1545390542.179 * [misc]progress: [Phase 1 of 3] Setting up. 1545390542.179 * * * [misc]progress: [1/2] Preparing points 1545390542.179 * * * * [misc]points: Sampling 256 additional inputs, on iter 0 have 0 / 256 1545390542.253 * * * * [misc]points: Filtering points with unrepresentable outputs 1545390542.253 * * * * [misc]points: Sampling 189 additional inputs, on iter 1 have 67 / 256 1545390542.321 * * * * [misc]points: Filtering points with unrepresentable outputs 1545390542.321 * * * * [misc]points: Sampling 139 additional inputs, on iter 2 have 117 / 256 1545390542.358 * * * * [misc]points: Filtering points with unrepresentable outputs 1545390542.358 * * * * [misc]points: Sampling 105 additional inputs, on iter 3 have 151 / 256 1545390542.432 * * * * [misc]points: Filtering points with unrepresentable outputs 1545390542.432 * * * * [misc]points: Sampling 83 additional inputs, on iter 4 have 173 / 256 1545390542.471 * * * * [misc]points: Filtering points with unrepresentable outputs 1545390542.472 * * * * [misc]points: Sampling 55 additional inputs, on iter 5 have 201 / 256 1545390542.497 * * * * [misc]points: Filtering points with unrepresentable outputs 1545390542.497 * * * * [misc]points: Sampling 38 additional inputs, on iter 6 have 218 / 256 1545390542.509 * * * * [misc]points: Filtering points with unrepresentable outputs 1545390542.509 * * * * [misc]points: Sampling 28 additional inputs, on iter 7 have 228 / 256 1545390542.517 * * * * [misc]points: Filtering points with unrepresentable outputs 1545390542.517 * * * * [misc]points: Sampling 18 additional inputs, on iter 8 have 238 / 256 1545390542.523 * * * * [misc]points: Filtering points with unrepresentable outputs 1545390542.523 * * * * [misc]points: Sampling 16 additional inputs, on iter 9 have 240 / 256 1545390542.528 * * * * [misc]points: Filtering points with unrepresentable outputs 1545390542.528 * * * * [misc]points: Sampling 12 additional inputs, on iter 10 have 244 / 256 1545390542.533 * * * * [misc]points: Filtering points with unrepresentable outputs 1545390542.533 * * * * [misc]points: Sampling 9 additional inputs, on iter 11 have 247 / 256 1545390542.537 * * * * [misc]points: Filtering points with unrepresentable outputs 1545390542.537 * * * * [misc]points: Sampling 6 additional inputs, on iter 12 have 250 / 256 1545390542.542 * * * * [misc]points: Filtering points with unrepresentable outputs 1545390542.542 * * * * [misc]points: Sampling 5 additional inputs, on iter 13 have 251 / 256 1545390542.583 * * * * [misc]points: Filtering points with unrepresentable outputs 1545390542.583 * * * * [misc]points: Sampling 4 additional inputs, on iter 14 have 253 / 256 1545390542.586 * * * * [misc]points: Filtering points with unrepresentable outputs 1545390542.586 * * * * [misc]points: Sampling 4 additional inputs, on iter 15 have 254 / 256 1545390542.589 * * * * [misc]points: Filtering points with unrepresentable outputs 1545390542.589 * * * * [exit]points: Sampled 256 points with exact outputs 1545390542.589 * * * [misc]progress: [2/2] Setting up program. 1545390542.595 * [misc]progress: [Phase 2 of 3] Improving. 1545390542.595 * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) 1545390542.595 * * [misc]simplify: iters left: 6 (13 enodes) 1545390542.598 * * [misc]simplify: iters left: 5 (28 enodes) 1545390542.605 * * [misc]simplify: iters left: 4 (44 enodes) 1545390542.618 * * [misc]simplify: iters left: 3 (54 enodes) 1545390542.629 * * [misc]simplify: iters left: 2 (57 enodes) 1545390542.635 * * [misc]simplify: iters left: 1 (65 enodes) 1545390542.643 * [exit]simplify: Simplified to (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)) 1545390542.650 * * [misc]progress: iteration 1 / 4 1545390542.650 * * * [misc]progress: picking best candidate 1545390542.657 * * * * [misc]pick: Picked # 1545390542.657 * * * [misc]progress: localizing error 1545390543.086 * * * [misc]progress: generating rewritten candidates 1545390543.086 * * * * [misc]progress: [ 1 / 3 ] rewriting at (2 1) 1545390543.093 * * * * [misc]progress: [ 2 / 3 ] rewriting at (2 1 1) 1545390543.098 * * * * [misc]progress: [ 3 / 3 ] rewriting at (2) 1545390543.114 * * * [misc]progress: generating series expansions 1545390543.114 * * * * [misc]progress: [ 1 / 3 ] generating series at (2 1) 1545390543.114 * [misc]backup-simplify: Simplify (pow (* PI (* n 2)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 1545390543.114 * [misc]approximate: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 1545390543.114 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1545390543.114 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1545390543.114 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1545390543.114 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1545390543.114 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390543.114 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390543.114 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1545390543.114 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390543.115 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390543.115 * [misc]taylor: Taking taylor expansion of k in k 1545390543.115 * [misc]backup-simplify: Simplify 0 into 0 1545390543.115 * [misc]backup-simplify: Simplify 1 into 1 1545390543.115 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1545390543.115 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1545390543.115 * [misc]taylor: Taking taylor expansion of 2 in k 1545390543.115 * [misc]backup-simplify: Simplify 2 into 2 1545390543.115 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1545390543.115 * [misc]taylor: Taking taylor expansion of n in k 1545390543.115 * [misc]backup-simplify: Simplify n into n 1545390543.115 * [misc]taylor: Taking taylor expansion of PI in k 1545390543.115 * [misc]backup-simplify: Simplify PI into PI 1545390543.115 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1545390543.115 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1545390543.115 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1545390543.116 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1545390543.117 * [misc]backup-simplify: Simplify (- 0) into 0 1545390543.117 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545390543.117 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1545390543.117 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1545390543.117 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1545390543.117 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1545390543.117 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1545390543.117 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1545390543.117 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390543.117 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390543.117 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1545390543.117 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390543.117 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390543.117 * [misc]taylor: Taking taylor expansion of k in n 1545390543.117 * [misc]backup-simplify: Simplify k into k 1545390543.117 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1545390543.117 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1545390543.117 * [misc]taylor: Taking taylor expansion of 2 in n 1545390543.117 * [misc]backup-simplify: Simplify 2 into 2 1545390543.117 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545390543.117 * [misc]taylor: Taking taylor expansion of n in n 1545390543.117 * [misc]backup-simplify: Simplify 0 into 0 1545390543.117 * [misc]backup-simplify: Simplify 1 into 1 1545390543.117 * [misc]taylor: Taking taylor expansion of PI in n 1545390543.117 * [misc]backup-simplify: Simplify PI into PI 1545390543.118 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1545390543.118 * [misc]backup-simplify: Simplify (* 2 0) into 0 1545390543.119 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1545390543.119 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1545390543.120 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545390543.120 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1545390543.120 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1545390543.120 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1545390543.121 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545390543.121 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 1545390543.122 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 1545390543.122 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1545390543.122 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1545390543.122 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1545390543.122 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1545390543.122 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390543.122 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390543.122 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1545390543.122 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390543.122 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390543.122 * [misc]taylor: Taking taylor expansion of k in n 1545390543.122 * [misc]backup-simplify: Simplify k into k 1545390543.122 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1545390543.122 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1545390543.122 * [misc]taylor: Taking taylor expansion of 2 in n 1545390543.122 * [misc]backup-simplify: Simplify 2 into 2 1545390543.122 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545390543.122 * [misc]taylor: Taking taylor expansion of n in n 1545390543.122 * [misc]backup-simplify: Simplify 0 into 0 1545390543.122 * [misc]backup-simplify: Simplify 1 into 1 1545390543.122 * [misc]taylor: Taking taylor expansion of PI in n 1545390543.122 * [misc]backup-simplify: Simplify PI into PI 1545390543.122 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1545390543.123 * [misc]backup-simplify: Simplify (* 2 0) into 0 1545390543.123 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1545390543.124 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1545390543.124 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545390543.124 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1545390543.124 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1545390543.125 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1545390543.125 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545390543.126 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 1545390543.126 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 1545390543.126 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1545390543.127 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1545390543.127 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1545390543.127 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390543.127 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390543.127 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1545390543.127 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390543.127 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390543.127 * [misc]taylor: Taking taylor expansion of k in k 1545390543.127 * [misc]backup-simplify: Simplify 0 into 0 1545390543.127 * [misc]backup-simplify: Simplify 1 into 1 1545390543.127 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1545390543.127 * [misc]taylor: Taking taylor expansion of (log n) in k 1545390543.127 * [misc]taylor: Taking taylor expansion of n in k 1545390543.127 * [misc]backup-simplify: Simplify n into n 1545390543.127 * [misc]backup-simplify: Simplify (log n) into (log n) 1545390543.127 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1545390543.127 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1545390543.127 * [misc]taylor: Taking taylor expansion of 2 in k 1545390543.127 * [misc]backup-simplify: Simplify 2 into 2 1545390543.127 * [misc]taylor: Taking taylor expansion of PI in k 1545390543.127 * [misc]backup-simplify: Simplify PI into PI 1545390543.127 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545390543.128 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545390543.128 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1545390543.128 * [misc]backup-simplify: Simplify (- 0) into 0 1545390543.128 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545390543.129 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545390543.129 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1545390543.130 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1545390543.130 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1545390543.131 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1545390543.132 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1545390543.135 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1545390543.135 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1545390543.135 * [misc]backup-simplify: Simplify (- 0) into 0 1545390543.136 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390543.136 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545390543.137 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1545390543.138 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1545390543.138 * [misc]taylor: Taking taylor expansion of 0 in k 1545390543.138 * [misc]backup-simplify: Simplify 0 into 0 1545390543.138 * [misc]backup-simplify: Simplify 0 into 0 1545390543.139 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1545390543.140 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1545390543.142 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1545390543.143 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390543.143 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1545390543.143 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1545390543.143 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1545390543.144 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1545390543.146 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 1545390543.147 * [misc]backup-simplify: Simplify (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 1545390543.149 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1545390543.150 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1545390543.155 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1545390543.156 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1545390543.156 * [misc]backup-simplify: Simplify (- 0) into 0 1545390543.156 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390543.157 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545390543.157 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1545390543.160 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1545390543.160 * [misc]taylor: Taking taylor expansion of 0 in k 1545390543.160 * [misc]backup-simplify: Simplify 0 into 0 1545390543.160 * [misc]backup-simplify: Simplify 0 into 0 1545390543.160 * [misc]backup-simplify: Simplify 0 into 0 1545390543.161 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1545390543.163 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1545390543.168 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1545390543.169 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390543.169 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1545390543.169 * [misc]backup-simplify: Simplify (- 0) into 0 1545390543.169 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390543.170 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1545390543.172 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 1545390543.174 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 1545390543.177 * [misc]backup-simplify: Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) 1545390543.177 * [misc]backup-simplify: Simplify (pow (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 1545390543.177 * [misc]approximate: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 1545390543.177 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1545390543.177 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1545390543.177 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1545390543.177 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1545390543.177 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390543.177 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390543.177 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545390543.177 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390543.177 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390543.177 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545390543.177 * [misc]taylor: Taking taylor expansion of k in k 1545390543.177 * [misc]backup-simplify: Simplify 0 into 0 1545390543.177 * [misc]backup-simplify: Simplify 1 into 1 1545390543.178 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545390543.178 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1545390543.178 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1545390543.178 * [misc]taylor: Taking taylor expansion of 2 in k 1545390543.178 * [misc]backup-simplify: Simplify 2 into 2 1545390543.178 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1545390543.178 * [misc]taylor: Taking taylor expansion of PI in k 1545390543.178 * [misc]backup-simplify: Simplify PI into PI 1545390543.178 * [misc]taylor: Taking taylor expansion of n in k 1545390543.178 * [misc]backup-simplify: Simplify n into n 1545390543.178 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1545390543.178 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1545390543.178 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1545390543.178 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545390543.178 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1545390543.178 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1545390543.178 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1545390543.178 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 1545390543.178 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1545390543.178 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1545390543.178 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1545390543.178 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1545390543.178 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390543.178 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390543.178 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545390543.178 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390543.178 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390543.178 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545390543.179 * [misc]taylor: Taking taylor expansion of k in n 1545390543.179 * [misc]backup-simplify: Simplify k into k 1545390543.179 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545390543.179 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1545390543.179 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1545390543.179 * [misc]taylor: Taking taylor expansion of 2 in n 1545390543.179 * [misc]backup-simplify: Simplify 2 into 2 1545390543.179 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390543.179 * [misc]taylor: Taking taylor expansion of PI in n 1545390543.179 * [misc]backup-simplify: Simplify PI into PI 1545390543.179 * [misc]taylor: Taking taylor expansion of n in n 1545390543.179 * [misc]backup-simplify: Simplify 0 into 0 1545390543.179 * [misc]backup-simplify: Simplify 1 into 1 1545390543.179 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390543.179 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545390543.180 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545390543.180 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545390543.180 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1545390543.180 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1545390543.180 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545390543.181 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 1545390543.181 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 1545390543.181 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1545390543.181 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1545390543.181 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1545390543.181 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1545390543.181 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390543.181 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390543.181 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545390543.181 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390543.181 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390543.181 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545390543.181 * [misc]taylor: Taking taylor expansion of k in n 1545390543.181 * [misc]backup-simplify: Simplify k into k 1545390543.181 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545390543.181 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1545390543.181 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1545390543.181 * [misc]taylor: Taking taylor expansion of 2 in n 1545390543.181 * [misc]backup-simplify: Simplify 2 into 2 1545390543.181 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390543.181 * [misc]taylor: Taking taylor expansion of PI in n 1545390543.181 * [misc]backup-simplify: Simplify PI into PI 1545390543.181 * [misc]taylor: Taking taylor expansion of n in n 1545390543.181 * [misc]backup-simplify: Simplify 0 into 0 1545390543.181 * [misc]backup-simplify: Simplify 1 into 1 1545390543.182 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390543.182 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545390543.182 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545390543.182 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545390543.182 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1545390543.182 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1545390543.183 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545390543.183 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 1545390543.183 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 1545390543.183 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1545390543.183 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1545390543.183 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1545390543.183 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390543.183 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390543.184 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545390543.184 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390543.184 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390543.184 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545390543.184 * [misc]taylor: Taking taylor expansion of k in k 1545390543.184 * [misc]backup-simplify: Simplify 0 into 0 1545390543.184 * [misc]backup-simplify: Simplify 1 into 1 1545390543.184 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545390543.184 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1545390543.184 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1545390543.184 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1545390543.184 * [misc]taylor: Taking taylor expansion of 2 in k 1545390543.184 * [misc]backup-simplify: Simplify 2 into 2 1545390543.184 * [misc]taylor: Taking taylor expansion of PI in k 1545390543.184 * [misc]backup-simplify: Simplify PI into PI 1545390543.184 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545390543.184 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545390543.184 * [misc]taylor: Taking taylor expansion of (log n) in k 1545390543.184 * [misc]taylor: Taking taylor expansion of n in k 1545390543.184 * [misc]backup-simplify: Simplify n into n 1545390543.184 * [misc]backup-simplify: Simplify (log n) into (log n) 1545390543.184 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545390543.185 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1545390543.185 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1545390543.185 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1545390543.185 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1545390543.185 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1545390543.186 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 1545390543.186 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 1545390543.187 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1545390543.187 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1545390543.189 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1545390543.189 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1545390543.189 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1545390543.189 * [misc]backup-simplify: Simplify (- 0) into 0 1545390543.189 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390543.190 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545390543.190 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1545390543.191 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1545390543.191 * [misc]taylor: Taking taylor expansion of 0 in k 1545390543.191 * [misc]backup-simplify: Simplify 0 into 0 1545390543.191 * [misc]backup-simplify: Simplify 0 into 0 1545390543.191 * [misc]backup-simplify: Simplify 0 into 0 1545390543.192 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390543.192 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1545390543.195 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1545390543.195 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545390543.196 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1545390543.196 * [misc]backup-simplify: Simplify (- 0) into 0 1545390543.196 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390543.196 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545390543.197 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1545390543.198 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1545390543.198 * [misc]taylor: Taking taylor expansion of 0 in k 1545390543.198 * [misc]backup-simplify: Simplify 0 into 0 1545390543.198 * [misc]backup-simplify: Simplify 0 into 0 1545390543.198 * [misc]backup-simplify: Simplify 0 into 0 1545390543.198 * [misc]backup-simplify: Simplify 0 into 0 1545390543.199 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390543.206 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1545390543.214 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 1545390543.214 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545390543.214 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1545390543.215 * [misc]backup-simplify: Simplify (- 0) into 0 1545390543.215 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390543.215 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545390543.216 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1545390543.220 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1545390543.220 * [misc]taylor: Taking taylor expansion of 0 in k 1545390543.220 * [misc]backup-simplify: Simplify 0 into 0 1545390543.220 * [misc]backup-simplify: Simplify 0 into 0 1545390543.221 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 1545390543.221 * [misc]backup-simplify: Simplify (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 1545390543.221 * [misc]approximate: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 1545390543.221 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1545390543.221 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1545390543.221 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1545390543.221 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1545390543.221 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545390543.221 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390543.221 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390543.221 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545390543.221 * [misc]taylor: Taking taylor expansion of k in k 1545390543.221 * [misc]backup-simplify: Simplify 0 into 0 1545390543.221 * [misc]backup-simplify: Simplify 1 into 1 1545390543.222 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545390543.222 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390543.222 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390543.222 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1545390543.222 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1545390543.222 * [misc]taylor: Taking taylor expansion of -2 in k 1545390543.222 * [misc]backup-simplify: Simplify -2 into -2 1545390543.222 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1545390543.222 * [misc]taylor: Taking taylor expansion of PI in k 1545390543.222 * [misc]backup-simplify: Simplify PI into PI 1545390543.222 * [misc]taylor: Taking taylor expansion of n in k 1545390543.222 * [misc]backup-simplify: Simplify n into n 1545390543.222 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1545390543.222 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1545390543.222 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1545390543.222 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545390543.222 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545390543.223 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1545390543.223 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) 1545390543.223 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1545390543.223 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1545390543.223 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1545390543.223 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1545390543.223 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545390543.223 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390543.223 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390543.223 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545390543.223 * [misc]taylor: Taking taylor expansion of k in n 1545390543.223 * [misc]backup-simplify: Simplify k into k 1545390543.223 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545390543.223 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390543.223 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390543.223 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1545390543.223 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1545390543.223 * [misc]taylor: Taking taylor expansion of -2 in n 1545390543.223 * [misc]backup-simplify: Simplify -2 into -2 1545390543.223 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390543.223 * [misc]taylor: Taking taylor expansion of PI in n 1545390543.223 * [misc]backup-simplify: Simplify PI into PI 1545390543.223 * [misc]taylor: Taking taylor expansion of n in n 1545390543.223 * [misc]backup-simplify: Simplify 0 into 0 1545390543.223 * [misc]backup-simplify: Simplify 1 into 1 1545390543.224 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390543.224 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1545390543.225 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1545390543.225 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545390543.225 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1545390543.225 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545390543.226 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1545390543.227 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 1545390543.227 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1545390543.227 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1545390543.227 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1545390543.227 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1545390543.227 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545390543.227 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390543.227 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390543.227 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545390543.227 * [misc]taylor: Taking taylor expansion of k in n 1545390543.227 * [misc]backup-simplify: Simplify k into k 1545390543.227 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545390543.227 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390543.227 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390543.227 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1545390543.227 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1545390543.227 * [misc]taylor: Taking taylor expansion of -2 in n 1545390543.227 * [misc]backup-simplify: Simplify -2 into -2 1545390543.227 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390543.227 * [misc]taylor: Taking taylor expansion of PI in n 1545390543.227 * [misc]backup-simplify: Simplify PI into PI 1545390543.227 * [misc]taylor: Taking taylor expansion of n in n 1545390543.227 * [misc]backup-simplify: Simplify 0 into 0 1545390543.227 * [misc]backup-simplify: Simplify 1 into 1 1545390543.228 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390543.228 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1545390543.228 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1545390543.228 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545390543.228 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1545390543.229 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545390543.229 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1545390543.229 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 1545390543.229 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1545390543.230 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1545390543.230 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1545390543.230 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545390543.230 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390543.230 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390543.230 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545390543.230 * [misc]taylor: Taking taylor expansion of k in k 1545390543.230 * [misc]backup-simplify: Simplify 0 into 0 1545390543.230 * [misc]backup-simplify: Simplify 1 into 1 1545390543.230 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545390543.230 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390543.230 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390543.230 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1545390543.230 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1545390543.230 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1545390543.230 * [misc]taylor: Taking taylor expansion of -2 in k 1545390543.230 * [misc]backup-simplify: Simplify -2 into -2 1545390543.230 * [misc]taylor: Taking taylor expansion of PI in k 1545390543.230 * [misc]backup-simplify: Simplify PI into PI 1545390543.230 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1545390543.230 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1545390543.230 * [misc]taylor: Taking taylor expansion of (log n) in k 1545390543.230 * [misc]taylor: Taking taylor expansion of n in k 1545390543.230 * [misc]backup-simplify: Simplify n into n 1545390543.230 * [misc]backup-simplify: Simplify (log n) into (log n) 1545390543.231 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545390543.231 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545390543.231 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1545390543.231 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1545390543.231 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1545390543.232 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 1545390543.232 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 1545390543.233 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1545390543.233 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1545390543.235 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1545390543.235 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1545390543.235 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1545390543.235 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390543.235 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545390543.236 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1545390543.237 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1545390543.237 * [misc]taylor: Taking taylor expansion of 0 in k 1545390543.237 * [misc]backup-simplify: Simplify 0 into 0 1545390543.237 * [misc]backup-simplify: Simplify 0 into 0 1545390543.237 * [misc]backup-simplify: Simplify 0 into 0 1545390543.238 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390543.238 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1545390543.241 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 1545390543.241 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545390543.241 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1545390543.242 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390543.242 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545390543.242 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1545390543.244 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1545390543.244 * [misc]taylor: Taking taylor expansion of 0 in k 1545390543.244 * [misc]backup-simplify: Simplify 0 into 0 1545390543.244 * [misc]backup-simplify: Simplify 0 into 0 1545390543.244 * [misc]backup-simplify: Simplify 0 into 0 1545390543.244 * [misc]backup-simplify: Simplify 0 into 0 1545390543.245 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390543.246 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1545390543.250 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0 1545390543.250 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545390543.251 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1545390543.251 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390543.251 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545390543.252 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 1545390543.254 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1545390543.254 * [misc]taylor: Taking taylor expansion of 0 in k 1545390543.254 * [misc]backup-simplify: Simplify 0 into 0 1545390543.254 * [misc]backup-simplify: Simplify 0 into 0 1545390543.254 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 1545390543.254 * * * * [misc]progress: [ 2 / 3 ] generating series at (2 1 1) 1545390543.254 * [misc]backup-simplify: Simplify (* PI (* n 2)) into (* 2 (* n PI)) 1545390543.254 * [misc]approximate: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1545390543.254 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1545390543.254 * [misc]taylor: Taking taylor expansion of 2 in n 1545390543.254 * [misc]backup-simplify: Simplify 2 into 2 1545390543.254 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545390543.254 * [misc]taylor: Taking taylor expansion of n in n 1545390543.254 * [misc]backup-simplify: Simplify 0 into 0 1545390543.254 * [misc]backup-simplify: Simplify 1 into 1 1545390543.255 * [misc]taylor: Taking taylor expansion of PI in n 1545390543.255 * [misc]backup-simplify: Simplify PI into PI 1545390543.255 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1545390543.255 * [misc]taylor: Taking taylor expansion of 2 in n 1545390543.255 * [misc]backup-simplify: Simplify 2 into 2 1545390543.255 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545390543.255 * [misc]taylor: Taking taylor expansion of n in n 1545390543.255 * [misc]backup-simplify: Simplify 0 into 0 1545390543.255 * [misc]backup-simplify: Simplify 1 into 1 1545390543.255 * [misc]taylor: Taking taylor expansion of PI in n 1545390543.255 * [misc]backup-simplify: Simplify PI into PI 1545390543.255 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1545390543.255 * [misc]backup-simplify: Simplify (* 2 0) into 0 1545390543.255 * [misc]backup-simplify: Simplify 0 into 0 1545390543.255 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1545390543.256 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1545390543.256 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545390543.257 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1545390543.257 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1545390543.257 * [misc]backup-simplify: Simplify 0 into 0 1545390543.258 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1545390543.259 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1545390543.259 * [misc]backup-simplify: Simplify 0 into 0 1545390543.260 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1545390543.261 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1545390543.261 * [misc]backup-simplify: Simplify 0 into 0 1545390543.263 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1545390543.264 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1545390543.264 * [misc]backup-simplify: Simplify 0 into 0 1545390543.266 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1545390543.268 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1545390543.268 * [misc]backup-simplify: Simplify 0 into 0 1545390543.270 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1545390543.273 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1545390543.273 * [misc]backup-simplify: Simplify 0 into 0 1545390543.273 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1545390543.273 * [misc]backup-simplify: Simplify (* PI (* (/ 1 n) 2)) into (* 2 (/ PI n)) 1545390543.273 * [misc]approximate: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1545390543.273 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1545390543.273 * [misc]taylor: Taking taylor expansion of 2 in n 1545390543.273 * [misc]backup-simplify: Simplify 2 into 2 1545390543.273 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390543.273 * [misc]taylor: Taking taylor expansion of PI in n 1545390543.273 * [misc]backup-simplify: Simplify PI into PI 1545390543.273 * [misc]taylor: Taking taylor expansion of n in n 1545390543.273 * [misc]backup-simplify: Simplify 0 into 0 1545390543.273 * [misc]backup-simplify: Simplify 1 into 1 1545390543.273 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390543.273 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1545390543.273 * [misc]taylor: Taking taylor expansion of 2 in n 1545390543.273 * [misc]backup-simplify: Simplify 2 into 2 1545390543.273 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390543.273 * [misc]taylor: Taking taylor expansion of PI in n 1545390543.273 * [misc]backup-simplify: Simplify PI into PI 1545390543.273 * [misc]taylor: Taking taylor expansion of n in n 1545390543.273 * [misc]backup-simplify: Simplify 0 into 0 1545390543.273 * [misc]backup-simplify: Simplify 1 into 1 1545390543.274 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390543.274 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545390543.274 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545390543.275 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1545390543.275 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1545390543.275 * [misc]backup-simplify: Simplify 0 into 0 1545390543.276 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390543.276 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1545390543.276 * [misc]backup-simplify: Simplify 0 into 0 1545390543.278 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390543.278 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1545390543.278 * [misc]backup-simplify: Simplify 0 into 0 1545390543.279 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390543.281 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1545390543.281 * [misc]backup-simplify: Simplify 0 into 0 1545390543.282 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390543.283 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1545390543.283 * [misc]backup-simplify: Simplify 0 into 0 1545390543.285 * [misc]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 1545390543.287 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1545390543.287 * [misc]backup-simplify: Simplify 0 into 0 1545390543.287 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 1545390543.287 * [misc]backup-simplify: Simplify (* PI (* (/ 1 (- n)) 2)) into (* -2 (/ PI n)) 1545390543.287 * [misc]approximate: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1545390543.287 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1545390543.287 * [misc]taylor: Taking taylor expansion of -2 in n 1545390543.287 * [misc]backup-simplify: Simplify -2 into -2 1545390543.287 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390543.287 * [misc]taylor: Taking taylor expansion of PI in n 1545390543.287 * [misc]backup-simplify: Simplify PI into PI 1545390543.287 * [misc]taylor: Taking taylor expansion of n in n 1545390543.287 * [misc]backup-simplify: Simplify 0 into 0 1545390543.287 * [misc]backup-simplify: Simplify 1 into 1 1545390543.287 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390543.287 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1545390543.287 * [misc]taylor: Taking taylor expansion of -2 in n 1545390543.287 * [misc]backup-simplify: Simplify -2 into -2 1545390543.287 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390543.287 * [misc]taylor: Taking taylor expansion of PI in n 1545390543.287 * [misc]backup-simplify: Simplify PI into PI 1545390543.287 * [misc]taylor: Taking taylor expansion of n in n 1545390543.287 * [misc]backup-simplify: Simplify 0 into 0 1545390543.287 * [misc]backup-simplify: Simplify 1 into 1 1545390543.288 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390543.288 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1545390543.288 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1545390543.289 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1545390543.289 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1545390543.289 * [misc]backup-simplify: Simplify 0 into 0 1545390543.290 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390543.290 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1545390543.290 * [misc]backup-simplify: Simplify 0 into 0 1545390543.291 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390543.292 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1545390543.292 * [misc]backup-simplify: Simplify 0 into 0 1545390543.293 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390543.294 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1545390543.295 * [misc]backup-simplify: Simplify 0 into 0 1545390543.296 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390543.297 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1545390543.297 * [misc]backup-simplify: Simplify 0 into 0 1545390543.299 * [misc]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 1545390543.301 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1545390543.301 * [misc]backup-simplify: Simplify 0 into 0 1545390543.301 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 1545390543.301 * * * * [misc]progress: [ 3 / 3 ] generating series at (2) 1545390543.302 * [misc]backup-simplify: Simplify (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)) into (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) 1545390543.302 * [misc]approximate: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (n k) around 0 1545390543.302 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 1545390543.302 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1545390543.302 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545390543.302 * [misc]taylor: Taking taylor expansion of k in k 1545390543.302 * [misc]backup-simplify: Simplify 0 into 0 1545390543.302 * [misc]backup-simplify: Simplify 1 into 1 1545390543.302 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545390543.302 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545390543.303 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1545390543.303 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1545390543.303 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1545390543.303 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1545390543.303 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1545390543.303 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390543.303 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390543.303 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1545390543.303 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390543.303 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390543.303 * [misc]taylor: Taking taylor expansion of k in k 1545390543.303 * [misc]backup-simplify: Simplify 0 into 0 1545390543.303 * [misc]backup-simplify: Simplify 1 into 