor expansion of PI in n 12.340 * [backup-simplify]: Simplify PI into PI 12.340 * [taylor]: Taking taylor expansion of (* n PI) in n 12.340 * [taylor]: Taking taylor expansion of n in n 12.340 * [backup-simplify]: Simplify 0 into 0 12.340 * [backup-simplify]: Simplify 1 into 1 12.340 * [taylor]: Taking taylor expansion of PI in n 12.340 * [backup-simplify]: Simplify PI into PI 12.340 * [backup-simplify]: Simplify (* 0 PI) into 0 12.340 * [backup-simplify]: Simplify 0 into 0 12.341 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.341 * [backup-simplify]: Simplify PI into PI 12.342 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 12.342 * [backup-simplify]: Simplify 0 into 0 12.343 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 12.343 * [backup-simplify]: Simplify 0 into 0 12.348 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 12.348 * [backup-simplify]: Simplify 0 into 0 12.349 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 12.349 * [backup-simplify]: Simplify 0 into 0 12.350 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 12.350 * [backup-simplify]: Simplify 0 into 0 12.351 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 12.351 * [backup-simplify]: Simplify 0 into 0 12.351 * [backup-simplify]: Simplify (* PI n) into (* n PI) 12.351 * [backup-simplify]: Simplify (* (/ 1 n) PI) into (/ PI n) 12.351 * [approximate]: Taking taylor expansion of (/ PI n) in (n) around 0 12.351 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.352 * [taylor]: Taking taylor expansion of PI in n 12.352 * [backup-simplify]: Simplify PI into PI 12.352 * [taylor]: Taking taylor expansion of n in n 12.352 * [backup-simplify]: Simplify 0 into 0 12.352 * [backup-simplify]: Simplify 1 into 1 12.352 * [backup-simplify]: Simplify (/ PI 1) into PI 12.352 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.352 * [taylor]: Taking taylor expansion of PI in n 12.352 * [backup-simplify]: Simplify PI into PI 12.352 * [taylor]: Taking taylor expansion of n in n 12.352 * [backup-simplify]: Simplify 0 into 0 12.352 * [backup-simplify]: Simplify 1 into 1 12.352 * [backup-simplify]: Simplify (/ PI 1) into PI 12.352 * [backup-simplify]: Simplify PI into PI 12.353 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.353 * [backup-simplify]: Simplify 0 into 0 12.354 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.354 * [backup-simplify]: Simplify 0 into 0 12.354 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.354 * [backup-simplify]: Simplify 0 into 0 12.355 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.355 * [backup-simplify]: Simplify 0 into 0 12.356 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.356 * [backup-simplify]: Simplify 0 into 0 12.357 * [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 12.357 * [backup-simplify]: Simplify 0 into 0 12.357 * [backup-simplify]: Simplify (* PI (/ 1 (/ 1 n))) into (* n PI) 12.357 * [backup-simplify]: Simplify (* (/ 1 (- n)) PI) into (* -1 (/ PI n)) 12.357 * [approximate]: Taking taylor expansion of (* -1 (/ PI n)) in (n) around 0 12.357 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n 12.357 * [taylor]: Taking taylor expansion of -1 in n 12.357 * [backup-simplify]: Simplify -1 into -1 12.357 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.357 * [taylor]: Taking taylor expansion of PI in n 12.357 * [backup-simplify]: Simplify PI into PI 12.357 * [taylor]: Taking taylor expansion of n in n 12.357 * [backup-simplify]: Simplify 0 into 0 12.357 * [backup-simplify]: Simplify 1 into 1 12.357 * [backup-simplify]: Simplify (/ PI 1) into PI 12.357 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n 12.357 * [taylor]: Taking taylor expansion of -1 in n 12.357 * [backup-simplify]: Simplify -1 into -1 12.357 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.357 * [taylor]: Taking taylor expansion of PI in n 12.357 * [backup-simplify]: Simplify PI into PI 12.357 * [taylor]: Taking taylor expansion of n in n 12.357 * [backup-simplify]: Simplify 0 into 0 12.357 * [backup-simplify]: Simplify 1 into 1 12.358 * [backup-simplify]: Simplify (/ PI 1) into PI 12.358 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI) 12.358 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI) 12.359 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.359 * [backup-simplify]: Simplify (+ (* -1 0) (* 0 PI)) into 0 12.359 * [backup-simplify]: Simplify 0 into 0 12.360 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.361 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 PI))) into 0 12.361 * [backup-simplify]: Simplify 0 into 0 12.361 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.362 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 12.362 * [backup-simplify]: Simplify 0 into 0 12.363 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.364 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 12.364 * [backup-simplify]: Simplify 0 into 0 12.364 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.365 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 12.365 * [backup-simplify]: Simplify 0 into 0 12.366 * [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 12.367 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 12.367 * [backup-simplify]: Simplify 0 into 0 12.367 * [backup-simplify]: Simplify (* (* -1 PI) (/ 1 (/ 1 (- n)))) into (* n PI) 12.367 * * * * [progress]: [ 3 / 4 ] generating series at (2 1) 12.367 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 12.367 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 12.367 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 12.367 * [taylor]: Taking taylor expansion of 1.0 in k 12.367 * [backup-simplify]: Simplify 1.0 into 1.0 12.367 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 12.367 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.367 * [taylor]: Taking taylor expansion of k in k 12.367 * [backup-simplify]: Simplify 0 into 0 12.367 * [backup-simplify]: Simplify 1 into 1 12.368 * [backup-simplify]: Simplify (/ 1 1) into 1 12.368 * [backup-simplify]: Simplify (sqrt 0) into 0 12.369 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 12.369 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 12.369 * [taylor]: Taking taylor expansion of 1.0 in k 12.369 * [backup-simplify]: Simplify 1.0 into 1.0 12.369 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 12.369 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.369 * [taylor]: Taking taylor expansion of k in k 12.369 * [backup-simplify]: Simplify 0 into 0 12.369 * [backup-simplify]: Simplify 1 into 1 12.369 * [backup-simplify]: Simplify (/ 1 1) into 1 12.369 * [backup-simplify]: Simplify (sqrt 0) into 0 12.370 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 12.370 * [backup-simplify]: Simplify (* 1.0 0) into 0 12.371 * [backup-simplify]: Simplify 0 into 0 12.371 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 12.372 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 12.372 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 12.374 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 12.375 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 12.375 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 12.376 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.378 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 12.380 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 12.380 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 12.381 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) 12.381 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 12.381 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 12.381 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 12.381 * [taylor]: Taking taylor expansion of 1.0 in k 12.381 * [backup-simplify]: Simplify 1.0 into 1.0 12.381 * [taylor]: Taking taylor expansion of (sqrt k) in k 12.381 * [taylor]: Taking taylor expansion of k in k 12.381 * [backup-simplify]: Simplify 0 into 0 12.381 * [backup-simplify]: Simplify 1 into 1 12.381 * [backup-simplify]: Simplify (sqrt 0) into 0 12.382 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 12.382 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 12.382 * [taylor]: Taking taylor expansion of 1.0 in k 12.382 * [backup-simplify]: Simplify 1.0 into 1.0 12.382 * [taylor]: Taking taylor expansion of (sqrt k) in k 12.382 * [taylor]: Taking taylor expansion of k in k 12.382 * [backup-simplify]: Simplify 0 into 0 12.382 * [backup-simplify]: Simplify 1 into 1 12.382 * [backup-simplify]: Simplify (sqrt 0) into 0 12.383 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 12.384 * [backup-simplify]: Simplify (* 1.0 0) into 0 12.384 * [backup-simplify]: Simplify 0 into 0 12.384 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 12.385 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 12.387 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 12.390 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 12.390 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 12.394 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 12.396 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 12.397 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 12.398 * [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)))))))) 12.399 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 12.399 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 12.399 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 12.399 * [taylor]: Taking taylor expansion of 1.0 in k 12.399 * [backup-simplify]: Simplify 1.0 into 1.0 12.399 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 12.399 * [taylor]: Taking taylor expansion of (/ -1 k) in k 12.399 * [taylor]: Taking taylor expansion of -1 in k 12.399 * [backup-simplify]: Simplify -1 into -1 12.399 * [taylor]: Taking taylor expansion of k in k 12.399 * [backup-simplify]: Simplify 0 into 0 12.399 * [backup-simplify]: Simplify 1 into 1 12.399 * [backup-simplify]: Simplify (/ -1 1) into -1 12.400 * [backup-simplify]: Simplify (sqrt 0) into 0 12.401 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 12.402 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 12.402 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 12.402 * [taylor]: Taking taylor expansion of 1.0 in k 12.402 * [backup-simplify]: Simplify 1.0 into 1.0 12.402 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 12.402 * [taylor]: Taking taylor expansion of (/ -1 k) in k 12.402 * [taylor]: Taking taylor expansion of -1 in k 12.402 * [backup-simplify]: Simplify -1 into -1 12.402 * [taylor]: Taking taylor expansion of k in k 12.402 * [backup-simplify]: Simplify 0 into 0 12.402 * [backup-simplify]: Simplify 1 into 1 12.402 * [backup-simplify]: Simplify (/ -1 1) into -1 12.403 * [backup-simplify]: Simplify (sqrt 0) into 0 12.404 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 12.404 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 12.405 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.406 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 12.409 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 12.412 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 12.412 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 12.413 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.417 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 12.420 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 12.420 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 12.421 * [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))))) 12.421 * * * * [progress]: [ 4 / 4 ] generating series at (2 2) 12.421 * [backup-simplify]: Simplify (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0))) into (* (pow 2.0 (* 0.5 (- 1.0 k))) (pow (* n PI) (* 0.5 (- 1.0 k)))) 12.421 * [approximate]: Taking taylor expansion of (* (pow 2.0 (* 0.5 (- 1.0 k))) (pow (* n PI) (* 0.5 (- 1.0 k)))) in (k n) around 0 12.421 * [taylor]: Taking taylor expansion of (* (pow 2.0 (* 0.5 (- 1.0 k))) (pow (* n PI) (* 0.5 (- 1.0 k)))) in n 12.421 * [taylor]: Taking taylor expansion of (pow 2.0 (* 0.5 (- 1.0 k))) in n 12.421 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log 2.0))) in n 12.421 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log 2.0)) in n 12.421 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 12.421 * [taylor]: Taking taylor expansion of 0.5 in n 12.421 * [backup-simplify]: Simplify 0.5 into 0.5 12.421 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 12.421 * [taylor]: Taking taylor expansion of 1.0 in n 12.421 * [backup-simplify]: Simplify 1.0 into 1.0 12.421 * [taylor]: Taking taylor expansion of k in n 12.421 * [backup-simplify]: Simplify k into k 12.421 * [taylor]: Taking taylor expansion of (log 2.0) in n 12.421 * [taylor]: Taking taylor expansion of 2.0 in n 12.421 * [backup-simplify]: Simplify 2.0 into 2.0 12.422 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 12.422 * [backup-simplify]: Simplify (- k) into (- k) 12.422 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 12.422 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 12.422 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (log 2.0)) into (* 0.5 (* (- 1.0 k) (log 2.0))) 12.422 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (log 2.0)))) into (exp (* 0.5 (* (- 1.0 k) (log 2.0)))) 12.422 * [taylor]: Taking taylor expansion of (pow (* n PI) (* 0.5 (- 1.0 k))) in n 12.422 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* n PI)))) in n 12.422 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* n PI))) in n 12.422 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 12.422 * [taylor]: Taking taylor expansion of 0.5 in n 12.422 * [backup-simplify]: Simplify 0.5 into 0.5 12.422 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 12.422 * [taylor]: Taking taylor expansion of 1.0 in n 12.423 * [backup-simplify]: Simplify 1.0 into 1.0 12.423 * [taylor]: Taking taylor expansion of k in n 12.423 * [backup-simplify]: Simplify k into k 12.423 * [taylor]: Taking taylor expansion of (log (* n PI)) in n 12.423 * [taylor]: Taking taylor expansion of (* n PI) in n 12.423 * [taylor]: Taking taylor expansion of n in n 12.423 * [backup-simplify]: Simplify 0 into 0 12.423 * [backup-simplify]: Simplify 1 into 1 12.423 * [taylor]: Taking taylor expansion of PI in n 12.423 * [backup-simplify]: Simplify PI into PI 12.423 * [backup-simplify]: Simplify (* 0 PI) into 0 12.424 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.424 * [backup-simplify]: Simplify (log PI) into (log PI) 12.425 * [backup-simplify]: Simplify (- k) into (- k) 12.425 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 12.425 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 12.425 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n)) 12.426 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log PI) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log PI) (log n)))) 12.426 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log PI) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log PI) (log n))))) 12.426 * [taylor]: Taking taylor expansion of (* (pow 2.0 (* 0.5 (- 1.0 k))) (pow (* n PI) (* 0.5 (- 1.0 k)))) in k 12.426 * [taylor]: Taking taylor expansion of (pow 2.0 (* 0.5 (- 1.0 k))) in k 12.426 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log 2.0))) in k 12.426 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log 2.0)) in k 12.426 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 12.426 * [taylor]: Taking taylor expansion of 0.5 in k 12.426 * [backup-simplify]: Simplify 0.5 into 0.5 12.426 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 12.426 * [taylor]: Taking taylor expansion of 1.0 in k 12.426 * [backup-simplify]: Simplify 1.0 into 1.0 12.426 * [taylor]: Taking taylor expansion of k in k 12.426 * [backup-simplify]: Simplify 0 into 0 12.426 * [backup-simplify]: Simplify 1 into 1 12.426 * [taylor]: Taking taylor expansion of (log 2.0) in k 12.426 * [taylor]: Taking taylor expansion of 2.0 in k 12.426 * [backup-simplify]: Simplify 2.0 into 2.0 12.426 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 12.427 * [backup-simplify]: Simplify (- 0) into 0 12.427 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 12.427 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 12.428 * [backup-simplify]: Simplify (* 0.5 (log 2.0)) into (* 0.5 (log 2.0)) 12.429 * [backup-simplify]: Simplify (exp (* 0.5 (log 2.0))) into (pow 2.0 0.5) 12.429 * [taylor]: Taking taylor expansion of (pow (* n PI) (* 0.5 (- 1.0 k))) in k 12.429 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* n PI)))) in k 12.429 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* n PI))) in k 12.429 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 12.429 * [taylor]: Taking taylor expansion of 0.5 in k 12.429 * [backup-simplify]: Simplify 0.5 into 0.5 12.429 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 12.429 * [taylor]: Taking taylor expansion of 1.0 in k 12.429 * [backup-simplify]: Simplify 1.0 into 1.0 12.429 * [taylor]: Taking taylor expansion of k in k 12.429 * [backup-simplify]: Simplify 0 into 0 12.429 * [backup-simplify]: Simplify 1 into 1 12.429 * [taylor]: Taking taylor expansion of (log (* n PI)) in k 12.429 * [taylor]: Taking taylor expansion of (* n PI) in k 12.429 * [taylor]: Taking taylor expansion of n in k 12.429 * [backup-simplify]: Simplify n into n 12.429 * [taylor]: Taking taylor expansion of PI in k 12.429 * [backup-simplify]: Simplify PI into PI 12.429 * [backup-simplify]: Simplify (* n PI) into (* n PI) 12.429 * [backup-simplify]: Simplify (log (* n PI)) into (log (* n PI)) 12.429 * [backup-simplify]: Simplify (- 0) into 0 12.430 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 12.430 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 12.430 * [backup-simplify]: Simplify (* 0.5 (log (* n PI))) into (* 0.5 (log (* n PI))) 12.430 * [backup-simplify]: Simplify (exp (* 0.5 (log (* n PI)))) into (pow (* n PI) 0.5) 12.430 * [taylor]: Taking taylor expansion of (* (pow 2.0 (* 0.5 (- 1.0 k))) (pow (* n PI) (* 0.5 (- 1.0 k)))) in k 12.430 * [taylor]: Taking taylor expansion of (pow 2.0 (* 0.5 (- 1.0 k))) in k 12.430 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log 2.0))) in k 12.430 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log 2.0)) in k 12.430 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 12.430 * [taylor]: Taking taylor expansion of 0.5 in k 12.430 * [backup-simplify]: Simplify 0.5 into 0.5 12.430 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 12.430 * [taylor]: Taking taylor expansion of 1.0 in k 12.430 * [backup-simplify]: Simplify 1.0 into 1.0 12.430 * [taylor]: Taking taylor expansion of k in k 12.430 * [backup-simplify]: Simplify 0 into 0 12.430 * [backup-simplify]: Simplify 1 into 1 12.430 * [taylor]: Taking taylor expansion of (log 2.0) in k 12.430 * [taylor]: Taking taylor expansion of 2.0 in k 12.430 * [backup-simplify]: Simplify 2.0 into 2.0 12.430 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 12.431 * [backup-simplify]: Simplify (- 0) into 0 12.431 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 12.431 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 12.432 * [backup-simplify]: Simplify (* 