1 1545390543.303 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1545390543.303 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1545390543.303 * [misc]taylor: Taking taylor expansion of 2 in k 1545390543.303 * [misc]backup-simplify: Simplify 2 into 2 1545390543.303 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1545390543.303 * [misc]taylor: Taking taylor expansion of n in k 1545390543.303 * [misc]backup-simplify: Simplify n into n 1545390543.303 * [misc]taylor: Taking taylor expansion of PI in k 1545390543.303 * [misc]backup-simplify: Simplify PI into PI 1545390543.303 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1545390543.303 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1545390543.304 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1545390543.304 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1545390543.304 * [misc]backup-simplify: Simplify (- 0) into 0 1545390543.304 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545390543.304 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1545390543.304 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1545390543.304 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 1545390543.304 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1545390543.304 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545390543.304 * [misc]taylor: Taking taylor expansion of k in n 1545390543.304 * [misc]backup-simplify: Simplify k into k 1545390543.304 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545390543.304 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1545390543.305 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1545390543.305 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1545390543.305 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1545390543.305 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1545390543.305 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1545390543.305 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1545390543.305 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390543.305 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390543.305 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1545390543.305 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390543.305 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390543.305 * [misc]taylor: Taking taylor expansion of k in n 1545390543.305 * [misc]backup-simplify: Simplify k into k 1545390543.305 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1545390543.305 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1545390543.305 * [misc]taylor: Taking taylor expansion of 2 in n 1545390543.305 * [misc]backup-simplify: Simplify 2 into 2 1545390543.305 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545390543.305 * [misc]taylor: Taking taylor expansion of n in n 1545390543.305 * [misc]backup-simplify: Simplify 0 into 0 1545390543.305 * [misc]backup-simplify: Simplify 1 into 1 1545390543.305 * [misc]taylor: Taking taylor expansion of PI in n 1545390543.305 * [misc]backup-simplify: Simplify PI into PI 1545390543.305 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1545390543.305 * [misc]backup-simplify: Simplify (* 2 0) into 0 1545390543.306 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1545390543.307 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1545390543.307 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545390543.307 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1545390543.307 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1545390543.307 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1545390543.309 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545390543.309 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 1545390543.310 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 1545390543.310 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 1545390543.310 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1545390543.310 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545390543.310 * [misc]taylor: Taking taylor expansion of k in n 1545390543.310 * [misc]backup-simplify: Simplify k into k 1545390543.310 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545390543.310 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1545390543.310 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1545390543.310 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1545390543.310 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1545390543.310 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1545390543.310 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1545390543.310 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1545390543.310 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390543.310 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390543.310 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1545390543.310 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390543.310 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390543.310 * [misc]taylor: Taking taylor expansion of k in n 1545390543.310 * [misc]backup-simplify: Simplify k into k 1545390543.311 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1545390543.311 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1545390543.311 * [misc]taylor: Taking taylor expansion of 2 in n 1545390543.311 * [misc]backup-simplify: Simplify 2 into 2 1545390543.311 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545390543.311 * [misc]taylor: Taking taylor expansion of n in n 1545390543.311 * [misc]backup-simplify: Simplify 0 into 0 1545390543.311 * [misc]backup-simplify: Simplify 1 into 1 1545390543.311 * [misc]taylor: Taking taylor expansion of PI in n 1545390543.311 * [misc]backup-simplify: Simplify PI into PI 1545390543.311 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1545390543.311 * [misc]backup-simplify: Simplify (* 2 0) into 0 1545390543.312 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1545390543.312 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1545390543.313 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545390543.313 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1545390543.313 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1545390543.313 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1545390543.313 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545390543.314 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 1545390543.314 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 1545390543.315 * [misc]backup-simplify: Simplify (* (sqrt (/ 1 k)) (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k))) 1545390543.315 * [misc]taylor: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k))) in k 1545390543.315 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1545390543.315 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1545390543.315 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1545390543.315 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390543.315 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390543.315 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1545390543.315 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390543.315 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390543.315 * [misc]taylor: Taking taylor expansion of k in k 1545390543.315 * [misc]backup-simplify: Simplify 0 into 0 1545390543.315 * [misc]backup-simplify: Simplify 1 into 1 1545390543.315 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1545390543.315 * [misc]taylor: Taking taylor expansion of (log n) in k 1545390543.316 * [misc]taylor: Taking taylor expansion of n in k 1545390543.316 * [misc]backup-simplify: Simplify n into n 1545390543.316 * [misc]backup-simplify: Simplify (log n) into (log n) 1545390543.316 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1545390543.316 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1545390543.316 * [misc]taylor: Taking taylor expansion of 2 in k 1545390543.316 * [misc]backup-simplify: Simplify 2 into 2 1545390543.316 * [misc]taylor: Taking taylor expansion of PI in k 1545390543.316 * [misc]backup-simplify: Simplify PI into PI 1545390543.316 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545390543.316 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545390543.316 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1545390543.317 * [misc]backup-simplify: Simplify (- 0) into 0 1545390543.317 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545390543.317 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545390543.318 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1545390543.318 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1545390543.318 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1545390543.318 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545390543.318 * [misc]taylor: Taking taylor expansion of k in k 1545390543.318 * [misc]backup-simplify: Simplify 0 into 0 1545390543.318 * [misc]backup-simplify: Simplify 1 into 1 1545390543.318 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545390543.319 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545390543.319 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1545390543.319 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) into 0 1545390543.320 * [misc]backup-simplify: Simplify 0 into 0 1545390543.320 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1545390543.321 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1545390543.324 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1545390543.324 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1545390543.324 * [misc]backup-simplify: Simplify (- 0) into 0 1545390543.324 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390543.325 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545390543.325 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1545390543.327 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1545390543.328 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 k)) 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))) into 0 1545390543.328 * [misc]taylor: Taking taylor expansion of 0 in k 1545390543.328 * [misc]backup-simplify: Simplify 0 into 0 1545390543.329 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1545390543.329 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1545390543.331 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1545390543.332 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390543.332 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1545390543.332 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1545390543.332 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1545390543.333 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1545390543.334 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 1545390543.336 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 0)) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 1545390543.336 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 1545390543.338 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1545390543.339 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1545390543.343 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1545390543.344 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1545390543.344 * [misc]backup-simplify: Simplify (- 0) into 0 1545390543.344 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390543.344 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545390543.345 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1545390543.347 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1545390543.347 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545390543.348 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 1545390543.349 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))))) into 0 1545390543.349 * [misc]taylor: Taking taylor expansion of 0 in k 1545390543.349 * [misc]backup-simplify: Simplify 0 into 0 1545390543.349 * [misc]backup-simplify: Simplify 0 into 0 1545390543.349 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1545390543.350 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1545390543.352 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1545390543.352 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1545390543.357 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1545390543.357 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390543.357 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1545390543.358 * [misc]backup-simplify: Simplify (- 0) into 0 1545390543.358 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390543.358 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1545390543.361 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 1545390543.365 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) +nan.0) (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 0))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) 1545390543.367 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) 1545390543.369 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1545390543.371 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1545390543.378 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 1545390543.378 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 1545390543.378 * [misc]backup-simplify: Simplify (- 0) into 0 1545390543.378 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390543.379 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545390543.380 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 1545390543.383 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1545390543.383 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545390543.383 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 1545390543.384 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))))) into 0 1545390543.384 * [misc]taylor: Taking taylor expansion of 0 in k 1545390543.384 * [misc]backup-simplify: Simplify 0 into 0 1545390543.384 * [misc]backup-simplify: Simplify 0 into 0 1545390543.384 * [misc]backup-simplify: Simplify 0 into 0 1545390543.385 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390543.386 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1545390543.388 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0 1545390543.389 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1545390543.395 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 1545390543.395 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390543.395 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1545390543.395 * [misc]backup-simplify: Simplify (- 0) into 0 1545390543.395 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390543.396 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 1545390543.398 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 3) 6)) (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 1545390543.403 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) +nan.0) (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) +nan.0) (* (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 0)))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) 1545390543.407 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) 1545390543.413 * [misc]backup-simplify: Simplify (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) (* k 1)) (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) into (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k)))))))))))))))))))))) 1545390543.413 * [misc]backup-simplify: Simplify (/ (pow (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) into (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 1545390543.413 * [misc]approximate: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0 1545390543.413 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 1545390543.413 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1545390543.413 * [misc]taylor: Taking taylor expansion of k in k 1545390543.413 * [misc]backup-simplify: Simplify 0 into 0 1545390543.413 * [misc]backup-simplify: Simplify 1 into 1 1545390543.413 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545390543.414 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1545390543.414 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1545390543.414 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1545390543.414 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1545390543.414 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1545390543.414 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390543.414 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390543.414 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545390543.414 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390543.414 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390543.414 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545390543.414 * [misc]taylor: Taking taylor expansion of k in k 1545390543.414 * [misc]backup-simplify: Simplify 0 into 0 1545390543.414 * [misc]backup-simplify: Simplify 1 into 1 1545390543.414 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545390543.414 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1545390543.414 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1545390543.414 * [misc]taylor: Taking taylor expansion of 2 in k 1545390543.414 * [misc]backup-simplify: Simplify 2 into 2 1545390543.414 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1545390543.414 * [misc]taylor: Taking taylor expansion of PI in k 1545390543.414 * [misc]backup-simplify: Simplify PI into PI 1545390543.414 * [misc]taylor: Taking taylor expansion of n in k 1545390543.414 * [misc]backup-simplify: Simplify n into n 1545390543.414 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1545390543.414 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1545390543.414 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1545390543.415 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545390543.415 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1545390543.415 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1545390543.415 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1545390543.415 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 1545390543.415 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1545390543.415 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1545390543.415 * [misc]taylor: Taking taylor expansion of k in n 1545390543.415 * [misc]backup-simplify: Simplify k into k 1545390543.415 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1545390543.415 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1545390543.415 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1545390543.415 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1545390543.415 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1545390543.415 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1545390543.415 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390543.415 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390543.415 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545390543.415 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390543.415 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390543.415 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545390543.415 * [misc]taylor: Taking taylor expansion of k in n 1545390543.415 * [misc]backup-simplify: Simplify k into k 1545390543.415 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545390543.415 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1545390543.415 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1545390543.415 * [misc]taylor: Taking taylor expansion of 2 in n 1545390543.415 * [misc]backup-simplify: Simplify 2 into 2 1545390543.415 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390543.415 * [misc]taylor: Taking taylor expansion of PI in n 1545390543.415 * [misc]backup-simplify: Simplify PI into PI 1545390543.415 * [misc]taylor: Taking taylor expansion of n in n 1545390543.415 * [misc]backup-simplify: Simplify 0 into 0 1545390543.415 * [misc]backup-simplify: Simplify 1 into 1 1545390543.416 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390543.416 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545390543.416 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545390543.416 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545390543.416 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1545390543.416 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1545390543.417 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545390543.417 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 1545390543.417 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 1545390543.418 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1545390543.418 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1545390543.418 * [misc]taylor: Taking taylor expansion of k in n 1545390543.418 * [misc]backup-simplify: Simplify k into k 1545390543.418 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1545390543.418 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1545390543.418 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1545390543.418 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1545390543.418 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1545390543.418 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1545390543.418 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390543.418 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390543.418 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545390543.418 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390543.418 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390543.418 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545390543.418 * [misc]taylor: Taking taylor expansion of k in n 1545390543.418 * [misc]backup-simplify: Simplify k into k 1545390543.418 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545390543.418 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1545390543.418 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1545390543.418 * [misc]taylor: Taking taylor expansion of 2 in n 1545390543.418 * [misc]backup-simplify: Simplify 2 into 2 1545390543.418 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390543.418 * [misc]taylor: Taking taylor expansion of PI in n 1545390543.418 * [misc]backup-simplify: Simplify PI into PI 1545390543.418 * [misc]taylor: Taking taylor expansion of n in n 1545390543.418 * [misc]backup-simplify: Simplify 0 into 0 1545390543.418 * [misc]backup-simplify: Simplify 1 into 1 1545390543.418 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390543.418 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545390543.419 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545390543.419 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545390543.419 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1545390543.419 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1545390543.419 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545390543.420 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 1545390543.420 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 1545390543.420 * [misc]backup-simplify: Simplify (* (sqrt k) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) 1545390543.421 * [misc]taylor: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) in k 1545390543.421 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1545390543.421 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1545390543.421 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1545390543.421 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390543.421 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390543.421 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545390543.421 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390543.421 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390543.421 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545390543.421 * [misc]taylor: Taking taylor expansion of k in k 1545390543.421 * [misc]backup-simplify: Simplify 0 into 0 1545390543.421 * [misc]backup-simplify: Simplify 1 into 1 1545390543.421 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545390543.421 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1545390543.421 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1545390543.421 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1545390543.421 * [misc]taylor: Taking taylor expansion of 2 in k 1545390543.421 * [misc]backup-simplify: Simplify 2 into 2 1545390543.421 * [misc]taylor: Taking taylor expansion of PI in k 1545390543.421 * [misc]backup-simplify: Simplify PI into PI 1545390543.421 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545390543.421 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545390543.421 * [misc]taylor: Taking taylor expansion of (log n) in k 1545390543.421 * [misc]taylor: Taking taylor expansion of n in k 1545390543.421 * [misc]backup-simplify: Simplify n into n 1545390543.421 * [misc]backup-simplify: Simplify (log n) into (log n) 1545390543.422 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545390543.422 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1545390543.422 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1545390543.422 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1545390543.422 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1545390543.422 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1545390543.423 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 1545390543.423 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1545390543.423 * [misc]taylor: Taking taylor expansion of k in k 1545390543.423 * [misc]backup-simplify: Simplify 0 into 0 1545390543.423 * [misc]backup-simplify: Simplify 1 into 1 1545390543.423 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545390543.423 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1545390543.424 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) into 0 1545390543.424 * [misc]backup-simplify: Simplify 0 into 0 1545390543.424 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1545390543.425 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1545390543.426 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1545390543.426 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1545390543.426 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1545390543.427 * [misc]backup-simplify: Simplify (- 0) into 0 1545390543.427 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390543.427 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545390543.427 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1545390543.429 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1545390543.429 * [misc]backup-simplify: Simplify (+ (* (sqrt k) 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0 1545390543.429 * [misc]taylor: Taking taylor expansion of 0 in k 1545390543.429 * [misc]backup-simplify: Simplify 0 into 0 1545390543.429 * [misc]backup-simplify: Simplify 0 into 0 1545390543.430 * [misc]backup-simplify: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 1545390543.431 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 1545390543.432 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390543.432 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1545390543.435 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1545390543.435 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545390543.435 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1545390543.436 * [misc]backup-simplify: Simplify (- 0) into 0 1545390543.436 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390543.436 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545390543.437 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1545390543.438 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1545390543.438 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 1545390543.439 * [misc]backup-simplify: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0 1545390543.439 * [misc]taylor: Taking taylor expansion of 0 in k 1545390543.439 * [misc]backup-simplify: Simplify 0 into 0 1545390543.439 * [misc]backup-simplify: Simplify 0 into 0 1545390543.439 * [misc]backup-simplify: Simplify 0 into 0 1545390543.440 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1545390543.440 * [misc]backup-simplify: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 1545390543.441 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 1545390543.442 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390543.442 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1545390543.450 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 1545390543.450 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545390543.451 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1545390543.451 * [misc]backup-simplify: Simplify (- 0) into 0 1545390543.451 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390543.452 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545390543.453 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1545390543.457 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1545390543.457 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 1545390543.458 * [misc]backup-simplify: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))) into 0 1545390543.458 * [misc]taylor: Taking taylor expansion of 0 in k 1545390543.458 * [misc]backup-simplify: Simplify 0 into 0 1545390543.458 * [misc]backup-simplify: Simplify 0 into 0 1545390543.458 * [misc]backup-simplify: Simplify 0 into 0 1545390543.458 * [misc]backup-simplify: Simplify 0 into 0 1545390543.460 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1545390543.460 * [misc]backup-simplify: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 1545390543.461 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 1545390543.464 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))))))) 1545390543.464 * [misc]backup-simplify: Simplify (/ (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) into (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) 1545390543.464 * [misc]approximate: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (n k) around 0 1545390543.464 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 1545390543.464 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1545390543.464 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1545390543.465 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1545390543.465 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1545390543.465 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545390543.465 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390543.465 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390543.465 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545390543.465 * [misc]taylor: Taking taylor expansion of k in k 1545390543.465 * [misc]backup-simplify: Simplify 0 into 0 1545390543.465 * [misc]backup-simplify: Simplify 1 into 1 1545390543.465 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545390543.465 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390543.465 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390543.465 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1545390543.465 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1545390543.465 * [misc]taylor: Taking taylor expansion of -2 in k 1545390543.465 * [misc]backup-simplify: Simplify -2 into -2 1545390543.465 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1545390543.465 * [misc]taylor: Taking taylor expansion of PI in k 1545390543.465 * [misc]backup-simplify: Simplify PI into PI 1545390543.465 * [misc]taylor: Taking taylor expansion of n in k 1545390543.465 * [misc]backup-simplify: Simplify n into n 1545390543.465 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1545390543.465 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1545390543.465 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1545390543.466 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545390543.466 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545390543.466 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1545390543.466 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) 1545390543.466 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1545390543.466 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1545390543.466 * [misc]taylor: Taking taylor expansion of -1 in k 1545390543.466 * [misc]backup-simplify: Simplify -1 into -1 1545390543.466 * [misc]taylor: Taking taylor expansion of k in k 1545390543.466 * [misc]backup-simplify: Simplify 0 into 0 1545390543.466 * [misc]backup-simplify: Simplify 1 into 1 1545390543.467 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1545390543.467 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545390543.467 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1545390543.468 * [misc]backup-simplify: Simplify (/ (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) +nan.0) into (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) 1545390543.468 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 1545390543.468 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1545390543.468 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1545390543.468 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1545390543.468 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1545390543.468 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545390543.468 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390543.468 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390543.468 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545390543.468 * [misc]taylor: Taking taylor expansion of k in n 1545390543.468 * [misc]backup-simplify: Simplify k into k 1545390543.468 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545390543.468 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390543.468 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390543.468 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1545390543.468 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1545390543.468 * [misc]taylor: Taking taylor expansion of -2 in n 1545390543.468 * [misc]backup-simplify: Simplify -2 into -2 1545390543.468 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390543.468 * [misc]taylor: Taking taylor expansion of PI in n 1545390543.468 * [misc]backup-simplify: Simplify PI into PI 1545390543.468 * [misc]taylor: Taking taylor expansion of n in n 1545390543.468 * [misc]backup-simplify: Simplify 0 into 0 1545390543.468 * [misc]backup-simplify: Simplify 1 into 1 1545390543.469 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390543.469 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1545390543.469 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1545390543.469 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545390543.470 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1545390543.470 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545390543.471 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1545390543.471 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 1545390543.471 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1545390543.471 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1545390543.472 * [misc]taylor: Taking taylor expansion of -1 in n 1545390543.472 * [misc]backup-simplify: Simplify -1 into -1 1545390543.472 * [misc]taylor: Taking taylor expansion of k in n 1545390543.472 * [misc]backup-simplify: Simplify k into k 1545390543.472 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1545390543.472 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1545390543.472 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1545390543.472 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1545390543.473 * [misc]backup-simplify: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) 1545390543.473 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 1545390543.473 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1545390543.473 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1545390543.473 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1545390543.473 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1545390543.473 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545390543.473 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390543.473 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390543.473 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545390543.473 * [misc]taylor: Taking taylor expansion of k in n 1545390543.473 * [misc]backup-simplify: Simplify k into k 1545390543.473 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545390543.473 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390543.473 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390543.473 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1545390543.473 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1545390543.473 * [misc]taylor: Taking taylor expansion of -2 in n 1545390543.473 * [misc]backup-simplify: Simplify -2 into -2 1545390543.473 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390543.473 * [misc]taylor: Taking taylor expansion of PI in n 1545390543.473 * [misc]backup-simplify: Simplify PI into PI 1545390543.473 * [misc]taylor: Taking taylor expansion of n in n 1545390543.473 * [misc]backup-simplify: Simplify 0 into 0 1545390543.473 * [misc]backup-simplify: Simplify 1 into 1 1545390543.474 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390543.474 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1545390543.474 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1545390543.475 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545390543.475 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1545390543.475 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545390543.476 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1545390543.477 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 1545390543.477 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1545390543.477 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1545390543.477 * [misc]taylor: Taking taylor expansion of -1 in n 1545390543.477 * [misc]backup-simplify: Simplify -1 into -1 1545390543.477 * [misc]taylor: Taking taylor expansion of k in n 1545390543.477 * [misc]backup-simplify: Simplify k into k 1545390543.477 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1545390543.477 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1545390543.477 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1545390543.477 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1545390543.478 * [misc]backup-simplify: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) 1545390543.478 * [misc]taylor: Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) in k 1545390543.478 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1545390543.478 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1545390543.478 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1545390543.478 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545390543.478 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390543.478 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390543.478 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545390543.478 * [misc]taylor: Taking taylor expansion of k in k 1545390543.479 * [misc]backup-simplify: Simplify 0 into 0 1545390543.479 * [misc]backup-simplify: Simplify 1 into 1 1545390543.479 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545390543.479 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390543.479 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390543.479 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1545390543.479 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1545390543.479 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1545390543.479 * [misc]taylor: Taking taylor expansion of -2 in k 1545390543.479 * [misc]backup-simplify: Simplify -2 into -2 1545390543.479 * [misc]taylor: Taking taylor expansion of PI in k 1545390543.479 * [misc]backup-simplify: Simplify PI into PI 1545390543.479 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1545390543.480 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1545390543.480 * [misc]taylor: Taking taylor expansion of (log n) in k 1545390543.480 * [misc]taylor: Taking taylor expansion of n in k 1545390543.480 * [misc]backup-simplify: Simplify n into n 1545390543.480 * [misc]backup-simplify: Simplify (log n) into (log n) 1545390543.480 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545390543.480 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545390543.480 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1545390543.481 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1545390543.481 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1545390543.482 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 1545390543.482 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1545390543.482 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1545390543.482 * [misc]taylor: Taking taylor expansion of -1 in k 1545390543.482 * [misc]backup-simplify: Simplify -1 into -1 1545390543.482 * [misc]taylor: Taking taylor expansion of k in k 1545390543.482 * [misc]backup-simplify: Simplify 0 into 0 1545390543.482 * [misc]backup-simplify: Simplify 1 into 1 1545390543.482 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1545390543.483 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545390543.483 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1545390543.484 * [misc]backup-simplify: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) +nan.0) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 1545390543.484 * [misc]backup-simplify: Simplify (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 1545390543.486 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1545390543.486 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1545390543.489 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1545390543.489 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1545390543.489 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1545390543.489 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390543.490 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545390543.491 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1545390543.492 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1545390543.493 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0 1545390543.493 * [misc]taylor: Taking taylor expansion of 0 in k 1545390543.493 * [misc]backup-simplify: Simplify 0 into 0 1545390543.493 * [misc]backup-simplify: Simplify 0 into 0 1545390543.494 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1545390543.495 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1545390543.496 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 1545390543.496 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 1545390543.498 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390543.499 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1545390543.504 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 1545390543.504 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545390543.504 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1545390543.505 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390543.505 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545390543.506 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1545390543.508 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1545390543.509 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545390543.509 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 1545390543.510 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0 1545390543.510 * [misc]taylor: Taking taylor expansion of 0 in k 1545390543.510 * [misc]backup-simplify: Simplify 0 into 0 1545390543.510 * [misc]backup-simplify: Simplify 0 into 0 1545390543.510 * [misc]backup-simplify: Simplify 0 into 0 1545390543.511 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390543.512 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1545390543.514 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 1545390543.515 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 1545390543.517 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))) 1545390543.517 * * * [misc]progress: simplifying candidates 1545390543.517 * * * * [misc]progress: [ 1 / 83 ] simplifiying candidate # 1545390543.517 * * * * [misc]progress: [ 2 / 83 ] simplifiying candidate # 1545390543.518 * * * * [misc]progress: [ 3 / 83 ] simplifiying candidate # 1545390543.518 * [enter]simplify: Simplifying (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) 1545390543.518 * * [misc]simplify: iters left: 6 (11 enodes) 1545390543.522 * * [misc]simplify: iters left: 5 (21 enodes) 1545390543.529 * * [misc]simplify: iters left: 4 (47 enodes) 1545390543.543 * * [misc]simplify: iters left: 3 (113 enodes) 1545390543.574 * * [misc]simplify: iters left: 2 (328 enodes) 1545390543.837 * [exit]simplify: Simplified to (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) 1545390543.837 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (exp (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI)))) (sqrt k))) 1545390543.837 * * * * [misc]progress: [ 4 / 83 ] simplifiying candidate # 1545390543.838 * * * * [misc]progress: [ 5 / 83 ] simplifiying candidate # 1545390543.838 * [enter]simplify: Simplifying (* PI (* n 2)) 1545390543.838 * * [misc]simplify: iters left: 4 (5 enodes) 1545390543.839 * * [misc]simplify: iters left: 3 (9 enodes) 1545390543.840 * * [misc]simplify: iters left: 2 (15 enodes) 1545390543.842 * * [misc]simplify: iters left: 1 (17 enodes) 1545390543.844 * [exit]simplify: Simplified to (* (* 2 n) PI) 1545390543.844 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* 2 n) PI) (* 1 (- 1/2 (/ k 2)))) (sqrt k))) 1545390543.844 * * * * [misc]progress: [ 6 / 83 ] simplifiying candidate # 1545390543.844 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (/ k 2)) 1545390543.844 * * [misc]simplify: iters left: 5 (8 enodes) 1545390543.846 * * [misc]simplify: iters left: 4 (12 enodes) 1545390543.847 * * [misc]simplify: iters left: 3 (18 enodes) 1545390543.850 * * [misc]simplify: iters left: 2 (20 enodes) 1545390543.852 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ k 2)) 1545390543.852 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (/ (pow (* PI (* n 2)) 1/2) (pow (* (* 2 n) PI) (/ k 2))) (sqrt k))) 1545390543.853 * * * * [misc]progress: [ 7 / 83 ] simplifiying candidate # 1545390543.853 * [enter]simplify: Simplifying (cbrt (- 1/2 (/ k 2))) 1545390543.853 * * [misc]simplify: iters left: 5 (6 enodes) 1545390543.854 * * [misc]simplify: iters left: 4 (8 enodes) 1545390543.855 * * [misc]simplify: iters left: 3 (11 enodes) 1545390543.857 * [exit]simplify: Simplified to (cbrt (- 1/2 (/ k 2))) 1545390543.857 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (pow (pow (* PI (* n 2)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))) (sqrt k))) 1545390543.857 * * * * [misc]progress: [ 8 / 83 ] simplifiying candidate # 1545390543.858 * [enter]simplify: Simplifying (sqrt (- 1/2 (/ k 2))) 1545390543.858 * * [misc]simplify: iters left: 5 (6 enodes) 1545390543.859 * * [misc]simplify: iters left: 4 (8 enodes) 1545390543.862 * * [misc]simplify: iters left: 3 (11 enodes) 1545390543.865 * [exit]simplify: Simplified to (sqrt (- 1/2 (/ k 2))) 1545390543.865 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (pow (pow (* PI (* n 2)) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))) (sqrt k))) 1545390543.865 * * * * [misc]progress: [ 9 / 83 ] simplifiying candidate # 1545390543.865 * [enter]simplify: Simplifying (- 1/2 (/ k 2)) 1545390543.865 * * [misc]simplify: iters left: 4 (5 enodes) 1545390543.867 * * [misc]simplify: iters left: 3 (7 enodes) 1545390543.869 * * [misc]simplify: iters left: 2 (10 enodes) 1545390543.871 * [exit]simplify: Simplified to (- 1/2 (/ k 2)) 1545390543.871 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (pow (pow (* PI (* n 2)) 1) (- 1/2 (/ k 2))) (sqrt k))) 1545390543.871 * * * * [misc]progress: [ 10 / 83 ] simplifiying candidate # 1545390543.872 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1545390543.872 * * [misc]simplify: iters left: 5 (9 enodes) 1545390543.874 * * [misc]simplify: iters left: 4 (15 enodes) 1545390543.879 * * [misc]simplify: iters left: 3 (21 enodes) 1545390543.884 * * [misc]simplify: iters left: 2 (22 enodes) 1545390543.890 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1545390543.890 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2)))) (sqrt k))) 1545390543.890 * * * * [misc]progress: [ 11 / 83 ] simplifiying candidate # 1545390543.890 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1545390543.890 * * [misc]simplify: iters left: 5 (9 enodes) 1545390543.892 * * [misc]simplify: iters left: 4 (15 enodes) 1545390543.894 * * [misc]simplify: iters left: 3 (21 enodes) 1545390543.897 * * [misc]simplify: iters left: 2 (22 enodes) 1545390543.899 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1545390543.899 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2)))) (sqrt k))) 1545390543.899 * * * * [misc]progress: [ 12 / 83 ] simplifiying candidate # 1545390543.900 * [enter]simplify: Simplifying (pow PI (- 1/2 (/ k 2))) 1545390543.900 * * [misc]simplify: iters left: 5 (7 enodes) 1545390543.901 * * [misc]simplify: iters left: 4 (9 enodes) 1545390543.902 * * [misc]simplify: iters left: 3 (12 enodes) 1545390543.903 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1545390543.903 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (* (pow PI (- 1/2 (/ k 2))) (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt k))) 1545390543.904 * * * * [misc]progress: [ 13 / 83 ] simplifiying candidate # 1545390543.904 * * * * [misc]progress: [ 14 / 83 ] simplifiying candidate # 1545390543.904 * * * * [misc]progress: [ 15 / 83 ] simplifiying candidate # 1545390543.904 * * * * [misc]progress: [ 16 / 83 ] simplifiying candidate # 1545390543.904 * * * * [misc]progress: [ 17 / 83 ] simplifiying candidate # 1545390543.904 * * * * [misc]progress: [ 18 / 83 ] simplifiying candidate # 1545390543.904 * * * * [misc]progress: [ 19 / 83 ] simplifiying candidate # 1545390543.904 * * * * [misc]progress: [ 20 / 83 ] simplifiying candidate # 1545390543.904 * * * * [misc]progress: [ 21 / 83 ] simplifiying candidate # 1545390543.904 * * * * [misc]progress: [ 22 / 83 ] simplifiying candidate # 1545390543.904 * * * * [misc]progress: [ 23 / 83 ] simplifiying candidate # 1545390543.904 * * * * [misc]progress: [ 24 / 83 ] simplifiying candidate # 1545390543.904 * * * * [misc]progress: [ 25 / 83 ] simplifiying candidate # 1545390543.904 * * * * [misc]progress: [ 26 / 83 ] simplifiying candidate # 1545390543.904 * * * * [misc]progress: [ 27 / 83 ] simplifiying candidate # 1545390543.904 * * * * [misc]progress: [ 28 / 83 ] simplifiying candidate # 1545390543.904 * * * * [misc]progress: [ 29 / 83 ] simplifiying candidate # 1545390543.904 * * * * [misc]progress: [ 30 / 83 ] simplifiying candidate # 1545390543.904 * * * * [misc]progress: [ 31 / 83 ] simplifiying candidate # 1545390543.904 * * * * [misc]progress: [ 32 / 83 ] simplifiying candidate # 1545390543.904 * * * * [misc]progress: [ 33 / 83 ] simplifiying candidate # 1545390543.904 * * * * [misc]progress: [ 34 / 83 ] simplifiying candidate # 1545390543.904 * [enter]simplify: Simplifying (- (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) (log (sqrt k))) 1545390543.905 * * [misc]simplify: iters left: 6 (14 enodes) 1545390543.907 * * [misc]simplify: iters left: 5 (27 enodes) 1545390543.913 * * [misc]simplify: iters left: 4 (55 enodes) 1545390543.924 * * [misc]simplify: iters left: 3 (144 enodes) 1545390543.976 * [exit]simplify: Simplified to (fma (- 1/2 (/ k 2)) (log (* (* 2 n) PI)) (- (log (sqrt k)))) 1545390543.976 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (- 1/2 (/ k 2)) (log (* (* 2 n) PI)) (- (log (sqrt k)))))) 1545390543.976 * * * * [misc]progress: [ 35 / 83 ] simplifiying candidate # 1545390543.977 * [enter]simplify: Simplifying (- (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) (log (sqrt k))) 1545390543.977 * * [misc]simplify: iters left: 6 (14 enodes) 1545390543.981 * * [misc]simplify: iters left: 5 (27 enodes) 1545390543.985 * * [misc]simplify: iters left: 4 (55 enodes) 1545390543.996 * * [misc]simplify: iters left: 3 (144 enodes) 1545390544.080 * [exit]simplify: Simplified to (fma (- 1/2 (/ k 2)) (log (* (* 2 n) PI)) (- (log (sqrt k)))) 1545390544.080 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (- 1/2 (/ k 2)) (log (* (* 2 n) PI)) (- (log (sqrt k)))))) 1545390544.080 * * * * [misc]progress: [ 36 / 83 ] simplifiying candidate # 1545390544.081 * [enter]simplify: Simplifying (- (log (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (log (sqrt k))) 1545390544.081 * * [misc]simplify: iters left: 6 (14 enodes) 1545390544.083 * * [misc]simplify: iters left: 5 (24 enodes) 1545390544.087 * * [misc]simplify: iters left: 4 (43 enodes) 1545390544.093 * * [misc]simplify: iters left: 3 (73 enodes) 1545390544.111 * * [misc]simplify: iters left: 2 (220 enodes) 1545390544.318 * [exit]simplify: Simplified to (fma (log (* (* PI 2) n)) (- 1/2 (/ k 2)) (- (log (sqrt k)))) 1545390544.319 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (log (* (* PI 2) n)) (- 1/2 (/ k 2)) (- (log (sqrt k)))))) 1545390544.319 * * * * [misc]progress: [ 37 / 83 ] simplifiying candidate # 1545390544.319 * * * * [misc]progress: [ 38 / 83 ] simplifiying candidate # 1545390544.319 * * * * [misc]progress: [ 39 / 83 ] simplifiying candidate # 1545390544.319 * [enter]simplify: Simplifying (/ (* (* (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k))) 1545390544.319 * * [misc]simplify: iters left: 6 (16 enodes) 1545390544.322 * * [misc]simplify: iters left: 5 (31 enodes) 1545390544.327 * * [misc]simplify: iters left: 4 (67 enodes) 1545390544.345 * * [misc]simplify: iters left: 3 (124 enodes) 1545390544.397 * * [misc]simplify: iters left: 2 (195 enodes) 1545390544.456 * * [misc]simplify: iters left: 1 (309 enodes) 1545390544.592 * [exit]simplify: Simplified to (* (* (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (* k (sqrt k)))) 1545390544.592 * [misc]simplify: Simplified (2 1) to (λ (k n) (cbrt (* (* (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (* k (sqrt k)))))) 1545390544.592 * * * * [misc]progress: [ 40 / 83 ] simplifiying candidate # 1545390544.592 * * * * [misc]progress: [ 41 / 83 ] simplifiying candidate # 1545390544.592 * * * * [misc]progress: [ 42 / 83 ] simplifiying candidate # 1545390544.592 * * * * [misc]progress: [ 43 / 83 ] simplifiying candidate # 1545390544.592 * * * * [misc]progress: [ 44 / 83 ] simplifiying candidate # 1545390544.593 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1545390544.593 * * [misc]simplify: iters left: 6 (12 enodes) 1545390544.597 * * [misc]simplify: iters left: 5 (19 enodes) 1545390544.602 * * [misc]simplify: iters left: 4 (25 enodes) 1545390544.609 * * [misc]simplify: iters left: 3 (26 enodes) 1545390544.616 * [exit]simplify: Simplified to (/ (sqrt (* (* 2 n) PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1545390544.616 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (* (* 2 n) PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (sqrt k))))) 1545390544.616 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (sqrt k))) 1545390544.616 * * [misc]simplify: iters left: 6 (12 enodes) 1545390544.620 * * [misc]simplify: iters left: 5 (18 enodes) 1545390544.625 * * [misc]simplify: iters left: 4 (24 enodes) 1545390544.634 * * [misc]simplify: iters left: 3 (25 enodes) 1545390544.641 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt k))) 1545390544.642 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (* (* 2 n) PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt k))))) 1545390544.642 * * * * [misc]progress: [ 45 / 83 ] simplifiying candidate # 1545390544.642 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (sqrt (sqrt k))) 1545390544.642 * * [misc]simplify: iters left: 6 (11 enodes) 1545390544.645 * * [misc]simplify: iters left: 5 (16 enodes) 1545390544.650 * * [misc]simplify: iters left: 4 (22 enodes) 1545390544.656 * * [misc]simplify: iters left: 3 (24 enodes) 1545390544.662 * [exit]simplify: Simplified to (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) 1545390544.662 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k))))) 1545390544.663 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k))) 1545390544.663 * * [misc]simplify: iters left: 6 (12 enodes) 1545390544.666 * * [misc]simplify: iters left: 5 (18 enodes) 1545390544.672 * * [misc]simplify: iters left: 4 (24 enodes) 1545390544.679 * * [misc]simplify: iters left: 3 (25 enodes) 1545390544.685 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k))) 1545390544.685 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k))))) 1545390544.685 * * * * [misc]progress: [ 46 / 83 ] simplifiying candidate # 1545390544.685 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) 1) 1545390544.685 * * [misc]simplify: iters left: 6 (9 enodes) 1545390544.688 * * [misc]simplify: iters left: 5 (16 enodes) 1545390544.694 * * [misc]simplify: iters left: 4 (24 enodes) 1545390544.699 * * [misc]simplify: iters left: 3 (26 enodes) 1545390544.704 * [exit]simplify: Simplified to (sqrt (* (* PI 2) n)) 1545390544.704 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) 1545390544.704 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)) 1545390544.704 * * [misc]simplify: iters left: 6 (11 enodes) 1545390544.708 * * [misc]simplify: iters left: 5 (17 enodes) 1545390544.712 * * [misc]simplify: iters left: 4 (23 enodes) 1545390544.718 * * [misc]simplify: iters left: 3 (24 enodes) 1545390544.724 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)) 1545390544.724 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)))) 1545390544.724 * * * * [misc]progress: [ 47 / 83 ] simplifiying candidate # 1545390544.724 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1545390544.724 * * [misc]simplify: iters left: 6 (12 enodes) 1545390544.727 * * [misc]simplify: iters left: 5 (19 enodes) 1545390544.732 * * [misc]simplify: iters left: 4 (25 enodes) 1545390544.739 * * [misc]simplify: iters left: 3 (26 enodes) 1545390544.745 * [exit]simplify: Simplified to (/ (sqrt (* (* 2 n) PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1545390544.745 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (* (* 2 n) PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (sqrt k))))) 1545390544.746 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (sqrt k))) 1545390544.746 * * [misc]simplify: iters left: 6 (12 enodes) 1545390544.750 * * [misc]simplify: iters left: 5 (18 enodes) 1545390544.755 * * [misc]simplify: iters left: 4 (24 enodes) 1545390544.761 * * [misc]simplify: iters left: 3 (25 enodes) 1545390544.767 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt k))) 1545390544.767 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (* (* 2 n) PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt k))))) 1545390544.767 * * * * [misc]progress: [ 48 / 83 ] simplifiying candidate # 1545390544.768 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (sqrt (sqrt k))) 1545390544.768 * * [misc]simplify: iters left: 6 (11 enodes) 1545390544.771 * * [misc]simplify: iters left: 5 (16 enodes) 1545390544.776 * * [misc]simplify: iters left: 4 (22 enodes) 1545390544.783 * * [misc]simplify: iters left: 3 (24 enodes) 1545390544.789 * [exit]simplify: Simplified to (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) 1545390544.789 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k))))) 1545390544.789 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k))) 1545390544.789 * * [misc]simplify: iters left: 6 (12 enodes) 1545390544.793 * * [misc]simplify: iters left: 5 (18 enodes) 1545390544.799 * * [misc]simplify: iters left: 4 (24 enodes) 1545390544.805 * * [misc]simplify: iters left: 3 (25 enodes) 1545390544.811 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k))) 1545390544.811 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k))))) 1545390544.811 * * * * [misc]progress: [ 49 / 83 ] simplifiying candidate # 1545390544.811 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) 1) 1545390544.812 * * [misc]simplify: iters left: 6 (9 enodes) 1545390544.814 * * [misc]simplify: iters left: 5 (16 enodes) 1545390544.820 * * [misc]simplify: iters left: 4 (24 enodes) 1545390544.825 * * [misc]simplify: iters left: 3 (26 enodes) 1545390544.831 * [exit]simplify: Simplified to (sqrt (* (* PI 2) n)) 1545390544.831 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) 1545390544.832 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)) 1545390544.832 * * [misc]simplify: iters left: 6 (11 enodes) 1545390544.835 * * [misc]simplify: iters left: 5 (17 enodes) 1545390544.840 * * [misc]simplify: iters left: 4 (23 enodes) 1545390544.846 * * [misc]simplify: iters left: 3 (24 enodes) 1545390544.852 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)) 1545390544.852 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)))) 1545390544.852 * * * * [misc]progress: [ 50 / 83 ] simplifiying candidate # 1545390544.852 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1545390544.853 * * [misc]simplify: iters left: 6 (11 enodes) 1545390544.856 * * [misc]simplify: iters left: 5 (15 enodes) 1545390544.861 * * [misc]simplify: iters left: 4 (18 enodes) 1545390544.866 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1545390544.866 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (pow PI (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))))) 1545390544.866 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1545390544.866 * * [misc]simplify: iters left: 6 (11 enodes) 1545390544.870 * * [misc]simplify: iters left: 5 (14 enodes) 1545390544.874 * * [misc]simplify: iters left: 4 (17 enodes) 1545390544.879 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1545390544.879 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (pow PI (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))))) 1545390544.879 * * * * [misc]progress: [ 51 / 83 ] simplifiying candidate # 1545390544.879 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1545390544.879 * * [misc]simplify: iters left: 6 (10 enodes) 1545390544.882 * * [misc]simplify: iters left: 5 (12 enodes) 1545390544.886 * * [misc]simplify: iters left: 4 (15 enodes) 1545390544.890 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1545390544.890 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) 1545390544.891 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1545390544.891 * * [misc]simplify: iters left: 6 (11 enodes) 1545390544.894 * * [misc]simplify: iters left: 5 (14 enodes) 1545390544.899 * * [misc]simplify: iters left: 4 (17 enodes) 1545390544.904 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1545390544.904 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) 1545390544.904 * * * * [misc]progress: [ 52 / 83 ] simplifiying candidate # 1545390544.904 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) 1) 1545390544.904 * * [misc]simplify: iters left: 6 (9 enodes) 1545390544.907 * * [misc]simplify: iters left: 5 (13 enodes) 1545390544.912 * * [misc]simplify: iters left: 4 (18 enodes) 1545390544.916 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1545390544.916 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1545390544.917 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)) 1545390544.917 * * [misc]simplify: iters left: 6 (10 enodes) 1545390544.920 * * [misc]simplify: iters left: 5 (13 enodes) 1545390544.924 * * [misc]simplify: iters left: 4 (16 enodes) 1545390544.929 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)) 1545390544.929 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1545390544.929 * * * * [misc]progress: [ 53 / 83 ] simplifiying candidate # 1545390544.930 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1545390544.930 * * [misc]simplify: iters left: 6 (16 enodes) 1545390544.937 * * [misc]simplify: iters left: 5 (28 enodes) 1545390544.945 * * [misc]simplify: iters left: 4 (46 enodes) 1545390544.958 * * [misc]simplify: iters left: 3 (50 enodes) 1545390544.970 * * [misc]simplify: iters left: 2 (53 enodes) 1545390544.984 * [exit]simplify: Simplified to (* (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))) 1545390544.984 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (* (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))) (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))) 1545390544.985 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1545390544.985 * * [misc]simplify: iters left: 6 (14 enodes) 1545390544.989 * * [misc]simplify: iters left: 5 (20 enodes) 1545390544.995 * * [misc]simplify: iters left: 4 (29 enodes) 1545390545.003 * * [misc]simplify: iters left: 3 (30 enodes) 1545390545.011 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1545390545.011 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))) 1545390545.011 * * * * [misc]progress: [ 54 / 83 ] simplifiying candidate # 1545390545.011 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) 1545390545.011 * * [misc]simplify: iters left: 6 (15 enodes) 1545390545.016 * * [misc]simplify: iters left: 5 (23 enodes) 1545390545.023 * * [misc]simplify: iters left: 4 (34 enodes) 1545390545.032 * * [misc]simplify: iters left: 3 (37 enodes) 1545390545.041 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (/ (sqrt (sqrt k)) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))))) 1545390545.042 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (/ (sqrt (sqrt k)) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))))) (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) 1545390545.042 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1545390545.042 * * [misc]simplify: iters left: 6 (14 enodes) 1545390545.046 * * [misc]simplify: iters left: 5 (20 enodes) 1545390545.052 * * [misc]simplify: iters left: 4 (29 enodes) 1545390545.060 * * [misc]simplify: iters left: 3 (30 enodes) 1545390545.068 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1545390545.068 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) 1545390545.068 * * * * [misc]progress: [ 55 / 83 ] simplifiying candidate # 1545390545.069 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1) 1545390545.069 * * [misc]simplify: iters left: 6 (14 enodes) 1545390545.074 * * [misc]simplify: iters left: 5 (24 enodes) 1545390545.082 * * [misc]simplify: iters left: 4 (39 enodes) 1545390545.093 * * [misc]simplify: iters left: 3 (54 enodes) 1545390545.100 * * [misc]simplify: iters left: 2 (80 enodes) 1545390545.109 * [exit]simplify: Simplified to (* (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))) 1545390545.110 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (* (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))) (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt k)))) 1545390545.110 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt k)) 1545390545.110 * * [misc]simplify: iters left: 6 (13 enodes) 1545390545.112 * * [misc]simplify: iters left: 5 (19 enodes) 1545390545.114 * * [misc]simplify: iters left: 4 (28 enodes) 1545390545.118 * * [misc]simplify: iters left: 3 (30 enodes) 1545390545.122 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt k)) 1545390545.122 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))) (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt k)))) 1545390545.122 * * * * [misc]progress: [ 56 / 83 ] simplifiying candidate # 1545390545.122 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1545390545.122 * * [misc]simplify: iters left: 6 (15 enodes) 1545390545.125 * * [misc]simplify: iters left: 5 (23 enodes) 1545390545.131 * * [misc]simplify: iters left: 4 (32 enodes) 1545390545.136 * * [misc]simplify: iters left: 3 (34 enodes) 1545390545.140 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1545390545.140 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))) 1545390545.140 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1545390545.140 * * [misc]simplify: iters left: 6 (14 enodes) 1545390545.142 * * [misc]simplify: iters left: 5 (20 enodes) 1545390545.145 * * [misc]simplify: iters left: 4 (29 enodes) 1545390545.149 * * [misc]simplify: iters left: 3 (30 enodes) 1545390545.152 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1545390545.152 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))) 1545390545.152 * * * * [misc]progress: [ 57 / 83 ] simplifiying candidate # 1545390545.152 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1545390545.153 * * [misc]simplify: iters left: 6 (14 enodes) 1545390545.154 * * [misc]simplify: iters left: 5 (20 enodes) 1545390545.157 * * [misc]simplify: iters left: 4 (29 enodes) 1545390545.163 * * [misc]simplify: iters left: 3 (30 enodes) 1545390545.171 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1545390545.172 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) 1545390545.172 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1545390545.172 * * [misc]simplify: iters left: 6 (14 enodes) 1545390545.176 * * [misc]simplify: iters left: 5 (20 enodes) 1545390545.182 * * [misc]simplify: iters left: 4 (29 enodes) 1545390545.190 * * [misc]simplify: iters left: 3 (30 enodes) 1545390545.198 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1545390545.198 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) 1545390545.198 * * * * [misc]progress: [ 58 / 83 ] simplifiying candidate # 1545390545.198 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1) 1545390545.198 * * [misc]simplify: iters left: 6 (13 enodes) 1545390545.203 * * [misc]simplify: iters left: 5 (21 enodes) 1545390545.209 * * [misc]simplify: iters left: 4 (32 enodes) 1545390545.217 * * [misc]simplify: iters left: 3 (33 enodes) 1545390545.224 * [exit]simplify: Simplified to (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) 1545390545.224 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt k)))) 1545390545.225 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt k)) 1545390545.225 * * [misc]simplify: iters left: 6 (13 enodes) 1545390545.229 * * [misc]simplify: iters left: 5 (19 enodes) 1545390545.234 * * [misc]simplify: iters left: 4 (28 enodes) 1545390545.242 * * [misc]simplify: iters left: 3 (30 enodes) 1545390545.249 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt k)) 1545390545.249 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt k)))) 1545390545.249 * * * * [misc]progress: [ 59 / 83 ] simplifiying candidate # 1545390545.250 * [enter]simplify: Simplifying (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1545390545.250 * * [misc]simplify: iters left: 6 (6 enodes) 1545390545.252 * * [misc]simplify: iters left: 5 (10 enodes) 1545390545.254 * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) 1545390545.254 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (cbrt (sqrt k))))) 1545390545.254 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1545390545.255 * * [misc]simplify: iters left: 6 (13 enodes) 1545390545.258 * * [misc]simplify: iters left: 5 (19 enodes) 1545390545.264 * * [misc]simplify: iters left: 4 (28 enodes) 1545390545.271 * * [misc]simplify: iters left: 3 (30 enodes) 1545390545.279 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1545390545.279 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (cbrt (sqrt k))))) 1545390545.279 * * * * [misc]progress: [ 60 / 83 ] simplifiying candidate # 1545390545.279 * [enter]simplify: Simplifying (/ 1 (sqrt (sqrt k))) 1545390545.279 * * [misc]simplify: iters left: 4 (5 enodes) 1545390545.281 * * [misc]simplify: iters left: 3 (7 enodes) 1545390545.282 * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt k))) 1545390545.282 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) 1545390545.283 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1545390545.283 * * [misc]simplify: iters left: 6 (13 enodes) 1545390545.287 * * [misc]simplify: iters left: 5 (19 enodes) 1545390545.293 * * [misc]simplify: iters left: 4 (28 enodes) 1545390545.300 * * [misc]simplify: iters left: 3 (30 enodes) 1545390545.308 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1545390545.308 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) 1545390545.308 * * * * [misc]progress: [ 61 / 83 ] simplifiying candidate # 1545390545.308 * [enter]simplify: Simplifying (/ 1 1) 1545390545.308 * * [misc]simplify: iters left: 2 (2 enodes) 1545390545.309 * * [misc]simplify: iters left: 1 (4 enodes) 1545390545.310 * [exit]simplify: Simplified to 1 1545390545.310 * [misc]simplify: Simplified (2 1) to (λ (k n) (* 1 (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))) 1545390545.310 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)) 1545390545.310 * * [misc]simplify: iters left: 6 (12 enodes) 1545390545.314 * * [misc]simplify: iters left: 5 (18 enodes) 1545390545.320 * * [misc]simplify: iters left: 4 (27 enodes) 1545390545.327 * * [misc]simplify: iters left: 3 (29 enodes) 1545390545.335 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k)) 1545390545.335 * [misc]simplify: Simplified (2 2) to (λ (k n) (* 1 (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k)))) 1545390545.335 * * * * [misc]progress: [ 62 / 83 ] simplifiying candidate # 1545390545.335 * * * * [misc]progress: [ 63 / 83 ] simplifiying candidate # 1545390545.335 * * * * [misc]progress: [ 64 / 83 ] simplifiying candidate # 1545390545.335 * * * * [misc]progress: [ 65 / 83 ] simplifiying candidate # 1545390545.335 * [enter]simplify: Simplifying (cbrt (sqrt k)) 1545390545.335 * * [misc]simplify: iters left: 2 (3 enodes) 1545390545.336 * [exit]simplify: Simplified to (cbrt (sqrt k)) 1545390545.336 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k)))) 1545390545.336 * * * * [misc]progress: [ 66 / 83 ] simplifiying candidate # 1545390545.336 * [enter]simplify: Simplifying (sqrt (sqrt k)) 1545390545.336 * * [misc]simplify: iters left: 2 (3 enodes) 1545390545.337 * [exit]simplify: Simplified to (sqrt (sqrt k)) 1545390545.337 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k)))) 1545390545.337 * * * * [misc]progress: [ 67 / 83 ] simplifiying candidate # 1545390545.338 * [enter]simplify: Simplifying (sqrt k) 1545390545.338 * * [misc]simplify: iters left: 1 (2 enodes) 1545390545.338 * [exit]simplify: Simplified to (sqrt k) 1545390545.338 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) 1) (sqrt k))) 1545390545.338 * * * * [misc]progress: [ 68 / 83 ] simplifiying candidate # 1545390545.339 * [enter]simplify: Simplifying (pow (* PI (* n 2)) 1/2) 1545390545.339 * * [misc]simplify: iters left: 5 (7 enodes) 1545390545.341 * * [misc]simplify: iters left: 4 (12 enodes) 1545390545.345 * * [misc]simplify: iters left: 3 (18 enodes) 1545390545.349 * * [misc]simplify: iters left: 2 (20 enodes) 1545390545.354 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1545390545.354 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2)))))) 1545390545.354 * * * * [misc]progress: [ 69 / 83 ] simplifiying candidate # 1545390545.355 * [enter]simplify: Simplifying (pow (* PI (* n 2)) 1/2) 1545390545.355 * * [misc]simplify: iters left: 5 (7 enodes) 1545390545.357 * * [misc]simplify: iters left: 4 (12 enodes) 1545390545.360 * * [misc]simplify: iters left: 3 (18 enodes) 1545390545.365 * * [misc]simplify: iters left: 2 (20 enodes) 1545390545.370 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1545390545.370 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2)))))) 1545390545.370 * * * * [misc]progress: [ 70 / 83 ] simplifiying candidate # 1545390545.370 * [enter]simplify: Simplifying (pow PI (- 1/2 (/ k 2))) 1545390545.370 * * [misc]simplify: iters left: 5 (7 enodes) 1545390545.372 * * [misc]simplify: iters left: 4 (9 enodes) 1545390545.375 * * [misc]simplify: iters left: 3 (12 enodes) 1545390545.378 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1545390545.378 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (pow PI (- 1/2 (/ k 2))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2)))))) 1545390545.378 * * * * [misc]progress: [ 71 / 83 ] simplifiying candidate # 1545390545.378 * [enter]simplify: Simplifying (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1545390545.378 * * [misc]simplify: iters left: 6 (12 enodes) 1545390545.382 * * [misc]simplify: iters left: 5 (18 enodes) 1545390545.388 * * [misc]simplify: iters left: 4 (27 enodes) 1545390545.395 * * [misc]simplify: iters left: 3 (29 enodes) 1545390545.403 * [exit]simplify: Simplified to (* (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) 1545390545.403 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (* (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) (/ (sqrt k) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))) 1545390545.403 * * * * [misc]progress: [ 72 / 83 ] simplifiying candidate # 1545390545.403 * [enter]simplify: Simplifying (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1545390545.403 * * [misc]simplify: iters left: 6 (11 enodes) 1545390545.407 * * [misc]simplify: iters left: 5 (17 enodes) 1545390545.412 * * [misc]simplify: iters left: 4 (26 enodes) 1545390545.419 * * [misc]simplify: iters left: 3 (27 enodes) 1545390545.426 * [exit]simplify: Simplified to (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) 1545390545.426 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))) 1545390545.426 * * * * [misc]progress: [ 73 / 83 ] simplifiying candidate # 1545390545.426 * * * * [misc]progress: [ 74 / 83 ] simplifiying candidate # 1545390545.426 * [enter]simplify: Simplifying (pow (* PI (* n 2)) 1/2) 1545390545.426 * * [misc]simplify: iters left: 5 (7 enodes) 1545390545.428 * * [misc]simplify: iters left: 4 (12 enodes) 1545390545.432 * * [misc]simplify: iters left: 3 (18 enodes) 1545390545.437 * * [misc]simplify: iters left: 2 (20 enodes) 1545390545.441 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1545390545.441 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2))))) 1545390545.441 * * * * [misc]progress: [ 75 / 83 ] simplifiying candidate # 1545390545.442 * [enter]simplify: Simplifying (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) 1545390545.443 * * [misc]simplify: iters left: 6 (37 enodes) 1545390545.458 * * [misc]simplify: iters left: 5 (108 enodes) 1545390545.482 * * [misc]simplify: iters left: 4 (368 enodes) 1545390545.751 * [exit]simplify: Simplified to (fma -1/2 (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) (fma (* (* (* k k) (log n)) (* (log (* PI 2)) 1/4)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (fma (* (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (log (* PI 2)) (log (* PI 2)))) (* (* k k) 1/8) (fma (* (* (* k k) (log n)) (* (log n) 1/8)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (pow n 1/2) (pow (* PI 2) 1/2)))))) 1545390545.751 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (fma -1/2 (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) (fma (* (* (* k k) (log n)) (* (log (* PI 2)) 1/4)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (fma (* (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (log (* PI 2)) (log (* PI 2)))) (* (* k k) 1/8) (fma (* (* (* k k) (log n)) (* (log n) 1/8)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (pow n 1/2) (pow (* PI 2) 1/2)))))) (sqrt k))) 1545390545.751 * * * * [misc]progress: [ 76 / 83 ] simplifiying candidate # 1545390545.752 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 1545390545.752 * * [misc]simplify: iters left: 6 (15 enodes) 1545390545.757 * * [misc]simplify: iters left: 5 (33 enodes) 1545390545.762 * * [misc]simplify: iters left: 4 (64 enodes) 1545390545.778 * * [misc]simplify: iters left: 3 (179 enodes) 1545390545.898 * [exit]simplify: Simplified to (* (pow (* 2 PI) (fma -1/2 k 1/2)) (pow n (fma -1/2 k 1/2))) 1545390545.898 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (* (pow (* 2 PI) (fma -1/2 k 1/2)) (pow n (fma -1/2 k 1/2))) (sqrt k))) 1545390545.898 * * * * [misc]progress: [ 77 / 83 ] simplifiying candidate # 1545390545.898 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 1545390545.898 * * [misc]simplify: iters left: 6 (15 enodes) 1545390545.901 * * [misc]simplify: iters left: 5 (30 enodes) 1545390545.907 * * [misc]simplify: iters left: 4 (65 enodes) 1545390545.921 * * [misc]simplify: iters left: 3 (208 enodes) 1545390546.099 * [exit]simplify: Simplified to (pow (exp (fma -1/2 k 1/2)) (- (log (* -2 PI)) (log (/ -1 n)))) 1545390546.099 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (pow (exp (fma -1/2 k 1/2)) (- (log (* -2 PI)) (log (/ -1 n)))) (sqrt k))) 1545390546.099 * * * * [misc]progress: [ 78 / 83 ] simplifiying candidate # 1545390546.100 * [enter]simplify: Simplifying (* 2 (* n PI)) 1545390546.100 * * [misc]simplify: iters left: 4 (5 enodes) 1545390546.101 * * [misc]simplify: iters left: 3 (9 enodes) 1545390546.104 * * [misc]simplify: iters left: 2 (15 enodes) 1545390546.108 * * [misc]simplify: iters left: 1 (17 enodes) 1545390546.111 * [exit]simplify: Simplified to (* (* PI n) 2) 1545390546.112 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt k))) 1545390546.112 * * * * [misc]progress: [ 79 / 83 ] simplifiying candidate # 1545390546.112 * [enter]simplify: Simplifying (* 2 (* n PI)) 1545390546.112 * * [misc]simplify: iters left: 4 (5 enodes) 1545390546.113 * * [misc]simplify: iters left: 3 (9 enodes) 1545390546.116 * * [misc]simplify: iters left: 2 (15 enodes) 1545390546.118 * * [misc]simplify: iters left: 1 (17 enodes) 1545390546.120 * [exit]simplify: Simplified to (* (* PI n) 2) 1545390546.120 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt k))) 1545390546.120 * * * * [misc]progress: [ 80 / 83 ] simplifiying candidate # 1545390546.121 * [enter]simplify: Simplifying (* 2 (* n PI)) 1545390546.121 * * [misc]simplify: iters left: 4 (5 enodes) 1545390546.121 * * [misc]simplify: iters left: 3 (9 enodes) 1545390546.123 * * [misc]simplify: iters left: 2 (15 enodes) 1545390546.125 * * [misc]simplify: iters left: 1 (17 enodes) 1545390546.127 * [exit]simplify: Simplified to (* (* PI n) 2) 1545390546.127 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt k))) 1545390546.127 * * * * [misc]progress: [ 81 / 83 ] simplifiying candidate # 1545390546.127 * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k)))))))))))))))))))))) 1545390546.127 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1545390546.127 * * * * [misc]progress: [ 82 / 83 ] simplifiying candidate # 1545390546.127 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))))))) 1545390546.127 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1545390546.127 * * * * [misc]progress: [ 83 / 83 ] simplifiying candidate # 1545390546.127 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))) 1545390546.127 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1545390546.128 * * * [misc]progress: adding candidates to table 1545390547.165 * * [misc]progress: iteration 2 / 4 1545390547.165 * * * [misc]progress: picking best candidate 1545390547.203 * * * * [misc]pick: Picked # 1545390547.203 * * * [misc]progress: localizing error 1545390547.245 * * * [misc]progress: generating rewritten candidates 1545390547.245 * * * * [misc]progress: [ 1 / 4 ] rewriting at (2 2) 1545390547.251 * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 2 1) 1545390547.260 * * * * [misc]progress: [ 3 / 4 ] rewriting at (2 1) 1545390547.264 * * * * [misc]progress: [ 4 / 4 ] rewriting at (2) 1545390547.281 * * * [misc]progress: generating series expansions 1545390547.281 * * * * [misc]progress: [ 1 / 4 ] generating series at (2 2) 1545390547.282 * [misc]backup-simplify: Simplify (pow (* (* 2 PI) n) (/ (- 1 k) 2)) into (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) 1545390547.282 * [misc]approximate: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in (n k) around 0 1545390547.282 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k 1545390547.282 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k 1545390547.282 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k 1545390547.282 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 k)) in k 1545390547.282 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390547.282 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390547.282 * [misc]taylor: Taking taylor expansion of (- 1 k) in k 1545390547.282 * [misc]taylor: Taking taylor expansion of 1 in k 1545390547.282 * [misc]backup-simplify: Simplify 1 into 1 1545390547.282 * [misc]taylor: Taking taylor expansion of k in k 1545390547.282 * [misc]backup-simplify: Simplify 0 into 0 1545390547.282 * [misc]backup-simplify: Simplify 1 into 1 1545390547.282 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1545390547.282 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1545390547.282 * [misc]taylor: Taking taylor expansion of 2 in k 1545390547.282 * [misc]backup-simplify: Simplify 2 into 2 1545390547.282 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1545390547.282 * [misc]taylor: Taking taylor expansion of n in k 1545390547.282 * [misc]backup-simplify: Simplify n into n 1545390547.282 * [misc]taylor: Taking taylor expansion of PI in k 1545390547.282 * [misc]backup-simplify: Simplify PI into PI 1545390547.282 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1545390547.282 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1545390547.282 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1545390547.282 * [misc]backup-simplify: Simplify (- 0) into 0 1545390547.283 * [misc]backup-simplify: Simplify (+ 1 0) into 1 1545390547.283 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545390547.283 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1545390547.283 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1545390547.283 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n 1545390547.283 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n 1545390547.283 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n 1545390547.283 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 k)) in n 1545390547.283 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390547.283 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390547.283 * [misc]taylor: Taking taylor expansion of (- 1 k) in n 1545390547.283 * [misc]taylor: Taking taylor expansion of 1 in n 1545390547.283 * [misc]backup-simplify: Simplify 1 into 1 1545390547.283 * [misc]taylor: Taking taylor expansion of k in n 1545390547.283 * [misc]backup-simplify: Simplify k into k 1545390547.283 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1545390547.283 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1545390547.283 * [misc]taylor: Taking taylor expansion of 2 in n 1545390547.283 * [misc]backup-simplify: Simplify 2 into 2 1545390547.283 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545390547.283 * [misc]taylor: Taking taylor expansion of n in n 1545390547.283 * [misc]backup-simplify: Simplify 0 into 0 1545390547.283 * [misc]backup-simplify: Simplify 1 into 1 1545390547.283 * [misc]taylor: Taking taylor expansion of PI in n 1545390547.283 * [misc]backup-simplify: Simplify PI into PI 1545390547.283 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1545390547.283 * [misc]backup-simplify: Simplify (* 2 0) into 0 1545390547.284 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1545390547.284 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1545390547.284 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545390547.285 * [misc]backup-simplify: Simplify (- k) into (- k) 1545390547.285 * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) 1545390547.285 * [misc]backup-simplify: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k)) 1545390547.285 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545390547.285 * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) 1545390547.286 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 1545390547.286 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n 1545390547.286 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n 1545390547.286 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n 1545390547.286 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 k)) in n 1545390547.286 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390547.286 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390547.286 * [misc]taylor: Taking taylor expansion of (- 1 k) in n 1545390547.286 * [misc]taylor: Taking taylor expansion of 1 in n 1545390547.286 * [misc]backup-simplify: Simplify 1 into 1 1545390547.286 * [misc]taylor: Taking taylor expansion of k in n 1545390547.286 * [misc]backup-simplify: Simplify k into k 1545390547.286 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1545390547.286 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1545390547.286 * [misc]taylor: Taking taylor expansion of 2 in n 1545390547.286 * [misc]backup-simplify: Simplify 2 into 2 1545390547.286 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545390547.286 * [misc]taylor: Taking taylor expansion of n in n 1545390547.286 * [misc]backup-simplify: Simplify 0 into 0 1545390547.286 * [misc]backup-simplify: Simplify 1 into 1 1545390547.286 * [misc]taylor: Taking taylor expansion of PI in n 1545390547.286 * [misc]backup-simplify: Simplify PI into PI 1545390547.286 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1545390547.286 * [misc]backup-simplify: Simplify (* 2 0) into 0 1545390547.287 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1545390547.287 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1545390547.287 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545390547.287 * [misc]backup-simplify: Simplify (- k) into (- k) 1545390547.287 * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) 1545390547.287 * [misc]backup-simplify: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k)) 1545390547.288 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545390547.288 * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) 1545390547.289 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 1545390547.289 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) in k 1545390547.289 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) in k 1545390547.289 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390547.289 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390547.289 * [misc]taylor: Taking taylor expansion of (* (- 1 k) (+ (log n) (log (* 2 PI)))) in k 1545390547.289 * [misc]taylor: Taking taylor expansion of (- 1 k) in k 1545390547.289 * [misc]taylor: Taking taylor expansion of 1 in k 1545390547.289 * [misc]backup-simplify: Simplify 1 into 1 1545390547.289 * [misc]taylor: Taking taylor expansion of k in k 1545390547.289 * [misc]backup-simplify: Simplify 0 into 0 1545390547.289 * [misc]backup-simplify: Simplify 1 into 1 1545390547.289 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1545390547.289 * [misc]taylor: Taking taylor expansion of (log n) in k 1545390547.289 * [misc]taylor: Taking taylor expansion of n in k 1545390547.289 * [misc]backup-simplify: Simplify n into n 1545390547.289 * [misc]backup-simplify: Simplify (log n) into (log n) 1545390547.289 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1545390547.289 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1545390547.289 * [misc]taylor: Taking taylor expansion of 2 in k 1545390547.289 * [misc]backup-simplify: Simplify 2 into 2 1545390547.289 * [misc]taylor: Taking taylor expansion of PI in k 1545390547.289 * [misc]backup-simplify: Simplify PI into PI 1545390547.289 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545390547.289 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545390547.290 * [misc]backup-simplify: Simplify (- 0) into 0 1545390547.290 * [misc]backup-simplify: Simplify (+ 1 0) into 1 1545390547.290 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545390547.290 * [misc]backup-simplify: Simplify (* 1 (+ (log n) (log (* 2 PI)))) into (+ (log n) (log (* 2 PI))) 1545390547.291 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1545390547.291 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1545390547.291 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1545390547.292 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1545390547.292 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1545390547.294 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1545390547.294 * [misc]backup-simplify: Simplify (- 0) into 0 1545390547.294 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390547.295 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- 1 k))) into 0 1545390547.295 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545390547.295 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1545390547.296 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0 1545390547.296 * [misc]taylor: Taking taylor expansion of 0 in k 1545390547.296 * [misc]backup-simplify: Simplify 0 into 0 1545390547.296 * [misc]backup-simplify: Simplify 0 into 0 1545390547.297 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1545390547.297 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1545390547.299 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1545390547.299 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390547.299 * [misc]backup-simplify: Simplify (- 1) into -1 1545390547.299 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 1545390547.300 * [misc]backup-simplify: Simplify (+ (* 1 0) (* -1 (+ (log n) (log (* 2 PI))))) into (- (+ (log (* 2 PI)) (log n))) 1545390547.300 * [misc]backup-simplify: Simplify (+ (* 1/2 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1545390547.301 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 1545390547.302 * [misc]backup-simplify: Simplify (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 1545390547.303 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1545390547.304 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1545390547.306 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1545390547.306 * [misc]backup-simplify: Simplify (- 0) into 0 1545390547.307 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390547.307 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0 1545390547.307 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545390547.308 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1545390547.309 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1545390547.309 * [misc]taylor: Taking taylor expansion of 0 in k 1545390547.309 * [misc]backup-simplify: Simplify 0 into 0 1545390547.309 * [misc]backup-simplify: Simplify 0 into 0 1545390547.309 * [misc]backup-simplify: Simplify 0 into 0 1545390547.310 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1545390547.311 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1545390547.314 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1545390547.314 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390547.314 * [misc]backup-simplify: Simplify (- 0) into 0 1545390547.314 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390547.314 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1545390547.315 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1545390547.316 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 1545390547.318 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 1545390547.322 * [misc]backup-simplify: Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) 1545390547.322 * [misc]backup-simplify: Simplify (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) into (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) 1545390547.322 * [misc]approximate: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in (n k) around 0 1545390547.322 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k 1545390547.323 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1545390547.323 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1545390547.323 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k 1545390547.323 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390547.323 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390547.323 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k 1545390547.323 * [misc]taylor: Taking taylor expansion of 1 in k 1545390547.323 * [misc]backup-simplify: Simplify 1 into 1 1545390547.323 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545390547.323 * [misc]taylor: Taking taylor expansion of k in k 1545390547.323 * [misc]backup-simplify: Simplify 0 into 0 1545390547.323 * [misc]backup-simplify: Simplify 1 into 1 1545390547.323 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545390547.323 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1545390547.323 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1545390547.323 * [misc]taylor: Taking taylor expansion of 2 in k 1545390547.323 * [misc]backup-simplify: Simplify 2 into 2 