0.5 (log 2.0)) into (* 0.5 (log 2.0)) 12.433 * [backup-simplify]: Simplify (exp (* 0.5 (log 2.0))) into (pow 2.0 0.5) 12.433 * [taylor]: Taking taylor expansion of (pow (* n PI) (* 0.5 (- 1.0 k))) in k 12.433 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* n PI)))) in k 12.433 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* n PI))) in k 12.433 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 12.433 * [taylor]: Taking taylor expansion of 0.5 in k 12.433 * [backup-simplify]: Simplify 0.5 into 0.5 12.433 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 12.433 * [taylor]: Taking taylor expansion of 1.0 in k 12.433 * [backup-simplify]: Simplify 1.0 into 1.0 12.433 * [taylor]: Taking taylor expansion of k in k 12.433 * [backup-simplify]: Simplify 0 into 0 12.433 * [backup-simplify]: Simplify 1 into 1 12.433 * [taylor]: Taking taylor expansion of (log (* n PI)) in k 12.433 * [taylor]: Taking taylor expansion of (* n PI) in k 12.433 * [taylor]: Taking taylor expansion of n in k 12.433 * [backup-simplify]: Simplify n into n 12.433 * [taylor]: Taking taylor expansion of PI in k 12.433 * [backup-simplify]: Simplify PI into PI 12.433 * [backup-simplify]: Simplify (* n PI) into (* n PI) 12.433 * [backup-simplify]: Simplify (log (* n PI)) into (log (* n PI)) 12.434 * [backup-simplify]: Simplify (- 0) into 0 12.434 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 12.434 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 12.434 * [backup-simplify]: Simplify (* 0.5 (log (* n PI))) into (* 0.5 (log (* n PI))) 12.434 * [backup-simplify]: Simplify (exp (* 0.5 (log (* n PI)))) into (pow (* n PI) 0.5) 12.435 * [backup-simplify]: Simplify (* (pow 2.0 0.5) (pow (* n PI) 0.5)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) 12.435 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 12.435 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 12.435 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 12.435 * [taylor]: Taking taylor expansion of 0.5 in n 12.435 * [backup-simplify]: Simplify 0.5 into 0.5 12.435 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 12.435 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 12.435 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 12.435 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 12.435 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 12.435 * [taylor]: Taking taylor expansion of 1.0 in n 12.435 * [backup-simplify]: Simplify 1.0 into 1.0 12.435 * [taylor]: Taking taylor expansion of (log PI) in n 12.435 * [taylor]: Taking taylor expansion of PI in n 12.435 * [backup-simplify]: Simplify PI into PI 12.435 * [backup-simplify]: Simplify (log PI) into (log PI) 12.436 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 12.437 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 12.437 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 12.437 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 12.437 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 12.437 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 12.437 * [taylor]: Taking taylor expansion of 1.0 in n 12.437 * [backup-simplify]: Simplify 1.0 into 1.0 12.437 * [taylor]: Taking taylor expansion of (log n) in n 12.437 * [taylor]: Taking taylor expansion of n in n 12.437 * [backup-simplify]: Simplify 0 into 0 12.437 * [backup-simplify]: Simplify 1 into 1 12.437 * [backup-simplify]: Simplify (log 1) into 0 12.437 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 12.438 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 12.438 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 12.438 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 12.438 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 12.438 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 12.438 * [taylor]: Taking taylor expansion of 1.0 in n 12.438 * [backup-simplify]: Simplify 1.0 into 1.0 12.438 * [taylor]: Taking taylor expansion of (log 2.0) in n 12.438 * [taylor]: Taking taylor expansion of 2.0 in n 12.438 * [backup-simplify]: Simplify 2.0 into 2.0 12.438 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 12.439 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 12.439 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 12.440 * [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) 12.441 * [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) 12.441 * [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)) 12.442 * [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))) 12.443 * [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) 12.444 * [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) into (pow (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) 1.0) 0.5) 12.444 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 12.445 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* n PI) 1)))) 1) into 0 12.445 * [backup-simplify]: Simplify (- 1) into -1 12.445 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.447 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5) 12.448 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* n PI)))) into (- (* 0.5 (log (* n PI)))) 12.448 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* n PI)))) (+ (* (/ (pow (- (* 0.5 (log (* n PI)))) 1) 1)))) into (* -0.5 (* (log (* n PI)) (pow (* (pow n 1.0) (pow PI 1.0)) 0.5))) 12.450 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0 12.450 * [backup-simplify]: Simplify (- 1) into -1 12.450 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.452 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5) 12.462 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log 2.0))) into (- (* 0.5 (log 2.0))) 12.471 * [backup-simplify]: Simplify (* (exp (* 0.5 (log 2.0))) (+ (* (/ (pow (- (* 0.5 (log 2.0))) 1) 1)))) into (* -0.5 (* (pow (pow 2.0 1.0) 0.5) (log 2.0))) 12.476 * [backup-simplify]: Simplify (+ (* (pow 2.0 0.5) (* -0.5 (* (log (* n PI)) (pow (* (pow n 1.0) (pow PI 1.0)) 0.5)))) (* (* -0.5 (* (pow (pow 2.0 1.0) 0.5) (log 2.0))) (pow (* n PI) 0.5))) into (- (+ (* 0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* n PI)))) (* 0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log 2.0))))) 12.476 * [taylor]: Taking taylor expansion of (- (+ (* 0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* n PI)))) (* 0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log 2.0))))) in n 12.476 * [taylor]: Taking taylor expansion of (+ (* 0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* n PI)))) (* 0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log 2.0)))) in n 12.476 * [taylor]: Taking taylor expansion of (* 0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* n PI)))) in n 12.476 * [taylor]: Taking taylor expansion of 0.5 in n 12.476 * [backup-simplify]: Simplify 0.5 into 0.5 12.476 * [taylor]: Taking taylor expansion of (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* n PI))) in n 12.476 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 12.476 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 12.476 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 12.476 * [taylor]: Taking taylor expansion of 0.5 in n 12.476 * [backup-simplify]: Simplify 0.5 into 0.5 12.476 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 12.476 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 12.477 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 12.477 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 12.477 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 12.477 * [taylor]: Taking taylor expansion of 1.0 in n 12.477 * [backup-simplify]: Simplify 1.0 into 1.0 12.477 * [taylor]: Taking taylor expansion of (log PI) in n 12.477 * [taylor]: Taking taylor expansion of PI in n 12.477 * [backup-simplify]: Simplify PI into PI 12.477 * [backup-simplify]: Simplify (log PI) into (log PI) 12.478 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 12.480 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 12.480 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 12.480 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 12.480 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 12.480 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 12.480 * [taylor]: Taking taylor expansion of 1.0 in n 12.480 * [backup-simplify]: Simplify 1.0 into 1.0 12.480 * [taylor]: Taking taylor expansion of (log n) in n 12.480 * [taylor]: Taking taylor expansion of n in n 12.480 * [backup-simplify]: Simplify 0 into 0 12.480 * [backup-simplify]: Simplify 1 into 1 12.481 * [backup-simplify]: Simplify (log 1) into 0 12.481 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 12.481 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 12.481 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 12.481 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 12.481 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 12.481 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 12.481 * [taylor]: Taking taylor expansion of 1.0 in n 12.482 * [backup-simplify]: Simplify 1.0 into 1.0 12.482 * [taylor]: Taking taylor expansion of (log 2.0) in n 12.482 * [taylor]: Taking taylor expansion of 2.0 in n 12.482 * [backup-simplify]: Simplify 2.0 into 2.0 12.482 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 12.483 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 12.485 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 12.485 * [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) 12.486 * [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) 12.488 * [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)) 12.489 * [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))) 12.490 * [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) 12.490 * [taylor]: Taking taylor expansion of (log (* n PI)) in n 12.490 * [taylor]: Taking taylor expansion of (* n PI) in n 12.490 * [taylor]: Taking taylor expansion of n in n 12.490 * [backup-simplify]: Simplify 0 into 0 12.490 * [backup-simplify]: Simplify 1 into 1 12.490 * [taylor]: Taking taylor expansion of PI in n 12.490 * [backup-simplify]: Simplify PI into PI 12.491 * [backup-simplify]: Simplify (* 0 PI) into 0 12.492 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.493 * [backup-simplify]: Simplify (log PI) into (log PI) 12.493 * [taylor]: Taking taylor expansion of (* 0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log 2.0))) in n 12.493 * [taylor]: Taking taylor expansion of 0.5 in n 12.493 * [backup-simplify]: Simplify 0.5 into 0.5 12.493 * [taylor]: Taking taylor expansion of (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log 2.0)) in n 12.493 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 12.493 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 12.493 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 12.493 * [taylor]: Taking taylor expansion of 0.5 in n 12.493 * [backup-simplify]: Simplify 0.5 into 0.5 12.493 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 12.493 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 12.493 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 12.493 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 12.493 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 12.493 * [taylor]: Taking taylor expansion of 1.0 in n 12.493 * [backup-simplify]: Simplify 1.0 into 1.0 12.493 * [taylor]: Taking taylor expansion of (log PI) in n 12.493 * [taylor]: Taking taylor expansion of PI in n 12.493 * [backup-simplify]: Simplify PI into PI 12.494 * [backup-simplify]: Simplify (log PI) into (log PI) 12.495 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 12.496 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 12.496 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 12.496 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 12.496 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 12.496 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 12.496 * [taylor]: Taking taylor expansion of 1.0 in n 12.496 * [backup-simplify]: Simplify 1.0 into 1.0 12.496 * [taylor]: Taking taylor expansion of (log n) in n 12.496 * [taylor]: Taking taylor expansion of n in n 12.496 * [backup-simplify]: Simplify 0 into 0 12.496 * [backup-simplify]: Simplify 1 into 1 12.497 * [backup-simplify]: Simplify (log 1) into 0 12.497 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 12.497 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 12.497 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 12.497 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 12.497 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 12.497 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 12.497 * [taylor]: Taking taylor expansion of 1.0 in n 12.497 * [backup-simplify]: Simplify 1.0 into 1.0 12.497 * [taylor]: Taking taylor expansion of (log 2.0) in n 12.497 * [taylor]: Taking taylor expansion of 2.0 in n 12.497 * [backup-simplify]: Simplify 2.0 into 2.0 12.498 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 12.499 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 12.500 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 12.500 * [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) 12.502 * [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) 12.503 * [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)) 12.504 * [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))) 12.505 * [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) 12.505 * [taylor]: Taking taylor expansion of (log 2.0) in n 12.505 * [taylor]: Taking taylor expansion of 2.0 in n 12.505 * [backup-simplify]: Simplify 2.0 into 2.0 12.506 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 12.506 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n)) 12.508 * [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 PI) (log n))) into (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (+ (log PI) (log n))) 12.510 * [backup-simplify]: Simplify (* 0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (+ (log PI) (log n)))) into (* 0.5 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (+ (log PI) (log n)))) 12.512 * [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)) into (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log 2.0)) 12.514 * [backup-simplify]: Simplify (* 0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log 2.0))) into (* 0.5 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log 2.0))) 12.518 * [backup-simplify]: Simplify (+ (* 0.5 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (+ (log PI) (log n)))) (* 0.5 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log 2.0)))) into (+ (* 0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (+ (* 0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log 2.0))) (* 0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log PI))))) 12.525 * [backup-simplify]: Simplify (- (+ (* 0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (+ (* 0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log 2.0))) (* 0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log PI)))))) into (- (+ (* 0.5 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log n))) (+ (* 0.5 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log PI))) (* 0.5 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log 2.0)))))) 12.531 * [backup-simplify]: Simplify (- (+ (* 0.5 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log n))) (+ (* 0.5 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log PI))) (* 0.5 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log 2.0)))))) into (- (+ (* 0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (+ (* 0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log 2.0))) (* 0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log PI)))))) 12.532 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0 12.533 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log 2.0))) into 0 12.535 * [backup-simplify]: Simplify (* (exp (* 1.0 (log 2.0))) (+ (* (/ (pow 0 1) 1)))) into 0 12.536 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 12.537 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 12.537 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log n))) into 0 12.538 * [backup-simplify]: Simplify (* (exp (* 1.0 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 12.538 * [backup-simplify]: Simplify (+ (* (pow n 1.0) 0) (* 0 (pow 2.0 1.0))) into 0 12.539 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 12.540 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log PI))) into 0 12.541 * [backup-simplify]: Simplify (* (exp (* 1.0 (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 12.541 * [backup-simplify]: Simplify (+ (* (pow PI 1.0) 0) (* 0 (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0))) into 0 12.543 * [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 12.544 * [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 12.545 * [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 12.545 * [backup-simplify]: Simplify 0 into 0 12.546 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 12.547 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* n PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* n PI) 1)))) 2) into 0 12.547 * [backup-simplify]: Simplify (- 0) into 0 12.547 * [backup-simplify]: Simplify (+ 0 0) into 0 12.548 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0 12.549 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* n PI))))) into 0 12.549 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* n PI)))) (+ (* (/ (pow (- (* 0.5 (log (* n PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 0.125 (* (pow (log (* n PI)) 2) (pow (* (pow n 1.0) (pow PI 1.0)) 0.5))) 12.551 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2.0 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2.0 1)))) 2) into 0 12.551 * [backup-simplify]: Simplify (- 0) into 0 12.552 * [backup-simplify]: Simplify (+ 0 0) into 0 12.552 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0 12.553 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log 2.0)))) into 0 12.559 * [backup-simplify]: Simplify (* (exp (* 0.5 (log 2.0))) (+ (* (/ (pow (- (* 0.5 (log 2.0))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 0.125 (* (pow (pow 2.0 1.0) 0.5) (pow (log 2.0) 2))) 12.566 * [backup-simplify]: Simplify (+ (* (pow 2.0 0.5) (* 0.125 (* (pow (log (* n PI)) 2) (pow (* (pow n 1.0) (pow PI 1.0)) 0.5)))) (+ (* (* -0.5 (* (pow (pow 2.0 1.0) 0.5) (log 2.0))) (* -0.5 (* (log (* n PI)) (pow (* (pow n 1.0) (pow PI 1.0)) 0.5)))) (* (* 0.125 (* (pow (pow 2.0 1.0) 0.5) (pow (log 2.0) 2))) (pow (* n PI) 0.5)))) into (+ (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* n PI)) 2))) (+ (* 0.25 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* n PI)) (log 2.0)))) (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log 2.0) 2))))) 12.566 * [taylor]: Taking taylor expansion of (+ (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* n PI)) 2))) (+ (* 0.25 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* n PI)) (log 2.0)))) (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log 2.0) 2))))) in n 12.566 * [taylor]: Taking taylor expansion of (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* n PI)) 2))) in n 12.566 * [taylor]: Taking taylor expansion of 0.125 in n 12.566 * [backup-simplify]: Simplify 0.125 into 0.125 12.566 * [taylor]: Taking taylor expansion of (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* n PI)) 2)) in n 12.566 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 12.566 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 12.566 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 12.566 * [taylor]: Taking taylor expansion of 0.5 in n 12.567 * [backup-simplify]: Simplify 0.5 into 0.5 12.567 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 12.567 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 12.567 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 12.567 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 12.567 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 12.567 * [taylor]: Taking taylor expansion of 1.0 in n 12.567 * [backup-simplify]: Simplify 1.0 into 1.0 12.567 * [taylor]: Taking taylor expansion of (log PI) in n 12.567 * [taylor]: Taking taylor expansion of PI in n 12.567 * [backup-simplify]: Simplify PI into PI 12.567 * [backup-simplify]: Simplify (log PI) into (log PI) 12.568 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 12.570 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 12.570 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 12.570 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 12.570 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 12.570 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 12.570 * [taylor]: Taking taylor expansion of 1.0 in n 12.570 * [backup-simplify]: Simplify 1.0 into 1.0 12.570 * [taylor]: Taking taylor expansion of (log n) in n 12.570 * [taylor]: Taking taylor expansion of n in n 12.570 * [backup-simplify]: Simplify 0 into 0 12.570 * [backup-simplify]: Simplify 1 into 1 12.571 * [backup-simplify]: Simplify (log 1) into 0 12.571 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 12.571 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 12.571 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 12.571 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 12.571 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 12.571 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 12.572 * [taylor]: Taking taylor expansion of 1.0 in n 12.572 * [backup-simplify]: Simplify 1.0 into 1.0 12.572 * [taylor]: Taking taylor expansion of (log 2.0) in n 12.572 * [taylor]: Taking taylor expansion of 2.0 in n 12.572 * [backup-simplify]: Simplify 2.0 into 2.0 12.572 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 12.573 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 12.574 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 12.575 * [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) 12.576 * [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) 12.578 * [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)) 12.579 * [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))) 12.580 * [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) 12.581 * [taylor]: Taking taylor expansion of (pow (log (* n PI)) 2) in n 12.581 * [taylor]: Taking taylor expansion of (log (* n PI)) in n 12.581 * [taylor]: Taking taylor expansion of (* n PI) in n 12.581 * [taylor]: Taking taylor expansion of n in n 12.581 * [backup-simplify]: Simplify 0 into 0 12.581 * [backup-simplify]: Simplify 1 into 1 12.581 * [taylor]: Taking taylor expansion of PI in n 12.581 * [backup-simplify]: Simplify PI into PI 12.581 * [backup-simplify]: Simplify (* 0 PI) into 0 12.583 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.583 * [backup-simplify]: Simplify (log PI) into (log PI) 12.584 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n)) 12.584 * [taylor]: Taking taylor expansion of (+ (* 0.25 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* n PI)) (log 2.0)))) (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log 2.0) 2)))) in n 12.584 * [taylor]: Taking taylor expansion of (* 0.25 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* n PI)) (log 2.0)))) in n 12.584 * [taylor]: Taking taylor expansion of 0.25 in n 12.584 * [backup-simplify]: Simplify 0.25 into 0.25 12.584 * [taylor]: Taking taylor expansion of (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* n PI)) (log 2.0))) in n 12.584 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 12.584 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 12.584 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 12.584 * [taylor]: Taking taylor expansion of 0.5 in n 12.584 * [backup-simplify]: Simplify 0.5 into 0.5 12.584 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 12.584 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 12.584 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 12.584 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 12.584 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 12.584 * [taylor]: Taking taylor expansion of 1.0 in n 12.584 * [backup-simplify]: Simplify 1.0 into 1.0 12.584 * [taylor]: Taking taylor expansion of (log PI) in n 12.585 * [taylor]: Taking taylor expansion of PI in n 12.585 * [backup-simplify]: Simplify PI into PI 12.585 * [backup-simplify]: Simplify (log PI) into (log PI) 12.586 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 12.594 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 12.594 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 12.594 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 12.594 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 12.594 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 12.594 * [taylor]: Taking taylor expansion of 1.0 in n 12.594 * [backup-simplify]: Simplify 1.0 into 1.0 12.594 * [taylor]: Taking taylor expansion of (log n) in n 12.594 * [taylor]: Taking taylor expansion of n in n 12.594 * [backup-simplify]: Simplify 0 into 0 12.594 * [backup-simplify]: Simplify 1 into 1 12.594 * [backup-simplify]: Simplify (log 1) into 0 12.595 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 12.595 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 12.595 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 12.595 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 12.595 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 12.595 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 12.595 * [taylor]: Taking taylor expansion of 1.0 in n 12.595 * [backup-simplify]: Simplify 1.0 into 1.0 12.595 * [taylor]: Taking taylor expansion of (log 2.0) in n 12.595 * [taylor]: Taking taylor expansion of 2.0 in n 12.595 * [backup-simplify]: Simplify 2.0 into 2.0 12.595 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 12.596 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 12.597 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 12.597 * [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) 12.598 * [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) 12.599 * [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)) 12.600 * [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))) 12.600 * [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) 12.600 * [taylor]: Taking taylor expansion of (* (log (* n PI)) (log 2.0)) in n 12.601 * [taylor]: Taking taylor expansion of (log (* n PI)) in n 12.601 * [taylor]: Taking taylor expansion of (* n PI) in n 12.601 * [taylor]: Taking taylor expansion of n in n 12.601 * [backup-simplify]: Simplify 0 into 0 12.601 * [backup-simplify]: Simplify 1 into 1 12.601 * [taylor]: Taking taylor expansion of PI in n 12.601 * [backup-simplify]: Simplify PI into PI 12.601 * [backup-simplify]: Simplify (* 0 PI) into 0 12.602 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.602 * [backup-simplify]: Simplify (log PI) into (log PI) 12.602 * [taylor]: Taking taylor expansion of (log 2.0) in n 12.602 * [taylor]: Taking taylor expansion of 2.0 in n 12.602 * [backup-simplify]: Simplify 2.0 into 2.0 12.602 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 12.602 * [taylor]: Taking taylor expansion of (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log 2.0) 2))) in n 12.603 * [taylor]: Taking taylor expansion of 0.125 in n 12.603 * [backup-simplify]: Simplify 0.125 into 0.125 12.603 * [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) 2)) in n 12.603 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 12.603 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 12.603 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 12.603 * [taylor]: Taking taylor expansion of 0.5 in n 12.603 * [backup-simplify]: Simplify 0.5 into 0.5 12.603 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 12.603 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 12.603 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 12.603 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 12.603 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 12.603 * [taylor]: Taking taylor expansion of 1.0 in n 12.603 * [backup-simplify]: Simplify 1.0 into 1.0 12.603 * [taylor]: Taking taylor expansion of (log PI) in n 12.603 * [taylor]: Taking taylor expansion of PI in n 12.603 * [backup-simplify]: Simplify PI into PI 12.603 * [backup-simplify]: Simplify (log PI) into (log PI) 12.604 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 12.605 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 12.605 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 12.605 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 12.605 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 12.605 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 12.605 * [taylor]: Taking taylor expansion of 1.0 in n 12.605 * [backup-simplify]: Simplify 1.0 into 1.0 12.605 * [taylor]: Taking taylor expansion of (log n) in n 12.605 * [taylor]: Taking taylor expansion of n in n 12.605 * [backup-simplify]: Simplify 0 into 0 12.605 * [backup-simplify]: Simplify 1 into 1 12.605 * [backup-simplify]: Simplify (log 1) into 0 12.605 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 12.605 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 12.606 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 12.606 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 12.606 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 12.606 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 12.606 * [taylor]: Taking taylor expansion of 1.0 in n 12.606 * [backup-simplify]: Simplify 1.0 into 1.0 12.606 * [taylor]: Taking taylor expansion of (log 2.0) in n 12.606 * [taylor]: Taking taylor expansion of 2.0 in n 12.606 * [backup-simplify]: Simplify 2.0 into 2.0 12.606 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 12.606 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 12.607 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 12.608 * [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) 12.609 * [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) 12.609 * [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)) 12.610 * [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))) 12.611 * [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) 12.611 * [taylor]: Taking taylor expansion of (pow (log 2.0) 2) in n 12.611 * [taylor]: Taking taylor expansion of (log 2.0) in n 12.611 * [taylor]: Taking taylor expansion of 2.0 in n 12.611 * [backup-simplify]: Simplify 2.0 into 2.0 12.611 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 12.612 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n)) 12.612 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n)) 12.613 * [backup-simplify]: Simplify (* (+ (log PI) (log n)) (+ (log PI) (log n))) into (pow (+ (log PI) (log n)) 2) 12.614 * [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 PI) (log n)) 2)) into (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (+ (log PI) (log n)) 2)) 12.615 * [backup-simplify]: Simplify (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (+ (log PI) (log n)) 2))) into (* 0.125 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (+ (log PI) (log n)) 2))) 12.616 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n)) 12.617 * [backup-simplify]: Simplify (* (+ (log PI) (log n)) (log 2.0)) into (* (+ (log PI) (log n)) (log 2.0)) 12.619 * [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 PI) (log n)) (log 2.0))) into (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (+ (log PI) (log n)) (log 2.0))) 12.621 * [backup-simplify]: Simplify (* 0.25 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (+ (log PI) (log n)) (log 2.0)))) into (* 0.25 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (+ (log PI) (log n)) (log 2.0)))) 12.622 * [backup-simplify]: Simplify (* (log 2.0) (log 2.0)) into (pow (log 2.0) 2) 12.625 * [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) 2)) into (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log 2.0) 2)) 12.627 * [backup-simplify]: Simplify (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log 2.0) 2))) into (* 0.125 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log 2.0) 2))) 12.632 * [backup-simplify]: Simplify (+ (* 0.25 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (+ (log PI) (log n)) (log 2.0)))) (* 0.125 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log 2.0) 2)))) into (+ (* 0.25 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log n) (log 2.0)))) (+ (* 0.25 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log PI) (log 2.0)))) (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log 2.0) 2))))) 12.641 * [backup-simplify]: Simplify (+ (* 0.125 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (+ (log PI) (log n)) 2))) (+ (* 0.25 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log n) (log 2.0)))) (+ (* 0.25 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log PI) (log 2.0)))) (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log 2.0) 2)))))) into (+ (* 0.25 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log PI) (log n)))) (+ (* 0.125 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log 2.0) 2))) (+ (* 0.25 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log n) (log 2.0)))) (+ (* 0.25 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log PI) (log 2.0)))) (+ (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log n) 2))) (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log PI) 2)))))))) 12.650 * [backup-simplify]: Simplify (+ (* 0.25 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log PI) (log n)))) (+ (* 0.125 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log 2.0) 2))) (+ (* 0.25 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log n) (log 2.0)))) (+ (* 0.25 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log PI) (log 2.0)))) (+ (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log n) 2))) (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log PI) 2)))))))) into (+ (* 0.125 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log n) 2))) (+ (* 0.25 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log PI) (log n)))) (+ (* 0.25 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log PI) (log 2.0)))) (+ (* 0.125 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log PI) 2))) (+ (* 0.25 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log n) (log 2.0)))) (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log 2.0) 2)))))))) 12.665 * [backup-simplify]: Simplify (+ (* (+ (* 0.125 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log n) 2))) (+ (* 0.25 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log PI) (log n)))) (+ (* 0.25 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log PI) (log 2.0)))) (+ (* 0.125 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log PI) 2))) (+ (* 0.25 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log n) (log 2.0)))) (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log 2.0) 2)))))))) (pow (* 1 k) 2)) (+ (* (- (+ (* 0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (+ (* 0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log 2.0))) (* 0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log PI)))))) (* 1 k)) (pow (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) 1.0) 0.5))) into (- (+ (* 0.25 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (pow k 2) (* (log PI) (log n))))) (+ (* 0.125 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (pow (log n) 2) (pow k 2)))) (+ (* 0.25 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (pow k 2) (* (log PI) (log 2.0))))) (+ (* 0.125 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (pow (log PI) 2) (pow k 2)))) (+ (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (pow k 2) (pow (log 2.0) 2)))) (+ (pow (pow (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) 1.0) 1.0) 0.5) (* 0.25 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (pow k 2) (* (log n) (log 2.0))))))))))) (+ (* 0.5 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* k (log 2.0)))) (+ (* 0.5 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log PI) k))) (* 0.5 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log n) k)))))) 12.665 * [backup-simplify]: Simplify (* (pow 2.0 (/ (- 1.0 (/ 1 k)) 2.0)) (pow (* (/ 1 n) PI) (/ (- 1.0 (/ 1 k)) 2.0))) into (* (pow (/ PI n) (* 0.5 (- 1.0 (/ 1 k)))) (pow 2.0 (* 0.5 (- 1.0 (/ 1 k))))) 12.665 * [approximate]: Taking taylor expansion of (* (pow (/ PI n) (* 0.5 (- 1.0 (/ 1 k)))) (pow 2.0 (* 0.5 (- 1.0 (/ 1 k))))) in (k n) around 0 12.665 * [taylor]: Taking taylor expansion of (* (pow (/ PI n) (* 0.5 (- 1.0 (/ 1 k)))) (pow 2.0 (* 0.5 (- 1.0 (/ 1 k))))) in n 12.665 * [taylor]: Taking taylor expansion of (pow (/ PI n) (* 0.5 (- 1.0 (/ 1 k)))) in n 12.665 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ PI n)))) in n 12.665 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ PI n))) in n 12.665 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 12.665 * [taylor]: Taking taylor expansion of 0.5 in n 12.665 * [backup-simplify]: Simplify 0.5 into 0.5 12.665 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 12.665 * [taylor]: Taking taylor expansion of 1.0 in n 12.665 * [backup-simplify]: Simplify 1.0 into 1.0 12.665 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.665 * [taylor]: Taking taylor expansion of k in n 12.666 * [backup-simplify]: Simplify k into k 12.666 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.666 * [taylor]: Taking taylor expansion of (log (/ PI n)) in n 12.666 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.666 * [taylor]: Taking taylor expansion of PI in n 12.666 * [backup-simplify]: Simplify PI into PI 12.666 * [taylor]: Taking taylor expansion of n in n 12.666 * [backup-simplify]: Simplify 0 into 0 12.666 * [backup-simplify]: Simplify 1 into 1 12.666 * [backup-simplify]: Simplify (/ PI 1) into PI 12.666 * [backup-simplify]: Simplify (log PI) into (log PI) 12.667 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 12.667 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 12.667 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 12.667 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 12.668 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log PI) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log PI) (log n)))) 12.668 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log