1545390547.323 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1545390547.323 * [misc]taylor: Taking taylor expansion of PI in k 1545390547.323 * [misc]backup-simplify: Simplify PI into PI 1545390547.323 * [misc]taylor: Taking taylor expansion of n in k 1545390547.323 * [misc]backup-simplify: Simplify n into n 1545390547.323 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1545390547.323 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1545390547.323 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1545390547.324 * [misc]backup-simplify: Simplify (- 1) into -1 1545390547.324 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 1545390547.324 * [misc]backup-simplify: Simplify (* 1/2 -1) into -1/2 1545390547.324 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1545390547.324 * [misc]backup-simplify: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 1545390547.324 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n 1545390547.324 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1545390547.324 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1545390547.324 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n 1545390547.324 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390547.325 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390547.325 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n 1545390547.325 * [misc]taylor: Taking taylor expansion of 1 in n 1545390547.325 * [misc]backup-simplify: Simplify 1 into 1 1545390547.325 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545390547.325 * [misc]taylor: Taking taylor expansion of k in n 1545390547.325 * [misc]backup-simplify: Simplify k into k 1545390547.325 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545390547.325 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1545390547.325 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1545390547.325 * [misc]taylor: Taking taylor expansion of 2 in n 1545390547.325 * [misc]backup-simplify: Simplify 2 into 2 1545390547.325 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390547.325 * [misc]taylor: Taking taylor expansion of PI in n 1545390547.325 * [misc]backup-simplify: Simplify PI into PI 1545390547.325 * [misc]taylor: Taking taylor expansion of n in n 1545390547.325 * [misc]backup-simplify: Simplify 0 into 0 1545390547.325 * [misc]backup-simplify: Simplify 1 into 1 1545390547.325 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390547.325 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545390547.326 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545390547.326 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1545390547.326 * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 1545390547.326 * [misc]backup-simplify: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k))) 1545390547.327 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545390547.327 * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 1545390547.328 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 1545390547.328 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n 1545390547.328 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1545390547.328 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1545390547.328 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n 1545390547.328 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390547.328 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390547.328 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n 1545390547.328 * [misc]taylor: Taking taylor expansion of 1 in n 1545390547.328 * [misc]backup-simplify: Simplify 1 into 1 1545390547.328 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545390547.328 * [misc]taylor: Taking taylor expansion of k in n 1545390547.328 * [misc]backup-simplify: Simplify k into k 1545390547.328 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545390547.328 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1545390547.328 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1545390547.328 * [misc]taylor: Taking taylor expansion of 2 in n 1545390547.329 * [misc]backup-simplify: Simplify 2 into 2 1545390547.329 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390547.329 * [misc]taylor: Taking taylor expansion of PI in n 1545390547.329 * [misc]backup-simplify: Simplify PI into PI 1545390547.329 * [misc]taylor: Taking taylor expansion of n in n 1545390547.329 * [misc]backup-simplify: Simplify 0 into 0 1545390547.329 * [misc]backup-simplify: Simplify 1 into 1 1545390547.329 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390547.329 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545390547.330 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545390547.330 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1545390547.330 * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 1545390547.330 * [misc]backup-simplify: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k))) 1545390547.330 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545390547.331 * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 1545390547.332 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 1545390547.332 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k 1545390547.332 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k 1545390547.332 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390547.332 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390547.332 * [misc]taylor: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k 1545390547.332 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k 1545390547.332 * [misc]taylor: Taking taylor expansion of 1 in k 1545390547.332 * [misc]backup-simplify: Simplify 1 into 1 1545390547.332 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545390547.332 * [misc]taylor: Taking taylor expansion of k in k 1545390547.332 * [misc]backup-simplify: Simplify 0 into 0 1545390547.332 * [misc]backup-simplify: Simplify 1 into 1 1545390547.332 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545390547.332 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1545390547.332 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1545390547.332 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1545390547.332 * [misc]taylor: Taking taylor expansion of 2 in k 1545390547.332 * [misc]backup-simplify: Simplify 2 into 2 1545390547.332 * [misc]taylor: Taking taylor expansion of PI in k 1545390547.332 * [misc]backup-simplify: Simplify PI into PI 1545390547.333 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545390547.333 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545390547.333 * [misc]taylor: Taking taylor expansion of (log n) in k 1545390547.333 * [misc]taylor: Taking taylor expansion of n in k 1545390547.333 * [misc]backup-simplify: Simplify n into n 1545390547.333 * [misc]backup-simplify: Simplify (log n) into (log n) 1545390547.333 * [misc]backup-simplify: Simplify (- 1) into -1 1545390547.334 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 1545390547.334 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1545390547.334 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1545390547.335 * [misc]backup-simplify: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n))) 1545390547.335 * [misc]backup-simplify: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1545390547.336 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 1545390547.336 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 1545390547.337 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1545390547.338 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1545390547.340 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1545390547.340 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1545390547.340 * [misc]backup-simplify: Simplify (- 0) into 0 1545390547.340 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390547.340 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- 1 (/ 1 k)))) into 0 1545390547.341 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545390547.341 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1545390547.342 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1545390547.342 * [misc]taylor: Taking taylor expansion of 0 in k 1545390547.342 * [misc]backup-simplify: Simplify 0 into 0 1545390547.342 * [misc]backup-simplify: Simplify 0 into 0 1545390547.342 * [misc]backup-simplify: Simplify 0 into 0 1545390547.343 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390547.344 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1545390547.347 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1545390547.347 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545390547.347 * [misc]backup-simplify: Simplify (- 0) into 0 1545390547.347 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390547.347 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0 1545390547.348 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545390547.348 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1545390547.349 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1545390547.349 * [misc]taylor: Taking taylor expansion of 0 in k 1545390547.349 * [misc]backup-simplify: Simplify 0 into 0 1545390547.350 * [misc]backup-simplify: Simplify 0 into 0 1545390547.350 * [misc]backup-simplify: Simplify 0 into 0 1545390547.350 * [misc]backup-simplify: Simplify 0 into 0 1545390547.351 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390547.351 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1545390547.356 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 1545390547.356 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545390547.356 * [misc]backup-simplify: Simplify (- 0) into 0 1545390547.356 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390547.356 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0 1545390547.357 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545390547.357 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1545390547.359 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1545390547.360 * [misc]taylor: Taking taylor expansion of 0 in k 1545390547.360 * [misc]backup-simplify: Simplify 0 into 0 1545390547.360 * [misc]backup-simplify: Simplify 0 into 0 1545390547.360 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) 1545390547.360 * [misc]backup-simplify: Simplify (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) into (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) 1545390547.360 * [misc]approximate: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in (n k) around 0 1545390547.360 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k 1545390547.360 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k 1545390547.361 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k 1545390547.361 * [misc]taylor: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k 1545390547.361 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390547.361 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390547.361 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in k 1545390547.361 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545390547.361 * [misc]taylor: Taking taylor expansion of k in k 1545390547.361 * [misc]backup-simplify: Simplify 0 into 0 1545390547.361 * [misc]backup-simplify: Simplify 1 into 1 1545390547.361 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545390547.361 * [misc]taylor: Taking taylor expansion of 1 in k 1545390547.361 * [misc]backup-simplify: Simplify 1 into 1 1545390547.361 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1545390547.361 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1545390547.361 * [misc]taylor: Taking taylor expansion of -2 in k 1545390547.361 * [misc]backup-simplify: Simplify -2 into -2 1545390547.361 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1545390547.361 * [misc]taylor: Taking taylor expansion of PI in k 1545390547.361 * [misc]backup-simplify: Simplify PI into PI 1545390547.361 * [misc]taylor: Taking taylor expansion of n in k 1545390547.361 * [misc]backup-simplify: Simplify n into n 1545390547.361 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1545390547.361 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1545390547.361 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1545390547.361 * [misc]backup-simplify: Simplify (+ 1 0) into 1 1545390547.361 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545390547.361 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1545390547.361 * [misc]backup-simplify: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) 1545390547.361 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n 1545390547.361 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n 1545390547.361 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n 1545390547.362 * [misc]taylor: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n 1545390547.362 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390547.362 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390547.362 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in n 1545390547.362 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545390547.362 * [misc]taylor: Taking taylor expansion of k in n 1545390547.362 * [misc]backup-simplify: Simplify k into k 1545390547.362 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545390547.362 * [misc]taylor: Taking taylor expansion of 1 in n 1545390547.362 * [misc]backup-simplify: Simplify 1 into 1 1545390547.362 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1545390547.362 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1545390547.362 * [misc]taylor: Taking taylor expansion of -2 in n 1545390547.362 * [misc]backup-simplify: Simplify -2 into -2 1545390547.362 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390547.362 * [misc]taylor: Taking taylor expansion of PI in n 1545390547.362 * [misc]backup-simplify: Simplify PI into PI 1545390547.362 * [misc]taylor: Taking taylor expansion of n in n 1545390547.362 * [misc]backup-simplify: Simplify 0 into 0 1545390547.362 * [misc]backup-simplify: Simplify 1 into 1 1545390547.362 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390547.362 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1545390547.362 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1545390547.362 * [misc]backup-simplify: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 1545390547.363 * [misc]backup-simplify: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1)) 1545390547.363 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545390547.365 * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 1545390547.366 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 1545390547.366 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n 1545390547.366 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n 1545390547.366 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n 1545390547.366 * [misc]taylor: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n 1545390547.366 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390547.366 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390547.366 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in n 1545390547.366 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545390547.366 * [misc]taylor: Taking taylor expansion of k in n 1545390547.366 * [misc]backup-simplify: Simplify k into k 1545390547.366 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545390547.366 * [misc]taylor: Taking taylor expansion of 1 in n 1545390547.366 * [misc]backup-simplify: Simplify 1 into 1 1545390547.366 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1545390547.366 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1545390547.366 * [misc]taylor: Taking taylor expansion of -2 in n 1545390547.366 * [misc]backup-simplify: Simplify -2 into -2 1545390547.366 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390547.366 * [misc]taylor: Taking taylor expansion of PI in n 1545390547.366 * [misc]backup-simplify: Simplify PI into PI 1545390547.366 * [misc]taylor: Taking taylor expansion of n in n 1545390547.366 * [misc]backup-simplify: Simplify 0 into 0 1545390547.366 * [misc]backup-simplify: Simplify 1 into 1 1545390547.367 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390547.367 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1545390547.367 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1545390547.368 * [misc]backup-simplify: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 1545390547.368 * [misc]backup-simplify: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1)) 1545390547.368 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545390547.369 * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 1545390547.369 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 1545390547.370 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k 1545390547.370 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) in k 1545390547.370 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390547.370 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390547.370 * [misc]taylor: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) in k 1545390547.370 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in k 1545390547.370 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545390547.370 * [misc]taylor: Taking taylor expansion of k in k 1545390547.370 * [misc]backup-simplify: Simplify 0 into 0 1545390547.370 * [misc]backup-simplify: Simplify 1 into 1 1545390547.370 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545390547.370 * [misc]taylor: Taking taylor expansion of 1 in k 1545390547.370 * [misc]backup-simplify: Simplify 1 into 1 1545390547.370 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1545390547.370 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1545390547.370 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1545390547.370 * [misc]taylor: Taking taylor expansion of -2 in k 1545390547.370 * [misc]backup-simplify: Simplify -2 into -2 1545390547.370 * [misc]taylor: Taking taylor expansion of PI in k 1545390547.370 * [misc]backup-simplify: Simplify PI into PI 1545390547.371 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1545390547.371 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1545390547.371 * [misc]taylor: Taking taylor expansion of (log n) in k 1545390547.371 * [misc]taylor: Taking taylor expansion of n in k 1545390547.371 * [misc]backup-simplify: Simplify n into n 1545390547.371 * [misc]backup-simplify: Simplify (log n) into (log n) 1545390547.371 * [misc]backup-simplify: Simplify (+ 1 0) into 1 1545390547.371 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1545390547.372 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1545390547.373 * [misc]backup-simplify: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n)) 1545390547.373 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1545390547.374 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 1545390547.374 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 1545390547.376 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1545390547.376 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1545390547.379 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1545390547.379 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1545390547.379 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390547.379 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (+ (/ 1 k) 1))) into 0 1545390547.380 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545390547.380 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1545390547.382 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1545390547.382 * [misc]taylor: Taking taylor expansion of 0 in k 1545390547.382 * [misc]backup-simplify: Simplify 0 into 0 1545390547.382 * [misc]backup-simplify: Simplify 0 into 0 1545390547.382 * [misc]backup-simplify: Simplify 0 into 0 1545390547.383 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390547.384 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1545390547.389 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 1545390547.389 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545390547.390 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390547.390 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0 1545390547.391 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545390547.391 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1545390547.394 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1545390547.394 * [misc]taylor: Taking taylor expansion of 0 in k 1545390547.394 * [misc]backup-simplify: Simplify 0 into 0 1545390547.394 * [misc]backup-simplify: Simplify 0 into 0 1545390547.394 * [misc]backup-simplify: Simplify 0 into 0 1545390547.394 * [misc]backup-simplify: Simplify 0 into 0 1545390547.396 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390547.397 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1545390547.401 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0 1545390547.401 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545390547.401 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390547.401 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1))))) into 0 1545390547.402 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545390547.402 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 1545390547.405 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1545390547.405 * [misc]taylor: Taking taylor expansion of 0 in k 1545390547.405 * [misc]backup-simplify: Simplify 0 into 0 1545390547.405 * [misc]backup-simplify: Simplify 0 into 0 1545390547.405 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) 1545390547.405 * * * * [misc]progress: [ 2 / 4 ] generating series at (2 2 1) 1545390547.405 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1545390547.405 * [misc]approximate: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1545390547.406 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1545390547.406 * [misc]taylor: Taking taylor expansion of 2 in n 1545390547.406 * [misc]backup-simplify: Simplify 2 into 2 1545390547.406 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545390547.406 * [misc]taylor: Taking taylor expansion of n in n 1545390547.406 * [misc]backup-simplify: Simplify 0 into 0 1545390547.406 * [misc]backup-simplify: Simplify 1 into 1 1545390547.406 * [misc]taylor: Taking taylor expansion of PI in n 1545390547.406 * [misc]backup-simplify: Simplify PI into PI 1545390547.406 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1545390547.406 * [misc]taylor: Taking taylor expansion of 2 in n 1545390547.406 * [misc]backup-simplify: Simplify 2 into 2 1545390547.406 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545390547.406 * [misc]taylor: Taking taylor expansion of n in n 1545390547.406 * [misc]backup-simplify: Simplify 0 into 0 1545390547.406 * [misc]backup-simplify: Simplify 1 into 1 1545390547.406 * [misc]taylor: Taking taylor expansion of PI in n 1545390547.406 * [misc]backup-simplify: Simplify PI into PI 1545390547.406 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1545390547.406 * [misc]backup-simplify: Simplify (* 2 0) into 0 1545390547.406 * [misc]backup-simplify: Simplify 0 into 0 1545390547.406 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1545390547.407 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1545390547.407 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545390547.408 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1545390547.408 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1545390547.408 * [misc]backup-simplify: Simplify 0 into 0 1545390547.409 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1545390547.410 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1545390547.410 * [misc]backup-simplify: Simplify 0 into 0 1545390547.411 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1545390547.412 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1545390547.412 * [misc]backup-simplify: Simplify 0 into 0 1545390547.414 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1545390547.415 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1545390547.415 * [misc]backup-simplify: Simplify 0 into 0 1545390547.417 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1545390547.419 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1545390547.419 * [misc]backup-simplify: Simplify 0 into 0 1545390547.421 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1545390547.423 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1545390547.423 * [misc]backup-simplify: Simplify 0 into 0 1545390547.424 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1545390547.424 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 n)) into (* 2 (/ PI n)) 1545390547.424 * [misc]approximate: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1545390547.424 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1545390547.424 * [misc]taylor: Taking taylor expansion of 2 in n 1545390547.424 * [misc]backup-simplify: Simplify 2 into 2 1545390547.424 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390547.424 * [misc]taylor: Taking taylor expansion of PI in n 1545390547.424 * [misc]backup-simplify: Simplify PI into PI 1545390547.424 * [misc]taylor: Taking taylor expansion of n in n 1545390547.424 * [misc]backup-simplify: Simplify 0 into 0 1545390547.424 * [misc]backup-simplify: Simplify 1 into 1 1545390547.424 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390547.424 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1545390547.424 * [misc]taylor: Taking taylor expansion of 2 in n 1545390547.424 * [misc]backup-simplify: Simplify 2 into 2 1545390547.424 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390547.424 * [misc]taylor: Taking taylor expansion of PI in n 1545390547.424 * [misc]backup-simplify: Simplify PI into PI 1545390547.424 * [misc]taylor: Taking taylor expansion of n in n 1545390547.424 * [misc]backup-simplify: Simplify 0 into 0 1545390547.424 * [misc]backup-simplify: Simplify 1 into 1 1545390547.424 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390547.425 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545390547.425 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545390547.425 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1545390547.426 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1545390547.426 * [misc]backup-simplify: Simplify 0 into 0 1545390547.427 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390547.427 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1545390547.427 * [misc]backup-simplify: Simplify 0 into 0 1545390547.428 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390547.429 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1545390547.429 * [misc]backup-simplify: Simplify 0 into 0 1545390547.430 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390547.431 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1545390547.431 * [misc]backup-simplify: Simplify 0 into 0 1545390547.432 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390547.434 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1545390547.434 * [misc]backup-simplify: Simplify 0 into 0 1545390547.435 * [misc]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 1545390547.437 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1545390547.437 * [misc]backup-simplify: Simplify 0 into 0 1545390547.437 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 1545390547.438 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (- n))) into (* -2 (/ PI n)) 1545390547.438 * [misc]approximate: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1545390547.438 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1545390547.438 * [misc]taylor: Taking taylor expansion of -2 in n 1545390547.438 * [misc]backup-simplify: Simplify -2 into -2 1545390547.438 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390547.438 * [misc]taylor: Taking taylor expansion of PI in n 1545390547.438 * [misc]backup-simplify: Simplify PI into PI 1545390547.438 * [misc]taylor: Taking taylor expansion of n in n 1545390547.438 * [misc]backup-simplify: Simplify 0 into 0 1545390547.438 * [misc]backup-simplify: Simplify 1 into 1 1545390547.438 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390547.438 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1545390547.438 * [misc]taylor: Taking taylor expansion of -2 in n 1545390547.438 * [misc]backup-simplify: Simplify -2 into -2 1545390547.438 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390547.438 * [misc]taylor: Taking taylor expansion of PI in n 1545390547.438 * [misc]backup-simplify: Simplify PI into PI 1545390547.438 * [misc]taylor: Taking taylor expansion of n in n 1545390547.438 * [misc]backup-simplify: Simplify 0 into 0 1545390547.438 * [misc]backup-simplify: Simplify 1 into 1 1545390547.438 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390547.438 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1545390547.438 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1545390547.439 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1545390547.440 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1545390547.440 * [misc]backup-simplify: Simplify 0 into 0 1545390547.440 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390547.441 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1545390547.441 * [misc]backup-simplify: Simplify 0 into 0 1545390547.442 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390547.443 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1545390547.443 * [misc]backup-simplify: Simplify 0 into 0 1545390547.444 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390547.445 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1545390547.445 * [misc]backup-simplify: Simplify 0 into 0 1545390547.446 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390547.448 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1545390547.448 * [misc]backup-simplify: Simplify 0 into 0 1545390547.449 * [misc]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 1545390547.451 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1545390547.451 * [misc]backup-simplify: Simplify 0 into 0 1545390547.451 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 1545390547.451 * * * * [misc]progress: [ 3 / 4 ] generating series at (2 1) 1545390547.451 * [misc]backup-simplify: Simplify (/ 1 (sqrt k)) into (sqrt (/ 1 k)) 1545390547.451 * [misc]approximate: Taking taylor expansion of (sqrt (/ 1 k)) in (k) around 0 1545390547.452 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1545390547.452 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545390547.452 * [misc]taylor: Taking taylor expansion of k in k 1545390547.452 * [misc]backup-simplify: Simplify 0 into 0 1545390547.452 * [misc]backup-simplify: Simplify 1 into 1 1545390547.452 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545390547.452 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545390547.452 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1545390547.452 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1545390547.452 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545390547.452 * [misc]taylor: Taking taylor expansion of k in k 1545390547.452 * [misc]backup-simplify: Simplify 0 into 0 1545390547.452 * [misc]backup-simplify: Simplify 1 into 1 1545390547.452 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545390547.452 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545390547.453 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1545390547.453 * [misc]backup-simplify: Simplify 0 into 0 1545390547.453 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545390547.453 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1545390547.454 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1545390547.454 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545390547.454 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390547.455 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1545390547.455 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545390547.455 * [misc]backup-simplify: Simplify (+ (* +nan.0 (pow k 2)) (+ (* +nan.0 k) +nan.0)) into (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) 1545390547.455 * [misc]backup-simplify: Simplify (/ 1 (sqrt (/ 1 k))) into (sqrt k) 1545390547.455 * [misc]approximate: Taking taylor expansion of (sqrt k) in (k) around 0 1545390547.455 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1545390547.455 * [misc]taylor: Taking taylor expansion of k in k 1545390547.455 * [misc]backup-simplify: Simplify 0 into 0 1545390547.455 * [misc]backup-simplify: Simplify 1 into 1 1545390547.455 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545390547.455 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1545390547.455 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1545390547.455 * [misc]taylor: Taking taylor expansion of k in k 1545390547.455 * [misc]backup-simplify: Simplify 0 into 0 1545390547.455 * [misc]backup-simplify: Simplify 1 into 1 1545390547.456 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545390547.456 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1545390547.456 * [misc]backup-simplify: Simplify 0 into 0 1545390547.456 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545390547.457 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1545390547.457 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545390547.459 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1545390547.459 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545390547.459 * [misc]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)))))))) 1545390547.459 * [misc]backup-simplify: Simplify (/ 1 (sqrt (/ 1 (- k)))) into (/ 1 (sqrt (/ -1 k))) 1545390547.459 * [misc]approximate: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in (k) around 0 1545390547.459 * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 1545390547.459 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1545390547.459 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1545390547.459 * [misc]taylor: Taking taylor expansion of -1 in k 1545390547.459 * [misc]backup-simplify: Simplify -1 into -1 1545390547.459 * [misc]taylor: Taking taylor expansion of k in k 1545390547.459 * [misc]backup-simplify: Simplify 0 into 0 1545390547.459 * [misc]backup-simplify: Simplify 1 into 1 1545390547.460 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1545390547.460 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545390547.460 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1545390547.460 * [misc]backup-simplify: Simplify (/ 1 +nan.0) into +nan.0 1545390547.460 * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 1545390547.460 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1545390547.460 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1545390547.460 * [misc]taylor: Taking taylor expansion of -1 in k 1545390547.460 * [misc]backup-simplify: Simplify -1 into -1 1545390547.461 * [misc]taylor: Taking taylor expansion of k in k 1545390547.461 * [misc]backup-simplify: Simplify 0 into 0 1545390547.461 * [misc]backup-simplify: Simplify 1 into 1 1545390547.461 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1545390547.461 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545390547.461 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1545390547.461 * [misc]backup-simplify: Simplify (/ 1 +nan.0) into +nan.0 1545390547.462 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545390547.462 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1545390547.463 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1545390547.464 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 1545390547.464 * [misc]backup-simplify: Simplify (- +nan.0) into (- +nan.0) 1545390547.464 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390547.465 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1545390547.467 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 1545390547.467 * [misc]backup-simplify: Simplify (- +nan.0) into (- +nan.0) 1545390547.467 * [misc]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))))) 1545390547.467 * * * * [misc]progress: [ 4 / 4 ] generating series at (2) 1545390547.468 * [misc]backup-simplify: Simplify (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) into (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) 1545390547.468 * [misc]approximate: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in (k n) around 0 1545390547.468 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in n 1545390547.468 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n 1545390547.468 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n 1545390547.468 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n 1545390547.468 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 k)) in n 1545390547.468 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390547.468 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390547.468 * [misc]taylor: Taking taylor expansion of (- 1 k) in n 1545390547.468 * [misc]taylor: Taking taylor expansion of 1 in n 1545390547.468 * [misc]backup-simplify: Simplify 1 into 1 1545390547.469 * [misc]taylor: Taking taylor expansion of k in n 1545390547.469 * [misc]backup-simplify: Simplify k into k 1545390547.469 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1545390547.469 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1545390547.469 * [misc]taylor: Taking taylor expansion of 2 in n 1545390547.469 * [misc]backup-simplify: Simplify 2 into 2 1545390547.469 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545390547.469 * [misc]taylor: Taking taylor expansion of n in n 1545390547.469 * [misc]backup-simplify: Simplify 0 into 0 1545390547.469 * [misc]backup-simplify: Simplify 1 into 1 1545390547.469 * [misc]taylor: Taking taylor expansion of PI in n 1545390547.469 * [misc]backup-simplify: Simplify PI into PI 1545390547.469 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1545390547.469 * [misc]backup-simplify: Simplify (* 2 0) into 0 1545390547.470 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1545390547.470 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1545390547.471 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545390547.471 * [misc]backup-simplify: Simplify (- k) into (- k) 1545390547.471 * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) 1545390547.471 * [misc]backup-simplify: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k)) 1545390547.472 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545390547.472 * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) 1545390547.473 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 1545390547.473 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1545390547.473 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545390547.473 * [misc]taylor: Taking taylor expansion of k in n 1545390547.473 * [misc]backup-simplify: Simplify k into k 1545390547.473 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545390547.473 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1545390547.473 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1545390547.473 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1545390547.473 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k 1545390547.473 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k 1545390547.474 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k 1545390547.474 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k 1545390547.474 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 k)) in k 1545390547.474 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390547.474 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390547.474 * [misc]taylor: Taking taylor expansion of (- 1 k) in k 1545390547.474 * [misc]taylor: Taking taylor expansion of 1 in k 1545390547.474 * [misc]backup-simplify: Simplify 1 into 1 1545390547.474 * [misc]taylor: Taking taylor expansion of k in k 1545390547.474 * [misc]backup-simplify: Simplify 0 into 0 1545390547.474 * [misc]backup-simplify: Simplify 1 into 1 1545390547.474 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1545390547.474 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1545390547.474 * [misc]taylor: Taking taylor expansion of 2 in k 1545390547.474 * [misc]backup-simplify: Simplify 2 into 2 1545390547.474 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1545390547.474 * [misc]taylor: Taking taylor expansion of n in k 1545390547.474 * [misc]backup-simplify: Simplify n into n 1545390547.474 * [misc]taylor: Taking taylor expansion of PI in k 1545390547.474 * [misc]backup-simplify: Simplify PI into PI 1545390547.474 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1545390547.474 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1545390547.474 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1545390547.474 * [misc]backup-simplify: Simplify (- 0) into 0 1545390547.475 * [misc]backup-simplify: Simplify (+ 1 0) into 1 1545390547.476 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545390547.476 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1545390547.476 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1545390547.476 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1545390547.476 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545390547.476 * [misc]taylor: Taking taylor expansion of k in k 1545390547.476 * [misc]backup-simplify: Simplify 0 into 0 1545390547.476 * [misc]backup-simplify: Simplify 1 into 1 1545390547.476 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545390547.476 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545390547.477 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1545390547.477 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k 1545390547.477 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k 1545390547.477 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k 1545390547.477 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k 1545390547.477 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 k)) in k 1545390547.477 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390547.477 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390547.477 * [misc]taylor: Taking taylor expansion of (- 1 k) in k 1545390547.477 * [misc]taylor: Taking taylor expansion of 1 in k 1545390547.477 * [misc]backup-simplify: Simplify 1 into 1 1545390547.477 * [misc]taylor: Taking taylor expansion of k in k 1545390547.477 * [misc]backup-simplify: Simplify 0 into 0 1545390547.477 * [misc]backup-simplify: Simplify 1 into 1 1545390547.477 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1545390547.477 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1545390547.477 * [misc]taylor: Taking taylor expansion of 2 in k 1545390547.477 * [misc]backup-simplify: Simplify 2 into 2 1545390547.477 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1545390547.477 * [misc]taylor: Taking taylor expansion of n in k 1545390547.477 * [misc]backup-simplify: Simplify n into n 1545390547.477 * [misc]taylor: Taking taylor expansion of PI in k 1545390547.477 * [misc]backup-simplify: Simplify PI into PI 1545390547.477 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1545390547.478 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1545390547.478 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1545390547.478 * [misc]backup-simplify: Simplify (- 0) into 0 1545390547.478 * [misc]backup-simplify: Simplify (+ 1 0) into 1 1545390547.478 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545390547.478 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1545390547.478 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1545390547.478 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1545390547.478 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545390547.478 * [misc]taylor: Taking taylor expansion of k in k 1545390547.478 * [misc]backup-simplify: Simplify 0 into 0 1545390547.479 * [misc]backup-simplify: Simplify 1 into 1 1545390547.479 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545390547.479 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545390547.479 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1545390547.480 * [misc]backup-simplify: Simplify (* (pow (* 2 (* n PI)) 1/2) 0) into 0 1545390547.480 * [misc]taylor: Taking taylor expansion of 0 in n 1545390547.480 * [misc]backup-simplify: Simplify 0 into 0 1545390547.480 * [misc]backup-simplify: Simplify 0 into 0 1545390547.480 * [misc]backup-simplify: Simplify (+ (* n 0) (* 0 PI)) into 0 1545390547.480 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0 1545390547.481 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 1545390547.481 * [misc]backup-simplify: Simplify (- 1) into -1 1545390547.481 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 1545390547.481 * [misc]backup-simplify: Simplify (+ (* 1/2 -1) (* 0 1)) into -1/2 1545390547.482 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI))))) 1545390547.482 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1)))) into (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) 1545390547.483 * [misc]backup-simplify: Simplify (+ (* (pow (* 2 (* n PI)) 1/2) +nan.0) (* (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) 0)) into (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) 1545390547.483 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 1545390547.483 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 1545390547.483 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1545390547.483 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545390547.483 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1545390547.483 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1545390547.483 * [misc]taylor: Taking taylor expansion of 2 in n 1545390547.483 * [misc]backup-simplify: Simplify 2 into 2 1545390547.483 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1545390547.483 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1545390547.483 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1545390547.483 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545390547.483 * [misc]taylor: Taking taylor expansion of n in n 1545390547.483 * [misc]backup-simplify: Simplify 0 into 0 1545390547.483 * [misc]backup-simplify: Simplify 1 into 1 1545390547.483 * [misc]taylor: Taking taylor expansion of PI in n 1545390547.483 * [misc]backup-simplify: Simplify PI into PI 1545390547.484 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1545390547.484 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1545390547.484 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545390547.485 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1545390547.485 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1545390547.485 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1545390547.485 * [misc]backup-simplify: Simplify (- 0) into 0 1545390547.485 * [misc]backup-simplify: Simplify 0 into 0 1545390547.485 * [misc]backup-simplify: Simplify 0 into 0 1545390547.486 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1545390547.487 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1545390547.487 * [misc]backup-simplify: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 1545390547.488 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 1545390547.489 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 1)))) 2) into 0 1545390547.489 * [misc]backup-simplify: Simplify (- 0) into 0 1545390547.489 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390547.489 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 -1) (* 0 1))) into 0 1545390547.489 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0 1545390547.490 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) 1545390547.490 * [misc]backup-simplify: Simplify (+ (* (pow (* 2 (* n PI)) 1/2) +nan.0) (+ (* (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) +nan.0) (* (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) 0))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) 1545390547.490 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) in n 1545390547.490 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))) in n 1545390547.490 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n 1545390547.490 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1545390547.490 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545390547.490 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n 1545390547.490 