PI) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log PI) (log n))))) 12.668 * [taylor]: Taking taylor expansion of (pow 2.0 (* 0.5 (- 1.0 (/ 1 k)))) in n 12.668 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log 2.0))) in n 12.668 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log 2.0)) in n 12.668 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 12.668 * [taylor]: Taking taylor expansion of 0.5 in n 12.668 * [backup-simplify]: Simplify 0.5 into 0.5 12.668 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 12.668 * [taylor]: Taking taylor expansion of 1.0 in n 12.668 * [backup-simplify]: Simplify 1.0 into 1.0 12.668 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.668 * [taylor]: Taking taylor expansion of k in n 12.668 * [backup-simplify]: Simplify k into k 12.668 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.668 * [taylor]: Taking taylor expansion of (log 2.0) in n 12.668 * [taylor]: Taking taylor expansion of 2.0 in n 12.668 * [backup-simplify]: Simplify 2.0 into 2.0 12.669 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 12.669 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 12.669 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 12.669 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 12.669 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (log 2.0)) into (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0))) 12.670 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0)))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0)))) 12.670 * [taylor]: Taking taylor expansion of (* (pow (/ PI n) (* 0.5 (- 1.0 (/ 1 k)))) (pow 2.0 (* 0.5 (- 1.0 (/ 1 k))))) in k 12.670 * [taylor]: Taking taylor expansion of (pow (/ PI n) (* 0.5 (- 1.0 (/ 1 k)))) in k 12.670 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ PI n)))) in k 12.670 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ PI n))) in k 12.670 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 12.670 * [taylor]: Taking taylor expansion of 0.5 in k 12.670 * [backup-simplify]: Simplify 0.5 into 0.5 12.670 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 12.670 * [taylor]: Taking taylor expansion of 1.0 in k 12.670 * [backup-simplify]: Simplify 1.0 into 1.0 12.670 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.670 * [taylor]: Taking taylor expansion of k in k 12.670 * [backup-simplify]: Simplify 0 into 0 12.670 * [backup-simplify]: Simplify 1 into 1 12.670 * [backup-simplify]: Simplify (/ 1 1) into 1 12.670 * [taylor]: Taking taylor expansion of (log (/ PI n)) in k 12.670 * [taylor]: Taking taylor expansion of (/ PI n) in k 12.670 * [taylor]: Taking taylor expansion of PI in k 12.670 * [backup-simplify]: Simplify PI into PI 12.670 * [taylor]: Taking taylor expansion of n in k 12.671 * [backup-simplify]: Simplify n into n 12.671 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 12.671 * [backup-simplify]: Simplify (log (/ PI n)) into (log (/ PI n)) 12.671 * [backup-simplify]: Simplify (- 1) into -1 12.671 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.672 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 12.672 * [backup-simplify]: Simplify (* -0.5 (log (/ PI n))) into (* -0.5 (log (/ PI n))) 12.672 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ PI n)))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (/ PI n))))) 12.672 * [taylor]: Taking taylor expansion of (pow 2.0 (* 0.5 (- 1.0 (/ 1 k)))) in k 12.672 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log 2.0))) in k 12.672 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log 2.0)) in k 12.672 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 12.672 * [taylor]: Taking taylor expansion of 0.5 in k 12.672 * [backup-simplify]: Simplify 0.5 into 0.5 12.672 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 12.673 * [taylor]: Taking taylor expansion of 1.0 in k 12.673 * [backup-simplify]: Simplify 1.0 into 1.0 12.673 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.673 * [taylor]: Taking taylor expansion of k in k 12.673 * [backup-simplify]: Simplify 0 into 0 12.673 * [backup-simplify]: Simplify 1 into 1 12.673 * [backup-simplify]: Simplify (/ 1 1) into 1 12.673 * [taylor]: Taking taylor expansion of (log 2.0) in k 12.673 * [taylor]: Taking taylor expansion of 2.0 in k 12.673 * [backup-simplify]: Simplify 2.0 into 2.0 12.674 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 12.674 * [backup-simplify]: Simplify (- 1) into -1 12.674 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.675 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 12.676 * [backup-simplify]: Simplify (* -0.5 (log 2.0)) into (* -0.5 (log 2.0)) 12.676 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log 2.0))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0)))) 12.676 * [taylor]: Taking taylor expansion of (* (pow (/ PI n) (* 0.5 (- 1.0 (/ 1 k)))) (pow 2.0 (* 0.5 (- 1.0 (/ 1 k))))) in k 12.676 * [taylor]: Taking taylor expansion of (pow (/ PI n) (* 0.5 (- 1.0 (/ 1 k)))) in k 12.676 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ PI n)))) in k 12.676 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ PI n))) in k 12.676 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 12.676 * [taylor]: Taking taylor expansion of 0.5 in k 12.676 * [backup-simplify]: Simplify 0.5 into 0.5 12.676 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 12.676 * [taylor]: Taking taylor expansion of 1.0 in k 12.677 * [backup-simplify]: Simplify 1.0 into 1.0 12.677 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.677 * [taylor]: Taking taylor expansion of k in k 12.677 * [backup-simplify]: Simplify 0 into 0 12.677 * [backup-simplify]: Simplify 1 into 1 12.677 * [backup-simplify]: Simplify (/ 1 1) into 1 12.677 * [taylor]: Taking taylor expansion of (log (/ PI n)) in k 12.677 * [taylor]: Taking taylor expansion of (/ PI n) in k 12.677 * [taylor]: Taking taylor expansion of PI in k 12.677 * [backup-simplify]: Simplify PI into PI 12.677 * [taylor]: Taking taylor expansion of n in k 12.677 * [backup-simplify]: Simplify n into n 12.677 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 12.677 * [backup-simplify]: Simplify (log (/ PI n)) into (log (/ PI n)) 12.678 * [backup-simplify]: Simplify (- 1) into -1 12.678 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.679 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 12.679 * [backup-simplify]: Simplify (* -0.5 (log (/ PI n))) into (* -0.5 (log (/ PI n))) 12.679 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ PI n)))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (/ PI n))))) 12.679 * [taylor]: Taking taylor expansion of (pow 2.0 (* 0.5 (- 1.0 (/ 1 k)))) in k 12.679 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log 2.0))) in k 12.679 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log 2.0)) in k 12.679 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 12.679 * [taylor]: Taking taylor expansion of 0.5 in k 12.679 * [backup-simplify]: Simplify 0.5 into 0.5 12.679 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 12.679 * [taylor]: Taking taylor expansion of 1.0 in k 12.679 * [backup-simplify]: Simplify 1.0 into 1.0 12.679 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.680 * [taylor]: Taking taylor expansion of k in k 12.680 * [backup-simplify]: Simplify 0 into 0 12.680 * [backup-simplify]: Simplify 1 into 1 12.680 * [backup-simplify]: Simplify (/ 1 1) into 1 12.680 * [taylor]: Taking taylor expansion of (log 2.0) in k 12.680 * [taylor]: Taking taylor expansion of 2.0 in k 12.680 * [backup-simplify]: Simplify 2.0 into 2.0 12.680 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 12.681 * [backup-simplify]: Simplify (- 1) into -1 12.681 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.682 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 12.683 * [backup-simplify]: Simplify (* -0.5 (log 2.0)) into (* -0.5 (log 2.0)) 12.683 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log 2.0))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0)))) 12.684 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (/ PI n))))) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0))))) into (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (/ PI n))))) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0))))) 12.684 * [taylor]: Taking taylor expansion of (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (/ PI n))))) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0))))) in n 12.684 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (/ PI n))))) in n 12.684 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (log (/ PI n)))) in n 12.684 * [taylor]: Taking taylor expansion of 0.5 in n 12.684 * [backup-simplify]: Simplify 0.5 into 0.5 12.684 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (log (/ PI n))) in n 12.684 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 12.684 * [taylor]: Taking taylor expansion of 1.0 in n 12.684 * [backup-simplify]: Simplify 1.0 into 1.0 12.684 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.684 * [taylor]: Taking taylor expansion of k in n 12.684 * [backup-simplify]: Simplify k into k 12.684 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.684 * [taylor]: Taking taylor expansion of (log (/ PI n)) in n 12.684 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.684 * [taylor]: Taking taylor expansion of PI in n 12.684 * [backup-simplify]: Simplify PI into PI 12.684 * [taylor]: Taking taylor expansion of n in n 12.684 * [backup-simplify]: Simplify 0 into 0 12.684 * [backup-simplify]: Simplify 1 into 1 12.685 * [backup-simplify]: Simplify (/ PI 1) into PI 12.685 * [backup-simplify]: Simplify (log PI) into (log PI) 12.686 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 12.686 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 12.686 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 12.687 * [backup-simplify]: Simplify (* (- 1.0 (/ 1 k)) (- (log PI) (log n))) into (* (- 1.0 (/ 1 k)) (- (log PI) (log n))) 12.688 * [backup-simplify]: Simplify (* 0.5 (* (- 1.0 (/ 1 k)) (- (log PI) (log n)))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log PI) (log n)))) 12.688 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log PI) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log PI) (log n))))) 12.688 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0)))) in n 12.688 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0))) in n 12.688 * [taylor]: Taking taylor expansion of 0.5 in n 12.688 * [backup-simplify]: Simplify 0.5 into 0.5 12.688 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (log 2.0)) in n 12.689 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 12.689 * [taylor]: Taking taylor expansion of 1.0 in n 12.689 * [backup-simplify]: Simplify 1.0 into 1.0 12.689 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.689 * [taylor]: Taking taylor expansion of k in n 12.689 * [backup-simplify]: Simplify k into k 12.689 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.689 * [taylor]: Taking taylor expansion of (log 2.0) in n 12.689 * [taylor]: Taking taylor expansion of 2.0 in n 12.689 * [backup-simplify]: Simplify 2.0 into 2.0 12.689 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 12.689 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 12.689 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 12.690 * [backup-simplify]: Simplify (* (- 1.0 (/ 1 k)) (log 2.0)) into (* (- 1.0 (/ 1 k)) (log 2.0)) 12.691 * [backup-simplify]: Simplify (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0))) into (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0))) 12.691 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0)))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0)))) 12.692 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log PI) (log n))))) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0))))) into (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0)))) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log PI) (log n)))))) 12.694 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0)))) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log PI) (log n)))))) into (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0)))) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log PI) (log n)))))) 12.695 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (/ PI n))))) 0) (* 0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0)))))) into 0 12.695 * [taylor]: Taking taylor expansion of 0 in n 12.695 * [backup-simplify]: Simplify 0 into 0 12.695 * [backup-simplify]: Simplify 0 into 0 12.696 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0 12.696 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 12.697 * [backup-simplify]: Simplify (- 0) into 0 12.697 * [backup-simplify]: Simplify (+ 0 0) into 0 12.698 * [backup-simplify]: Simplify (+ (* (- 1.0 (/ 1 k)) 0) (* 0 (log 2.0))) into 0 12.699 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- 1.0 (/ 1 k)) (log 2.0)))) into 0 12.700 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 12.702 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.703 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 12.703 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 12.704 * [backup-simplify]: Simplify (- 0) into 0 12.704 * [backup-simplify]: Simplify (+ 0 0) into 0 12.705 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 12.706 * [backup-simplify]: Simplify (+ (* (- 1.0 (/ 1 k)) 0) (* 0 (- (log PI) (log n)))) into 0 12.707 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- 1.0 (/ 1 k)) (- (log PI) (log n))))) into 0 12.708 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log PI) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 12.709 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log PI) (log n))))) 0) (* 0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0)))))) into 0 12.709 * [backup-simplify]: Simplify 0 into 0 12.711 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (/ PI n))))) 0) (+ (* 0 0) (* 0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0))))))) into 0 12.711 * [taylor]: Taking taylor expansion of 0 in n 12.711 * [backup-simplify]: Simplify 0 into 0 12.711 * [backup-simplify]: Simplify 0 into 0 12.711 * [backup-simplify]: Simplify 0 into 0 12.720 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2.0 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2.0 1)))) 2) into 0 12.721 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.722 * [backup-simplify]: Simplify (- 0) into 0 12.722 * [backup-simplify]: Simplify (+ 0 0) into 0 12.723 * [backup-simplify]: Simplify (+ (* (- 1.0 (/ 1 k)) 0) (+ (* 0 0) (* 0 (log 2.0)))) into 0 12.725 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (* (- 1.0 (/ 1 k)) (log 2.0))))) into 0 12.727 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 12.729 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.733 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 12.733 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.733 * [backup-simplify]: Simplify (- 0) into 0 12.734 * [backup-simplify]: Simplify (+ 0 0) into 0 12.734 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 12.735 * [backup-simplify]: Simplify (+ (* (- 1.0 (/ 1 k)) 0) (+ (* 0 0) (* 0 (- (log PI) (log n))))) into 0 12.736 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (* (- 1.0 (/ 1 k)) (- (log PI) (log n)))))) into 0 12.737 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log PI) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 12.738 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log PI) (log n))))) 0) (+ (* 0 0) (* 0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0))))))) into 0 12.738 * [backup-simplify]: Simplify 0 into 0 12.739 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (/ PI n))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0)))))))) 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 12.739 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (log 2.0)))) (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log PI) (log (/ 1 n))))))) into (* (exp (* 0.5 (* (- 1.0 k) (log 2.0)))) (exp (* 0.5 (* (- 1.0 k) (- (log PI) (log (/ 1 n))))))) 12.740 * [backup-simplify]: Simplify (* (pow 2.0 (/ (- 1.0 (/ 1 (- k))) 2.0)) (pow (* (/ 1 (- n)) PI) (/ (- 1.0 (/ 1 (- k))) 2.0))) into (* (pow (* -1 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (pow 2.0 (* 0.5 (+ (/ 1 k) 1.0)))) 12.740 * [approximate]: Taking taylor expansion of (* (pow (* -1 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (pow 2.0 (* 0.5 (+ (/ 1 k) 1.0)))) in (k n) around 0 12.740 * [taylor]: Taking taylor expansion of (* (pow (* -1 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (pow 2.0 (* 0.5 (+ (/ 1 k) 1.0)))) in n 12.740 * [taylor]: Taking taylor expansion of (pow (* -1 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 12.740 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -1 (/ PI n))))) in n 12.740 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -1 (/ PI n)))) in n 12.740 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 12.740 * [taylor]: Taking taylor expansion of 0.5 in n 12.740 * [backup-simplify]: Simplify 0.5 into 0.5 12.740 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 12.740 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.740 * [taylor]: Taking taylor expansion of k in n 12.740 * [backup-simplify]: Simplify k into k 12.740 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.740 * [taylor]: Taking taylor expansion of 1.0 in n 12.740 * [backup-simplify]: Simplify 1.0 into 1.0 12.740 * [taylor]: Taking taylor expansion of (log (* -1 (/ PI n))) in n 12.740 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n 12.740 * [taylor]: Taking taylor expansion of -1 in n 12.740 * [backup-simplify]: Simplify -1 into -1 12.740 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.740 * [taylor]: Taking taylor expansion of PI in n 12.740 * [backup-simplify]: Simplify PI into PI 12.740 * [taylor]: Taking taylor expansion of n in n 12.740 * [backup-simplify]: Simplify 0 into 0 12.740 * [backup-simplify]: Simplify 1 into 1 12.741 * [backup-simplify]: Simplify (/ PI 1) into PI 12.741 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI) 12.742 * [backup-simplify]: Simplify (log (* -1 PI)) into (log (* -1 PI)) 12.742 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 12.742 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 12.743 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 12.744 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -1 PI)) (log n))) into (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0))) 12.744 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) 12.745 * [taylor]: Taking taylor expansion of (pow 2.0 (* 0.5 (+ (/ 1 k) 1.0))) in n 12.745 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log 2.0))) in n 12.745 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log 2.0)) in n 12.745 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 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 (+ (/ 1 k) 1.0) in n 12.745 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.745 * [taylor]: Taking taylor expansion of k in n 12.745 * [backup-simplify]: Simplify k into k 12.745 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 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 2.0) in n 12.745 * [taylor]: Taking taylor expansion of 2.0 in n 12.745 * [backup-simplify]: Simplify 2.0 into 2.0 12.745 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 12.745 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 12.745 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 12.745 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (log 2.0)) into (* 0.5 (* (log 2.0) (+ (/ 1 k) 1.0))) 12.746 * [backup-simplify]: Simplify (exp (* 0.5 (* (log 2.0) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (log 2.0) (+ (/ 1 k) 1.0)))) 12.746 * [taylor]: Taking taylor expansion of (* (pow (* -1 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (pow 2.0 (* 0.5 (+ (/ 1 k) 1.0)))) in k 12.746 * [taylor]: Taking taylor expansion of (pow (* -1 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 12.746 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -1 (/ PI n))))) in k 12.746 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -1 (/ PI n)))) in k 12.746 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 12.746 * [taylor]: Taking taylor expansion of 0.5 in k 12.746 * [backup-simplify]: Simplify 0.5 into 0.5 12.746 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 12.746 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.746 * [taylor]: Taking taylor expansion of k in k 12.746 * [backup-simplify]: Simplify 0 into 0 12.746 * [backup-simplify]: Simplify 1 into 1 12.746 * [backup-simplify]: Simplify (/ 1 1) into 1 12.746 * [taylor]: Taking taylor expansion of 1.0 in k 12.746 * [backup-simplify]: Simplify 1.0 into 1.0 12.746 * [taylor]: Taking taylor expansion of (log (* -1 (/ PI n))) in k 12.746 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in k 12.746 * [taylor]: Taking taylor expansion of -1 in k 12.746 * [backup-simplify]: Simplify -1 into -1 12.746 * [taylor]: Taking taylor expansion of (/ PI n) in k 12.746 * [taylor]: Taking taylor expansion of PI in k 12.746 * [backup-simplify]: Simplify PI into PI 12.746 * [taylor]: Taking taylor expansion of n in k 12.746 * [backup-simplify]: Simplify n into n 12.746 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 12.747 * [backup-simplify]: Simplify (* -1 (/ PI n)) into (* -1 (/ PI n)) 12.747 * [backup-simplify]: Simplify (log (* -1 (/ PI n))) into (log (* -1 (/ PI n))) 12.747 * [backup-simplify]: Simplify (+ 1 0) into 1 12.747 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 12.747 * [backup-simplify]: Simplify (* 0.5 (log (* -1 (/ PI n)))) into (* 0.5 (log (* -1 (/ PI n)))) 12.747 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -1 (/ PI n))))) into (exp (* 0.5 (* (log (* -1 (/ PI n))) (+ (/ 1 k) 1.0)))) 12.747 * [taylor]: Taking taylor expansion of (pow 2.0 (* 0.5 (+ (/ 1 k) 1.0))) in k 12.747 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log 2.0))) in k 12.747 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log 2.0)) in k 12.747 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 12.747 * [taylor]: Taking taylor expansion of 0.5 in k 12.747 * [backup-simplify]: Simplify 0.5 into 0.5 12.748 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 12.748 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.748 * [taylor]: Taking taylor expansion of k in k 12.748 * [backup-simplify]: Simplify 0 into 0 12.748 * [backup-simplify]: Simplify 1 into 1 12.748 * [backup-simplify]: Simplify (/ 1 1) into 1 12.748 * [taylor]: Taking taylor expansion of 1.0 in k 12.748 * [backup-simplify]: Simplify 1.0 into 1.0 12.748 * [taylor]: Taking taylor expansion of (log 2.0) in k 12.748 * [taylor]: Taking taylor expansion of 2.0 in k 12.748 * [backup-simplify]: Simplify 2.0 into 2.0 12.748 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 12.748 * [backup-simplify]: Simplify (+ 1 0) into 1 12.749 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 12.749 * [backup-simplify]: Simplify (* 0.5 (log 2.0)) into (* 0.5 (log 2.0)) 12.750 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log 2.0))) into (exp (* 0.5 (* (log 2.0) (+ (/ 1 k) 1.0)))) 12.750 * [taylor]: Taking taylor expansion of (* (pow (* -1 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (pow 2.0 (* 0.5 (+ (/ 1 k) 1.0)))) in k 12.750 * [taylor]: Taking taylor expansion of (pow (* -1 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 12.750 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -1 (/ PI n))))) in k 12.750 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -1 (/ PI n)))) in k 12.750 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 12.750 * [taylor]: Taking taylor expansion of 0.5 in k 12.750 * [backup-simplify]: Simplify 0.5 into 0.5 12.750 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 12.750 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.750 * [taylor]: Taking taylor expansion of k in k 12.750 * [backup-simplify]: Simplify 0 into 0 12.750 * [backup-simplify]: Simplify 1 into 1 12.750 * [backup-simplify]: Simplify (/ 1 1) into 1 12.750 * [taylor]: Taking taylor expansion of 1.0 in k 12.750 * [backup-simplify]: Simplify 1.0 into 1.0 12.750 * [taylor]: Taking taylor expansion of (log (* -1 (/ PI n))) in k 12.750 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in k 12.750 * [taylor]: Taking taylor expansion of -1 in k 12.750 * [backup-simplify]: Simplify -1 into -1 12.750 * [taylor]: Taking taylor expansion of (/ PI n) in k 12.750 * [taylor]: Taking taylor expansion of PI in k 12.750 * [backup-simplify]: Simplify PI into PI 12.750 * [taylor]: Taking taylor expansion of n in k 12.750 * [backup-simplify]: Simplify n into n 12.750 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 12.750 * [backup-simplify]: Simplify (* -1 (/ PI n)) into (* -1 (/ PI n)) 12.750 * [backup-simplify]: Simplify (log (* -1 (/ PI n))) into (log (* -1 (/ PI n))) 12.751 * [backup-simplify]: Simplify (+ 1 0) into 1 12.751 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 12.751 * [backup-simplify]: Simplify (* 0.5 (log (* -1 (/ PI n)))) into (* 0.5 (log (* -1 (/ PI n)))) 12.751 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -1 (/ PI n))))) into (exp (* 0.5 (* (log (* -1 (/ PI n))) (+ (/ 1 k) 1.0)))) 12.751 * [taylor]: Taking taylor expansion of (pow 2.0 (* 0.5 (+ (/ 1 k) 1.0))) in k 12.751 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log 2.0))) in k 12.751 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log 2.0)) in k 12.751 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 12.751 * [taylor]: Taking taylor expansion of 0.5 in k 12.751 * [backup-simplify]: Simplify 0.5 into 0.5 12.751 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 12.751 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.751 * [taylor]: Taking taylor expansion of k in k 12.751 * [backup-simplify]: Simplify 0 into 0 12.751 * [backup-simplify]: Simplify 1 into 1 12.752 * [backup-simplify]: Simplify (/ 1 1) into 1 12.752 * [taylor]: Taking taylor expansion of 1.0 in k 12.752 * [backup-simplify]: Simplify 1.0 into 1.0 12.752 * [taylor]: Taking taylor expansion of (log 2.0) in k 12.752 * [taylor]: Taking taylor expansion of 2.0 in k 12.752 * [backup-simplify]: Simplify 2.0 into 2.0 12.752 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 12.752 * [backup-simplify]: Simplify (+ 1 0) into 1 12.752 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 12.753 * [backup-simplify]: Simplify (* 0.5 (log 2.0)) into (* 0.5 (log 2.0)) 12.753 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log 2.0))) into (exp (* 0.5 (* (log 2.0) (+ (/ 1 k) 1.0)))) 12.754 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (log (* -1 (/ PI n))) (+ (/ 1 k) 1.0)))) (exp (* 0.5 (* (log 2.0) (+ (/ 1 k) 1.0))))) into (* (exp (* 0.5 (* (log (* -1 (/ PI n))) (+ (/ 1 k) 1.0)))) (exp (* 0.5 (* (log 2.0) (+ (/ 1 k) 1.0))))) 12.754 * [taylor]: Taking taylor expansion of (* (exp (* 0.5 (* (log (* -1 (/ PI n))) (+ (/ 1 k) 1.0)))) (exp (* 0.5 (* (log 2.0) (+ (/ 1 k) 1.0))))) in n 12.754 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* -1 (/ PI n))) (+ (/ 1 k) 1.0)))) in n 12.754 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* -1 (/ PI n))) (+ (/ 1 k) 1.0))) in n 12.754 * [taylor]: Taking taylor expansion of 0.5 in n 12.754 * [backup-simplify]: Simplify 0.5 into 0.5 12.754 * [taylor]: Taking taylor expansion of (* (log (* -1 (/ PI n))) (+ (/ 1 k) 1.0)) in n 12.754 * [taylor]: Taking taylor expansion of (log (* -1 (/ PI n))) in n 12.754 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n 12.754 * [taylor]: Taking taylor expansion of -1 in n 12.754 * [backup-simplify]: Simplify -1 into -1 12.754 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.754 * [taylor]: Taking taylor expansion of PI in n 12.754 * [backup-simplify]: Simplify PI into PI 12.754 * [taylor]: Taking taylor expansion of n in n 12.754 * [backup-simplify]: Simplify 0 into 0 12.754 * [backup-simplify]: Simplify 1 into 1 12.754 * [backup-simplify]: Simplify (/ PI 1) into PI 12.755 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI) 12.755 * [backup-simplify]: Simplify (log (* -1 PI)) into (log (* -1 PI)) 12.755 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 12.755 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.755 * [taylor]: Taking taylor expansion of k in n 12.755 * [backup-simplify]: Simplify k into k 12.755 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.756 * [taylor]: Taking taylor expansion of 1.0 in n 12.756 * [backup-simplify]: Simplify 1.0 into 1.0 12.756 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 12.756 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 12.757 * [backup-simplify]: Simplify (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)) into (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)) 12.758 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0))) into (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0))) 12.759 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) 12.759 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log 2.0) (+ (/ 1 k) 1.0)))) in n 12.759 * [taylor]: Taking taylor expansion of (* 0.5 (* (log 2.0) (+ (/ 1 k) 1.0))) in n 12.759 * [taylor]: Taking taylor expansion of 0.5 in n 12.759 * [backup-simplify]: Simplify 0.5 into 0.5 12.759 * [taylor]: Taking taylor expansion of (* (log 2.0) (+ (/ 1 k) 1.0)) in n 12.759 * [taylor]: Taking taylor expansion of (log 2.0) in n 12.759 * [taylor]: Taking taylor expansion of 2.0 in n 12.759 * [backup-simplify]: Simplify 2.0 into 2.0 12.759 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 12.759 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 12.759 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.759 * [taylor]: Taking taylor expansion of k in n 12.759 * [backup-simplify]: Simplify k into k 12.759 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.759 * [taylor]: Taking taylor expansion of 1.0 in n 12.759 * [backup-simplify]: Simplify 1.0 into 1.0 12.759 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 12.760 * [backup-simplify]: Simplify (* (log 2.0) (+ (/ 1 k) 1.0)) into (* (+ (/ 1 k) 1.0) (log 2.0)) 12.760 * [backup-simplify]: Simplify (* 0.5 (* (+ (/ 1 k) 1.0) (log 2.0))) into (* 0.5 (* (+ (/ 1 k) 1.0) (log 2.0))) 12.760 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log 2.0)))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log 2.0)))) 12.761 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log 2.0))))) into (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log 2.0)))) (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0))))) 12.762 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log 2.0)))) (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0))))) into (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log 2.0)))) (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0))))) 12.763 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (log (* -1 (/ PI n))) (+ (/ 1 k) 1.0)))) 0) (* 0 (exp (* 0.5 (* (log 2.0) (+ (/ 1 k) 1.0)))))) into 0 12.763 * [taylor]: Taking taylor expansion of 0 in n 12.763 * [backup-simplify]: Simplify 0 into 0 12.763 * [backup-simplify]: Simplify 0 into 0 12.763 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 12.763 * [backup-simplify]: Simplify (+ 0 0) into 0 12.764 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0 12.765 * [backup-simplify]: Simplify (+ (* (log 2.0) 0) (* 0 (+ (/ 1 k) 1.0))) into 0 12.765 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (+ (/ 1 k) 1.0) (log 2.0)))) into 0 12.767 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log 2.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 12.768 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 12.768 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 12.769 * [backup-simplify]: Simplify (+ 0 0) into 0 12.769 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.770 * [backup-simplify]: Simplify (+ (* -1 0) (* 0 PI)) into 0 12.772 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -1 PI) 1)))) 1) into 0 12.773 * [backup-simplify]: Simplify (+ (* (- (log (* -1 PI)) (log n)) 0) (* 0 (+ (/ 1 k) 1.0))) into 0 12.775 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) into 0 12.777 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 12.779 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) 0) (* 0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log 2.0)))))) into 0 12.779 * [backup-simplify]: Simplify 0 into 0 12.780 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (log (* -1 (/ PI n))) (+ (/ 1 k) 1.0)))) 0) (+ (* 0 0) (* 0 (exp (* 0.5 (* (log 2.0) (+ (/ 1 k) 1.0))))))) into 0 12.780 * [taylor]: Taking taylor expansion of 0 in n 12.780 * [backup-simplify]: Simplify 0 into 0 12.780 * [backup-simplify]: Simplify 0 into 0 12.780 * [backup-simplify]: Simplify 0 into 0 12.780 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.781 * [backup-simplify]: Simplify (+ 0 0) into 0 12.784 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2.0 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2.0 1)))) 2) into 0 12.785 * [backup-simplify]: Simplify (+ (* (log 2.0) 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 12.786 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (* (+ (/ 1 k) 1.0) (log 2.0))))) into 0 12.788 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log 2.0)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 12.790 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 12.790 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.791 * [backup-simplify]: Simplify (+ 0 0) into 0 12.792 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.793 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 PI))) into 0 12.796 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -1 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -1 PI) 1)))) 2) into 0 12.798 * [backup-simplify]: Simplify (+ (* (- (log (* -1 PI)) (log n)) 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 12.800 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0))))) into 0 12.803 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 12.805 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) 0) (+ (* 0 0) (* 0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log 2.0))))))) into 0 12.805 * [backup-simplify]: Simplify 0 into 0 12.806 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (log (* -1 (/ PI n))) (+ (/ 1 k) 1.0)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 0.5 (* (log 2.0) (+ (/ 1 k) 1.0)))))))) into 0 12.807 * [taylor]: Taking taylor expansion of 0 in n 12.807 * [backup-simplify]: Simplify 0 into 0 12.807 * [backup-simplify]: Simplify 0 into 0 12.809 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (log 2.0)))) (exp (* 0.5 (* (- (log (* -1 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0))))) into (* (exp (* 0.5 (* (- 1.0 k) (log 2.0)))) (exp (* 0.5 (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1.0 k))))) 12.809 * * * [progress]: simplifying candidates 12.812 * [simplify]: Simplifying: (* (+ (log n) (log PI)) (/ (- 1.0 k) 2.0)) (* (log (* n PI)) (/ (- 1.0 k) 2.0)) (* (log (* n PI)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ 1.0 2.0)) (pow (* n PI) (/ k 2.0)) (pow (* n PI) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* n PI) (sqrt (/ (- 1.0 k) 2.0))) (pow (* n PI) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* n PI) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* n PI) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* n PI) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* n PI) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* n PI) (/ (sqrt (- 1.0 k)) 1)) (pow (* n PI) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* n PI) (/ 1 (sqrt 2.0))) (pow (* n PI) (/ 1 1)) (pow (* n PI) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* n PI) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* n PI) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* n PI) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* n PI) (/ 1 (sqrt 2.0))) (pow (* n PI) (/ 1 1)) (pow (* n PI) 1) (pow (* n PI) (- 1.0 k)) (pow n (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0)) (log (pow (* n PI) (/ (- 1.0 k) 2.0))) (exp (pow (* n PI) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* n PI) (/ (- 1.0 k) 2.0))) (cbrt (pow (* n PI) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* n PI) (/ (- 1.0 k) 2.0))) (* (* (pow (* n PI) (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0))) (pow (* n PI) (/ (- 1.0 k) 2.0))) (sqrt (pow (* n PI) (/ (- 1.0 k) 2.0))) (sqrt (pow (* n PI) (/ (- 1.0 k) 2.0))) (pow (* n PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* n PI) (/ (/ (- 1.0 k) 2.0) 2)) (* n PI) (+ (log n) (log PI)) (log (* n PI)) (exp (* n PI)) (* (* (* n n) n) (* (* PI PI) PI)) (* (cbrt (* n PI)) (cbrt (* n PI))) (cbrt (* n PI)) (* (* (* n PI) (* n PI)) (* n PI)) (sqrt (* n PI)) (sqrt (* n PI)) (* (sqrt n) (sqrt PI)) (* (sqrt n) (sqrt PI)) (* n (* (cbrt PI) (cbrt PI))) (* n (sqrt PI)) (* n 1) (* (cbrt n) PI) (* (sqrt n) PI) (* n PI) (- (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) (* 2.0 (* n PI)) (+ (* (log 2.0) (/ (- 1.0 k) 2.0)) (* (+ (log n) (log PI)) (/ (- 1.0 k) 2.0))) (+ (* (log 2.0) (/ (- 1.0 k) 2.0)) (* (log (* n PI)) (/ (- 1.0 k) 2.0))) (+ (* (log 2.0) (/ (- 1.0 k) 2.0)) (* (log (* n PI)) (/ (- 1.0 k) 2.0))) (+ (* (log 2.0) (/ (- 1.0 k) 2.0)) (log (pow (* n PI) (/ (- 1.0 k) 2.0)))) (+ (* (log 2.0) (/ (- 1.0 k) 2.0)) (* (+ (log n) (log PI)) (/ (- 1.0 k) 2.0))) (+ (* (log 2.0) (/ (- 1.0 k) 2.0)) (* (log (* n PI)) (/ (- 1.0 k) 2.0))) (+ (* (log 2.0) (/ (- 1.0 k) 2.0)) (* (log (* n PI)) (/ (- 1.0 k) 2.0))) (+ (* (log 2.0) (/ (- 1.0 k) 2.0)) (log (pow (* n PI) (/ (- 1.0 k) 2.0)))) (+ (log (pow 2.0 (/ (- 1.0 k) 2.0))) (* (+ (log n) (log PI)) (/ (- 1.0 k) 2.0))) (+ (log (pow 2.0 (/ (- 1.0 k) 2.0))) (* (log (* n PI)) (/ (- 1.0 k) 2.0))) (+ (log (pow 2.0 (/ (- 1.0 k) 2.0))) (* (log (* n PI)) (/ (- 1.0 k) 2.0))) (+ (log (pow 2.0 (/ (- 1.0 k) 2.0))) (log (pow (* n PI) (/ (- 1.0 k) 2.0)))) (log (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0)))) (exp (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0)))) (* (* (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow 2.0 (/ (- 1.0 k) 2.0))) (pow 2.0 (/ (- 1.0 k) 2.0))) (* (* (pow (* n PI) (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0))) (pow (* n PI) (/ (- 1.0 k) 2.0)))) (* (cbrt (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0)))) (cbrt (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0))))) (cbrt (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0)))) (* (* (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0))) (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0)))) (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0)))) (sqrt (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0)))) (sqrt (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0)))) (* (pow 2.0 (/ 1.0 2.0)) (pow (* n PI) (/ 1.0 2.0))) (* (pow 2.0 (/ k 2.0)) (pow (* n PI) (/ k 2.0))) (* (pow (sqrt 2.0) (/ (- 1.0 k) 2.0)) (sqrt (pow (* n PI) (/ (- 1.0 k) 2.0)))) (* (pow (sqrt 2.0) (/ (- 1.0 k) 2.0)) (sqrt (pow (* n PI) (/ (- 1.0 k) 2.0)))) (* (pow (sqrt 2.0) (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (/ (- 1.0 k) 2.0) 2))) (* (pow (sqrt 2.0) (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (/ (- 1.0 k) 2.0) 2))) (* (sqrt (pow 2.0 (/ (- 1.0 k) 2.0))) (sqrt (pow (* n PI) (/ (- 1.0 k) 2.0)))) (* (sqrt (pow 2.0 (/ (- 1.0 k) 2.0))) (sqrt (pow (* n PI) (/ (- 1.0 k) 2.0)))) (* (sqrt (pow 2.0 (/ (- 1.0 k) 2.0))) (pow (* n PI) (/ (/ (- 1.0 k) 2.0) 2))) (* (sqrt (pow 2.0 (/ (- 1.0 k) 2.0))) (pow (* n PI) (/ (/ (- 1.0 k) 2.0) 2))) (* (pow 2.0 (/ (/ (- 1.0 k) 2.0) 2)) (sqrt (pow (* n PI) (/ (- 1.0 k) 2.0)))) (* (pow 2.0 (/ (/ (- 1.0 k) 2.0) 2)) (sqrt (pow (* n PI) (/ (- 1.0 k) 2.0)))) (* (pow 2.0 (/ (/ (- 1.0 k) 2.0) 2)) (pow (* n PI) (/ (/ (- 1.0 k) 2.0) 2))) (* (pow 2.0 (/ (/ (- 1.0 k) 2.0) 2)) (pow (* n PI) (/ (/ (- 1.0 k) 2.0) 2))) (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0))) (* (pow 2.0 (/ (- 1.0 k) 2.0)) (* (cbrt (pow (* n PI) (/ (- 1.0 k) 2.0))) (cbrt (pow (* n PI) (/ (- 1.0 k) 2.0))))) (* (pow 2.0 (/ (- 1.0 k) 2.0)) (sqrt (pow (* n PI) (/ (- 1.0 k) 2.0)))) (* (pow 2.0 (/ (- 1.0 k) 2.0)) 1) (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (/ (- 1.0 k) 2.0) 2))) (* (pow (cbrt 2.0) (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0))) (* (pow (sqrt 2.0) (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0))) (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0))) (* (cbrt (pow 2.0 (/ (- 1.0 k) 2.0))) (pow (* n PI) (/ (- 1.0 k) 2.0))) (* (sqrt (pow 2.0 (/ (- 1.0 k) 2.0))) (pow (* n PI) (/ (- 1.0 k) 2.0))) (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0))) (* (pow 2.0 (/ (/ (- 1.0 k) 2.0) 2)) (pow (* n PI) (/ (- 1.0 k) 2.0))) (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ 1.0 2.0))) (* (pow 2.0 (/ 1.0 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0))) (- (+ (exp (* 0.5 (+ (log PI) (log n)))) (+ (* 0.125 (* (exp (* 0.5 (+ (log PI) (log n)))) (* (pow (log PI) 2) (pow k 2)))) (+ (* 0.125 (* (exp (* 0.5 (+ (log PI) (log n)))) (* (pow (log n) 2) (pow k 2)))) (* 0.25 (* (exp (* 0.5 (+ (log PI) (log n)))) (* (log PI) (* (log n) (pow k 2)))))))) (+ (* 0.5 (* (exp (* 0.5 (+ (log PI) (log n)))) (* (log n) k))) (* 0.5 (* (exp (* 0.5 (+ (log PI) (log n)))) (* (log PI) k))))) (exp (* 0.5 (* (- 1.0 k) (- (log PI) (log (/ 1 n)))))) (exp (* 0.5 (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1.0 k)))) (* n PI) (* n PI) (* 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))))) (- (+ (* 0.25 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (pow k 2) (* (log PI) (log n))))) (+ (* 0.125 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (pow (log n) 2) (pow k 2)))) (+ (* 0.25 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (pow k 2) (* (log PI) (log 2.0))))) (+ (* 0.125 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (pow (log PI) 2) (pow k 2)))) (+ (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (pow k 2) (pow (log 2.0) 2)))) (+ (pow (pow (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) 1.0) 1.0) 0.5) (* 0.25 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (pow k 2) (* (log n) (log 2.0))))))))))) (+ (* 0.5 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* k (log 2.0)))) (+ (* 0.5 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log PI) k))) (* 0.5 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log n) k)))))) (* (exp (* 0.5 (* (- 1.0 k) (log 2.0)))) (exp (* 0.5 (* (- 1.0 k) (- (log PI) (log (/ 1 n))))))) (* (exp (* 0.5 (* (- 1.0 k) (log 2.0)))) (exp (* 0.5 (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1.0 k))))) 12.818 * * [simplify]: iteration 0: 332 enodes 12.966 * * [simplify]: iteration 1: 888 enodes 13.349 * * [simplify]: iteration 2: 2836 enodes 14.179 * * [simplify]: iteration complete: 5003 enodes 14.179 * * [simplify]: Extracting #0: cost 115 inf + 0 14.181 * * [simplify]: Extracting #1: cost 619 inf + 85 14.188 * * [simplify]: Extracting #2: cost 1266 inf + 3891 14.204 * * [simplify]: Extracting #3: cost 1494 inf + 38430 14.249 * * [simplify]: Extracting #4: cost 1106 inf + 144584 14.322 * * [simplify]: Extracting #5: cost 655 inf + 358307 14.410 * * [simplify]: Extracting #6: cost 356 inf + 565321 14.516 * * [simplify]: Extracting #7: cost 151 inf + 767702 14.620 * * [simplify]: Extracting #8: cost 114 inf + 811688 14.762 * * [simplify]: Extracting #9: cost 110 inf + 817131 14.903 * * [simplify]: Extracting #10: cost 113 inf + 822726 15.043 * * [simplify]: Extracting #11: cost 105 inf + 839572 15.210 * * [simplify]: Extracting #12: cost 65 inf + 902802 15.359 * * [simplify]: Extracting #13: cost 22 inf + 1017152 15.556 * * [simplify]: Extracting #14: cost 1 inf + 1064498 15.726 * * [simplify]: Extracting #15: cost 0 inf + 1065463 15.951 * [simplify]: Simplified to: (* (/ (- 1.0 k) 2.0) (log (* n PI))) (* (/ (- 1.0 k) 2.0) (log (* n PI))) (* (/ (- 1.0 k) 2.0) (log (* n PI))) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (pow (* n PI) (/ 1.0 2.0)) (pow (* n PI) (/ k 2.0)) (pow (* n PI) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* n PI) (sqrt (/ (- 1.0 k) 2.0))) (pow (* n PI) (* (/ (cbrt (- 1.0 k)) (cbrt 2.0)) (/ (cbrt (- 1.0 k)) (cbrt 2.0)))) (pow (* n PI) (/ (cbrt (- 1.0 k)) (/ (sqrt 2.0) (cbrt (- 1.0 k))))) (pow (* n PI) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* n PI) (/ (/ (sqrt (- 1.0 k)) (cbrt 2.0)) (cbrt 2.0))) (pow (* n PI) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* n PI) (sqrt (- 1.0 k))) (pow (* n PI) (/ (/ 1 (cbrt 2.0)) (cbrt 2.0))) (pow (* n PI) (/ 1 (sqrt 2.0))) (* n PI) (pow (* n PI) (/ (/ (+ (sqrt 1.0) (sqrt k)) (cbrt 2.0)) (cbrt 2.0))) (pow (* n PI) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* n PI) (+ (sqrt 1.0) (sqrt k))) (pow (* n PI) (/ (/ 1 (cbrt 2.0)) (cbrt 2.0))) (pow (* n PI) (/ 1 (sqrt 2.0))) (* n PI) (* n PI) (pow (* n PI) (- 1.0 k)) (pow n (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0)) (* (/ (- 1.0 k) 2.0) (log (* n PI))) (exp (pow (* n PI) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* n PI) (/ (- 1.0 k) 2.0))) (cbrt (pow (* n PI) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* n PI) (/ (- 1.0 k) 2.0))) (* (pow (* n PI) (/ (- 1.0 k) 2.0)) (* (pow (* n PI) (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0)))) (sqrt (pow (* n PI) (/ (- 1.0 k) 2.0))) (sqrt (pow (* n PI) (/ (- 1.0 k) 2.0))) (pow (* n PI) (/ (/ (- 1.0 k) 2) 2.0)) (pow (* n PI) (/ (/ (- 1.0 k) 2) 2.0)) (* n PI) (log (* n PI)) (log (* n PI)) (exp (* n PI)) (* (* (* n PI) (* n PI)) (* n PI)) (* (cbrt (* n PI)) (cbrt (* n PI))) (cbrt (* n PI)) (* (* (* n PI) (* n PI)) (* n PI)) (sqrt (* n PI)) (sqrt (* n PI)) (* (sqrt PI) (sqrt n)) (* (sqrt PI) (sqrt n)) (* n (* (cbrt PI) (cbrt PI))) (* (sqrt PI) n) n (* PI (cbrt n)) (* PI (sqrt n)) (* n PI) (log (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (* (/ (* 1.0 1.0) 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) (sqrt (sqrt k))) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (cbrt 1.0)) (/ (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) (* 2.0 (* n PI)) (* (/ (- 1.0 k) 2.0) (+ (log (* n PI)) (log 2.0))) (* (/ (- 1.0 k) 2.0) (+ (log (* n PI)) (log 2.0))) (* (/ (- 1.0 k) 2.0) (+ (log (* n PI)) (log 2.0))) (* (/ (- 1.0 k) 2.0) (+ (log (* n PI)) (log 2.0))) (* (/ (- 1.0 k) 2.0) (+ (log (* n PI)) (log 2.0))) (* (/ (- 1.0 k) 2.0) (+ (log (* n PI)) (log 2.0))) (* (/ (- 1.0 k) 2.0) (+ (log (* n PI)) (log 2.0))) (* (/ (- 1.0 k) 2.0) (+ (log (* n PI)) (log 2.0))) (* (/ (- 1.0 k) 2.0) (+ (log (* n PI)) (log 2.0))) (* (/ (- 1.0 k) 2.0) (+ (log (* n PI)) (log 2.0))) (* (/ (- 1.0 k) 2.0) (+ (log (* n PI)) (log 2.0))) (* (/ (- 1.0 k) 2.0) (+ (log (* n PI)) (log 2.0))) (* (/ (- 1.0 k) 2.0) (+ (log (* n PI)) (log 2.0))) (exp (* (pow (* n PI) (/ (- 1.0 k) 2.0)) (pow 2.0 (/ (- 1.0 k) 2.0)))) (* (* (pow (* n PI) (/ (- 1.0 k) 2.0)) (pow 2.0 (/ (- 1.0 k) 2.0))) (* (* (pow (* n PI) (/ (- 1.0 k) 2.0)) (pow 2.0 (/ (- 1.0 k) 2.0))) (* (pow (* n PI) (/ (- 1.0 k) 2.0)) (pow 2.0 (/ (- 1.0 k) 2.0))))) (* (cbrt (* (pow (* n PI) (/ (- 1.0 k) 2.0)) (pow 2.0 (/ (- 1.0 k) 2.0)))) (cbrt (* (pow (* n PI) (/ (- 1.0 k) 2.0)) (pow 2.0 (/ (- 1.0 k) 2.0))))) (cbrt (* (pow (* n PI) (/ (- 1.0 k) 2.0)) (pow 2.0 (/ (- 1.0 k) 2.0)))) (* (* (pow (* n PI) (/ (- 1.0 k) 2.0)) (pow 2.0 (/ (- 1.0 k) 2.0))) (* (* (pow (* n PI) (/ (- 1.0 k) 2.0)) (pow 2.0 (/ (- 1.0 k) 2.0))) (* (pow (* n PI) (/ (- 1.0 k) 2.0)) (pow 2.0 (/ (- 1.0 k) 2.0))))) (sqrt (* (pow (* n PI) (/ (- 1.0 k) 2.0)) (pow 2.0 (/ (- 1.0 k) 2.0)))) (sqrt (* (pow (* n PI) (/ (- 1.0 k) 2.0)) (pow 2.0 (/ (- 1.0 k) 2.0)))) (* (pow 2.0 (/ 1.0 2.0)) (pow (* n PI) (/ 1.0 2.0))) (* (pow 2.0 (/ k 2.0)) (pow (* n PI) (/ k 2.0))) (* (sqrt (pow (* n PI) (/ (- 1.0 k) 2.0))) (pow (sqrt 2.0) (/ (- 1.0 k) 2.0))) (* (sqrt (pow (* n PI) (/ (- 1.0 k) 2.0))) (pow (sqrt 2.0) (/ (- 1.0 k) 2.0))) (* (pow (* n PI) (/ (/ (- 1.0 k) 2.0) 4)) (* (pow (* n PI) (/ (/ (- 1.0 k) 2.0) 4)) (pow (sqrt 2.0) (/ (- 1.0 k) 2.0)))) (* (pow (* n PI) (/ (/ (- 1.0 k) 2.0) 4)) (* (pow (* n PI) (/ (/ (- 1.0 k) 2.0) 4)) (pow (sqrt 2.0) (/ (- 1.0 k) 2.0)))) (* (sqrt (pow 2.0 (/ (- 1.0 k) 2.0))) (sqrt (pow (* n PI) (/ (- 1.0 k) 2.0)))) (* (sqrt (pow 2.0 (/ (- 1.0 k) 2.0))) (sqrt (pow (* n PI) (/ (- 1.0 k) 2.0)))) (* (* (sqrt (pow 2.0 (/ (- 1.0 k) 2.0))) (pow (* n PI) (/ (/ (- 1.0 k) 2.0) 4))) (pow (* n PI) (/ (/ (- 1.0 k) 2.0) 4))) (* (* (sqrt (pow 2.0 (/ (- 1.0 k) 2.0))) (pow (* n PI) (/ (/ (- 1.0 k) 2.0) 4))) (pow (* n PI) (/ (/ (- 1.0 k) 2.0) 4))) (* (pow 2.0 (/ (/ (- 1.0 k) 2) 2.0)) (sqrt (pow (* n PI) (/ (- 1.0 k) 2.0)))) (* (pow 2.0 (/ (/ (- 1.0 k) 2) 2.0)) (sqrt (pow (* n PI) (/ (- 1.0 k) 2.0)))) (* (pow (* n PI) (/ (/ (- 1.0 k) 2) 2.0)) (pow 2.0 (/ (/ (- 1.0 k) 2) 2.0))) (* (pow (* n PI) (/ (/ (- 1.0 k) 2) 2.0)) (pow 2.0 (/ (/ (- 1.0 k) 2) 2.0))) (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0))) (* (* (pow 2.0 (/ (- 1.0 k) 2.0)) (cbrt (pow (* n PI) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* n PI) (/ (- 1.0 k) 2.0)))) (* (sqrt (pow (* n PI) (/ (- 1.0 k) 2.0))) (pow 2.0 (/ (- 1.0 k) 2.0))) (pow 2.0 (/ (- 1.0 k) 2.0)) (* (pow (* n PI) (/ (/ (- 1.0 k) 2.0) 4)) (* (pow (* n PI) (/ (/ (- 1.0 k) 2.0) 4)) (pow 2.0 (/ (- 1.0 k) 2.0)))) (* (pow (cbrt 2.0) (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0))) (* (pow (sqrt 2.0) (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0))) (* (pow (* n PI) (/ (- 1.0 k) 2.0)) (pow 2.0 (/ (- 1.0 k) 2.0))) (* (cbrt (pow 2.0 (/ (- 1.0 k) 2.0))) (pow (* n PI) (/ (- 1.0 k) 2.0))) (* (sqrt (pow 2.0 (/ (- 1.0 k) 2.0))) (pow (* n PI) (/ (- 1.0 k) 2.0))) (* (pow (* n PI) (/ (- 1.0 k) 2.0)) (pow 2.0 (/ (- 1.0 k) 2.0))) (* (pow 2.0 (/ (/ (- 1.0 k) 2) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0))) (* (pow (* n PI) (/ 1.0 2.0)) (pow 2.0 (/ (- 1.0 k) 2.0))) (* (pow (* n PI) (/ (- 1.0 k) 2.0)) (pow 2.0 (/ 1.0 2.0))) (+ (+ (* (* 0.25 (exp (* 0.5 (log (* n PI))))) (* (* k k) (* (log PI) (log n)))) (* (* (exp (* 0.5 (log (* n PI)))) 0.125) (+ (* (* (* k k) (log PI)) (log PI)) (* (log n) (* (* k k) (log n)))))) (- (exp (* 0.5 (log (* n PI)))) (* (* 0.5 (exp (* 0.5 (log (* n PI))))) (+ (* k (log PI)) (* k (log n)))))) (exp (* (* 0.5 (log (* n PI))) (- 1.0 k))) (exp (* (- 1.0 k) (* 0.5 (- (log (- PI)) (log (/ -1 n)))))) (* n PI) (* n PI) (* n PI) (- (+ (- (* (* k k) +nan.0) +nan.0) (* +nan.0 k))) (+ (- (/ +nan.0 k) (/ +nan.0 (* k (* k k)))) (- (/ +nan.0 (* k k)))) (- (+ (- (/ +nan.0 (* k k)) (/ +nan.0 k)) +nan.0)) (- (+ (+ (* (* 0.125 (* (* (log n) k) (* (log n) k))) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5)) (* (* 0.25 (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5)) (* (* k k) (* (log PI) (log n))))) (- (+ (+ (* (* 0.25 (* (* (log 2.0) (log PI)) (* k k))) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5)) (* 0.125 (+ (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (* (* (log PI) k) (* (log PI) k))) (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (* (* k (log 2.0)) (* k (log 2.0))))))) (+ (pow (pow (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 1.0) 1.0) 1.0) 1.0) 1.0) 1.0) 0.5) (* (* 0.25 (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5)) (* (log 2.0) (* (* k k) (log n)))))) (* (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) 0.5) (* k (log 2.0))))) (* (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) 0.5) (+ (* k (log PI)) (* k (log n))))) (exp (* (* (- 1.0 k) 0.5) (+ (log 2.0) (log (* n PI))))) (exp (* 0.5 (+ (* (log 2.0) (- 1.0 k)) (* (- 1.0 k) (- (log (- PI)) (log (/ -1 n))))))) 15.973 * * * [progress]: adding candidates to table 16.787 * * [progress]: iteration 4 / 4 16.787 * * * [progress]: picking best candidate 16.855 * * * * [pick]: Picked # 16.855 * * * [progress]: localizing error 16.915 * * * [progress]: generating rewritten candidates 16.916 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 1 2 2) 16.917 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1 2 1 2) 16.919 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2) 17.020 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1 2) 17.042 * * * [progress]: generating series expansions 17.042 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 1 2 2) 17.042 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1 2 1 2) 17.042 * * * * [progress]: [ 3 / 4 ] generating series at (2 2) 17.043 * [backup-simplify]: Simplify (pow (* 2.0 (* (* n (sqrt PI)) (sqrt PI))) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 17.043 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 17.043 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 17.043 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 17.043 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 17.043 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 17.043 * [taylor]: Taking taylor expansion of 0.5 in k 17.043 * [backup-simplify]: Simplify 0.5 into 0.5 17.043 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 17.043 * [taylor]: Taking taylor expansion of 1.0 in k 17.043 * [backup-simplify]: Simplify 1.0 into 1.0 17.043 * [taylor]: Taking taylor expansion of k in k 17.043 * [backup-simplify]: Simplify 0 into 0 17.043 * [backup-simplify]: Simplify 1 into 1 17.043 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 17.043 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 17.043 * [taylor]: Taking taylor expansion of 2.0 in k 17.043 * [backup-simplify]: Simplify 2.0 into 2.0 17.043 * [taylor]: Taking taylor expansion of (* n PI) in k 17.043 * [taylor]: Taking taylor expansion of n in k 17.043 * [backup-simplify]: Simplify n into n 17.043 * [taylor]: Taking taylor expansion of PI in k 17.043 * [backup-simplify]: Simplify PI into PI 17.043 * [backup-simplify]: Simplify (* n PI) into (* n PI) 17.043 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 17.043 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 17.044 * [backup-simplify]: Simplify (- 0) into 0 17.046 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 17.047 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 17.047 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 17.047 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 17.047 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 17.047 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 17.047 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 17.047 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 17.047 * [taylor]: Taking taylor expansion of 0.5 in n 17.047 * [backup-simplify]: Simplify 0.5 into 0.5 17.047 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 17.047 * [taylor]: Taking taylor expansion of 1.0 in n 17.047 * [backup-simplify]: Simplify 1.0 into 1.0 17.047 * [taylor]: Taking taylor expansion of k in n 17.047 * [backup-simplify]: Simplify k into k 17.047 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 17.047 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 17.047 * [taylor]: Taking taylor expansion of 2.0 in n 17.047 * [backup-simplify]: Simplify 2.0 into 2.0 17.047 * [taylor]: Taking taylor expansion of (* n PI) in n 17.047 * [taylor]: Taking taylor expansion of n in n 17.047 * [backup-simplify]: Simplify 0 into 0 17.047 * [backup-simplify]: Simplify 1 into 1 17.047 * [taylor]: Taking taylor expansion of PI in n 17.047 * [backup-simplify]: Simplify PI into PI 17.048 * [backup-simplify]: Simplify (* 0 PI) into 0 17.048 * [backup-simplify]: Simplify (* 2.0 0) into 0 17.049 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 17.050 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 17.051 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 17.051 * [backup-simplify]: Simplify (- k) into (- k) 17.051 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 17.051 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 17.052 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 17.053 * [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)))) 17.053 * [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))))) 17.053 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 17.053 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 17.053 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 17.054 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 17.054 * [taylor]: Taking taylor expansion of 0.5 in n 17.054 * [backup-simplify]: Simplify 0.5 into 0.5 17.054 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 17.054 * [taylor]: Taking taylor expansion of 1.0 in n 17.054 * [backup-simplify]: Simplify 1.0 into 1.0 17.054 * [taylor]: Taking taylor expansion of k in n 17.054 * [backup-simplify]: Simplify k into k 17.054 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 17.054 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 17.054 * [taylor]: Taking taylor expansion of 2.0 in n 17.054 * [backup-simplify]: Simplify 2.0 into 2.0 17.054 * [taylor]: Taking taylor expansion of (* n PI) in n 17.054 * [taylor]: Taking taylor expansion of n in n 17.054 * [backup-simplify]: Simplify 0 into 0 17.054 * [backup-simplify]: Simplify 1 into 1 17.054 * [taylor]: Taking taylor expansion of PI in n 17.054 * [backup-simplify]: Simplify PI into PI 17.054 * [backup-simplify]: Simplify (* 0 PI) into 0 17.054 * [backup-simplify]: Simplify (* 2.0 0) into 0 17.055 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 17.056 