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n 1545390547.490 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1545390547.490 * [misc]taylor: Taking taylor expansion of 2 in n 1545390547.490 * [misc]backup-simplify: Simplify 2 into 2 1545390547.490 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1545390547.491 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1545390547.491 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1545390547.491 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1545390547.491 * [misc]taylor: Taking taylor expansion of 2 in n 1545390547.491 * [misc]backup-simplify: Simplify 2 into 2 1545390547.491 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545390547.491 * [misc]taylor: Taking taylor expansion of n in n 1545390547.491 * [misc]backup-simplify: Simplify 0 into 0 1545390547.491 * [misc]backup-simplify: Simplify 1 into 1 1545390547.491 * [misc]taylor: Taking taylor expansion of PI in n 1545390547.491 * [misc]backup-simplify: Simplify PI into PI 1545390547.491 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1545390547.491 * [misc]backup-simplify: Simplify (* 2 0) into 0 1545390547.491 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1545390547.492 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1545390547.492 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545390547.492 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1545390547.492 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545390547.492 * [misc]taylor: Taking taylor expansion of n in n 1545390547.492 * [misc]backup-simplify: Simplify 0 into 0 1545390547.492 * [misc]backup-simplify: Simplify 1 into 1 1545390547.492 * [misc]taylor: Taking taylor expansion of PI in n 1545390547.492 * [misc]backup-simplify: Simplify PI into PI 1545390547.492 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1545390547.493 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1545390547.493 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545390547.493 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1545390547.493 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 1545390547.493 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 1545390547.493 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1545390547.493 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545390547.493 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1545390547.493 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1545390547.493 * [misc]taylor: Taking taylor expansion of 2 in n 1545390547.493 * [misc]backup-simplify: Simplify 2 into 2 1545390547.493 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1545390547.493 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1545390547.494 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1545390547.494 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545390547.494 * [misc]taylor: Taking taylor expansion of n in n 1545390547.494 * [misc]backup-simplify: Simplify 0 into 0 1545390547.494 * [misc]backup-simplify: Simplify 1 into 1 1545390547.494 * [misc]taylor: Taking taylor expansion of PI in n 1545390547.494 * [misc]backup-simplify: Simplify PI into PI 1545390547.494 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1545390547.494 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1545390547.494 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545390547.494 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1545390547.495 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545390547.495 * [misc]backup-simplify: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 1545390547.496 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0 1545390547.496 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1545390547.496 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1545390547.496 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1545390547.496 * [misc]backup-simplify: Simplify (- 0) into 0 1545390547.497 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390547.497 * [misc]backup-simplify: Simplify (- 0) into 0 1545390547.497 * [misc]backup-simplify: Simplify 0 into 0 1545390547.497 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1545390547.499 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1545390547.499 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 1545390547.500 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI))) 1545390547.500 * [misc]backup-simplify: Simplify 0 into 0 1545390547.500 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390547.501 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1545390547.501 * [misc]backup-simplify: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1545390547.502 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 1545390547.503 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 (* n PI)) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 (* n PI)) 1)))) 6) into 0 1545390547.503 * [misc]backup-simplify: Simplify (- 0) into 0 1545390547.504 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390547.504 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1)))) into 0 1545390547.504 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log (* 2 (* n PI))))))) into 0 1545390547.505 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 3) 6)) (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 3))) 1545390547.506 * [misc]backup-simplify: Simplify (+ (* (pow (* 2 (* n PI)) 1/2) +nan.0) (+ (* (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) +nan.0) (+ (* (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) +nan.0) (* (* -1/48 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 3))) 0)))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))))))) 1545390547.506 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))))))) in n 1545390547.506 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))))))) in n 1545390547.506 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n 1545390547.506 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1545390547.506 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545390547.506 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n 1545390547.506 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n 1545390547.506 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1545390547.506 * [misc]taylor: Taking taylor expansion of 2 in n 1545390547.506 * [misc]backup-simplify: Simplify 2 into 2 1545390547.506 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1545390547.506 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1545390547.506 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1545390547.506 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1545390547.506 * [misc]taylor: Taking taylor expansion of 2 in n 1545390547.506 * [misc]backup-simplify: Simplify 2 into 2 1545390547.506 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545390547.506 * [misc]taylor: Taking taylor expansion of n in n 1545390547.506 * [misc]backup-simplify: Simplify 0 into 0 1545390547.506 * [misc]backup-simplify: Simplify 1 into 1 1545390547.506 * [misc]taylor: Taking taylor expansion of PI in n 1545390547.506 * [misc]backup-simplify: Simplify PI into PI 1545390547.507 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1545390547.507 * [misc]backup-simplify: Simplify (* 2 0) into 0 1545390547.507 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1545390547.507 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1545390547.508 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545390547.508 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1545390547.508 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545390547.508 * [misc]taylor: Taking taylor expansion of n in n 1545390547.508 * [misc]backup-simplify: Simplify 0 into 0 1545390547.508 * [misc]backup-simplify: Simplify 1 into 1 1545390547.508 * [misc]taylor: Taking taylor expansion of PI in n 1545390547.508 * [misc]backup-simplify: Simplify PI into PI 1545390547.508 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1545390547.508 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1545390547.508 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545390547.509 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1545390547.509 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))))) in n 1545390547.509 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))))) in n 1545390547.509 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 1545390547.509 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1545390547.509 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545390547.509 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1545390547.509 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1545390547.509 * [misc]taylor: Taking taylor expansion of 2 in n 1545390547.509 * [misc]backup-simplify: Simplify 2 into 2 1545390547.509 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1545390547.509 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1545390547.509 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1545390547.509 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545390547.509 * [misc]taylor: Taking taylor expansion of n in n 1545390547.509 * [misc]backup-simplify: Simplify 0 into 0 1545390547.509 * [misc]backup-simplify: Simplify 1 into 1 1545390547.509 * [misc]taylor: Taking taylor expansion of PI in n 1545390547.509 * [misc]backup-simplify: Simplify PI into PI 1545390547.509 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1545390547.510 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1545390547.510 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545390547.510 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1545390547.510 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))) in n 1545390547.510 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) in n 1545390547.510 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1545390547.510 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545390547.510 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))) in n 1545390547.510 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) in n 1545390547.510 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1545390547.510 * [misc]taylor: Taking taylor expansion of 2 in n 1545390547.510 * [misc]backup-simplify: Simplify 2 into 2 1545390547.510 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1545390547.511 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1545390547.511 * [misc]taylor: Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n 1545390547.511 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1545390547.511 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1545390547.511 * [misc]taylor: Taking taylor expansion of 2 in n 1545390547.511 * [misc]backup-simplify: Simplify 2 into 2 1545390547.511 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545390547.511 * [misc]taylor: Taking taylor expansion of n in n 1545390547.511 * [misc]backup-simplify: Simplify 0 into 0 1545390547.511 * [misc]backup-simplify: Simplify 1 into 1 1545390547.511 * [misc]taylor: Taking taylor expansion of PI in n 1545390547.511 * [misc]backup-simplify: Simplify PI into PI 1545390547.511 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1545390547.511 * [misc]backup-simplify: Simplify (* 2 0) into 0 1545390547.511 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1545390547.512 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1545390547.512 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545390547.512 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545390547.512 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1545390547.512 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545390547.512 * [misc]taylor: Taking taylor expansion of n in n 1545390547.512 * [misc]backup-simplify: Simplify 0 into 0 1545390547.513 * [misc]backup-simplify: Simplify 1 into 1 1545390547.513 * [misc]taylor: Taking taylor expansion of PI in n 1545390547.513 * [misc]backup-simplify: Simplify PI into PI 1545390547.513 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1545390547.513 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1545390547.513 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545390547.513 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1545390547.514 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545390547.514 * [misc]backup-simplify: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 1545390547.515 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0 1545390547.515 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1545390547.515 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1545390547.515 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1545390547.515 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545390547.516 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545390547.517 * [misc]backup-simplify: Simplify (* (+ (log n) (log (* 2 PI))) (+ (log n) (log (* 2 PI)))) into (pow (+ (log n) (log (* 2 PI))) 2) 1545390547.517 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) into (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 1545390547.517 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 0) into 0 1545390547.518 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1545390547.518 * [misc]backup-simplify: Simplify (- 0) into 0 1545390547.518 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390547.518 * [misc]backup-simplify: Simplify (- 0) into 0 1545390547.518 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390547.518 * [misc]backup-simplify: Simplify (- 0) into 0 1545390547.518 * [misc]backup-simplify: Simplify 0 into 0 1545390547.519 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1545390547.519 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1545390547.521 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1545390547.521 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545390547.522 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1545390547.522 * [misc]backup-simplify: Simplify (+ (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) (* +nan.0 PI)) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) 1545390547.524 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) 1545390547.525 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1545390547.526 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1545390547.526 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 1545390547.528 * [misc]backup-simplify: Simplify (+ (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) (- (* +nan.0 (* (sqrt 2) PI)))) into (- (+ (* +nan.0 (* (sqrt 2) PI)) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))))) 1545390547.530 * [misc]backup-simplify: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) PI)) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) 1545390547.532 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) 1545390547.533 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1545390547.534 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 1545390547.534 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1545390547.536 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 (pow PI 2))) (+ (* 0 (* +nan.0 PI)) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 1545390547.538 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) (+ (* 0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 1545390547.539 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 1545390547.540 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 1545390547.547 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) (pow (* n 1) 2)) (+ (* (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) (* n k)) (* (- (* +nan.0 (* (sqrt 2) PI))) (* n 1)))) into (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))))))) 1545390547.547 * [misc]backup-simplify: Simplify (* (/ 1 (sqrt (/ 1 k))) (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2))) into (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) 1545390547.547 * [misc]approximate: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in (k n) around 0 1545390547.547 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in n 1545390547.547 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n 1545390547.547 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1545390547.548 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1545390547.548 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n 1545390547.548 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390547.548 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390547.548 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n 1545390547.548 * [misc]taylor: Taking taylor expansion of 1 in n 1545390547.548 * [misc]backup-simplify: Simplify 1 into 1 1545390547.548 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545390547.548 * [misc]taylor: Taking taylor expansion of k in n 1545390547.548 * [misc]backup-simplify: Simplify k into k 1545390547.548 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545390547.548 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1545390547.548 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1545390547.548 * [misc]taylor: Taking taylor expansion of 2 in n 1545390547.548 * [misc]backup-simplify: Simplify 2 into 2 1545390547.548 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390547.548 * [misc]taylor: Taking taylor expansion of PI in n 1545390547.548 * [misc]backup-simplify: Simplify PI into PI 1545390547.548 * [misc]taylor: Taking taylor expansion of n in n 1545390547.548 * [misc]backup-simplify: Simplify 0 into 0 1545390547.548 * [misc]backup-simplify: Simplify 1 into 1 1545390547.548 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390547.548 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545390547.549 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545390547.549 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1545390547.549 * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 1545390547.549 * [misc]backup-simplify: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k))) 1545390547.550 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545390547.550 * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 1545390547.551 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 1545390547.551 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1545390547.551 * [misc]taylor: Taking taylor expansion of k in n 1545390547.551 * [misc]backup-simplify: Simplify k into k 1545390547.551 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1545390547.551 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1545390547.551 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k 1545390547.551 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k 1545390547.551 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1545390547.551 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1545390547.551 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k 1545390547.551 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390547.551 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390547.551 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k 1545390547.552 * [misc]taylor: Taking taylor expansion of 1 in k 1545390547.552 * [misc]backup-simplify: Simplify 1 into 1 1545390547.552 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545390547.552 * [misc]taylor: Taking taylor expansion of k in k 1545390547.552 * [misc]backup-simplify: Simplify 0 into 0 1545390547.552 * [misc]backup-simplify: Simplify 1 into 1 1545390547.552 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545390547.552 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1545390547.552 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1545390547.552 * [misc]taylor: Taking taylor expansion of 2 in k 1545390547.552 * [misc]backup-simplify: Simplify 2 into 2 1545390547.552 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1545390547.552 * [misc]taylor: Taking taylor expansion of PI in k 1545390547.552 * [misc]backup-simplify: Simplify PI into PI 1545390547.552 * [misc]taylor: Taking taylor expansion of n in k 1545390547.552 * [misc]backup-simplify: Simplify n into n 1545390547.552 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1545390547.552 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1545390547.552 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1545390547.552 * [misc]backup-simplify: Simplify (- 1) into -1 1545390547.552 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 1545390547.553 * [misc]backup-simplify: Simplify (* 1/2 -1) into -1/2 1545390547.553 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1545390547.553 * [misc]backup-simplify: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 1545390547.553 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1545390547.553 * [misc]taylor: Taking taylor expansion of k in k 1545390547.553 * [misc]backup-simplify: Simplify 0 into 0 1545390547.553 * [misc]backup-simplify: Simplify 1 into 1 1545390547.553 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545390547.554 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1545390547.554 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k 1545390547.554 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k 1545390547.554 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1545390547.554 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1545390547.554 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k 1545390547.554 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390547.554 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390547.554 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k 1545390547.554 * [misc]taylor: Taking taylor expansion of 1 in k 1545390547.554 * [misc]backup-simplify: Simplify 1 into 1 1545390547.554 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545390547.554 * [misc]taylor: Taking taylor expansion of k in k 1545390547.554 * [misc]backup-simplify: Simplify 0 into 0 1545390547.554 * [misc]backup-simplify: Simplify 1 into 1 1545390547.554 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545390547.554 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1545390547.554 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1545390547.554 * [misc]taylor: Taking taylor expansion of 2 in k 1545390547.554 * [misc]backup-simplify: Simplify 2 into 2 1545390547.554 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1545390547.554 * [misc]taylor: Taking taylor expansion of PI in k 1545390547.554 * [misc]backup-simplify: Simplify PI into PI 1545390547.554 * [misc]taylor: Taking taylor expansion of n in k 1545390547.554 * [misc]backup-simplify: Simplify n into n 1545390547.554 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1545390547.554 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1545390547.555 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1545390547.555 * [misc]backup-simplify: Simplify (- 1) into -1 1545390547.555 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 1545390547.555 * [misc]backup-simplify: Simplify (* 1/2 -1) into -1/2 1545390547.555 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1545390547.555 * [misc]backup-simplify: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 1545390547.555 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1545390547.555 * [misc]taylor: Taking taylor expansion of k in k 1545390547.555 * [misc]backup-simplify: Simplify 0 into 0 1545390547.555 * [misc]backup-simplify: Simplify 1 into 1 1545390547.556 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545390547.556 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1545390547.556 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 0) into 0 1545390547.556 * [misc]taylor: Taking taylor expansion of 0 in n 1545390547.556 * [misc]backup-simplify: Simplify 0 into 0 1545390547.556 * [misc]backup-simplify: Simplify 0 into 0 1545390547.557 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) 1545390547.557 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n 1545390547.557 * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n 1545390547.557 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1545390547.557 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545390547.557 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n 1545390547.557 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n 1545390547.557 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390547.557 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390547.557 * [misc]taylor: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n 1545390547.557 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n 1545390547.557 * [misc]taylor: Taking taylor expansion of 1 in n 1545390547.557 * [misc]backup-simplify: Simplify 1 into 1 1545390547.557 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545390547.557 * [misc]taylor: Taking taylor expansion of k in n 1545390547.557 * [misc]backup-simplify: Simplify k into k 1545390547.557 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545390547.557 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1545390547.557 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1545390547.557 * [misc]taylor: Taking taylor expansion of 2 in n 1545390547.557 * [misc]backup-simplify: Simplify 2 into 2 1545390547.557 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390547.558 * [misc]taylor: Taking taylor expansion of PI in n 1545390547.558 * [misc]backup-simplify: Simplify PI into PI 1545390547.558 * [misc]taylor: Taking taylor expansion of n in n 1545390547.558 * [misc]backup-simplify: Simplify 0 into 0 1545390547.558 * [misc]backup-simplify: Simplify 1 into 1 1545390547.558 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390547.558 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545390547.559 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545390547.559 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1545390547.559 * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 1545390547.559 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545390547.560 * [misc]backup-simplify: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) 1545390547.561 * [misc]backup-simplify: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 1545390547.561 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 1545390547.562 * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) 1545390547.562 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 1545390547.563 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 1545390547.563 * [misc]backup-simplify: Simplify 0 into 0 1545390547.564 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1545390547.565 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) 1545390547.565 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n 1545390547.565 * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n 1545390547.565 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1545390547.565 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545390547.565 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n 1545390547.565 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n 1545390547.565 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390547.565 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390547.565 * [misc]taylor: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n 1545390547.565 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n 1545390547.565 * [misc]taylor: Taking taylor expansion of 1 in n 1545390547.565 * [misc]backup-simplify: Simplify 1 into 1 1545390547.565 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545390547.565 * [misc]taylor: Taking taylor expansion of k in n 1545390547.565 * [misc]backup-simplify: Simplify k into k 1545390547.565 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545390547.565 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1545390547.565 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1545390547.565 * [misc]taylor: Taking taylor expansion of 2 in n 1545390547.565 * [misc]backup-simplify: Simplify 2 into 2 1545390547.565 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390547.565 * [misc]taylor: Taking taylor expansion of PI in n 1545390547.565 * [misc]backup-simplify: Simplify PI into PI 1545390547.565 * [misc]taylor: Taking taylor expansion of n in n 1545390547.565 * [misc]backup-simplify: Simplify 0 into 0 1545390547.565 * [misc]backup-simplify: Simplify 1 into 1 1545390547.566 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390547.566 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545390547.566 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545390547.567 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1545390547.567 * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 1545390547.567 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545390547.568 * [misc]backup-simplify: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) 1545390547.568 * [misc]backup-simplify: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 1545390547.569 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 1545390547.570 * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) 1545390547.570 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 1545390547.571 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 1545390547.572 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1545390547.573 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1545390547.575 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1545390547.575 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1545390547.576 * [misc]backup-simplify: Simplify (- 0) into 0 1545390547.576 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390547.576 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545390547.577 * [misc]backup-simplify: Simplify (+ (* (- 1 (/ 1 k)) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1545390547.578 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into 0 1545390547.579 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1545390547.580 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into 0 1545390547.580 * [misc]backup-simplify: Simplify (- 0) into 0 1545390547.580 * [misc]backup-simplify: Simplify 0 into 0 1545390547.580 * [misc]backup-simplify: Simplify 0 into 0 1545390547.581 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1545390547.582 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) 1545390547.582 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n 1545390547.582 * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n 1545390547.582 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1545390547.582 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545390547.582 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n 1545390547.582 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n 1545390547.582 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390547.582 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390547.582 * [misc]taylor: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n 1545390547.582 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n 1545390547.582 * [misc]taylor: Taking taylor expansion of 1 in n 1545390547.582 * [misc]backup-simplify: Simplify 1 into 1 1545390547.582 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545390547.582 * [misc]taylor: Taking taylor expansion of k in n 1545390547.582 * [misc]backup-simplify: Simplify k into k 1545390547.582 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545390547.582 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1545390547.583 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1545390547.583 * [misc]taylor: Taking taylor expansion of 2 in n 1545390547.583 * [misc]backup-simplify: Simplify 2 into 2 1545390547.583 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390547.583 * [misc]taylor: Taking taylor expansion of PI in n 1545390547.583 * [misc]backup-simplify: Simplify PI into PI 1545390547.583 * [misc]taylor: Taking taylor expansion of n in n 1545390547.583 * [misc]backup-simplify: Simplify 0 into 0 1545390547.583 * [misc]backup-simplify: Simplify 1 into 1 1545390547.583 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390547.583 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545390547.584 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545390547.584 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1545390547.584 * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 1545390547.584 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545390547.585 * [misc]backup-simplify: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) 1545390547.586 * [misc]backup-simplify: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 1545390547.586 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 1545390547.587 * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) 1545390547.588 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 1545390547.588 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 1545390547.591 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3)))))))) 1545390547.591 * [misc]backup-simplify: Simplify (* (/ 1 (sqrt (/ 1 (- k)))) (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2))) into (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) 1545390547.591 * [misc]approximate: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in (k n) around 0 1545390547.591 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in n 1545390547.592 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n 1545390547.592 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n 1545390547.592 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n 1545390547.592 * [misc]taylor: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n 1545390547.592 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390547.592 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390547.592 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in n 1545390547.592 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545390547.592 * [misc]taylor: Taking taylor expansion of k in n 1545390547.592 * [misc]backup-simplify: Simplify k into k 1545390547.592 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545390547.592 * [misc]taylor: Taking taylor expansion of 1 in n 1545390547.592 * [misc]backup-simplify: Simplify 1 into 1 1545390547.592 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1545390547.592 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1545390547.592 * [misc]taylor: Taking taylor expansion of -2 in n 1545390547.592 * [misc]backup-simplify: Simplify -2 into -2 1545390547.592 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390547.592 * [misc]taylor: Taking taylor expansion of PI in n 1545390547.592 * [misc]backup-simplify: Simplify PI into PI 1545390547.592 * [misc]taylor: Taking taylor expansion of n in n 1545390547.592 * [misc]backup-simplify: Simplify 0 into 0 1545390547.592 * [misc]backup-simplify: Simplify 1 into 1 1545390547.592 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390547.593 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1545390547.593 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1545390547.593 * [misc]backup-simplify: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 1545390547.593 * [misc]backup-simplify: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1)) 1545390547.594 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545390547.594 * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 1545390547.595 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 1545390547.595 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1545390547.595 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1545390547.595 * [misc]taylor: Taking taylor expansion of -1 in n 1545390547.595 * [misc]backup-simplify: Simplify -1 into -1 1545390547.595 * [misc]taylor: Taking taylor expansion of k in n 1545390547.595 * [misc]backup-simplify: Simplify k into k 1545390547.595 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1545390547.595 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1545390547.596 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1545390547.596 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1545390547.596 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) 1545390547.596 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in k 1545390547.597 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k 1545390547.597 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k 1545390547.597 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k 1545390547.597 * [misc]taylor: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k 1545390547.597 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390547.597 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390547.597 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in k 1545390547.597 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545390547.597 * [misc]taylor: Taking taylor expansion of k in k 1545390547.597 * [misc]backup-simplify: Simplify 0 into 0 1545390547.597 * [misc]backup-simplify: Simplify 1 into 1 1545390547.597 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545390547.597 * [misc]taylor: Taking taylor expansion of 1 in k 1545390547.597 * [misc]backup-simplify: Simplify 1 into 1 1545390547.597 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1545390547.597 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1545390547.597 * [misc]taylor: Taking taylor expansion of -2 in k 1545390547.597 * [misc]backup-simplify: Simplify -2 into -2 1545390547.597 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1545390547.597 * [misc]taylor: Taking taylor expansion of PI in k 1545390547.597 * [misc]backup-simplify: Simplify PI into PI 1545390547.597 * [misc]taylor: Taking taylor expansion of n in k 1545390547.597 * [misc]backup-simplify: Simplify n into n 1545390547.597 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1545390547.597 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1545390547.598 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1545390547.598 * [misc]backup-simplify: Simplify (+ 1 0) into 1 1545390547.598 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545390547.598 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1545390547.598 * [misc]backup-simplify: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) 1545390547.598 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1545390547.598 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1545390547.598 * [misc]taylor: Taking taylor expansion of -1 in k 1545390547.598 * [misc]backup-simplify: Simplify -1 into -1 1545390547.598 * [misc]taylor: Taking taylor expansion of k in k 1545390547.598 * [misc]backup-simplify: Simplify 0 into 0 1545390547.598 * [misc]backup-simplify: Simplify 1 into 1 1545390547.599 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1545390547.599 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545390547.599 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1545390547.599 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) 1545390547.599 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in k 1545390547.599 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k 1545390547.599 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k 1545390547.599 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k 1545390547.599 * [misc]taylor: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k 1545390547.600 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390547.600 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390547.600 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in k 1545390547.600 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545390547.600 * [misc]taylor: Taking taylor expansion of k in k 1545390547.600 * [misc]backup-simplify: Simplify 0 into 0 1545390547.600 * [misc]backup-simplify: Simplify 1 into 1 1545390547.600 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545390547.600 * [misc]taylor: Taking taylor expansion of 1 in k 1545390547.600 * [misc]backup-simplify: Simplify 1 into 1 1545390547.600 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1545390547.600 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1545390547.600 * [misc]taylor: Taking taylor expansion of -2 in k 1545390547.600 * [misc]backup-simplify: Simplify -2 into -2 1545390547.600 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1545390547.600 * [misc]taylor: Taking taylor expansion of PI in k 1545390547.600 * [misc]backup-simplify: Simplify PI into PI 1545390547.600 * [misc]taylor: Taking taylor expansion of n in k 1545390547.600 * [misc]backup-simplify: Simplify n into n 1545390547.600 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1545390547.600 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1545390547.600 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1545390547.600 * [misc]backup-simplify: Simplify (+ 1 0) into 1 1545390547.600 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545390547.601 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1545390547.601 * [misc]backup-simplify: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) 1545390547.601 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1545390547.601 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1545390547.601 * [misc]taylor: Taking taylor expansion of -1 in k 1545390547.601 * [misc]backup-simplify: Simplify -1 into -1 1545390547.601 * [misc]taylor: Taking taylor expansion of k in k 1545390547.601 * [misc]backup-simplify: Simplify 0 into 0 1545390547.601 * [misc]backup-simplify: Simplify 1 into 1 1545390547.601 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1545390547.601 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545390547.602 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1545390547.602 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) 1545390547.602 * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n 1545390547.602 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1545390547.602 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545390547.602 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n 1545390547.602 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n 1545390547.602 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390547.602 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390547.602 * [misc]taylor: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n 1545390547.602 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1545390547.602 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1545390547.602 * [misc]taylor: Taking taylor expansion of -2 in n 1545390547.602 * [misc]backup-simplify: Simplify -2 into -2 1545390547.602 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390547.602 * [misc]taylor: Taking taylor expansion of PI in n 1545390547.602 * [misc]backup-simplify: Simplify PI into PI 1545390547.602 * [misc]taylor: Taking taylor expansion of n in n 1545390547.602 * [misc]backup-simplify: Simplify 0 into 0 1545390547.602 * [misc]backup-simplify: Simplify 1 into 1 1545390547.602 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390547.602 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1545390547.603 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1545390547.603 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in n 1545390547.603 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545390547.603 * [misc]taylor: Taking taylor expansion of k in n 1545390547.603 * [misc]backup-simplify: Simplify k into k 1545390547.603 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545390547.603 * [misc]taylor: Taking taylor expansion of 1 in n 1545390547.603 * [misc]backup-simplify: Simplify 1 into 1 1545390547.603 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545390547.603 * [misc]backup-simplify: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 1545390547.604 * [misc]backup-simplify: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) 1545390547.604 * [misc]backup-simplify: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 1545390547.604 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 1545390547.605 * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) 1545390547.605 * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) 1545390547.605 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1545390547.606 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1545390547.606 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) 1545390547.606 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n 1545390547.606 * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n 1545390547.607 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1545390547.607 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545390547.607 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n 1545390547.607 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n 1545390547.607 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390547.607 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390547.607 * [misc]taylor: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n 1545390547.607 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1545390547.607 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1545390547.607 * [misc]taylor: Taking taylor expansion of -2 in n 1545390547.607 * [misc]backup-simplify: Simplify -2 into -2 1545390547.607 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390547.607 * [misc]taylor: Taking taylor expansion of PI in n 1545390547.607 * [misc]backup-simplify: Simplify PI into PI 1545390547.607 * [misc]taylor: Taking taylor expansion of n in n 1545390547.607 * [misc]backup-simplify: Simplify 0 into 0 1545390547.607 * [misc]backup-simplify: Simplify 1 into 1 1545390547.607 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390547.607 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1545390547.607 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1545390547.607 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in n 1545390547.607 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545390547.607 * [misc]taylor: Taking taylor expansion of k in n 1545390547.607 * [misc]backup-simplify: Simplify k into k 1545390547.607 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545390547.608 * [misc]taylor: Taking taylor expansion of 1 in n 1545390547.608 * [misc]backup-simplify: Simplify 1 into 1 1545390547.608 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545390547.608 * [misc]backup-simplify: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 1545390547.608 * [misc]backup-simplify: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) 1545390547.609 * [misc]backup-simplify: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 1545390547.609 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 1545390547.609 * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) 1545390547.610 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) 1545390547.610 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) 1545390547.611 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545390547.611 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1545390547.611 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390547.612 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1545390547.612 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1545390547.613 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1545390547.614 * [misc]backup-simplify: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (/ 1 k) 1))) into 0 1545390547.614 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into 0 1545390547.615 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1545390547.616 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into 0 1545390547.616 * [misc]backup-simplify: Simplify 0 into 0 1545390547.616 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390547.617 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1545390547.617 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) 1545390547.617 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n 1545390547.617 * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n 1545390547.617 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1545390547.617 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545390547.617 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n 1545390547.617 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n 1545390547.617 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390547.617 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390547.617 * [misc]taylor: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n 1545390547.617 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1545390547.617 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1545390547.617 * [misc]taylor: Taking taylor expansion of -2 in n 1545390547.617 * [misc]backup-simplify: Simplify -2 into -2 1545390547.617 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390547.617 * [misc]taylor: Taking taylor expansion of PI in n 1545390547.618 * [misc]backup-simplify: Simplify PI into PI 1545390547.618 * [misc]taylor: Taking taylor expansion of n in n 1545390547.618 * [misc]backup-simplify: Simplify 0 into 0 1545390547.618 * [misc]backup-simplify: Simplify 1 into 1 1545390547.618 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390547.618 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1545390547.618 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1545390547.618 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in n 1545390547.618 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545390547.618 * [misc]taylor: Taking taylor expansion of k in n 1545390547.618 * [misc]backup-simplify: Simplify k into k 1545390547.618 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545390547.618 * [misc]taylor: Taking taylor expansion of 1 in n 1545390547.618 * [misc]backup-simplify: Simplify 1 into 1 1545390547.619 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545390547.619 * [misc]backup-simplify: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 1545390547.619 * [misc]backup-simplify: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) 1545390547.619 * [misc]backup-simplify: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 1545390547.620 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 1545390547.620 * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) 1545390547.621 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) 1545390547.621 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) 1545390547.623 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (* 1 (/ 1 (- k)))) (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))))))))) 1545390547.623 * * * [misc]progress: simplifying candidates 1545390547.623 * * * * [misc]progress: [ 1 / 88 ] simplifiying candidate # 1545390547.623 * * * * [misc]progress: [ 2 / 88 ] simplifiying candidate # 1545390547.623 * * * * [misc]progress: [ 3 / 88 ] simplifiying candidate # 1545390547.623 * [enter]simplify: Simplifying (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)) 1545390547.623 * * [misc]simplify: iters left: 6 (11 enodes) 1545390547.625 * * [misc]simplify: iters left: 5 (29 enodes) 1545390547.633 * * [misc]simplify: iters left: 4 (59 enodes) 1545390547.655 * * [misc]simplify: iters left: 3 (146 enodes) 1545390547.745 * [exit]simplify: Simplified to (* (- 1/2 (/ k 2)) (log (* (* 2 PI) n))) 1545390547.745 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ 1 (sqrt k)) (exp (* (- 1/2 (/ k 2)) (log (* (* 2 PI) n)))))) 1545390547.745 * * * * [misc]progress: [ 4 / 88 ] simplifiying candidate # 1545390547.746 * * * * [misc]progress: [ 5 / 88 ] simplifiying candidate # 1545390547.746 * [enter]simplify: Simplifying (* (* 2 PI) n) 1545390547.746 * * [misc]simplify: iters left: 4 (5 enodes) 1545390547.747 * * [misc]simplify: iters left: 3 (9 enodes) 1545390547.750 * * [misc]simplify: iters left: 2 (15 enodes) 1545390547.754 * * [misc]simplify: iters left: 1 (17 enodes) 1545390547.758 * [exit]simplify: Simplified to (* (* 2 PI) n) 1545390547.758 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (* 1 (/ (- 1 k) 2))))) 1545390547.758 * * * * [misc]progress: [ 6 / 88 ] simplifiying candidate # 1545390547.758 * [enter]simplify: Simplifying (pow (* (* 2 PI) n) (/ k 2)) 1545390547.759 * * [misc]simplify: iters left: 5 (8 enodes) 1545390547.761 * * [misc]simplify: iters left: 4 (12 enodes) 1545390547.765 * * [misc]simplify: iters left: 3 (18 enodes) 1545390547.770 * * [misc]simplify: iters left: 2 (20 enodes) 1545390547.775 * [exit]simplify: Simplified to (pow (* 2 (* n PI)) (/ k 2)) 1545390547.775 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ 1 (sqrt k)) (/ (pow (* (* 2 PI) n) (/ 1 2)) (pow (* 2 (* n PI)) (/ k 2))))) 1545390547.775 * * * * [misc]progress: [ 7 / 88 ] simplifiying candidate # 1545390547.776 * [enter]simplify: Simplifying (cbrt (/ (- 1 k) 2)) 1545390547.776 * * [misc]simplify: iters left: 5 (6 enodes) 1545390547.779 * * [misc]simplify: iters left: 4 (14 enodes) 1545390547.782 * * [misc]simplify: iters left: 3 (17 enodes) 1545390547.786 * * [misc]simplify: iters left: 2 (19 enodes) 1545390547.791 * [exit]simplify: Simplified to (cbrt (/ (- 1 k) 2)) 1545390547.791 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) (cbrt (/ (- 1 k) 2))))) 1545390547.791 * * * * [misc]progress: [ 8 / 88 ] simplifiying candidate # 1545390547.791 * [enter]simplify: Simplifying (sqrt (/ (- 1 k) 2)) 1545390547.791 * * [misc]simplify: iters left: 5 (6 enodes) 1545390547.794 * * [misc]simplify: iters left: 4 (14 enodes) 1545390547.798 * * [misc]simplify: iters left: 3 (17 enodes) 1545390547.802 * * [misc]simplify: iters left: 2 (19 enodes) 1545390547.807 * [exit]simplify: Simplified to (sqrt (/ (- 1 k) 2)) 1545390547.807 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (sqrt (/ (- 1 k) 2))) (sqrt (/ (- 1 k) 2))))) 1545390547.807 * * * * [misc]progress: [ 9 / 88 ] simplifiying candidate # 1545390547.807 * [enter]simplify: Simplifying (/ (- 1 k) 2) 1545390547.807 * * [misc]simplify: iters left: 4 (5 enodes) 1545390547.810 * * [misc]simplify: iters left: 3 (13 enodes) 1545390547.813 * * [misc]simplify: iters left: 2 (16 enodes) 1545390547.817 * * [misc]simplify: iters left: 1 (18 enodes) 1545390547.821 * [exit]simplify: Simplified to (/ (- 1 k) 2) 1545390547.821 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) 1) (/ (- 1 k) 2)))) 1545390547.821 * * * * [misc]progress: [ 10 / 88 ] simplifiying candidate # 1545390547.822 * [enter]simplify: Simplifying (/ 1 2) 1545390547.822 * * [misc]simplify: iters left: 2 (3 enodes) 1545390547.824 * * [misc]simplify: iters left: 1 (6 enodes) 1545390547.825 * [exit]simplify: Simplified to 1/2 1545390547.825 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (- 1 k)) 1/2))) 1545390547.825 * * * * [misc]progress: [ 11 / 88 ] simplifiying candidate # 1545390547.825 * [enter]simplify: Simplifying (pow (* 2 PI) (/ (- 1 k) 2)) 1545390547.825 * * [misc]simplify: iters left: 5 (8 enodes) 1545390547.829 * * [misc]simplify: iters left: 4 (17 enodes) 1545390547.833 * * [misc]simplify: iters left: 3 (20 enodes) 1545390547.838 * * [misc]simplify: iters left: 2 (22 enodes) 1545390547.843 * [exit]simplify: Simplified to (pow (* 2 PI) (- 1/2 (/ k 2))) 1545390547.843 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* 2 PI) (- 1/2 (/ k 2))) (pow n (/ (- 1 k) 2))))) 1545390547.843 * * * * [misc]progress: [ 12 / 88 ] simplifiying candidate # 1545390547.843 * * * * [misc]progress: [ 13 / 88 ] simplifiying candidate # 1545390547.843 * * * * [misc]progress: [ 14 / 88 ] simplifiying candidate # 1545390547.844 * * * * [misc]progress: [ 15 / 88 ] simplifiying candidate # 1545390547.844 * * * * [misc]progress: [ 16 / 88 ] simplifiying candidate # 1545390547.844 * * * * [misc]progress: [ 17 / 88 ] simplifiying candidate # 1545390547.844 * * * * [misc]progress: [ 18 / 88 ] simplifiying candidate # 1545390547.844 * * * * [misc]progress: [ 19 / 88 ] simplifiying candidate # 1545390547.844 * * * * [misc]progress: [ 20 / 88 ] simplifiying candidate # 1545390547.844 * * * * [misc]progress: [ 21 / 88 ] simplifiying candidate # 1545390547.844 * * * * [misc]progress: [ 22 / 88 ] simplifiying candidate # 1545390547.844 * * * * [misc]progress: [ 23 / 88 ] simplifiying candidate # 1545390547.844 * * * * [misc]progress: [ 24 / 88 ] simplifiying candidate # 1545390547.844 * * * * [misc]progress: [ 25 / 88 ] simplifiying candidate # 1545390547.844 * * * * [misc]progress: [ 26 / 88 ] simplifiying candidate # 1545390547.844 * * * * [misc]progress: [ 27 / 88 ] simplifiying candidate # 1545390547.844 * * * * [misc]progress: [ 28 / 88 ] simplifiying candidate # 1545390547.844 * * * * [misc]progress: [ 29 / 88 ] simplifiying candidate # 1545390547.844 * * * * [misc]progress: [ 30 / 88 ] simplifiying candidate # 1545390547.845 * * * * [misc]progress: [ 31 / 88 ] simplifiying candidate # 1545390547.845 * * * * [misc]progress: [ 32 / 88 ] simplifiying candidate # 1545390547.845 * * * * [misc]progress: [ 33 / 88 ] simplifiying candidate # 1545390547.845 * [enter]simplify: Simplifying (- 1/2) 1545390547.845 * * [misc]simplify: iters left: 2 (2 enodes) 1545390547.846 * * [misc]simplify: iters left: 1 (3 enodes) 1545390547.847 * [exit]simplify: Simplified to -1/2 1545390547.847 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) 1545390547.847 * * * * [misc]progress: [ 34 / 88 ] simplifiying candidate # 1545390547.847 * [enter]simplify: Simplifying (- 1) 1545390547.847 * * [misc]simplify: iters left: 2 (2 enodes) 1545390547.848 * * [misc]simplify: iters left: 1 (5 enodes) 1545390547.849 * [exit]simplify: Simplified to -1 1545390547.849 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (pow (sqrt k) -1) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) 1545390547.849 * * * * [misc]progress: [ 35 / 88 ] simplifiying candidate # 1545390547.849 * * * * [misc]progress: [ 36 / 88 ] simplifiying candidate # 1545390547.849 * * * * [misc]progress: [ 37 / 88 ] simplifiying candidate # 1545390547.849 * * * * [misc]progress: [ 38 / 88 ] simplifiying candidate # 1545390547.850 * * * * [misc]progress: [ 39 / 88 ] simplifiying candidate # 1545390547.850 * * * * [misc]progress: [ 40 / 88 ] simplifiying candidate # 1545390547.850 * * * * [misc]progress: [ 41 / 88 ] simplifiying candidate # 1545390547.850 * * * * [misc]progress: [ 42 / 88 ] simplifiying candidate # 1545390547.850 * * * * [misc]progress: [ 43 / 88 ] simplifiying candidate # 1545390547.850 * * * * [misc]progress: [ 44 / 88 ] simplifiying candidate # 1545390547.850 * * * * [misc]progress: [ 45 / 88 ] simplifiying candidate # 1545390547.850 * * * * [misc]progress: [ 46 / 88 ] simplifiying candidate # 1545390547.850 * [enter]simplify: Simplifying (cbrt (sqrt k)) 1545390547.850 * * [misc]simplify: iters left: 2 (3 enodes) 1545390547.851 * [exit]simplify: Simplified to (cbrt (sqrt k)) 1545390547.851 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (/ (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) 1545390547.851 * * * * [misc]progress: [ 47 / 88 ] simplifiying candidate # 1545390547.854 * [enter]simplify: Simplifying (sqrt (sqrt k)) 1545390547.854 * * [misc]simplify: iters left: 2 (3 enodes) 1545390547.855 * [exit]simplify: Simplified to (sqrt (sqrt k)) 1545390547.855 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) 1545390547.855 * * * * [misc]progress: [ 48 / 88 ] simplifiying candidate # 1545390547.855 * [enter]simplify: Simplifying (sqrt k) 1545390547.855 * * [misc]simplify: iters left: 1 (2 enodes) 1545390547.856 * [exit]simplify: Simplified to (sqrt k) 1545390547.856 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (/ (/ 1 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) 1545390547.856 * * * * [misc]progress: [ 49 / 88 ] simplifiying candidate # 1545390547.856 * * * * [misc]progress: [ 50 / 88 ] simplifiying candidate # 1545390547.856 * * * * [misc]progress: [ 51 / 88 ] simplifiying candidate # 1545390547.856 * * * * [misc]progress: [ 52 / 88 ] simplifiying candidate # 1545390547.856 * [enter]simplify: Simplifying (+ (- (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))) 1545390547.856 * * [misc]simplify: iters left: 6 (15 enodes) 1545390547.862 * * [misc]simplify: iters left: 5 (34 enodes) 1545390547.873 * * [misc]simplify: iters left: 4 (67 enodes) 1545390547.897 * * [misc]simplify: iters left: 3 (165 enodes) 1545390547.998 * [exit]simplify: Simplified to (fma (log (* (* n PI) 2)) (- 1/2 (/ k 2)) (- (log (sqrt k)))) 1545390547.999 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (log (* (* n PI) 2)) (- 1/2 (/ k 2)) (- (log (sqrt k)))))) 1545390547.999 * * * * [misc]progress: [ 53 / 88 ] simplifiying candidate # 1545390547.999 * [enter]simplify: Simplifying (+ (- (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))) 1545390547.999 * * [misc]simplify: iters left: 6 (15 enodes) 1545390548.005 * * [misc]simplify: iters left: 5 (34 enodes) 1545390548.016 * * [misc]simplify: iters left: 4 (67 enodes) 1545390548.040 * * [misc]simplify: iters left: 3 (165 enodes) 1545390548.124 * [exit]simplify: Simplified to (fma (log (* (* n PI) 2)) (- 1/2 (/ k 2)) (- (log (sqrt k)))) 1545390548.124 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (log (* (* n PI) 2)) (- 1/2 (/ k 2)) (- (log (sqrt k)))))) 1545390548.124 * * * * [misc]progress: [ 54 / 88 ] simplifiying candidate # 1545390548.124 * [enter]simplify: Simplifying (+ (- (log (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) 1545390548.125 * * [misc]simplify: iters left: 6 (15 enodes) 1545390548.131 * * [misc]simplify: iters left: 5 (30 enodes) 1545390548.140 * * [misc]simplify: iters left: 4 (51 enodes) 1545390548.154 * * [misc]simplify: iters left: 3 (99 enodes) 1545390548.201 * * [misc]simplify: iters left: 2 (301 enodes) 1545390548.405 * [exit]simplify: Simplified to (fma (log (* 2 (* n PI))) (/ (- 1 k) 2) (- (log (sqrt k)))) 1545390548.405 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (log (* 2 (* n PI))) (/ (- 1 k) 2) (- (log (sqrt k)))))) 1545390548.405 * * * * [misc]progress: [ 55 / 88 ] simplifiying candidate # 1545390548.405 * [enter]simplify: Simplifying (+ (log (/ 1 (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))) 1545390548.405 * * [misc]simplify: iters left: 6 (15 enodes) 1545390548.409 * * [misc]simplify: iters left: 5 (38 enodes) 1545390548.414 * * [misc]simplify: iters left: 4 (71 enodes) 1545390548.430 * * [misc]simplify: iters left: 3 (173 enodes) 1545390548.537 * [exit]simplify: Simplified to (fma (/ (- 1 k) 2) (log (* (* n 2) PI)) (- (log (sqrt k)))) 1545390548.538 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (/ (- 1 k) 2) (log (* (* n 2) PI)) (- (log (sqrt k)))))) 1545390548.538 * * * * [misc]progress: [ 56 / 88 ] simplifiying candidate # 1545390548.538 * [enter]simplify: Simplifying (+ (log (/ 1 (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))) 1545390548.538 * * [misc]simplify: iters left: 6 (15 enodes) 1545390548.543 * * [misc]simplify: iters left: 5 (38 enodes) 1545390548.557 * * [misc]simplify: iters left: 4 (71 enodes) 1545390548.577 * * [misc]simplify: iters left: 3 (173 enodes) 1545390548.700 * [exit]simplify: Simplified to (fma (/ (- 1 k) 2) (log (* (* n 2) PI)) (- (log (sqrt k)))) 1545390548.700 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (/ (- 1 k) 2) (log (* (* n 2) PI)) (- (log (sqrt k)))))) 1545390548.700 * * * * [misc]progress: [ 57 / 88 ] simplifiying candidate # 1545390548.701 * [enter]simplify: Simplifying (+ (log (/ 1 (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) 1545390548.701 * * [misc]simplify: iters left: 6 (15 enodes) 1545390548.707 * * [misc]simplify: iters left: 5 (34 enodes) 1545390548.717 * * [misc]simplify: iters left: 4 (55 enodes) 1545390548.730 * * [misc]simplify: iters left: 3 (107 enodes) 1545390548.761 * * [misc]simplify: iters left: 2 (347 enodes) 1545390549.161 * [exit]simplify: Simplified to (fma (- 1/2 (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k)))) 1545390549.162 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (- 1/2 (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k)))))) 1545390549.162 * * * * [misc]progress: [ 58 / 88 ] simplifiying candidate # 1545390549.162 * * * * [misc]progress: [ 59 / 88 ] simplifiying candidate # 1545390549.162 * * * * [misc]progress: [ 60 / 88 ] simplifiying candidate # 1545390549.162 * [enter]simplify: Simplifying (* (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k))) (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) 1545390549.163 * * [misc]simplify: iters left: 6 (17 enodes) 1545390549.170 * * [misc]simplify: iters left: 5 (42 enodes) 1545390549.184 * * [misc]simplify: iters left: 4 (98 enodes) 1545390549.233 * * [misc]simplify: iters left: 3 (175 enodes) 1545390549.279 * * [misc]simplify: iters left: 2 (325 enodes) 1545390549.409 * * [misc]simplify: iters left: 1 (454 enodes) 1545390549.577 * [exit]simplify: Simplified to (* (* (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (* (sqrt k) k))) 1545390549.577 * [misc]simplify: Simplified (2 1) to (λ (k n) (cbrt (* (* (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (* (sqrt k) k))))) 1545390549.577 * * * * [misc]progress: [ 61 / 88 ] simplifiying candidate # 1545390549.577 * * * * [misc]progress: [ 62 / 88 ] simplifiying candidate # 1545390549.577 * * * * [misc]progress: [ 63 / 88 ] simplifiying candidate # 1545390549.577 * * * * [misc]progress: [ 64 / 88 ] simplifiying candidate # 1545390549.577 * [enter]simplify: Simplifying (* 1 (pow (* (* 2 PI) n) (/ 1 2))) 1545390549.577 * * [misc]simplify: iters left: 6 (9 enodes) 1545390549.580 * * [misc]simplify: iters left: 5 (17 enodes) 1545390549.583 * * [misc]simplify: iters left: 4 (26 enodes) 1545390549.586 * * [misc]simplify: iters left: 3 (27 enodes) 1545390549.589 * [exit]simplify: Simplified to (sqrt (* PI (* 2 n))) 1545390549.589 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* PI (* 2 n))) (* (sqrt k) (pow (* (* 2 PI) n) (/ k 2))))) 1545390549.589 * [enter]simplify: Simplifying (* (sqrt k) (pow (* (* 2 PI) n) (/ k 2))) 1545390549.589 * * [misc]simplify: iters left: 6 (10 enodes) 1545390549.592 * * [misc]simplify: iters left: 5 (15 enodes) 1545390549.597 * * [misc]simplify: iters left: 4 (21 enodes) 1545390549.602 * * [misc]simplify: iters left: 3 (22 enodes) 1545390549.608 * [exit]simplify: Simplified to (* (pow (* (* 2 PI) n) (/ k 2)) (sqrt k)) 1545390549.608 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (sqrt (* PI (* 2 n))) (* (pow (* (* 2 PI) n) (/ k 2)) (sqrt k)))) 1545390549.608 * * * * [misc]progress: [ 65 / 88 ] simplifiying candidate # 1545390549.608 * * * * [misc]progress: [ 66 / 88 ] simplifiying candidate # 1545390549.609 * [enter]simplify: Simplifying (pow n (/ (- 1 k) 2)) 1545390549.609 * * [misc]simplify: iters left: 5 (7 enodes) 1545390549.612 * * [misc]simplify: iters left: 4 (15 enodes) 1545390549.616 * * [misc]simplify: iters left: 3 (18 enodes) 1545390549.620 * * [misc]simplify: iters left: 2 (20 enodes) 1545390549.625 * [exit]simplify: Simplified to (pow n (- 1/2 (/ k 2))) 1545390549.625 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ 1 (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2))) (pow n (- 1/2 (/ k 2))))) 1545390549.625 * * * * [misc]progress: [ 67 / 88 ] simplifiying candidate # 1545390549.625 * [enter]simplify: Simplifying (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) 1545390549.626 * * [misc]simplify: iters left: 6 (11 enodes) 1545390549.630 * * [misc]simplify: iters left: 5 (23 enodes) 1545390549.636 * * [misc]simplify: iters left: 4 (32 enodes) 1545390549.643 * * [misc]simplify: iters left: 3 (35 enodes) 1545390549.651 * [exit]simplify: Simplified to (cbrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) 1545390549.651 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ 1 (sqrt k)) (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) (cbrt (pow (* PI (* n 2)) (/ (- 1 k) 2))))) 1545390549.651 * * * * [misc]progress: [ 68 / 88 ] simplifiying candidate # 1545390549.652 * [enter]simplify: Simplifying (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) 1545390549.652 * * [misc]simplify: iters left: 6 (11 enodes) 1545390549.656 * * [misc]simplify: iters left: 5 (23 enodes) 1545390549.662 * * [misc]simplify: iters left: 4 (32 enodes) 1545390549.669 * * [misc]simplify: iters left: 3 (35 enodes) 1545390549.678 * [exit]simplify: Simplified to (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) 1545390549.678 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ 1 (sqrt k)) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))))) 1545390549.679 * * * * [misc]progress: [ 69 / 88 ] simplifiying candidate # 1545390549.679 * [enter]simplify: Simplifying (pow (* (* 2 PI) n) (/ (- 1 k) 2)) 1545390549.679 * * [misc]simplify: iters left: 5 (10 enodes) 1545390549.683 * * [misc]simplify: iters left: 4 (22 enodes) 1545390549.688 * * [misc]simplify: iters left: 3 (31 enodes) 1545390549.696 * * [misc]simplify: iters left: 2 (34 enodes) 1545390549.704 * [exit]simplify: Simplified to (pow (* (* n 2) PI) (/ (- 1 k) 2)) 1545390549.704 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ 1 (sqrt k)) 1) (pow (* (* n 2) PI) (/ (- 1 k) 2)))) 1545390549.704 * * * * [misc]progress: [ 70 / 88 ] simplifiying candidate # 1545390549.704 * [enter]simplify: Simplifying (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k)))) 1545390549.704 * * [misc]simplify: iters left: 6 (6 enodes) 1545390549.706 * * [misc]simplify: iters left: 5 (8 enodes) 1545390549.708 * [exit]simplify: Simplified to (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k)))) 1545390549.708 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k)))) (* (cbrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) 1545390549.709 * * * * [misc]progress: [ 71 / 88 ] simplifiying candidate # 1545390549.709 * [enter]simplify: Simplifying (sqrt (/ 1 (sqrt k))) 1545390549.709 * * [misc]simplify: iters left: 4 (5 enodes) 1545390549.710 * * [misc]simplify: iters left: 3 (7 enodes) 1545390549.712 * [exit]simplify: Simplified to (sqrt (/ 1 (sqrt k))) 1545390549.712 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (/ 1 (sqrt k))) (* (sqrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) 1545390549.712 * * * * [misc]progress: [ 72 / 88 ] simplifiying candidate # 1545390549.712 * * * * [misc]progress: [ 73 / 88 ] simplifiying candidate # 1545390549.712 * * * * [misc]progress: [ 74 / 88 ] simplifiying candidate # 1545390549.713 * [enter]simplify: Simplifying (pow (* (* 2 PI) n) (/ k 2)) 1545390549.713 * * [misc]simplify: iters left: 5 (8 enodes) 1545390549.715 * * [misc]simplify: iters left: 4 (12 enodes) 1545390549.719 * * [misc]simplify: iters left: 3 (18 enodes) 1545390549.724 * * [misc]simplify: iters left: 2 (20 enodes) 1545390549.729 * [exit]simplify: Simplified to (pow (* 2 (* n PI)) (/ k 2)) 1545390549.729 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ 1 2))) (pow (* 2 (* n PI)) (/ k 2)))) 1545390549.729 * * * * [misc]progress: [ 75 / 88 ] simplifiying candidate # 1545390549.729 * [enter]simplify: Simplifying (* 1 (pow (* (* 2 PI) n) (/ (- 1 k) 2))) 1545390549.729 * * [misc]simplify: iters left: 6 (11 enodes) 1545390549.734 * * [misc]simplify: iters left: 5 (24 enodes) 1545390549.742 * * [misc]simplify: iters left: 4 (35 enodes) 1545390549.750 * * [misc]simplify: iters left: 3 (38 enodes) 1545390549.759 * [exit]simplify: Simplified to (pow (* (* n PI) 2) (- 1/2 (/ k 2))) 1545390549.759 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (pow (* (* n PI) 2) (- 1/2 (/ k 2))) (sqrt k))) 1545390549.759 * * * * [misc]progress: [ 76 / 88 ] simplifiying candidate # 1545390549.759 * * * * [misc]progress: [ 77 / 88 ] simplifiying candidate # 1545390549.759 * [enter]simplify: Simplifying (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) 1545390549.760 * * [misc]simplify: iters left: 6 (37 enodes) 1545390549.775 * * [misc]simplify: iters left: 5 (108 enodes) 1545390549.819 * * [misc]simplify: iters left: 4 (368 enodes) 1545390550.091 * [exit]simplify: Simplified to (fma -1/2 (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) (fma (* (* (* k k) (log n)) (* (log (* PI 2)) 1/4)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (fma (* (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (log (* PI 2)) (log (* PI 2)))) (* (* k k) 1/8) (fma (* (* (* k k) (log n)) (* (log n) 1/8)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (pow n 1/2) (pow (* PI 2) 1/2)))))) 1545390550.091 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ 1 (sqrt k)) (fma -1/2 (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) (fma (* (* (* k k) (log n)) (* (log (* PI 2)) 1/4)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (fma (* (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (log (* PI 2)) (log (* PI 2)))) (* (* k k) 1/8) (fma (* (* (* k k) (log n)) (* (log n) 1/8)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (pow n 1/2) (pow (* PI 2) 1/2)))))))) 1545390550.091 * * * * [misc]progress: [ 78 / 88 ] simplifiying candidate # 1545390550.091 * [enter]simplify: Simplifying (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) 1545390550.091 * * [misc]simplify: iters left: 6 (15 enodes) 1545390550.098 * * [misc]simplify: iters left: 5 (35 enodes) 1545390550.110 * * [misc]simplify: iters left: 4 (72 enodes) 1545390550.126 * * [misc]simplify: iters left: 3 (240 enodes) 1545390550.256 * [exit]simplify: Simplified to (pow (exp (- 1/2 (* 1/2 k))) (+ (log (* 2 PI)) (log n))) 1545390550.256 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ 1 (sqrt k)) (pow (exp (- 1/2 (* 1/2 k))) (+ (log (* 2 PI)) (log n))))) 1545390550.256 * * * * [misc]progress: [ 79 / 88 ] simplifiying candidate # 1545390550.257 * [enter]simplify: Simplifying (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) 1545390550.257 * * [misc]simplify: iters left: 6 (16 enodes) 1545390550.263 * * [misc]simplify: iters left: 5 (35 enodes) 1545390550.277 * * [misc]simplify: iters left: 4 (76 enodes) 1545390550.311 * * [misc]simplify: iters left: 3 (278 enodes) 1545390550.516 * [exit]simplify: Simplified to (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))) 1545390550.516 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ 1 (sqrt k)) (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))))) 1545390550.516 * * * * [misc]progress: [ 80 / 88 ] simplifiying candidate # 1545390550.516 * [enter]simplify: Simplifying (* 2 (* n PI)) 1545390550.517 * * [misc]simplify: iters left: 4 (5 enodes) 1545390550.518 * * [misc]simplify: iters left: 3 (9 enodes) 1545390550.521 * * [misc]simplify: iters left: 2 (15 enodes) 1545390550.524 * * [misc]simplify: iters left: 1 (17 enodes) 1545390550.527 * [exit]simplify: Simplified to (* (* PI n) 2) 1545390550.528 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* PI n) 2) (/ (- 1 k) 2)))) 1545390550.528 * * * * [misc]progress: [ 81 / 88 ] simplifiying candidate # 1545390550.528 * [enter]simplify: Simplifying (* 2 (* n PI)) 1545390550.528 * * [misc]simplify: iters left: 4 (5 enodes) 1545390550.529 * * [misc]simplify: iters left: 3 (9 enodes) 1545390550.532 * * [misc]simplify: iters left: 2 (15 enodes) 1545390550.535 * * [misc]simplify: iters left: 1 (17 enodes) 1545390550.539 * [exit]simplify: Simplified to (* (* PI n) 2) 1545390550.539 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* PI n) 2) (/ (- 1 k) 2)))) 1545390550.539 * * * * [misc]progress: [ 82 / 88 ] simplifiying candidate # 1545390550.539 * [enter]simplify: Simplifying (* 2 (* n PI)) 1545390550.539 * * [misc]simplify: iters left: 4 (5 enodes) 1545390550.541 * * [misc]simplify: iters left: 3 (9 enodes) 1545390550.547 * * [misc]simplify: iters left: 2 (15 enodes) 1545390550.550 * * [misc]simplify: iters left: 1 (17 enodes) 1545390550.554 * [exit]simplify: Simplified to (* (* PI n) 2) 1545390550.554 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* PI n) 2) (/ (- 1 k) 2)))) 1545390550.554 * * * * [misc]progress: [ 83 / 88 ] simplifiying candidate # 1545390550.554 * [enter]simplify: Simplifying (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) 1545390550.554 * [misc]simplify: Simplified (2 1) to (λ (k n) (* +nan.0 (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) 1545390550.555 * * * * [misc]progress: [ 84 / 88 ] simplifiying candidate # 1545390550.555 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) 1545390550.555 * [misc]simplify: Simplified (2 1) to (λ (k n) (* +nan.0 (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) 1545390550.555 * * * * [misc]progress: [ 85 / 88 ] simplifiying candidate # 1545390550.555 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) 1545390550.555 * [misc]simplify: Simplified (2 1) to (λ (k n) (* +nan.0 (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) 1545390550.555 * * * * [misc]progress: [ 86 / 88 ] simplifiying candidate # 1545390550.555 * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))))))) 1545390550.555 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1545390550.555 * * * * [misc]progress: [ 87 / 88 ] simplifiying candidate # 1545390550.556 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3)))))))) 1545390550.556 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1545390550.556 * * * * [misc]progress: [ 88 / 88 ] simplifiying candidate # 1545390550.556 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))))))))) 1545390550.556 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1545390550.556 * * * [misc]progress: adding candidates to table 1545390551.565 * * [misc]progress: iteration 3 / 4 1545390551.565 * * * [misc]progress: picking best candidate 1545390551.598 * * * * [misc]pick: Picked # 1545390551.598 * * * [misc]progress: localizing error 1545390551.608 * * * [misc]progress: generating rewritten candidates 1545390551.608 * * * * [misc]progress: [ 1 / 4 ] rewriting at (2 2 2 1) 1545390551.616 * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 1 1) 1545390551.623 * * * * [misc]progress: [ 3 / 4 ] rewriting at (2 2 2 1 1) 1545390551.628 * * * * [misc]progress: [ 4 / 4 ] rewriting at (2 1 1 1) 1545390551.634 * * * [misc]progress: generating series expansions 1545390551.634 * * * * [misc]progress: [ 1 / 4 ] generating series at (2 2 2 1) 1545390551.634 * [misc]backup-simplify: Simplify (pow (* PI (* n 2)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 1545390551.634 * [misc]approximate: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 1545390551.634 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1545390551.634 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1545390551.634 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1545390551.634 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1545390551.634 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390551.634 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390551.634 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1545390551.634 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390551.634 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390551.634 * [misc]taylor: Taking taylor expansion of k in k 1545390551.634 * [misc]backup-simplify: Simplify 0 into 0 1545390551.634 * [misc]backup-simplify: Simplify 1 into 1 1545390551.635 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1545390551.635 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1545390551.635 * [misc]taylor: Taking taylor expansion of 2 in k 1545390551.635 * [misc]backup-simplify: Simplify 2 into 2 1545390551.635 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1545390551.635 * [misc]taylor: Taking taylor expansion of n in k 1545390551.635 * [misc]backup-simplify: Simplify n into n 1545390551.635 * [misc]taylor: Taking taylor expansion of PI in k 1545390551.635 * [misc]backup-simplify: Simplify PI into PI 1545390551.635 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1545390551.635 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1545390551.635 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1545390551.635 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1545390551.636 * [misc]backup-simplify: Simplify (- 0) into 0 1545390551.636 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545390551.636 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1545390551.636 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1545390551.636 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1545390551.636 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1545390551.636 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1545390551.636 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1545390551.636 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390551.636 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390551.636 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1545390551.636 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390551.636 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390551.636 * [misc]taylor: Taking taylor expansion of k in n 1545390551.636 * [misc]backup-simplify: Simplify k into k 1545390551.636 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1545390551.636 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1545390551.636 * [misc]taylor: Taking taylor expansion of 2 in n 1545390551.636 * [misc]backup-simplify: Simplify 2 into 2 1545390551.636 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545390551.636 * [misc]taylor: Taking taylor expansion of n in n 1545390551.636 * [misc]backup-simplify: Simplify 0 into 0 1545390551.637 * [misc]backup-simplify: Simplify 1 into 1 1545390551.637 * [misc]taylor: Taking taylor expansion of PI in n 1545390551.637 * [misc]backup-simplify: Simplify PI into PI 1545390551.637 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1545390551.637 * [misc]backup-simplify: Simplify (* 2 0) into 0 1545390551.638 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1545390551.639 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1545390551.639 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545390551.639 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1545390551.639 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1545390551.639 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1545390551.640 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545390551.641 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 1545390551.641 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 1545390551.641 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1545390551.641 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1545390551.641 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1545390551.641 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1545390551.641 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390551.641 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390551.641 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1545390551.641 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390551.641 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390551.641 * [misc]taylor: Taking taylor expansion of k in n 1545390551.641 * [misc]backup-simplify: Simplify k into k 1545390551.642 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1545390551.642 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1545390551.642 * [misc]taylor: Taking taylor expansion of 2 in n 1545390551.642 * [misc]backup-simplify: Simplify 2 into 2 1545390551.642 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545390551.642 * [misc]taylor: Taking taylor expansion of n in n 1545390551.642 * [misc]backup-simplify: Simplify 0 into 0 1545390551.642 * [misc]backup-simplify: Simplify 1 into 1 1545390551.642 * [misc]taylor: Taking taylor expansion of PI in n 1545390551.642 * [misc]backup-simplify: Simplify PI into PI 1545390551.642 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1545390551.642 * [misc]backup-simplify: Simplify (* 2 0) into 0 1545390551.643 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1545390551.644 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1545390551.644 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545390551.644 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1545390551.644 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1545390551.645 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1545390551.645 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545390551.646 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 1545390551.646 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 1545390551.646 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1545390551.647 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1545390551.647 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1545390551.647 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390551.647 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390551.647 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1545390551.647 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390551.647 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390551.647 * [misc]taylor: Taking taylor expansion of k in k 1545390551.647 * [misc]backup-simplify: Simplify 0 into 0 1545390551.647 * [misc]backup-simplify: Simplify 1 into 1 1545390551.647 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1545390551.647 * [misc]taylor: Taking taylor expansion of (log n) in k 1545390551.647 * [misc]taylor: Taking taylor expansion of n in k 1545390551.647 * [misc]backup-simplify: Simplify n into n 1545390551.647 * [misc]backup-simplify: Simplify (log n) into (log n) 1545390551.647 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1545390551.647 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1545390551.647 * [misc]taylor: Taking taylor expansion of 2 in k 1545390551.647 * [misc]backup-simplify: Simplify 2 into 2 1545390551.647 * [misc]taylor: Taking taylor expansion of PI in k 1545390551.647 * [misc]backup-simplify: Simplify PI into PI 1545390551.647 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545390551.648 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545390551.648 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1545390551.648 * [misc]backup-simplify: Simplify (- 0) into 0 1545390551.648 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545390551.649 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545390551.649 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1545390551.650 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1545390551.650 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1545390551.652 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1545390551.653 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1545390551.655 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1545390551.656 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1545390551.656 * [misc]backup-simplify: Simplify (- 0) into 0 1545390551.656 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390551.656 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545390551.657 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1545390551.659 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1545390551.659 * [misc]taylor: Taking taylor expansion of 0 in k 1545390551.659 * [misc]backup-simplify: Simplify 0 into 0 1545390551.659 * [misc]backup-simplify: Simplify 0 into 0 1545390551.660 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1545390551.660 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1545390551.663 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1545390551.663 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390551.663 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1545390551.663 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1545390551.663 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1545390551.664 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1545390551.666 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 1545390551.667 * [misc]backup-simplify: Simplify (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 1545390551.668 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1545390551.670 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1545390551.673 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1545390551.674 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1545390551.674 * [misc]backup-simplify: Simplify (- 0) into 0 1545390551.674 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390551.674 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545390551.675 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1545390551.676 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1545390551.676 * [misc]taylor: Taking taylor expansion of 0 in k 1545390551.676 * [misc]backup-simplify: Simplify 0 into 0 1545390551.676 * [misc]backup-simplify: Simplify 0 into 0 1545390551.676 * [misc]backup-simplify: Simplify 0 into 0 1545390551.677 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1545390551.678 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1545390551.681 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1545390551.681 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390551.681 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1545390551.681 * [misc]backup-simplify: Simplify (- 0) into 0 1545390551.681 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390551.682 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1545390551.683 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 1545390551.684 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 1545390551.687 * [misc]backup-simplify: Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) 1545390551.687 * [misc]backup-simplify: Simplify (pow (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 1545390551.687 * [misc]approximate: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 1545390551.688 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1545390551.688 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1545390551.688 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1545390551.688 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1545390551.688 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390551.688 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390551.688 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545390551.688 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390551.688 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390551.688 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545390551.688 * [misc]taylor: Taking taylor expansion of k in k 1545390551.688 * [misc]backup-simplify: Simplify 0 into 0 1545390551.688 * [misc]backup-simplify: Simplify 1 into 1 1545390551.688 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545390551.688 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1545390551.688 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1545390551.688 * [misc]taylor: Taking taylor expansion of 2 in k 1545390551.688 * [misc]backup-simplify: Simplify 2 into 2 1545390551.688 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1545390551.688 * [misc]taylor: Taking taylor expansion of PI in k 1545390551.688 * [misc]backup-simplify: Simplify PI into PI 1545390551.688 * [misc]taylor: Taking taylor expansion of n in k 1545390551.688 * [misc]backup-simplify: Simplify n into n 1545390551.688 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1545390551.688 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1545390551.688 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1545390551.688 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545390551.688 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1545390551.688 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1545390551.689 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1545390551.689 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 1545390551.689 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1545390551.689 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1545390551.689 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1545390551.689 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1545390551.689 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390551.689 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390551.689 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545390551.689 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390551.689 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390551.689 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545390551.689 * [misc]taylor: Taking taylor expansion of k in n 1545390551.689 * [misc]backup-simplify: Simplify k into k 1545390551.689 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545390551.689 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1545390551.689 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1545390551.689 * [misc]taylor: Taking taylor expansion of 2 in n 1545390551.689 * [misc]backup-simplify: Simplify 2 into 2 1545390551.689 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390551.689 * [misc]taylor: Taking taylor expansion of PI in n 1545390551.689 * [misc]backup-simplify: Simplify PI into PI 1545390551.689 * [misc]taylor: Taking taylor expansion of n in n 1545390551.689 * [misc]backup-simplify: Simplify 0 into 0 1545390551.689 * [misc]backup-simplify: Simplify 1 into 1 1545390551.689 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390551.689 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545390551.690 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545390551.690 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545390551.690 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1545390551.690 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1545390551.690 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545390551.691 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 1545390551.691 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 1545390551.691 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1545390551.691 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1545390551.691 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1545390551.691 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1545390551.691 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390551.691 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390551.691 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545390551.691 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390551.691 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390551.691 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545390551.691 * [misc]taylor: Taking taylor expansion of k in n 1545390551.691 * [misc]backup-simplify: Simplify k into k 1545390551.691 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545390551.691 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1545390551.691 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1545390551.691 * [misc]taylor: Taking taylor expansion of 2 in n 1545390551.691 * [misc]backup-simplify: Simplify 2 into 2 1545390551.691 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390551.691 * [misc]taylor: Taking taylor expansion of PI in n 1545390551.691 * [misc]backup-simplify: Simplify PI into PI 1545390551.692 * [misc]taylor: Taking taylor expansion of n in n 1545390551.692 * [misc]backup-simplify: Simplify 0 into 0 1545390551.692 * [misc]backup-simplify: Simplify 1 into 1 1545390551.692 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390551.692 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545390551.692 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545390551.692 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545390551.692 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1545390551.692 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1545390551.693 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545390551.693 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 1545390551.694 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 1545390551.694 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1545390551.694 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1545390551.694 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1545390551.694 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390551.694 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390551.694 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545390551.694 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390551.694 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390551.694 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545390551.694 * [misc]taylor: Taking taylor expansion of k in k 1545390551.694 * [misc]backup-simplify: Simplify 0 into 0 1545390551.694 * [misc]backup-simplify: Simplify 1 into 1 1545390551.694 