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 17.057 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 17.057 * [backup-simplify]: Simplify (- k) into (- k) 17.057 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 17.057 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 17.058 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 17.059 * [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)))) 17.059 * [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))))) 17.060 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 17.060 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 17.060 * [taylor]: Taking taylor expansion of 0.5 in k 17.060 * [backup-simplify]: Simplify 0.5 into 0.5 17.060 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 17.060 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 17.060 * [taylor]: Taking taylor expansion of 1.0 in k 17.060 * [backup-simplify]: Simplify 1.0 into 1.0 17.060 * [taylor]: Taking taylor expansion of k in k 17.060 * [backup-simplify]: Simplify 0 into 0 17.060 * [backup-simplify]: Simplify 1 into 1 17.060 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 17.060 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 17.060 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 17.060 * [taylor]: Taking taylor expansion of 2.0 in k 17.060 * [backup-simplify]: Simplify 2.0 into 2.0 17.060 * [taylor]: Taking taylor expansion of PI in k 17.060 * [backup-simplify]: Simplify PI into PI 17.060 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 17.061 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 17.061 * [taylor]: Taking taylor expansion of (log n) in k 17.061 * [taylor]: Taking taylor expansion of n in k 17.061 * [backup-simplify]: Simplify n into n 17.061 * [backup-simplify]: Simplify (log n) into (log n) 17.062 * [backup-simplify]: Simplify (- 0) into 0 17.062 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 17.063 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 17.063 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 17.064 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 17.065 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 17.066 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 17.067 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 17.068 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 17.069 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 17.070 * [backup-simplify]: Simplify (- 0) into 0 17.070 * [backup-simplify]: Simplify (+ 0 0) into 0 17.071 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 17.072 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 17.073 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 17.075 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 17.075 * [taylor]: Taking taylor expansion of 0 in k 17.075 * [backup-simplify]: Simplify 0 into 0 17.075 * [backup-simplify]: Simplify 0 into 0 17.076 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 17.078 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 17.079 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 17.079 * [backup-simplify]: Simplify (+ 0 0) into 0 17.079 * [backup-simplify]: Simplify (- 1) into -1 17.080 * [backup-simplify]: Simplify (+ 0 -1) into -1 17.081 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 17.083 * [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)))) 17.087 * [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)))))) 17.090 * [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)))))) 17.091 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 17.092 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 17.096 * [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 17.096 * [backup-simplify]: Simplify (- 0) into 0 17.097 * [backup-simplify]: Simplify (+ 0 0) into 0 17.097 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 17.098 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 17.099 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 17.101 * [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 17.101 * [taylor]: Taking taylor expansion of 0 in k 17.101 * [backup-simplify]: Simplify 0 into 0 17.101 * [backup-simplify]: Simplify 0 into 0 17.101 * [backup-simplify]: Simplify 0 into 0 17.102 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 17.104 * [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 17.105 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 17.105 * [backup-simplify]: Simplify (+ 0 0) into 0 17.105 * [backup-simplify]: Simplify (- 0) into 0 17.106 * [backup-simplify]: Simplify (+ 0 0) into 0 17.107 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 17.109 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 17.111 * [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)))))) 17.114 * [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)))))) 17.121 * [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))))) 17.122 * [backup-simplify]: Simplify (pow (* 2.0 (* (* (/ 1 n) (sqrt PI)) (sqrt PI))) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) 17.122 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 17.122 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 17.122 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 17.122 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 17.122 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 17.122 * [taylor]: Taking taylor expansion of 0.5 in k 17.122 * [backup-simplify]: Simplify 0.5 into 0.5 17.122 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 17.122 * [taylor]: Taking taylor expansion of 1.0 in k 17.122 * [backup-simplify]: Simplify 1.0 into 1.0 17.122 * [taylor]: Taking taylor expansion of (/ 1 k) in k 17.122 * [taylor]: Taking taylor expansion of k in k 17.122 * [backup-simplify]: Simplify 0 into 0 17.122 * [backup-simplify]: Simplify 1 into 1 17.122 * [backup-simplify]: Simplify (/ 1 1) into 1 17.122 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 17.122 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 17.122 * [taylor]: Taking taylor expansion of 2.0 in k 17.122 * [backup-simplify]: Simplify 2.0 into 2.0 17.122 * [taylor]: Taking taylor expansion of (/ PI n) in k 17.122 * [taylor]: Taking taylor expansion of PI in k 17.122 * [backup-simplify]: Simplify PI into PI 17.122 * [taylor]: Taking taylor expansion of n in k 17.122 * [backup-simplify]: Simplify n into n 17.122 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 17.122 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 17.123 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 17.123 * [backup-simplify]: Simplify (- 1) into -1 17.123 * [backup-simplify]: Simplify (+ 0 -1) into -1 17.123 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 17.123 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 17.124 * [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)))))) 17.124 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 17.124 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 17.124 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 17.124 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 17.124 * [taylor]: Taking taylor expansion of 0.5 in n 17.124 * [backup-simplify]: Simplify 0.5 into 0.5 17.124 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 17.124 * [taylor]: Taking taylor expansion of 1.0 in n 17.124 * [backup-simplify]: Simplify 1.0 into 1.0 17.124 * [taylor]: Taking taylor expansion of (/ 1 k) in n 17.124 * [taylor]: Taking taylor expansion of k in n 17.124 * [backup-simplify]: Simplify k into k 17.124 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 17.124 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 17.124 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 17.124 * [taylor]: Taking taylor expansion of 2.0 in n 17.124 * [backup-simplify]: Simplify 2.0 into 2.0 17.124 * [taylor]: Taking taylor expansion of (/ PI n) in n 17.124 * [taylor]: Taking taylor expansion of PI in n 17.124 * [backup-simplify]: Simplify PI into PI 17.124 * [taylor]: Taking taylor expansion of n in n 17.124 * [backup-simplify]: Simplify 0 into 0 17.124 * [backup-simplify]: Simplify 1 into 1 17.124 * [backup-simplify]: Simplify (/ PI 1) into PI 17.125 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 17.125 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 17.125 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 17.125 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 17.125 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 17.126 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 17.127 * [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)))) 17.128 * [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))))) 17.128 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 17.128 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 17.128 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 17.128 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 17.128 * [taylor]: Taking taylor expansion of 0.5 in n 17.128 * [backup-simplify]: Simplify 0.5 into 0.5 17.128 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 17.128 * [taylor]: Taking taylor expansion of 1.0 in n 17.128 * [backup-simplify]: Simplify 1.0 into 1.0 17.128 * [taylor]: Taking taylor expansion of (/ 1 k) in n 17.128 * [taylor]: Taking taylor expansion of k in n 17.128 * [backup-simplify]: Simplify k into k 17.128 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 17.128 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 17.128 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 17.128 * [taylor]: Taking taylor expansion of 2.0 in n 17.128 * [backup-simplify]: Simplify 2.0 into 2.0 17.128 * [taylor]: Taking taylor expansion of (/ PI n) in n 17.128 * [taylor]: Taking taylor expansion of PI in n 17.128 * [backup-simplify]: Simplify PI into PI 17.128 * [taylor]: Taking taylor expansion of n in n 17.128 * [backup-simplify]: Simplify 0 into 0 17.128 * [backup-simplify]: Simplify 1 into 1 17.129 * [backup-simplify]: Simplify (/ PI 1) into PI 17.129 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 17.130 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 17.130 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 17.130 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 17.130 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 17.131 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 17.132 * [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)))) 17.133 * [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))))) 17.133 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) in k 17.133 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) in k 17.133 * [taylor]: Taking taylor expansion of 0.5 in k 17.133 * [backup-simplify]: Simplify 0.5 into 0.5 17.133 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) in k 17.133 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 17.133 * [taylor]: Taking taylor expansion of 1.0 in k 17.133 * [backup-simplify]: Simplify 1.0 into 1.0 17.133 * [taylor]: Taking taylor expansion of (/ 1 k) in k 17.133 * [taylor]: Taking taylor expansion of k in k 17.133 * [backup-simplify]: Simplify 0 into 0 17.133 * [backup-simplify]: Simplify 1 into 1 17.133 * [backup-simplify]: Simplify (/ 1 1) into 1 17.133 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 17.133 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 17.133 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 17.133 * [taylor]: Taking taylor expansion of 2.0 in k 17.133 * [backup-simplify]: Simplify 2.0 into 2.0 17.133 * [taylor]: Taking taylor expansion of PI in k 17.133 * [backup-simplify]: Simplify PI into PI 17.134 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 17.134 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 17.134 * [taylor]: Taking taylor expansion of (log n) in k 17.134 * [taylor]: Taking taylor expansion of n in k 17.134 * [backup-simplify]: Simplify n into n 17.134 * [backup-simplify]: Simplify (log n) into (log n) 17.135 * [backup-simplify]: Simplify (- 1) into -1 17.135 * [backup-simplify]: Simplify (+ 0 -1) into -1 17.135 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 17.136 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 17.137 * [backup-simplify]: Simplify (* -1 (- (log (* 2.0 PI)) (log n))) into (* -1 (- (log (* 2.0 PI)) (log n))) 17.137 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 17.139 * [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))))) 17.140 * [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))))) 17.141 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 17.142 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 17.143 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 17.144 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 17.144 * [backup-simplify]: Simplify (- 0) into 0 17.145 * [backup-simplify]: Simplify (+ 0 0) into 0 17.145 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 17.147 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 17.149 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 17.151 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 17.151 * [taylor]: Taking taylor expansion of 0 in k 17.151 * [backup-simplify]: Simplify 0 into 0 17.151 * [backup-simplify]: Simplify 0 into 0 17.151 * [backup-simplify]: Simplify 0 into 0 17.153 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.154 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 17.165 * [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 17.166 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 17.166 * [backup-simplify]: Simplify (- 0) into 0 17.167 * [backup-simplify]: Simplify (+ 0 0) into 0 17.168 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 17.169 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 17.171 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 17.174 * [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 17.174 * [taylor]: Taking taylor expansion of 0 in k 17.174 * [backup-simplify]: Simplify 0 into 0 17.174 * [backup-simplify]: Simplify 0 into 0 17.174 * [backup-simplify]: Simplify 0 into 0 17.174 * [backup-simplify]: Simplify 0 into 0 17.175 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.176 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 17.181 * [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 17.182 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 17.182 * [backup-simplify]: Simplify (- 0) into 0 17.182 * [backup-simplify]: Simplify (+ 0 0) into 0 17.183 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 17.184 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 17.185 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 17.187 * [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 17.187 * [taylor]: Taking taylor expansion of 0 in k 17.187 * [backup-simplify]: Simplify 0 into 0 17.187 * [backup-simplify]: Simplify 0 into 0 17.188 * [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)))))) 17.189 * [backup-simplify]: Simplify (pow (* 2.0 (* (* (/ 1 (- n)) (sqrt PI)) (sqrt PI))) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) 17.189 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 17.189 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 17.189 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 17.189 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 17.189 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 17.189 * [taylor]: Taking taylor expansion of 0.5 in k 17.189 * [backup-simplify]: Simplify 0.5 into 0.5 17.189 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 17.189 * [taylor]: Taking taylor expansion of (/ 1 k) in k 17.189 * [taylor]: Taking taylor expansion of k in k 17.189 * [backup-simplify]: Simplify 0 into 0 17.189 * [backup-simplify]: Simplify 1 into 1 17.189 * [backup-simplify]: Simplify (/ 1 1) into 1 17.189 * [taylor]: Taking taylor expansion of 1.0 in k 17.189 * [backup-simplify]: Simplify 1.0 into 1.0 17.189 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 17.189 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 17.189 * [taylor]: Taking taylor expansion of -2.0 in k 17.189 * [backup-simplify]: Simplify -2.0 into -2.0 17.189 * [taylor]: Taking taylor expansion of (/ PI n) in k 17.189 * [taylor]: Taking taylor expansion of PI in k 17.189 * [backup-simplify]: Simplify PI into PI 17.189 * [taylor]: Taking taylor expansion of n in k 17.189 * [backup-simplify]: Simplify n into n 17.189 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 17.189 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 17.189 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 17.190 * [backup-simplify]: Simplify (+ 1 0) into 1 17.190 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 17.190 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 17.190 * [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)))) 17.190 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 17.190 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 17.190 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 17.190 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 17.190 * [taylor]: Taking taylor expansion of 0.5 in n 17.190 * [backup-simplify]: Simplify 0.5 into 0.5 17.190 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 17.190 * [taylor]: Taking taylor expansion of (/ 1 k) in n 17.190 * [taylor]: Taking taylor expansion of k in n 17.190 * [backup-simplify]: Simplify k into k 17.190 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 17.190 * [taylor]: Taking taylor expansion of 1.0 in n 17.190 * [backup-simplify]: Simplify 1.0 into 1.0 17.190 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 17.190 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 17.190 * [taylor]: Taking taylor expansion of -2.0 in n 17.191 * [backup-simplify]: Simplify -2.0 into -2.0 17.191 * [taylor]: Taking taylor expansion of (/ PI n) in n 17.191 * [taylor]: Taking taylor expansion of PI in n 17.191 * [backup-simplify]: Simplify PI into PI 17.191 * [taylor]: Taking taylor expansion of n in n 17.191 * [backup-simplify]: Simplify 0 into 0 17.191 * [backup-simplify]: Simplify 1 into 1 17.191 * [backup-simplify]: Simplify (/ PI 1) into PI 17.191 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 17.192 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 17.192 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 17.192 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 17.193 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 17.194 * [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))) 17.194 * [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)))) 17.194 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 17.194 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 17.195 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 17.195 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 17.195 * [taylor]: Taking taylor expansion of 0.5 in n 17.195 * [backup-simplify]: Simplify 0.5 into 0.5 17.195 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 17.195 * [taylor]: Taking taylor expansion of (/ 1 k) in n 17.195 * [taylor]: Taking taylor expansion of k in n 17.195 * [backup-simplify]: Simplify k into k 17.195 