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545390551.694 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1545390551.694 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1545390551.694 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1545390551.694 * [misc]taylor: Taking taylor expansion of 2 in k 1545390551.694 * [misc]backup-simplify: Simplify 2 into 2 1545390551.694 * [misc]taylor: Taking taylor expansion of PI in k 1545390551.694 * [misc]backup-simplify: Simplify PI into PI 1545390551.694 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545390551.695 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545390551.695 * [misc]taylor: Taking taylor expansion of (log n) in k 1545390551.695 * [misc]taylor: Taking taylor expansion of n in k 1545390551.695 * [misc]backup-simplify: Simplify n into n 1545390551.695 * [misc]backup-simplify: Simplify (log n) into (log n) 1545390551.695 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545390551.695 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1545390551.695 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1545390551.695 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1545390551.695 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1545390551.696 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1545390551.696 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 1545390551.696 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 1545390551.697 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1545390551.698 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1545390551.699 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1545390551.699 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1545390551.699 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1545390551.699 * [misc]backup-simplify: Simplify (- 0) into 0 1545390551.699 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390551.700 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545390551.700 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1545390551.701 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1545390551.701 * [misc]taylor: Taking taylor expansion of 0 in k 1545390551.701 * [misc]backup-simplify: Simplify 0 into 0 1545390551.701 * [misc]backup-simplify: Simplify 0 into 0 1545390551.701 * [misc]backup-simplify: Simplify 0 into 0 1545390551.702 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390551.703 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1545390551.707 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1545390551.707 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545390551.708 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1545390551.708 * [misc]backup-simplify: Simplify (- 0) into 0 1545390551.708 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390551.709 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545390551.709 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1545390551.712 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1545390551.712 * [misc]taylor: Taking taylor expansion of 0 in k 1545390551.712 * [misc]backup-simplify: Simplify 0 into 0 1545390551.712 * [misc]backup-simplify: Simplify 0 into 0 1545390551.712 * [misc]backup-simplify: Simplify 0 into 0 1545390551.712 * [misc]backup-simplify: Simplify 0 into 0 1545390551.713 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390551.715 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1545390551.719 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 1545390551.719 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545390551.720 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1545390551.720 * [misc]backup-simplify: Simplify (- 0) into 0 1545390551.720 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390551.720 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545390551.721 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1545390551.724 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1545390551.725 * [misc]taylor: Taking taylor expansion of 0 in k 1545390551.725 * [misc]backup-simplify: Simplify 0 into 0 1545390551.725 * [misc]backup-simplify: Simplify 0 into 0 1545390551.725 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 1545390551.725 * [misc]backup-simplify: Simplify (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 1545390551.725 * [misc]approximate: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 1545390551.725 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1545390551.725 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1545390551.725 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1545390551.725 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1545390551.725 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545390551.725 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390551.725 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390551.725 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545390551.725 * [misc]taylor: Taking taylor expansion of k in k 1545390551.725 * [misc]backup-simplify: Simplify 0 into 0 1545390551.725 * [misc]backup-simplify: Simplify 1 into 1 1545390551.725 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545390551.725 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390551.726 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390551.726 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1545390551.726 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1545390551.726 * [misc]taylor: Taking taylor expansion of -2 in k 1545390551.726 * [misc]backup-simplify: Simplify -2 into -2 1545390551.726 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1545390551.726 * [misc]taylor: Taking taylor expansion of PI in k 1545390551.726 * [misc]backup-simplify: Simplify PI into PI 1545390551.726 * [misc]taylor: Taking taylor expansion of n in k 1545390551.726 * [misc]backup-simplify: Simplify n into n 1545390551.726 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1545390551.726 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1545390551.726 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1545390551.726 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545390551.726 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545390551.726 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1545390551.726 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) 1545390551.726 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1545390551.726 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1545390551.726 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1545390551.726 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1545390551.726 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545390551.726 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390551.726 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390551.726 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545390551.726 * [misc]taylor: Taking taylor expansion of k in n 1545390551.726 * [misc]backup-simplify: Simplify k into k 1545390551.726 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545390551.726 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390551.726 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390551.726 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1545390551.726 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1545390551.726 * [misc]taylor: Taking taylor expansion of -2 in n 1545390551.726 * [misc]backup-simplify: Simplify -2 into -2 1545390551.726 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390551.726 * [misc]taylor: Taking taylor expansion of PI in n 1545390551.726 * [misc]backup-simplify: Simplify PI into PI 1545390551.726 * [misc]taylor: Taking taylor expansion of n in n 1545390551.727 * [misc]backup-simplify: Simplify 0 into 0 1545390551.727 * [misc]backup-simplify: Simplify 1 into 1 1545390551.727 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390551.727 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1545390551.727 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1545390551.727 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545390551.727 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1545390551.728 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545390551.728 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1545390551.728 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 1545390551.729 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1545390551.729 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1545390551.729 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1545390551.729 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1545390551.729 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545390551.729 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390551.729 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390551.729 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545390551.729 * [misc]taylor: Taking taylor expansion of k in n 1545390551.729 * [misc]backup-simplify: Simplify k into k 1545390551.729 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545390551.729 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390551.729 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390551.729 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1545390551.729 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1545390551.729 * [misc]taylor: Taking taylor expansion of -2 in n 1545390551.729 * [misc]backup-simplify: Simplify -2 into -2 1545390551.729 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390551.729 * [misc]taylor: Taking taylor expansion of PI in n 1545390551.729 * [misc]backup-simplify: Simplify PI into PI 1545390551.729 * [misc]taylor: Taking taylor expansion of n in n 1545390551.729 * [misc]backup-simplify: Simplify 0 into 0 1545390551.729 * [misc]backup-simplify: Simplify 1 into 1 1545390551.729 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390551.729 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1545390551.729 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1545390551.730 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545390551.730 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1545390551.730 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545390551.730 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1545390551.731 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 1545390551.731 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1545390551.731 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1545390551.731 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1545390551.731 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545390551.731 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390551.731 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390551.731 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545390551.731 * [misc]taylor: Taking taylor expansion of k in k 1545390551.731 * [misc]backup-simplify: Simplify 0 into 0 1545390551.731 * [misc]backup-simplify: Simplify 1 into 1 1545390551.731 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545390551.731 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390551.731 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390551.731 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1545390551.731 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1545390551.731 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1545390551.731 * [misc]taylor: Taking taylor expansion of -2 in k 1545390551.731 * [misc]backup-simplify: Simplify -2 into -2 1545390551.731 * [misc]taylor: Taking taylor expansion of PI in k 1545390551.731 * [misc]backup-simplify: Simplify PI into PI 1545390551.731 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1545390551.732 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1545390551.732 * [misc]taylor: Taking taylor expansion of (log n) in k 1545390551.732 * [misc]taylor: Taking taylor expansion of n in k 1545390551.732 * [misc]backup-simplify: Simplify n into n 1545390551.732 * [misc]backup-simplify: Simplify (log n) into (log n) 1545390551.732 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545390551.732 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545390551.732 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1545390551.732 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1545390551.733 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1545390551.733 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 1545390551.733 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 1545390551.734 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1545390551.734 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1545390551.736 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1545390551.736 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1545390551.736 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1545390551.736 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390551.737 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545390551.737 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1545390551.738 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1545390551.738 * [misc]taylor: Taking taylor expansion of 0 in k 1545390551.738 * [misc]backup-simplify: Simplify 0 into 0 1545390551.738 * [misc]backup-simplify: Simplify 0 into 0 1545390551.738 * [misc]backup-simplify: Simplify 0 into 0 1545390551.739 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390551.740 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1545390551.742 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 1545390551.742 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545390551.743 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1545390551.743 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390551.743 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545390551.744 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1545390551.745 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1545390551.745 * [misc]taylor: Taking taylor expansion of 0 in k 1545390551.745 * [misc]backup-simplify: Simplify 0 into 0 1545390551.745 * [misc]backup-simplify: Simplify 0 into 0 1545390551.745 * [misc]backup-simplify: Simplify 0 into 0 1545390551.745 * [misc]backup-simplify: Simplify 0 into 0 1545390551.746 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390551.747 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1545390551.752 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0 1545390551.752 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545390551.752 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1545390551.753 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390551.753 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545390551.754 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 1545390551.758 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1545390551.758 * [misc]taylor: Taking taylor expansion of 0 in k 1545390551.758 * [misc]backup-simplify: Simplify 0 into 0 1545390551.758 * [misc]backup-simplify: Simplify 0 into 0 1545390551.759 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 1545390551.759 * * * * [misc]progress: [ 2 / 4 ] generating series at (2 1 1) 1545390551.759 * [misc]backup-simplify: Simplify (pow (* PI (* n 2)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 1545390551.759 * [misc]approximate: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 1545390551.759 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1545390551.759 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1545390551.759 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1545390551.759 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1545390551.759 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390551.759 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390551.759 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1545390551.759 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390551.759 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390551.759 * [misc]taylor: Taking taylor expansion of k in k 1545390551.759 * [misc]backup-simplify: Simplify 0 into 0 1545390551.759 * [misc]backup-simplify: Simplify 1 into 1 1545390551.759 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1545390551.759 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1545390551.759 * [misc]taylor: Taking taylor expansion of 2 in k 1545390551.759 * [misc]backup-simplify: Simplify 2 into 2 1545390551.759 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1545390551.759 * [misc]taylor: Taking taylor expansion of n in k 1545390551.760 * [misc]backup-simplify: Simplify n into n 1545390551.760 * [misc]taylor: Taking taylor expansion of PI in k 1545390551.760 * [misc]backup-simplify: Simplify PI into PI 1545390551.760 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1545390551.760 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1545390551.760 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1545390551.760 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1545390551.760 * [misc]backup-simplify: Simplify (- 0) into 0 1545390551.760 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545390551.760 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1545390551.760 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1545390551.761 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1545390551.761 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1545390551.761 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1545390551.761 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1545390551.761 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390551.761 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390551.761 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1545390551.761 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390551.761 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390551.761 * [misc]taylor: Taking taylor expansion of k in n 1545390551.761 * [misc]backup-simplify: Simplify k into k 1545390551.761 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1545390551.761 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1545390551.761 * [misc]taylor: Taking taylor expansion of 2 in n 1545390551.761 * [misc]backup-simplify: Simplify 2 into 2 1545390551.761 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545390551.761 * [misc]taylor: Taking taylor expansion of n in n 1545390551.761 * [misc]backup-simplify: Simplify 0 into 0 1545390551.761 * [misc]backup-simplify: Simplify 1 into 1 1545390551.761 * [misc]taylor: Taking taylor expansion of PI in n 1545390551.761 * [misc]backup-simplify: Simplify PI into PI 1545390551.761 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1545390551.762 * [misc]backup-simplify: Simplify (* 2 0) into 0 1545390551.762 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1545390551.763 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1545390551.763 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545390551.763 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1545390551.763 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1545390551.763 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1545390551.764 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545390551.765 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 1545390551.765 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 1545390551.765 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1545390551.765 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1545390551.765 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1545390551.765 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1545390551.765 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390551.765 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390551.765 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1545390551.765 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390551.766 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390551.766 * [misc]taylor: Taking taylor expansion of k in n 1545390551.766 * [misc]backup-simplify: Simplify k into k 1545390551.766 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1545390551.766 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1545390551.766 * [misc]taylor: Taking taylor expansion of 2 in n 1545390551.766 * [misc]backup-simplify: Simplify 2 into 2 1545390551.766 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545390551.766 * [misc]taylor: Taking taylor expansion of n in n 1545390551.766 * [misc]backup-simplify: Simplify 0 into 0 1545390551.766 * [misc]backup-simplify: Simplify 1 into 1 1545390551.766 * [misc]taylor: Taking taylor expansion of PI in n 1545390551.766 * [misc]backup-simplify: Simplify PI into PI 1545390551.766 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1545390551.766 * [misc]backup-simplify: Simplify (* 2 0) into 0 1545390551.767 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1545390551.767 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1545390551.768 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545390551.768 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1545390551.768 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1545390551.768 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1545390551.769 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545390551.769 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 1545390551.770 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 1545390551.770 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1545390551.770 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1545390551.770 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1545390551.770 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390551.770 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390551.770 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1545390551.770 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390551.770 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390551.770 * [misc]taylor: Taking taylor expansion of k in k 1545390551.770 * [misc]backup-simplify: Simplify 0 into 0 1545390551.770 * [misc]backup-simplify: Simplify 1 into 1 1545390551.770 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1545390551.770 * [misc]taylor: Taking taylor expansion of (log n) in k 1545390551.770 * [misc]taylor: Taking taylor expansion of n in k 1545390551.770 * [misc]backup-simplify: Simplify n into n 1545390551.770 * [misc]backup-simplify: Simplify (log n) into (log n) 1545390551.770 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1545390551.770 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1545390551.770 * [misc]taylor: Taking taylor expansion of 2 in k 1545390551.771 * [misc]backup-simplify: Simplify 2 into 2 1545390551.771 * [misc]taylor: Taking taylor expansion of PI in k 1545390551.771 * [misc]backup-simplify: Simplify PI into PI 1545390551.771 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545390551.771 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545390551.771 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1545390551.772 * [misc]backup-simplify: Simplify (- 0) into 0 1545390551.772 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545390551.772 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545390551.773 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1545390551.773 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1545390551.774 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1545390551.775 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1545390551.776 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1545390551.778 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1545390551.779 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1545390551.779 * [misc]backup-simplify: Simplify (- 0) into 0 1545390551.779 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390551.779 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545390551.780 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1545390551.781 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1545390551.781 * [misc]taylor: Taking taylor expansion of 0 in k 1545390551.781 * [misc]backup-simplify: Simplify 0 into 0 1545390551.781 * [misc]backup-simplify: Simplify 0 into 0 1545390551.781 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1545390551.782 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1545390551.783 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1545390551.783 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390551.783 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1545390551.784 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1545390551.784 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1545390551.784 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1545390551.785 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 1545390551.786 * [misc]backup-simplify: Simplify (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 1545390551.787 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1545390551.788 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1545390551.790 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1545390551.790 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1545390551.791 * [misc]backup-simplify: Simplify (- 0) into 0 1545390551.791 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390551.791 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545390551.792 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1545390551.793 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1545390551.793 * [misc]taylor: Taking taylor expansion of 0 in k 1545390551.793 * [misc]backup-simplify: Simplify 0 into 0 1545390551.793 * [misc]backup-simplify: Simplify 0 into 0 1545390551.793 * [misc]backup-simplify: Simplify 0 into 0 1545390551.794 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1545390551.794 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1545390551.797 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1545390551.798 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390551.798 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1545390551.798 * [misc]backup-simplify: Simplify (- 0) into 0 1545390551.798 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390551.799 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1545390551.800 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 1545390551.801 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 1545390551.804 * [misc]backup-simplify: Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) 1545390551.805 * [misc]backup-simplify: Simplify (pow (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 1545390551.805 * [misc]approximate: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 1545390551.805 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1545390551.805 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1545390551.805 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1545390551.805 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1545390551.805 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390551.805 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390551.805 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545390551.805 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390551.805 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390551.805 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545390551.805 * [misc]taylor: Taking taylor expansion of k in k 1545390551.805 * [misc]backup-simplify: Simplify 0 into 0 1545390551.805 * [misc]backup-simplify: Simplify 1 into 1 1545390551.805 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545390551.805 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1545390551.805 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1545390551.805 * [misc]taylor: Taking taylor expansion of 2 in k 1545390551.805 * [misc]backup-simplify: Simplify 2 into 2 1545390551.805 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1545390551.805 * [misc]taylor: Taking taylor expansion of PI in k 1545390551.805 * [misc]backup-simplify: Simplify PI into PI 1545390551.805 * [misc]taylor: Taking taylor expansion of n in k 1545390551.805 * [misc]backup-simplify: Simplify n into n 1545390551.805 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1545390551.805 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1545390551.805 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1545390551.805 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545390551.805 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1545390551.806 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1545390551.806 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1545390551.806 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 1545390551.806 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1545390551.806 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1545390551.806 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1545390551.806 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1545390551.806 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390551.806 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390551.806 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545390551.806 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390551.806 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390551.806 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545390551.806 * [misc]taylor: Taking taylor expansion of k in n 1545390551.806 * [misc]backup-simplify: Simplify k into k 1545390551.806 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545390551.806 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1545390551.806 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1545390551.806 * [misc]taylor: Taking taylor expansion of 2 in n 1545390551.806 * [misc]backup-simplify: Simplify 2 into 2 1545390551.806 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390551.806 * [misc]taylor: Taking taylor expansion of PI in n 1545390551.806 * [misc]backup-simplify: Simplify PI into PI 1545390551.806 * [misc]taylor: Taking taylor expansion of n in n 1545390551.806 * [misc]backup-simplify: Simplify 0 into 0 1545390551.806 * [misc]backup-simplify: Simplify 1 into 1 1545390551.806 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390551.807 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545390551.807 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545390551.807 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545390551.807 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1545390551.807 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1545390551.808 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545390551.808 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 1545390551.808 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 1545390551.808 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1545390551.808 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1545390551.808 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1545390551.808 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1545390551.808 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390551.808 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390551.809 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545390551.809 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390551.809 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390551.809 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545390551.809 * [misc]taylor: Taking taylor expansion of k in n 1545390551.809 * [misc]backup-simplify: Simplify k into k 1545390551.809 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545390551.809 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1545390551.809 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1545390551.809 * [misc]taylor: Taking taylor expansion of 2 in n 1545390551.809 * [misc]backup-simplify: Simplify 2 into 2 1545390551.809 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390551.809 * [misc]taylor: Taking taylor expansion of PI in n 1545390551.809 * [misc]backup-simplify: Simplify PI into PI 1545390551.809 * [misc]taylor: Taking taylor expansion of n in n 1545390551.809 * [misc]backup-simplify: Simplify 0 into 0 1545390551.809 * [misc]backup-simplify: Simplify 1 into 1 1545390551.809 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390551.809 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545390551.809 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545390551.809 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545390551.809 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1545390551.810 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1545390551.810 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545390551.810 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 1545390551.811 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 1545390551.811 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1545390551.811 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1545390551.811 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1545390551.811 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390551.811 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390551.811 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545390551.811 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390551.811 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390551.811 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545390551.811 * [misc]taylor: Taking taylor expansion of k in k 1545390551.811 * [misc]backup-simplify: Simplify 0 into 0 1545390551.811 * [misc]backup-simplify: Simplify 1 into 1 1545390551.811 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545390551.811 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1545390551.811 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1545390551.811 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1545390551.811 * [misc]taylor: Taking taylor expansion of 2 in k 1545390551.811 * [misc]backup-simplify: Simplify 2 into 2 1545390551.811 * [misc]taylor: Taking taylor expansion of PI in k 1545390551.811 * [misc]backup-simplify: Simplify PI into PI 1545390551.811 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545390551.812 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545390551.812 * [misc]taylor: Taking taylor expansion of (log n) in k 1545390551.812 * [misc]taylor: Taking taylor expansion of n in k 1545390551.812 * [misc]backup-simplify: Simplify n into n 1545390551.812 * [misc]backup-simplify: Simplify (log n) into (log n) 1545390551.812 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545390551.812 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1545390551.812 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1545390551.813 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1545390551.813 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1545390551.814 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1545390551.814 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 1545390551.815 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 1545390551.816 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1545390551.816 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1545390551.819 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1545390551.819 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1545390551.819 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1545390551.819 * [misc]backup-simplify: Simplify (- 0) into 0 1545390551.820 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390551.820 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545390551.821 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1545390551.822 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1545390551.822 * [misc]taylor: Taking taylor expansion of 0 in k 1545390551.822 * [misc]backup-simplify: Simplify 0 into 0 1545390551.822 * [misc]backup-simplify: Simplify 0 into 0 1545390551.823 * [misc]backup-simplify: Simplify 0 into 0 1545390551.824 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390551.825 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1545390551.829 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1545390551.830 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545390551.830 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1545390551.830 * [misc]backup-simplify: Simplify (- 0) into 0 1545390551.830 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390551.831 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545390551.832 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1545390551.834 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1545390551.834 * [misc]taylor: Taking taylor expansion of 0 in k 1545390551.834 * [misc]backup-simplify: Simplify 0 into 0 1545390551.834 * [misc]backup-simplify: Simplify 0 into 0 1545390551.834 * [misc]backup-simplify: Simplify 0 into 0 1545390551.834 * [misc]backup-simplify: Simplify 0 into 0 1545390551.836 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390551.837 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1545390551.845 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 1545390551.845 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545390551.847 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1545390551.847 * [misc]backup-simplify: Simplify (- 0) into 0 1545390551.847 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390551.848 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545390551.849 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1545390551.852 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1545390551.852 * [misc]taylor: Taking taylor expansion of 0 in k 1545390551.852 * [misc]backup-simplify: Simplify 0 into 0 1545390551.853 * [misc]backup-simplify: Simplify 0 into 0 1545390551.853 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 1545390551.854 * [misc]backup-simplify: Simplify (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 1545390551.854 * [misc]approximate: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 1545390551.854 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1545390551.854 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1545390551.854 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1545390551.854 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1545390551.854 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545390551.854 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390551.854 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390551.854 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545390551.854 * [misc]taylor: Taking taylor expansion of k in k 1545390551.854 * [misc]backup-simplify: Simplify 0 into 0 1545390551.854 * [misc]backup-simplify: Simplify 1 into 1 1545390551.854 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545390551.854 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390551.854 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390551.854 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1545390551.854 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1545390551.854 * [misc]taylor: Taking taylor expansion of -2 in k 1545390551.854 * [misc]backup-simplify: Simplify -2 into -2 1545390551.854 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1545390551.854 * [misc]taylor: Taking taylor expansion of PI in k 1545390551.855 * [misc]backup-simplify: Simplify PI into PI 1545390551.855 * [misc]taylor: Taking taylor expansion of n in k 1545390551.855 * [misc]backup-simplify: Simplify n into n 1545390551.855 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1545390551.855 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1545390551.855 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1545390551.855 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545390551.855 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545390551.855 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1545390551.855 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) 1545390551.855 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1545390551.855 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1545390551.855 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1545390551.855 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1545390551.855 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545390551.855 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390551.855 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390551.855 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545390551.855 * [misc]taylor: Taking taylor expansion of k in n 1545390551.856 * [misc]backup-simplify: Simplify k into k 1545390551.856 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545390551.856 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390551.856 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390551.856 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1545390551.856 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1545390551.856 * [misc]taylor: Taking taylor expansion of -2 in n 1545390551.856 * [misc]backup-simplify: Simplify -2 into -2 1545390551.856 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390551.856 * [misc]taylor: Taking taylor expansion of PI in n 1545390551.856 * [misc]backup-simplify: Simplify PI into PI 1545390551.856 * [misc]taylor: Taking taylor expansion of n in n 1545390551.856 * [misc]backup-simplify: Simplify 0 into 0 1545390551.856 * [misc]backup-simplify: Simplify 1 into 1 1545390551.856 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390551.856 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1545390551.856 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1545390551.856 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545390551.857 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1545390551.857 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545390551.857 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1545390551.858 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 1545390551.858 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1545390551.858 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1545390551.858 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1545390551.858 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1545390551.858 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545390551.858 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390551.858 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390551.858 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545390551.858 * [misc]taylor: Taking taylor expansion of k in n 1545390551.858 * [misc]backup-simplify: Simplify k into k 1545390551.858 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545390551.858 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390551.858 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390551.858 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1545390551.858 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1545390551.858 * [misc]taylor: Taking taylor expansion of -2 in n 1545390551.858 * [misc]backup-simplify: Simplify -2 into -2 1545390551.858 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390551.858 * [misc]taylor: Taking taylor expansion of PI in n 1545390551.858 * [misc]backup-simplify: Simplify PI into PI 1545390551.858 * [misc]taylor: Taking taylor expansion of n in n 1545390551.858 * [misc]backup-simplify: Simplify 0 into 0 1545390551.858 * [misc]backup-simplify: Simplify 1 into 1 1545390551.858 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390551.858 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1545390551.859 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1545390551.859 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545390551.859 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1545390551.859 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545390551.860 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1545390551.860 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 1545390551.860 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1545390551.860 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1545390551.860 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1545390551.860 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545390551.860 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390551.860 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390551.860 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545390551.860 * [misc]taylor: Taking taylor expansion of k in k 1545390551.860 * [misc]backup-simplify: Simplify 0 into 0 1545390551.860 * [misc]backup-simplify: Simplify 1 into 1 1545390551.860 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545390551.860 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390551.860 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390551.860 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1545390551.860 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1545390551.860 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1545390551.860 * [misc]taylor: Taking taylor expansion of -2 in k 1545390551.860 * [misc]backup-simplify: Simplify -2 into -2 1545390551.860 * [misc]taylor: Taking taylor expansion of PI in k 1545390551.861 * [misc]backup-simplify: Simplify PI into PI 1545390551.861 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1545390551.861 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1545390551.861 * [misc]taylor: Taking taylor expansion of (log n) in k 1545390551.861 * [misc]taylor: Taking taylor expansion of n in k 1545390551.861 * [misc]backup-simplify: Simplify n into n 1545390551.861 * [misc]backup-simplify: Simplify (log n) into (log n) 1545390551.861 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545390551.861 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545390551.861 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1545390551.862 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1545390551.862 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1545390551.862 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 1545390551.863 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 1545390551.863 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1545390551.864 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1545390551.865 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1545390551.865 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1545390551.866 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1545390551.866 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390551.866 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545390551.866 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1545390551.867 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1545390551.867 * [misc]taylor: Taking taylor expansion of 0 in k 1545390551.867 * [misc]backup-simplify: Simplify 0 into 0 1545390551.867 * [misc]backup-simplify: Simplify 0 into 0 1545390551.868 * [misc]backup-simplify: Simplify 0 into 0 1545390551.868 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390551.869 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1545390551.872 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 1545390551.872 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545390551.872 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1545390551.872 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390551.873 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545390551.873 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1545390551.874 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1545390551.875 * [misc]taylor: Taking taylor expansion of 0 in k 1545390551.875 * [misc]backup-simplify: Simplify 0 into 0 1545390551.875 * [misc]backup-simplify: Simplify 0 into 0 1545390551.875 * [misc]backup-simplify: Simplify 0 into 0 1545390551.875 * [misc]backup-simplify: Simplify 0 into 0 1545390551.876 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390551.876 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1545390551.881 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0 