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 17.195 * [taylor]: Taking taylor expansion of 1.0 in n 17.195 * [backup-simplify]: Simplify 1.0 into 1.0 17.195 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 17.195 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 17.195 * [taylor]: Taking taylor expansion of -2.0 in n 17.195 * [backup-simplify]: Simplify -2.0 into -2.0 17.195 * [taylor]: Taking taylor expansion of (/ PI n) in n 17.195 * [taylor]: Taking taylor expansion of PI in n 17.195 * [backup-simplify]: Simplify PI into PI 17.195 * [taylor]: Taking taylor expansion of n in n 17.195 * [backup-simplify]: Simplify 0 into 0 17.195 * [backup-simplify]: Simplify 1 into 1 17.195 * [backup-simplify]: Simplify (/ PI 1) into PI 17.195 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 17.196 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 17.196 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 17.196 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 17.197 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 17.198 * [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))) 17.199 * [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)))) 17.199 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) in k 17.199 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) in k 17.199 * [taylor]: Taking taylor expansion of 0.5 in k 17.199 * [backup-simplify]: Simplify 0.5 into 0.5 17.199 * [taylor]: Taking taylor expansion of (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) in k 17.199 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 17.199 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 17.199 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 17.199 * [taylor]: Taking taylor expansion of -2.0 in k 17.199 * [backup-simplify]: Simplify -2.0 into -2.0 17.199 * [taylor]: Taking taylor expansion of PI in k 17.199 * [backup-simplify]: Simplify PI into PI 17.199 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 17.200 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 17.200 * [taylor]: Taking taylor expansion of (log n) in k 17.200 * [taylor]: Taking taylor expansion of n in k 17.200 * [backup-simplify]: Simplify n into n 17.200 * [backup-simplify]: Simplify (log n) into (log n) 17.200 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 17.200 * [taylor]: Taking taylor expansion of (/ 1 k) in k 17.200 * [taylor]: Taking taylor expansion of k in k 17.200 * [backup-simplify]: Simplify 0 into 0 17.200 * [backup-simplify]: Simplify 1 into 1 17.200 * [backup-simplify]: Simplify (/ 1 1) into 1 17.200 * [taylor]: Taking taylor expansion of 1.0 in k 17.200 * [backup-simplify]: Simplify 1.0 into 1.0 17.200 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 17.201 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 17.201 * [backup-simplify]: Simplify (+ 1 0) into 1 17.202 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) 1) into (- (log (* -2.0 PI)) (log n)) 17.203 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 17.204 * [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)))) 17.204 * [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)))) 17.205 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 17.205 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 17.206 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 17.207 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 17.207 * [backup-simplify]: Simplify (+ 0 0) into 0 17.207 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 17.208 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 17.209 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 17.210 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 17.210 * [taylor]: Taking taylor expansion of 0 in k 17.210 * [backup-simplify]: Simplify 0 into 0 17.210 * [backup-simplify]: Simplify 0 into 0 17.210 * [backup-simplify]: Simplify 0 into 0 17.211 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.211 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 17.213 * [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 17.213 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 17.214 * [backup-simplify]: Simplify (+ 0 0) into 0 17.214 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 17.215 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 17.216 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 17.218 * [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 17.218 * [taylor]: Taking taylor expansion of 0 in k 17.218 * [backup-simplify]: Simplify 0 into 0 17.218 * [backup-simplify]: Simplify 0 into 0 17.218 * [backup-simplify]: Simplify 0 into 0 17.218 * [backup-simplify]: Simplify 0 into 0 17.219 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.219 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 17.223 * [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 17.223 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 17.223 * [backup-simplify]: Simplify (+ 0 0) into 0 17.224 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 17.225 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 17.226 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 17.228 * [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 17.228 * [taylor]: Taking taylor expansion of 0 in k 17.228 * [backup-simplify]: Simplify 0 into 0 17.228 * [backup-simplify]: Simplify 0 into 0 17.228 * [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)))))) 17.229 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1 2) 17.229 * [backup-simplify]: Simplify (* (* n (sqrt PI)) (sqrt PI)) into (* n PI) 17.229 * [approximate]: Taking taylor expansion of (* n PI) in (n) around 0 17.229 * [taylor]: Taking taylor expansion of (* n PI) in n 17.229 * [taylor]: Taking taylor expansion of n in n 17.229 * [backup-simplify]: Simplify 0 into 0 17.229 * [backup-simplify]: Simplify 1 into 1 17.229 * [taylor]: Taking taylor expansion of PI in n 17.229 * [backup-simplify]: Simplify PI into PI 17.229 * [taylor]: Taking taylor expansion of (* n PI) in n 17.229 * [taylor]: Taking taylor expansion of n in n 17.229 * [backup-simplify]: Simplify 0 into 0 17.230 * [backup-simplify]: Simplify 1 into 1 17.230 * [taylor]: Taking taylor expansion of PI in n 17.230 * [backup-simplify]: Simplify PI into PI 17.230 * [backup-simplify]: Simplify (* 0 PI) into 0 17.230 * [backup-simplify]: Simplify 0 into 0 17.232 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 17.232 * [backup-simplify]: Simplify PI into PI 17.233 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 17.233 * [backup-simplify]: Simplify 0 into 0 17.234 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 17.234 * [backup-simplify]: Simplify 0 into 0 17.236 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 17.236 * [backup-simplify]: Simplify 0 into 0 17.238 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 17.238 * [backup-simplify]: Simplify 0 into 0 17.240 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 17.240 * [backup-simplify]: Simplify 0 into 0 17.242 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 17.242 * [backup-simplify]: Simplify 0 into 0 17.242 * [backup-simplify]: Simplify (* PI n) into (* n PI) 17.243 * [backup-simplify]: Simplify (* (* (/ 1 n) (sqrt PI)) (sqrt PI)) into (/ PI n) 17.243 * [approximate]: Taking taylor expansion of (/ PI n) in (n) around 0 17.243 * [taylor]: Taking taylor expansion of (/ PI n) in n 17.243 * [taylor]: Taking taylor expansion of PI in n 17.243 * [backup-simplify]: Simplify PI into PI 17.243 * [taylor]: Taking taylor expansion of n in n 17.243 * [backup-simplify]: Simplify 0 into 0 17.243 * [backup-simplify]: Simplify 1 into 1 17.244 * [backup-simplify]: Simplify (/ PI 1) into PI 17.244 * [taylor]: Taking taylor expansion of (/ PI n) in n 17.244 * [taylor]: Taking taylor expansion of PI in n 17.244 * [backup-simplify]: Simplify PI into PI 17.244 * [taylor]: Taking taylor expansion of n in n 17.244 * [backup-simplify]: Simplify 0 into 0 17.244 * [backup-simplify]: Simplify 1 into 1 17.244 * [backup-simplify]: Simplify (/ PI 1) into PI 17.244 * [backup-simplify]: Simplify PI into PI 17.245 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 17.245 * [backup-simplify]: Simplify 0 into 0 17.246 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.246 * [backup-simplify]: Simplify 0 into 0 17.247 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.247 * [backup-simplify]: Simplify 0 into 0 17.247 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.247 * [backup-simplify]: Simplify 0 into 0 17.248 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.248 * [backup-simplify]: Simplify 0 into 0 17.249 * [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 17.249 * [backup-simplify]: Simplify 0 into 0 17.249 * [backup-simplify]: Simplify (* PI (/ 1 (/ 1 n))) into (* n PI) 17.249 * [backup-simplify]: Simplify (* (* (/ 1 (- n)) (sqrt PI)) (sqrt PI)) into (* -1 (/ PI n)) 17.249 * [approximate]: Taking taylor expansion of (* -1 (/ PI n)) in (n) around 0 17.249 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n 17.249 * [taylor]: Taking taylor expansion of -1 in n 17.249 * [backup-simplify]: Simplify -1 into -1 17.249 * [taylor]: Taking taylor expansion of (/ PI n) in n 17.249 * [taylor]: Taking taylor expansion of PI in n 17.249 * [backup-simplify]: Simplify PI into PI 17.249 * [taylor]: Taking taylor expansion of n in n 17.250 * [backup-simplify]: Simplify 0 into 0 17.250 * [backup-simplify]: Simplify 1 into 1 17.250 * [backup-simplify]: Simplify (/ PI 1) into PI 17.250 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n 17.250 * [taylor]: Taking taylor expansion of -1 in n 17.250 * [backup-simplify]: Simplify -1 into -1 17.250 * [taylor]: Taking taylor expansion of (/ PI n) in n 17.250 * [taylor]: Taking taylor expansion of PI in n 17.250 * [backup-simplify]: Simplify PI into PI 17.250 * [taylor]: Taking taylor expansion of n in n 17.250 * [backup-simplify]: Simplify 0 into 0 17.250 * [backup-simplify]: Simplify 1 into 1 17.250 * [backup-simplify]: Simplify (/ PI 1) into PI 17.251 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI) 17.251 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI) 17.251 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 17.252 * [backup-simplify]: Simplify (+ (* -1 0) (* 0 PI)) into 0 17.252 * [backup-simplify]: Simplify 0 into 0 17.253 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.253 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 PI))) into 0 17.253 * [backup-simplify]: Simplify 0 into 0 17.254 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.255 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 17.255 * [backup-simplify]: Simplify 0 into 0 17.255 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.256 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 17.256 * [backup-simplify]: Simplify 0 into 0 17.257 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.258 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 17.258 * [backup-simplify]: Simplify 0 into 0 17.259 * [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 17.260 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 17.260 * [backup-simplify]: Simplify 0 into 0 17.260 * [backup-simplify]: Simplify (* (* -1 PI) (/ 1 (/ 1 (- n)))) into (* n PI) 17.260 * * * [progress]: simplifying candidates 17.262 * [simplify]: Simplifying: (log (sqrt PI)) (exp (sqrt PI)) (* (cbrt (sqrt PI)) (cbrt (sqrt PI))) (cbrt (sqrt PI)) (* (* (sqrt PI) (sqrt PI)) (sqrt PI)) (sqrt (* (cbrt PI) (cbrt PI))) (sqrt (cbrt PI)) (sqrt (sqrt PI)) (sqrt (sqrt PI)) (sqrt 1) (sqrt PI) (/ 1 2) (sqrt (sqrt PI)) (sqrt (sqrt PI)) (log (sqrt PI)) (exp (sqrt PI)) (* (cbrt (sqrt PI)) (cbrt (sqrt PI))) (cbrt (sqrt PI)) (* (* (sqrt PI) (sqrt PI)) (sqrt PI)) (sqrt (* (cbrt PI) (cbrt PI))) (sqrt (cbrt PI)) (sqrt (sqrt PI)) (sqrt (sqrt PI)) (sqrt 1) (sqrt PI) (/ 1 2) (sqrt (sqrt PI)) (sqrt (sqrt PI)) (* (+ (log 2.0) (+ (+ (log n) (log (sqrt PI))) (log (sqrt PI)))) (/ (- 1.0 k) 2.0)) (* (+ (log 2.0) (+ (log (* n (sqrt PI))) (log (sqrt PI)))) (/ (- 1.0 k) 2.0)) (* (+ (log 2.0) (log (* (* n (sqrt PI)) (sqrt PI)))) (/ (- 1.0 k) 2.0)) (* (log (* 2.0 (* (* n (sqrt PI)) (sqrt PI)))) (/ (- 1.0 k) 2.0)) (* (log (* 2.0 (* (* n (sqrt PI)) (sqrt PI)))) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 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 (* (* n (sqrt PI)) (sqrt PI))) (/ 1.0 2.0)) (pow (* 2.0 (* (* n (sqrt PI)) (sqrt PI))) (/ k 2.0)) (pow (* 2.0 (* (* n (sqrt PI)) (sqrt PI))) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* 2.0 (* (* n (sqrt PI)) (sqrt PI))) (sqrt (/ (- 1.0 k) 2.0))) (pow (* 2.0 (* (* n (sqrt PI)) (sqrt PI))) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* (* n (sqrt PI)) (sqrt PI))) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* 2.0 (* (* n (sqrt PI)) (sqrt PI))) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* 2.0 (* (* n (sqrt PI)) (sqrt PI))) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* (* n (sqrt PI)) (sqrt PI))) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* 2.0 (* (* n (sqrt PI)) (sqrt PI))) (/ (sqrt (- 1.0 k)) 1)) (pow (* 2.0 (* (* n (sqrt PI)) (sqrt PI))) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* (* n (sqrt PI)) (sqrt PI))) (/ 1 (sqrt 2.0))) (pow (* 2.0 (* (* n (sqrt PI)) (sqrt PI))) (/ 1 1)) (pow (* 2.0 (* (* n (sqrt PI)) (sqrt PI))) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* (* n (sqrt PI)) (sqrt PI))) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* 2.0 (* (* n (sqrt PI)) (sqrt PI))) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* 2.0 (* (* n (sqrt PI)) (sqrt PI))) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* (* n (sqrt PI)) (sqrt PI))) (/ 1 (sqrt 2.0))) (pow (* 2.0 (* (* n (sqrt PI)) (sqrt PI))) (/ 1 1)) (pow (* 2.0 (* (* n (sqrt PI)) (sqrt PI))) 1) (pow (* 2.0 (* (* n (sqrt PI)) (sqrt PI))) (- 1.0 k)) (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* (* n (sqrt PI)) (sqrt PI)) (/ (- 1.0 k) 2.0)) (log (pow (* 2.0 (* (* n (sqrt PI)) (sqrt PI))) (/ (- 1.0 k) 2.0))) (exp (pow (* 2.0 (* (* n (sqrt PI)) (sqrt PI))) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* 2.0 (* (* n (sqrt PI)) (sqrt PI))) (/ (- 1.0 k) 2.0))) (cbrt (pow (* 2.0 (* (* n (sqrt PI)) (sqrt PI))) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* 2.0 (* (* n (sqrt PI)) (sqrt PI))) (/ (- 1.0 k) 2.0))) (* (* (pow (* 2.0 (* (* n (sqrt PI)) (sqrt PI))) (/ (- 1.0 k) 2.0)) (pow (* 2.0 (* (* n (sqrt PI)) (sqrt PI))) (/ (- 1.0 k) 2.0))) (pow (* 2.0 (* (* n (sqrt PI)) (sqrt PI))) (/ (- 1.0 k) 2.0))) (sqrt (pow (* 2.0 (* (* n (sqrt PI)) (sqrt PI))) (/ (- 1.0 k) 2.0))) (sqrt (pow (* 2.0 (* (* n (sqrt PI)) (sqrt PI))) (/ (- 1.0 k) 2.0))) (pow (* 2.0 (* (* n (sqrt PI)) (sqrt PI))) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* 2.0 (* (* n (sqrt PI)) (sqrt PI))) (/ (/ (- 1.0 k) 2.0) 2)) (* (* n (sqrt PI)) (sqrt PI)) (* (* n (sqrt PI)) (sqrt PI)) (+ (+ (log n) (log (sqrt PI))) (log (sqrt PI))) (+ (log (* n (sqrt PI))) (log (sqrt PI))) (log (* (* n (sqrt PI)) (sqrt PI))) (exp (* (* n (sqrt PI)) (sqrt PI))) (* (* (* (* n n) n) (* (* (sqrt PI) (sqrt PI)) (sqrt PI))) (* (* (sqrt PI) (sqrt PI)) (sqrt PI))) (* (* (* (* n (sqrt PI)) (* n (sqrt PI))) (* n (sqrt PI))) (* (* (sqrt PI) (sqrt PI)) (sqrt PI))) (* (cbrt (* (* n (sqrt PI)) (sqrt PI))) (cbrt (* (* n (sqrt PI)) (sqrt PI)))) (cbrt (* (* n (sqrt PI)) (sqrt PI))) (* (* (* (* n (sqrt PI)) (sqrt PI)) (* (* n (sqrt PI)) (sqrt PI))) (* (* n (sqrt PI)) (sqrt PI))) (sqrt (* (* n (sqrt PI)) (sqrt PI))) (sqrt (* (* n (sqrt PI)) (sqrt PI))) (* (* n (sqrt PI)) (* (cbrt (sqrt PI)) (cbrt (sqrt PI)))) (* (* n (sqrt PI)) (sqrt (* (cbrt PI) (cbrt PI)))) (* (* n (sqrt PI)) (sqrt (sqrt PI))) (* (* n (sqrt PI)) (sqrt 1)) (* (* n (sqrt PI)) (sqrt (sqrt PI))) (* (* n (sqrt PI)) 1) (* (sqrt PI) (sqrt PI)) (* n (sqrt PI)) (* n (sqrt PI)) (- (+ (* 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)))))) (* n PI) (* n PI) (* n PI) 17.263 * * [simplify]: iteration 0: 165 enodes 17.333 * * [simplify]: iteration 1: 454 enodes 17.537 * * [simplify]: iteration 2: 1473 enodes 18.509 * * [simplify]: iteration complete: 5000 enodes 18.509 * * [simplify]: Extracting #0: cost 53 inf + 0 18.510 * * [simplify]: Extracting #1: cost 533 inf + 3 18.524 * * [simplify]: Extracting #2: cost 1339 inf + 7048 18.549 * * [simplify]: Extracting #3: cost 1657 inf + 51479 18.603 * * [simplify]: Extracting #4: cost 1133 inf + 188573 18.671 * * [simplify]: Extracting #5: cost 461 inf + 419166 18.807 * * [simplify]: Extracting #6: cost 181 inf + 566035 18.939 * * [simplify]: Extracting #7: cost 29 inf + 624588 19.111 * * [simplify]: Extracting #8: cost 0 inf + 635438 19.264 * [simplify]: Simplified to: (log (sqrt PI)) (exp (sqrt PI)) (* (cbrt (sqrt PI)) (cbrt (sqrt PI))) (cbrt (sqrt PI)) (* PI (sqrt PI)) (fabs (cbrt PI)) (sqrt (cbrt PI)) (sqrt (sqrt PI)) (sqrt (sqrt PI)) 1 (sqrt PI) 1/2 (sqrt (sqrt PI)) (sqrt (sqrt PI)) (log (sqrt PI)) (exp (sqrt PI)) (* (cbrt (sqrt PI)) (cbrt (sqrt PI))) (cbrt (sqrt PI)) (* PI (sqrt PI)) (fabs (cbrt PI)) (sqrt (cbrt PI)) (sqrt (sqrt PI)) (sqrt (sqrt PI)) 1 (sqrt PI) 1/2 (sqrt (sqrt PI)) (sqrt (sqrt PI)) (* (/ (- 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) (log (* 2.0 (* PI n)))) (/ (- 1.0 k) 2.0) (/ (- 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 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))) (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 (/ (- 1.0 k) 2.0)) (pow (* PI 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) 2.0) 2)) (pow (* 2.0 (* PI n)) (/ (/ (- 1.0 k) 2.0) 2)) (* PI n) (* PI n) (log (* PI n)) (log (* PI n)) (log (* PI n)) (exp (* PI n)) (* (* (* PI n) (* PI n)) (* PI n)) (* (* (* PI n) (* PI n)) (* PI n)) (* (cbrt (* PI n)) (cbrt (* PI n))) (cbrt (* PI n)) (* (* (* PI n) (* PI n)) (* PI n)) (sqrt (* PI n)) (sqrt (* PI n)) (* n (* (* (sqrt PI) (cbrt (sqrt PI))) (cbrt (sqrt PI)))) (* (* (sqrt PI) n) (fabs (cbrt PI))) (* (sqrt (sqrt PI)) (* (sqrt PI) n)) (* (sqrt PI) n) (* (sqrt (sqrt PI)) (* (sqrt PI) n)) (* (sqrt PI) n) PI (* (sqrt PI) n) (* (sqrt PI) n) (+ (+ (* (exp (* (log (* 2.0 (* PI n))) 0.5)) (+ (* 0.125 (* (* k (log n)) (* k (log n)))) (* (* (log (* 2.0 PI)) 0.25) (* (* (log n) k) k)))) (* 0.125 (* (exp (* (log (* 2.0 (* PI n))) 0.5)) (* (* k (log (* 2.0 PI))) (* k (log (* 2.0 PI))))))) (- (exp (* (log (* 2.0 (* PI n))) 0.5)) (* (* (* k (exp (* (log (* 2.0 (* PI n))) 0.5))) (log (* 2.0 (* PI n)))) 0.5))) (exp (* (* (- 1.0 k) 0.5) (log (* 2.0 (* PI n))))) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ -1 n))) (- 1.0 k)))) (* PI n) (* PI n) (* PI n) 19.276 * * * [progress]: adding candidates to table 19.767 * [progress]: [Phase 3 of 3] Extracting. 19.767 * * [regime]: Finding splitpoints for: (# # # # # # # #) 19.770 * * * [regime-changes]: Trying 3 branch expressions: ((* (* 2.0 PI) n) n k) 19.770 * * * * [regimes]: Trying to branch on (* (* 2.0 PI) n) from (# # # # # # # #) 19.854 * * * * [regimes]: Trying to branch on (* (* 2.0 PI) n) from (# # #) 19.926 * * * * [regimes]: Trying to branch on n from (# # # # # # # #) 20.025 * * * * [regimes]: Trying to branch on k from (# # # # # # # #) 20.119 * * * [regime]: Found split indices: #