1545390551.881 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545390551.881 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1545390551.882 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390551.882 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545390551.883 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 1545390551.886 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1545390551.886 * [misc]taylor: Taking taylor expansion of 0 in k 1545390551.886 * [misc]backup-simplify: Simplify 0 into 0 1545390551.886 * [misc]backup-simplify: Simplify 0 into 0 1545390551.887 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 1545390551.887 * * * * [misc]progress: [ 3 / 4 ] generating series at (2 2 2 1 1) 1545390551.887 * [misc]backup-simplify: Simplify (* PI (* n 2)) into (* 2 (* n PI)) 1545390551.887 * [misc]approximate: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1545390551.887 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1545390551.887 * [misc]taylor: Taking taylor expansion of 2 in n 1545390551.887 * [misc]backup-simplify: Simplify 2 into 2 1545390551.887 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545390551.887 * [misc]taylor: Taking taylor expansion of n in n 1545390551.887 * [misc]backup-simplify: Simplify 0 into 0 1545390551.887 * [misc]backup-simplify: Simplify 1 into 1 1545390551.887 * [misc]taylor: Taking taylor expansion of PI in n 1545390551.887 * [misc]backup-simplify: Simplify PI into PI 1545390551.887 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1545390551.887 * [misc]taylor: Taking taylor expansion of 2 in n 1545390551.887 * [misc]backup-simplify: Simplify 2 into 2 1545390551.887 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545390551.887 * [misc]taylor: Taking taylor expansion of n in n 1545390551.887 * [misc]backup-simplify: Simplify 0 into 0 1545390551.887 * [misc]backup-simplify: Simplify 1 into 1 1545390551.887 * [misc]taylor: Taking taylor expansion of PI in n 1545390551.887 * [misc]backup-simplify: Simplify PI into PI 1545390551.888 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1545390551.888 * [misc]backup-simplify: Simplify (* 2 0) into 0 1545390551.888 * [misc]backup-simplify: Simplify 0 into 0 1545390551.889 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1545390551.889 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1545390551.890 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545390551.891 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1545390551.892 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1545390551.892 * [misc]backup-simplify: Simplify 0 into 0 1545390551.893 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1545390551.895 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1545390551.895 * [misc]backup-simplify: Simplify 0 into 0 1545390551.897 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1545390551.899 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1545390551.899 * [misc]backup-simplify: Simplify 0 into 0 1545390551.902 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1545390551.905 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1545390551.905 * [misc]backup-simplify: Simplify 0 into 0 1545390551.908 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1545390551.912 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1545390551.912 * [misc]backup-simplify: Simplify 0 into 0 1545390551.915 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1545390551.918 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1545390551.918 * [misc]backup-simplify: Simplify 0 into 0 1545390551.918 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1545390551.918 * [misc]backup-simplify: Simplify (* PI (* (/ 1 n) 2)) into (* 2 (/ PI n)) 1545390551.918 * [misc]approximate: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1545390551.918 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1545390551.918 * [misc]taylor: Taking taylor expansion of 2 in n 1545390551.918 * [misc]backup-simplify: Simplify 2 into 2 1545390551.918 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390551.918 * [misc]taylor: Taking taylor expansion of PI in n 1545390551.918 * [misc]backup-simplify: Simplify PI into PI 1545390551.918 * [misc]taylor: Taking taylor expansion of n in n 1545390551.918 * [misc]backup-simplify: Simplify 0 into 0 1545390551.918 * [misc]backup-simplify: Simplify 1 into 1 1545390551.918 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390551.919 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1545390551.919 * [misc]taylor: Taking taylor expansion of 2 in n 1545390551.919 * [misc]backup-simplify: Simplify 2 into 2 1545390551.919 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390551.919 * [misc]taylor: Taking taylor expansion of PI in n 1545390551.919 * [misc]backup-simplify: Simplify PI into PI 1545390551.919 * [misc]taylor: Taking taylor expansion of n in n 1545390551.919 * [misc]backup-simplify: Simplify 0 into 0 1545390551.919 * [misc]backup-simplify: Simplify 1 into 1 1545390551.919 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390551.919 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545390551.919 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545390551.920 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1545390551.920 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1545390551.920 * [misc]backup-simplify: Simplify 0 into 0 1545390551.921 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390551.922 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1545390551.922 * [misc]backup-simplify: Simplify 0 into 0 1545390551.923 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390551.923 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1545390551.923 * [misc]backup-simplify: Simplify 0 into 0 1545390551.925 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390551.926 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1545390551.926 * [misc]backup-simplify: Simplify 0 into 0 1545390551.927 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390551.928 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1545390551.928 * [misc]backup-simplify: Simplify 0 into 0 1545390551.930 * [misc]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 1545390551.932 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1545390551.932 * [misc]backup-simplify: Simplify 0 into 0 1545390551.932 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 1545390551.932 * [misc]backup-simplify: Simplify (* PI (* (/ 1 (- n)) 2)) into (* -2 (/ PI n)) 1545390551.932 * [misc]approximate: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1545390551.933 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1545390551.933 * [misc]taylor: Taking taylor expansion of -2 in n 1545390551.933 * [misc]backup-simplify: Simplify -2 into -2 1545390551.933 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390551.933 * [misc]taylor: Taking taylor expansion of PI in n 1545390551.933 * [misc]backup-simplify: Simplify PI into PI 1545390551.933 * [misc]taylor: Taking taylor expansion of n in n 1545390551.933 * [misc]backup-simplify: Simplify 0 into 0 1545390551.933 * [misc]backup-simplify: Simplify 1 into 1 1545390551.933 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390551.933 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1545390551.933 * [misc]taylor: Taking taylor expansion of -2 in n 1545390551.933 * [misc]backup-simplify: Simplify -2 into -2 1545390551.933 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390551.933 * [misc]taylor: Taking taylor expansion of PI in n 1545390551.933 * [misc]backup-simplify: Simplify PI into PI 1545390551.933 * [misc]taylor: Taking taylor expansion of n in n 1545390551.933 * [misc]backup-simplify: Simplify 0 into 0 1545390551.933 * [misc]backup-simplify: Simplify 1 into 1 1545390551.933 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390551.933 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1545390551.934 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1545390551.934 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1545390551.935 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1545390551.935 * [misc]backup-simplify: Simplify 0 into 0 1545390551.935 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390551.936 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1545390551.936 * [misc]backup-simplify: Simplify 0 into 0 1545390551.937 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390551.938 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1545390551.938 * [misc]backup-simplify: Simplify 0 into 0 1545390551.939 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390551.940 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1545390551.940 * [misc]backup-simplify: Simplify 0 into 0 1545390551.941 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390551.943 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1545390551.943 * [misc]backup-simplify: Simplify 0 into 0 1545390551.945 * [misc]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 1545390551.948 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1545390551.948 * [misc]backup-simplify: Simplify 0 into 0 1545390551.948 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 1545390551.949 * * * * [misc]progress: [ 4 / 4 ] generating series at (2 1 1 1) 1545390551.949 * [misc]backup-simplify: Simplify (* PI (* n 2)) into (* 2 (* n PI)) 1545390551.949 * [misc]approximate: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1545390551.949 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1545390551.949 * [misc]taylor: Taking taylor expansion of 2 in n 1545390551.949 * [misc]backup-simplify: Simplify 2 into 2 1545390551.949 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545390551.949 * [misc]taylor: Taking taylor expansion of n in n 1545390551.949 * [misc]backup-simplify: Simplify 0 into 0 1545390551.949 * [misc]backup-simplify: Simplify 1 into 1 1545390551.949 * [misc]taylor: Taking taylor expansion of PI in n 1545390551.949 * [misc]backup-simplify: Simplify PI into PI 1545390551.949 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1545390551.949 * [misc]taylor: Taking taylor expansion of 2 in n 1545390551.949 * [misc]backup-simplify: Simplify 2 into 2 1545390551.949 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545390551.949 * [misc]taylor: Taking taylor expansion of n in n 1545390551.949 * [misc]backup-simplify: Simplify 0 into 0 1545390551.949 * [misc]backup-simplify: Simplify 1 into 1 1545390551.949 * [misc]taylor: Taking taylor expansion of PI in n 1545390551.949 * [misc]backup-simplify: Simplify PI into PI 1545390551.950 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1545390551.950 * [misc]backup-simplify: Simplify (* 2 0) into 0 1545390551.950 * [misc]backup-simplify: Simplify 0 into 0 1545390551.950 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1545390551.951 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1545390551.951 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545390551.952 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1545390551.953 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1545390551.953 * [misc]backup-simplify: Simplify 0 into 0 1545390551.955 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1545390551.956 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1545390551.957 * [misc]backup-simplify: Simplify 0 into 0 1545390551.959 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1545390551.960 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1545390551.960 * [misc]backup-simplify: Simplify 0 into 0 1545390551.963 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1545390551.964 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1545390551.964 * [misc]backup-simplify: Simplify 0 into 0 1545390551.966 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1545390551.968 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1545390551.968 * [misc]backup-simplify: Simplify 0 into 0 1545390551.970 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1545390551.972 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1545390551.973 * [misc]backup-simplify: Simplify 0 into 0 1545390551.973 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1545390551.973 * [misc]backup-simplify: Simplify (* PI (* (/ 1 n) 2)) into (* 2 (/ PI n)) 1545390551.973 * [misc]approximate: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1545390551.973 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1545390551.973 * [misc]taylor: Taking taylor expansion of 2 in n 1545390551.973 * [misc]backup-simplify: Simplify 2 into 2 1545390551.973 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390551.973 * [misc]taylor: Taking taylor expansion of PI in n 1545390551.973 * [misc]backup-simplify: Simplify PI into PI 1545390551.973 * [misc]taylor: Taking taylor expansion of n in n 1545390551.973 * [misc]backup-simplify: Simplify 0 into 0 1545390551.973 * [misc]backup-simplify: Simplify 1 into 1 1545390551.973 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390551.973 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1545390551.973 * [misc]taylor: Taking taylor expansion of 2 in n 1545390551.973 * [misc]backup-simplify: Simplify 2 into 2 1545390551.973 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390551.973 * [misc]taylor: Taking taylor expansion of PI in n 1545390551.973 * [misc]backup-simplify: Simplify PI into PI 1545390551.973 * [misc]taylor: Taking taylor expansion of n in n 1545390551.973 * [misc]backup-simplify: Simplify 0 into 0 1545390551.973 * [misc]backup-simplify: Simplify 1 into 1 1545390551.974 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390551.974 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545390551.974 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545390551.975 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1545390551.975 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1545390551.975 * [misc]backup-simplify: Simplify 0 into 0 1545390551.976 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390551.976 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1545390551.976 * [misc]backup-simplify: Simplify 0 into 0 1545390551.977 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390551.978 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1545390551.978 * [misc]backup-simplify: Simplify 0 into 0 1545390551.979 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390551.980 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1545390551.980 * [misc]backup-simplify: Simplify 0 into 0 1545390551.982 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390551.983 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1545390551.983 * [misc]backup-simplify: Simplify 0 into 0 1545390551.985 * [misc]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 1545390551.986 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1545390551.986 * [misc]backup-simplify: Simplify 0 into 0 1545390551.987 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 1545390551.987 * [misc]backup-simplify: Simplify (* PI (* (/ 1 (- n)) 2)) into (* -2 (/ PI n)) 1545390551.987 * [misc]approximate: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1545390551.987 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1545390551.987 * [misc]taylor: Taking taylor expansion of -2 in n 1545390551.987 * [misc]backup-simplify: Simplify -2 into -2 1545390551.987 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390551.987 * [misc]taylor: Taking taylor expansion of PI in n 1545390551.987 * [misc]backup-simplify: Simplify PI into PI 1545390551.987 * [misc]taylor: Taking taylor expansion of n in n 1545390551.987 * [misc]backup-simplify: Simplify 0 into 0 1545390551.987 * [misc]backup-simplify: Simplify 1 into 1 1545390551.987 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390551.987 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1545390551.987 * [misc]taylor: Taking taylor expansion of -2 in n 1545390551.987 * [misc]backup-simplify: Simplify -2 into -2 1545390551.987 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390551.987 * [misc]taylor: Taking taylor expansion of PI in n 1545390551.987 * [misc]backup-simplify: Simplify PI into PI 1545390551.987 * [misc]taylor: Taking taylor expansion of n in n 1545390551.987 * [misc]backup-simplify: Simplify 0 into 0 1545390551.987 * [misc]backup-simplify: Simplify 1 into 1 1545390551.987 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390551.988 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1545390551.988 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1545390551.988 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1545390551.989 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1545390551.989 * [misc]backup-simplify: Simplify 0 into 0 1545390551.989 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390551.990 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1545390551.990 * [misc]backup-simplify: Simplify 0 into 0 1545390551.991 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390551.992 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1545390551.992 * [misc]backup-simplify: Simplify 0 into 0 1545390551.993 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390551.994 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1545390551.994 * [misc]backup-simplify: Simplify 0 into 0 1545390551.996 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390551.997 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1545390551.997 * [misc]backup-simplify: Simplify 0 into 0 1545390551.998 * [misc]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 1545390552.000 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1545390552.001 * [misc]backup-simplify: Simplify 0 into 0 1545390552.001 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 1545390552.001 * * * [misc]progress: simplifying candidates 1545390552.001 * * * * [misc]progress: [ 1 / 72 ] simplifiying candidate # 1545390552.001 * * * * [misc]progress: [ 2 / 72 ] simplifiying candidate # 1545390552.001 * * * * [misc]progress: [ 3 / 72 ] simplifiying candidate # 1545390552.001 * [enter]simplify: Simplifying (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) 1545390552.001 * * [misc]simplify: iters left: 6 (11 enodes) 1545390552.003 * * [misc]simplify: iters left: 5 (21 enodes) 1545390552.007 * * [misc]simplify: iters left: 4 (47 enodes) 1545390552.016 * * [misc]simplify: iters left: 3 (113 enodes) 1545390552.051 * * [misc]simplify: iters left: 2 (328 enodes) 1545390552.335 * [exit]simplify: Simplified to (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) 1545390552.335 * [misc]simplify: Simplified (2 2 2 1 1) to (λ (k n) (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (exp (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI)))))))) 1545390552.335 * * * * [misc]progress: [ 4 / 72 ] simplifiying candidate # 1545390552.335 * * * * [misc]progress: [ 5 / 72 ] simplifiying candidate # 1545390552.335 * [enter]simplify: Simplifying (* PI (* n 2)) 1545390552.336 * * [misc]simplify: iters left: 4 (5 enodes) 1545390552.337 * * [misc]simplify: iters left: 3 (9 enodes) 1545390552.340 * * [misc]simplify: iters left: 2 (15 enodes) 1545390552.344 * * [misc]simplify: iters left: 1 (17 enodes) 1545390552.348 * [exit]simplify: Simplified to (* (* 2 n) PI) 1545390552.348 * [misc]simplify: Simplified (2 2 2 1 1) to (λ (k n) (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* (* 2 n) PI) (* 1 (- 1/2 (/ k 2)))))))) 1545390552.348 * * * * [misc]progress: [ 6 / 72 ] simplifiying candidate # 1545390552.348 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (/ k 2)) 1545390552.348 * * [misc]simplify: iters left: 5 (8 enodes) 1545390552.351 * * [misc]simplify: iters left: 4 (12 enodes) 1545390552.354 * * [misc]simplify: iters left: 3 (18 enodes) 1545390552.357 * * [misc]simplify: iters left: 2 (20 enodes) 1545390552.359 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ k 2)) 1545390552.359 * [misc]simplify: Simplified (2 2 2 1 2) to (λ (k n) (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (/ (pow (* PI (* n 2)) 1/2) (pow (* (* 2 n) PI) (/ k 2))))))) 1545390552.359 * * * * [misc]progress: [ 7 / 72 ] simplifiying candidate # 1545390552.360 * [enter]simplify: Simplifying (cbrt (- 1/2 (/ k 2))) 1545390552.360 * * [misc]simplify: iters left: 5 (6 enodes) 1545390552.361 * * [misc]simplify: iters left: 4 (8 enodes) 1545390552.362 * * [misc]simplify: iters left: 3 (11 enodes) 1545390552.363 * [exit]simplify: Simplified to (cbrt (- 1/2 (/ k 2))) 1545390552.363 * [misc]simplify: Simplified (2 2 2 1 2) to (λ (k n) (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (pow (* PI (* n 2)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))))))) 1545390552.363 * * * * [misc]progress: [ 8 / 72 ] simplifiying candidate # 1545390552.363 * [enter]simplify: Simplifying (sqrt (- 1/2 (/ k 2))) 1545390552.363 * * [misc]simplify: iters left: 5 (6 enodes) 1545390552.364 * * [misc]simplify: iters left: 4 (8 enodes) 1545390552.365 * * [misc]simplify: iters left: 3 (11 enodes) 1545390552.367 * [exit]simplify: Simplified to (sqrt (- 1/2 (/ k 2))) 1545390552.367 * [misc]simplify: Simplified (2 2 2 1 2) to (λ (k n) (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (pow (* PI (* n 2)) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))))))) 1545390552.367 * * * * [misc]progress: [ 9 / 72 ] simplifiying candidate # 1545390552.367 * [enter]simplify: Simplifying (- 1/2 (/ k 2)) 1545390552.367 * * [misc]simplify: iters left: 4 (5 enodes) 1545390552.368 * * [misc]simplify: iters left: 3 (7 enodes) 1545390552.369 * * [misc]simplify: iters left: 2 (10 enodes) 1545390552.370 * [exit]simplify: Simplified to (- 1/2 (/ k 2)) 1545390552.370 * [misc]simplify: Simplified (2 2 2 1 2) to (λ (k n) (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (pow (* PI (* n 2)) 1) (- 1/2 (/ k 2))))))) 1545390552.370 * * * * [misc]progress: [ 10 / 72 ] simplifiying candidate # 1545390552.370 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1545390552.370 * * [misc]simplify: iters left: 5 (9 enodes) 1545390552.371 * * [misc]simplify: iters left: 4 (15 enodes) 1545390552.373 * * [misc]simplify: iters left: 3 (21 enodes) 1545390552.376 * * [misc]simplify: iters left: 2 (22 enodes) 1545390552.379 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1545390552.379 * [misc]simplify: Simplified (2 2 2 1 2) to (λ (k n) (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2)))))))) 1545390552.379 * * * * [misc]progress: [ 11 / 72 ] simplifiying candidate # 1545390552.379 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1545390552.379 * * [misc]simplify: iters left: 5 (9 enodes) 1545390552.380 * * [misc]simplify: iters left: 4 (15 enodes) 1545390552.382 * * [misc]simplify: iters left: 3 (21 enodes) 1545390552.385 * * [misc]simplify: iters left: 2 (22 enodes) 1545390552.388 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1545390552.388 * [misc]simplify: Simplified (2 2 2 1 2) to (λ (k n) (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2)))))))) 1545390552.388 * * * * [misc]progress: [ 12 / 72 ] simplifiying candidate # 1545390552.388 * [enter]simplify: Simplifying (pow PI (- 1/2 (/ k 2))) 1545390552.388 * * [misc]simplify: iters left: 5 (7 enodes) 1545390552.389 * * [misc]simplify: iters left: 4 (9 enodes) 1545390552.390 * * [misc]simplify: iters left: 3 (12 enodes) 1545390552.392 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1545390552.392 * [misc]simplify: Simplified (2 2 2 1 1) to (λ (k n) (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow PI (- 1/2 (/ k 2))) (pow (* n 2) (- 1/2 (/ k 2)))))))) 1545390552.392 * * * * [misc]progress: [ 13 / 72 ] simplifiying candidate # 1545390552.392 * * * * [misc]progress: [ 14 / 72 ] simplifiying candidate # 1545390552.392 * * * * [misc]progress: [ 15 / 72 ] simplifiying candidate # 1545390552.392 * * * * [misc]progress: [ 16 / 72 ] simplifiying candidate # 1545390552.392 * * * * [misc]progress: [ 17 / 72 ] simplifiying candidate # 1545390552.392 * * * * [misc]progress: [ 18 / 72 ] simplifiying candidate # 1545390552.392 * * * * [misc]progress: [ 19 / 72 ] simplifiying candidate # 1545390552.392 * * * * [misc]progress: [ 20 / 72 ] simplifiying candidate # 1545390552.392 * * * * [misc]progress: [ 21 / 72 ] simplifiying candidate # 1545390552.392 * * * * [misc]progress: [ 22 / 72 ] simplifiying candidate # 1545390552.392 * [enter]simplify: Simplifying (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) 1545390552.392 * * [misc]simplify: iters left: 6 (11 enodes) 1545390552.394 * * [misc]simplify: iters left: 5 (21 enodes) 1545390552.398 * * [misc]simplify: iters left: 4 (47 enodes) 1545390552.408 * * [misc]simplify: iters left: 3 (113 enodes) 1545390552.447 * * [misc]simplify: iters left: 2 (328 enodes) 1545390552.670 * [exit]simplify: Simplified to (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) 1545390552.671 * [misc]simplify: Simplified (2 1 1 1) to (λ (k n) (/ (sqrt (exp (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))))) (/ (sqrt k) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))) 1545390552.671 * * * * [misc]progress: [ 23 / 72 ] simplifiying candidate # 1545390552.671 * * * * [misc]progress: [ 24 / 72 ] simplifiying candidate # 1545390552.671 * [enter]simplify: Simplifying (* PI (* n 2)) 1545390552.671 * * [misc]simplify: iters left: 4 (5 enodes) 1545390552.673 * * [misc]simplify: iters left: 3 (9 enodes) 1545390552.675 * * [misc]simplify: iters left: 2 (15 enodes) 1545390552.679 * * [misc]simplify: iters left: 1 (17 enodes) 1545390552.684 * [exit]simplify: Simplified to (* (* 2 n) PI) 1545390552.684 * [misc]simplify: Simplified (2 1 1 1) to (λ (k n) (/ (sqrt (pow (* (* 2 n) PI) (* 1 (- 1/2 (/ k 2))))) (/ (sqrt k) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))) 1545390552.684 * * * * [misc]progress: [ 25 / 72 ] simplifiying candidate # 1545390552.684 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (/ k 2)) 1545390552.684 * * [misc]simplify: iters left: 5 (8 enodes) 1545390552.687 * * [misc]simplify: iters left: 4 (12 enodes) 1545390552.690 * * [misc]simplify: iters left: 3 (18 enodes) 1545390552.695 * * [misc]simplify: iters left: 2 (20 enodes) 1545390552.700 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ k 2)) 1545390552.700 * [misc]simplify: Simplified (2 1 1 2) to (λ (k n) (/ (sqrt (/ (pow (* PI (* n 2)) 1/2) (pow (* (* 2 n) PI) (/ k 2)))) (/ (sqrt k) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))) 1545390552.700 * * * * [misc]progress: [ 26 / 72 ] simplifiying candidate # 1545390552.700 * [enter]simplify: Simplifying (cbrt (- 1/2 (/ k 2))) 1545390552.701 * * [misc]simplify: iters left: 5 (6 enodes) 1545390552.702 * * [misc]simplify: iters left: 4 (8 enodes) 1545390552.705 * * [misc]simplify: iters left: 3 (11 enodes) 1545390552.708 * [exit]simplify: Simplified to (cbrt (- 1/2 (/ k 2))) 1545390552.708 * [misc]simplify: Simplified (2 1 1 2) to (λ (k n) (/ (sqrt (pow (pow (* PI (* n 2)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2))))) (/ (sqrt k) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))) 1545390552.708 * * * * [misc]progress: [ 27 / 72 ] simplifiying candidate # 1545390552.708 * [enter]simplify: Simplifying (sqrt (- 1/2 (/ k 2))) 1545390552.708 * * [misc]simplify: iters left: 5 (6 enodes) 1545390552.710 * * [misc]simplify: iters left: 4 (8 enodes) 1545390552.712 * * [misc]simplify: iters left: 3 (11 enodes) 1545390552.715 * [exit]simplify: Simplified to (sqrt (- 1/2 (/ k 2))) 1545390552.715 * [misc]simplify: Simplified (2 1 1 2) to (λ (k n) (/ (sqrt (pow (pow (* PI (* n 2)) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2))))) (/ (sqrt k) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))) 1545390552.715 * * * * [misc]progress: [ 28 / 72 ] simplifiying candidate # 1545390552.716 * [enter]simplify: Simplifying (- 1/2 (/ k 2)) 1545390552.716 * * [misc]simplify: iters left: 4 (5 enodes) 1545390552.717 * * [misc]simplify: iters left: 3 (7 enodes) 1545390552.719 * * [misc]simplify: iters left: 2 (10 enodes) 1545390552.722 * [exit]simplify: Simplified to (- 1/2 (/ k 2)) 1545390552.722 * [misc]simplify: Simplified (2 1 1 2) to (λ (k n) (/ (sqrt (pow (pow (* PI (* n 2)) 1) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))) 1545390552.722 * * * * [misc]progress: [ 29 / 72 ] simplifiying candidate # 1545390552.723 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1545390552.723 * * [misc]simplify: iters left: 5 (9 enodes) 1545390552.726 * * [misc]simplify: iters left: 4 (15 enodes) 1545390552.730 * * [misc]simplify: iters left: 3 (21 enodes) 1545390552.735 * * [misc]simplify: iters left: 2 (22 enodes) 1545390552.745 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1545390552.745 * [misc]simplify: Simplified (2 1 1 2) to (λ (k n) (/ (sqrt (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2))))) (/ (sqrt k) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))) 1545390552.745 * * * * [misc]progress: [ 30 / 72 ] simplifiying candidate # 1545390552.745 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1545390552.745 * * [misc]simplify: iters left: 5 (9 enodes) 1545390552.748 * * [misc]simplify: iters left: 4 (15 enodes) 1545390552.753 * * [misc]simplify: iters left: 3 (21 enodes) 1545390552.758 * * [misc]simplify: iters left: 2 (22 enodes) 1545390552.763 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1545390552.764 * [misc]simplify: Simplified (2 1 1 2) to (λ (k n) (/ (sqrt (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2))))) (/ (sqrt k) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))) 1545390552.764 * * * * [misc]progress: [ 31 / 72 ] simplifiying candidate # 1545390552.764 * [enter]simplify: Simplifying (pow PI (- 1/2 (/ k 2))) 1545390552.764 * * [misc]simplify: iters left: 5 (7 enodes) 1545390552.766 * * [misc]simplify: iters left: 4 (9 enodes) 1545390552.769 * * [misc]simplify: iters left: 3 (12 enodes) 1545390552.772 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1545390552.772 * [misc]simplify: Simplified (2 1 1 1) to (λ (k n) (/ (sqrt (* (pow PI (- 1/2 (/ k 2))) (pow (* n 2) (- 1/2 (/ k 2))))) (/ (sqrt k) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))) 1545390552.772 * * * * [misc]progress: [ 32 / 72 ] simplifiying candidate # 1545390552.772 * * * * [misc]progress: [ 33 / 72 ] simplifiying candidate # 1545390552.772 * * * * [misc]progress: [ 34 / 72 ] simplifiying candidate # 1545390552.772 * * * * [misc]progress: [ 35 / 72 ] simplifiying candidate # 1545390552.772 * * * * [misc]progress: [ 36 / 72 ] simplifiying candidate # 1545390552.773 * * * * [misc]progress: [ 37 / 72 ] simplifiying candidate # 1545390552.773 * * * * [misc]progress: [ 38 / 72 ] simplifiying candidate # 1545390552.773 * * * * [misc]progress: [ 39 / 72 ] simplifiying candidate # 1545390552.773 * * * * [misc]progress: [ 40 / 72 ] simplifiying candidate # 1545390552.773 * * * * [misc]progress: [ 41 / 72 ] simplifiying candidate # 1545390552.773 * * * * [misc]progress: [ 42 / 72 ] simplifiying candidate # 1545390552.773 * * * * [misc]progress: [ 43 / 72 ] simplifiying candidate # 1545390552.773 * * * * [misc]progress: [ 44 / 72 ] simplifiying candidate # 1545390552.773 * * * * [misc]progress: [ 45 / 72 ] simplifiying candidate # 1545390552.773 * * * * [misc]progress: [ 46 / 72 ] simplifiying candidate # 1545390552.773 * * * * [misc]progress: [ 47 / 72 ] simplifiying candidate # 1545390552.773 * * * * [misc]progress: [ 48 / 72 ] simplifiying candidate # 1545390552.773 * * * * [misc]progress: [ 49 / 72 ] simplifiying candidate # 1545390552.773 * * * * [misc]progress: [ 50 / 72 ] simplifiying candidate # 1545390552.773 * * * * [misc]progress: [ 51 / 72 ] simplifiying candidate # 1545390552.774 * * * * [misc]progress: [ 52 / 72 ] simplifiying candidate # 1545390552.774 * * * * [misc]progress: [ 53 / 72 ] simplifiying candidate # 1545390552.774 * * * * [misc]progress: [ 54 / 72 ] simplifiying candidate # 1545390552.774 * * * * [misc]progress: [ 55 / 72 ] simplifiying candidate # 1545390552.774 * * * * [misc]progress: [ 56 / 72 ] simplifiying candidate # 1545390552.774 * * * * [misc]progress: [ 57 / 72 ] simplifiying candidate # 1545390552.774 * * * * [misc]progress: [ 58 / 72 ] simplifiying candidate # 1545390552.774 * * * * [misc]progress: [ 59 / 72 ] simplifiying candidate # 1545390552.774 * * * * [misc]progress: [ 60 / 72 ] simplifiying candidate # 1545390552.774 * * * * [misc]progress: [ 61 / 72 ] simplifiying candidate # 1545390552.774 * [enter]simplify: Simplifying (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) 1545390552.775 * * [misc]simplify: iters left: 6 (37 enodes) 1545390552.789 * * [misc]simplify: iters left: 5 (108 enodes) 1545390552.813 * * [misc]simplify: iters left: 4 (368 enodes) 1545390553.056 * [exit]simplify: Simplified to (fma -1/2 (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) (fma (* (* (* k k) (log n)) (* (log (* PI 2)) 1/4)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (fma (* (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (log (* PI 2)) (log (* PI 2)))) (* (* k k) 1/8) (fma (* (* (* k k) (log n)) (* (log n) 1/8)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (pow n 1/2) (pow (* PI 2) 1/2)))))) 1545390553.057 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (fma -1/2 (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) (fma (* (* (* k k) (log n)) (* (log (* PI 2)) 1/4)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (fma (* (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (log (* PI 2)) (log (* PI 2)))) (* (* k k) 1/8) (fma (* (* (* k k) (log n)) (* (log n) 1/8)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (pow n 1/2) (pow (* PI 2) 1/2)))))))))) 1545390553.057 * * * * [misc]progress: [ 62 / 72 ] simplifiying candidate # 1545390553.057 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 1545390553.057 * * [misc]simplify: iters left: 6 (15 enodes) 1545390553.060 * * [misc]simplify: iters left: 5 (33 enodes) 1545390553.065 * * [misc]simplify: iters left: 4 (64 enodes) 1545390553.080 * * [misc]simplify: iters left: 3 (179 enodes) 1545390553.177 * [exit]simplify: Simplified to (* (pow (* 2 PI) (fma -1/2 k 1/2)) (pow n (fma -1/2 k 1/2))) 1545390553.177 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow (* 2 PI) (fma -1/2 k 1/2)) (pow n (fma -1/2 k 1/2))))))) 1545390553.177 * * * * [misc]progress: [ 63 / 72 ] simplifiying candidate # 1545390553.178 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 1545390553.178 * * [misc]simplify: iters left: 6 (15 enodes) 1545390553.181 * * [misc]simplify: iters left: 5 (30 enodes) 1545390553.186 * * [misc]simplify: iters left: 4 (65 enodes) 1545390553.206 * * [misc]simplify: iters left: 3 (208 enodes) 1545390553.316 * [exit]simplify: Simplified to (pow (exp (fma -1/2 k 1/2)) (- (log (* -2 PI)) (log (/ -1 n)))) 1545390553.316 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (exp (fma -1/2 k 1/2)) (- (log (* -2 PI)) (log (/ -1 n)))))))) 1545390553.316 * * * * [misc]progress: [ 64 / 72 ] simplifiying candidate # 1545390553.316 * [enter]simplify: Simplifying (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) 1545390553.316 * * [misc]simplify: iters left: 6 (37 enodes) 1545390553.324 * * [misc]simplify: iters left: 5 (108 enodes) 1545390553.354 * * [misc]simplify: iters left: 4 (368 enodes) 1545390553.577 * [exit]simplify: Simplified to (fma -1/2 (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) (fma (* (* (* k k) (log n)) (* (log (* PI 2)) 1/4)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (fma (* (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (log (* PI 2)) (log (* PI 2)))) (* (* k k) 1/8) (fma (* (* (* k k) (log n)) (* (log n) 1/8)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (pow n 1/2) (pow (* PI 2) 1/2)))))) 1545390553.577 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (sqrt (fma -1/2 (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) (fma (* (* (* k k) (log n)) (* (log (* PI 2)) 1/4)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (fma (* (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (log (* PI 2)) (log (* PI 2)))) (* (* k k) 1/8) (fma (* (* (* k k) (log n)) (* (log n) 1/8)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (pow n 1/2) (pow (* PI 2) 1/2))))))) (/ (sqrt k) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))) 1545390553.577 * * * * [misc]progress: [ 65 / 72 ] simplifiying candidate # 1545390553.577 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 1545390553.577 * * [misc]simplify: iters left: 6 (15 enodes) 1545390553.580 * * [misc]simplify: iters left: 5 (33 enodes) 1545390553.586 * * [misc]simplify: iters left: 4 (64 enodes) 1545390553.605 * * [misc]simplify: iters left: 3 (179 enodes) 1545390553.744 * [exit]simplify: Simplified to (* (pow (* 2 PI) (fma -1/2 k 1/2)) (pow n (fma -1/2 k 1/2))) 1545390553.744 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (sqrt (* (pow (* 2 PI) (fma -1/2 k 1/2)) (pow n (fma -1/2 k 1/2)))) (/ (sqrt k) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))) 1545390553.744 * * * * [misc]progress: [ 66 / 72 ] simplifiying candidate # 1545390553.744 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 1545390553.744 * * [misc]simplify: iters left: 6 (15 enodes) 1545390553.750 * * [misc]simplify: iters left: 5 (30 enodes) 1545390553.761 * * [misc]simplify: iters left: 4 (65 enodes) 1545390553.790 * * [misc]simplify: iters left: 3 (208 enodes) 1545390553.946 * [exit]simplify: Simplified to (pow (exp (fma -1/2 k 1/2)) (- (log (* -2 PI)) (log (/ -1 n)))) 1545390553.946 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (sqrt (pow (exp (fma -1/2 k 1/2)) (- (log (* -2 PI)) (log (/ -1 n))))) (/ (sqrt k) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))) 1545390553.946 * * * * [misc]progress: [ 67 / 72 ] simplifiying candidate # 1545390553.946 * [enter]simplify: Simplifying (* 2 (* n PI)) 1545390553.946 * * [misc]simplify: iters left: 4 (5 enodes) 1545390553.948 * * [misc]simplify: iters left: 3 (9 enodes) 1545390553.951 * * [misc]simplify: iters left: 2 (15 enodes) 1545390553.955 * * [misc]simplify: iters left: 1 (17 enodes) 1545390553.959 * [exit]simplify: Simplified to (* (* PI n) 2) 1545390553.959 * [misc]simplify: Simplified (2 2 2 1 1) to (λ (k n) (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))))) 1545390553.959 * * * * [misc]progress: [ 68 / 72 ] simplifiying candidate # 1545390553.959 * [enter]simplify: Simplifying (* 2 (* n PI)) 1545390553.960 * * [misc]simplify: iters left: 4 (5 enodes) 1545390553.961 * * [misc]simplify: iters left: 3 (9 enodes) 1545390553.964 * * [misc]simplify: iters left: 2 (15 enodes) 1545390553.968 * * [misc]simplify: iters left: 1 (17 enodes) 1545390553.972 * [exit]simplify: Simplified to (* (* PI n) 2) 1545390553.972 * [misc]simplify: Simplified (2 2 2 1 1) to (λ (k n) (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))))) 1545390553.972 * * * * [misc]progress: [ 69 / 72 ] simplifiying candidate # 1545390553.973 * [enter]simplify: Simplifying (* 2 (* n PI)) 1545390553.973 * * [misc]simplify: iters left: 4 (5 enodes) 1545390553.974 * * [misc]simplify: iters left: 3 (9 enodes) 1545390553.977 * * [misc]simplify: iters left: 2 (15 enodes) 1545390553.981 * * [misc]simplify: iters left: 1 (17 enodes) 1545390553.985 * [exit]simplify: Simplified to (* (* PI n) 2) 1545390553.985 * [misc]simplify: Simplified (2 2 2 1 1) to (λ (k n) (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))))) 1545390553.985 * * * * [misc]progress: [ 70 / 72 ] simplifiying candidate # 1545390553.985 * [enter]simplify: Simplifying (* 2 (* n PI)) 1545390553.985 * * [misc]simplify: iters left: 4 (5 enodes) 1545390553.987 * * [misc]simplify: iters left: 3 (9 enodes) 1545390553.990 * * [misc]simplify: iters left: 2 (15 enodes) 1545390553.994 * * [misc]simplify: iters left: 1 (17 enodes) 1545390553.998 * [exit]simplify: Simplified to (* (* PI n) 2) 1545390553.998 * [misc]simplify: Simplified (2 1 1 1) to (λ (k n) (/ (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))) 1545390553.998 * * * * [misc]progress: [ 71 / 72 ] simplifiying candidate # 1545390553.998 * [enter]simplify: Simplifying (* 2 (* n PI)) 1545390553.998 * * [misc]simplify: iters left: 4 (5 enodes) 1545390554.000 * * [misc]simplify: iters left: 3 (9 enodes) 1545390554.002 * * [misc]simplify: iters left: 2 (15 enodes) 1545390554.007 * * [misc]simplify: iters left: 1 (17 enodes) 1545390554.011 * [exit]simplify: Simplified to (* (* PI n) 2) 1545390554.011 * [misc]simplify: Simplified (2 1 1 1) to (λ (k n) (/ (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))) 1545390554.011 * * * * [misc]progress: [ 72 / 72 ] simplifiying candidate # 1545390554.011 * [enter]simplify: Simplifying (* 2 (* n PI)) 1545390554.011 * * [misc]simplify: iters left: 4 (5 enodes) 1545390554.013 * * [misc]simplify: iters left: 3 (9 enodes) 1545390554.015 * * [misc]simplify: iters left: 2 (15 enodes) 1545390554.019 * * [misc]simplify: iters left: 1 (17 enodes) 1545390554.023 * [exit]simplify: Simplified to (* (* PI n) 2) 1545390554.023 * [misc]simplify: Simplified (2 1 1 1) to (λ (k n) (/ (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))) 1545390554.024 * * * [misc]progress: adding candidates to table 1545390555.127 * * [misc]progress: iteration 4 / 4 1545390555.127 * * * [misc]progress: picking best candidate 1545390555.158 * * * * [misc]pick: Picked # 1545390555.158 * * * [misc]progress: localizing error 1545390555.165 * * * [misc]progress: generating rewritten candidates 1545390555.165 * * * * [misc]progress: [ 1 / 4 ] rewriting at (2 2 1 2) 1545390555.168 * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 1 1 2) 1545390555.170 * * * * [misc]progress: [ 3 / 4 ] rewriting at (2) 1545390555.230 * * * * [misc]progress: [ 4 / 4 ] rewriting at (2 2 1 2 1) 1545390555.236 * * * [misc]progress: generating series expansions 1545390555.236 * * * * [misc]progress: [ 1 / 4 ] generating series at (2 2 1 2) 1545390555.237 * [misc]backup-simplify: Simplify (pow (* (* 2 PI) n) (/ (- 1 k) 2)) into (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) 1545390555.237 * [misc]approximate: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in (n k) around 0 1545390555.237 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k 1545390555.237 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k 1545390555.237 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k 1545390555.237 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 k)) in k 1545390555.237 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390555.237 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390555.237 * [misc]taylor: Taking taylor expansion of (- 1 k) in k 1545390555.237 * [misc]taylor: Taking taylor expansion of 1 in k 1545390555.237 * [misc]backup-simplify: Simplify 1 into 1 1545390555.237 * [misc]taylor: Taking taylor expansion of k in k 1545390555.237 * [misc]backup-simplify: Simplify 0 into 0 1545390555.238 * [misc]backup-simplify: Simplify 1 into 1 1545390555.238 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1545390555.238 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1545390555.238 * [misc]taylor: Taking taylor expansion of 2 in k 1545390555.238 * [misc]backup-simplify: Simplify 2 into 2 1545390555.238 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1545390555.238 * [misc]taylor: Taking taylor expansion of n in k 1545390555.238 * [misc]backup-simplify: Simplify n into n 1545390555.238 * [misc]taylor: Taking taylor expansion of PI in k 1545390555.238 * [misc]backup-simplify: Simplify PI into PI 1545390555.238 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1545390555.238 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1545390555.238 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1545390555.238 * [misc]backup-simplify: Simplify (- 0) into 0 1545390555.238 * [misc]backup-simplify: Simplify (+ 1 0) into 1 1545390555.239 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545390555.239 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1545390555.239 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1545390555.239 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n 1545390555.239 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n 1545390555.239 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n 1545390555.239 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 k)) in n 1545390555.239 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390555.239 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390555.239 * [misc]taylor: Taking taylor expansion of (- 1 k) in n 1545390555.239 * [misc]taylor: Taking taylor expansion of 1 in n 1545390555.239 * [misc]backup-simplify: Simplify 1 into 1 1545390555.239 * [misc]taylor: Taking taylor expansion of k in n 1545390555.239 * [misc]backup-simplify: Simplify k into k 1545390555.239 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1545390555.239 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1545390555.239 * [misc]taylor: Taking taylor expansion of 2 in n 1545390555.239 * [misc]backup-simplify: Simplify 2 into 2 1545390555.239 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545390555.239 * [misc]taylor: Taking taylor expansion of n in n 1545390555.239 * [misc]backup-simplify: Simplify 0 into 0 1545390555.239 * [misc]backup-simplify: Simplify 1 into 1 1545390555.239 * [misc]taylor: Taking taylor expansion of PI in n 1545390555.239 * [misc]backup-simplify: Simplify PI into PI 1545390555.240 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1545390555.240 * [misc]backup-simplify: Simplify (* 2 0) into 0 1545390555.241 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1545390555.241 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1545390555.242 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545390555.242 * [misc]backup-simplify: Simplify (- k) into (- k) 1545390555.242 * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) 1545390555.242 * [misc]backup-simplify: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k)) 1545390555.243 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545390555.243 * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) 1545390555.244 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 1545390555.244 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n 1545390555.244 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n 1545390555.244 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n 1545390555.244 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 k)) in n 1545390555.244 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390555.244 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390555.244 * [misc]taylor: Taking taylor expansion of (- 1 k) in n 1545390555.244 * [misc]taylor: Taking taylor expansion of 1 in n 1545390555.244 * [misc]backup-simplify: Simplify 1 into 1 1545390555.244 * [misc]taylor: Taking taylor expansion of k in n 1545390555.244 * [misc]backup-simplify: Simplify k into k 1545390555.244 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1545390555.245 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1545390555.245 * [misc]taylor: Taking taylor expansion of 2 in n 1545390555.245 * [misc]backup-simplify: Simplify 2 into 2 1545390555.245 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545390555.245 * [misc]taylor: Taking taylor expansion of n in n 1545390555.245 * [misc]backup-simplify: Simplify 0 into 0 1545390555.245 * [misc]backup-simplify: Simplify 1 into 1 1545390555.245 * [misc]taylor: Taking taylor expansion of PI in n 1545390555.245 * [misc]backup-simplify: Simplify PI into PI 1545390555.245 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1545390555.245 * [misc]backup-simplify: Simplify (* 2 0) into 0 1545390555.246 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1545390555.246 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1545390555.247 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545390555.247 * [misc]backup-simplify: Simplify (- k) into (- k) 1545390555.247 * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) 1545390555.247 * [misc]backup-simplify: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k)) 1545390555.248 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545390555.248 * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) 1545390555.248 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 1545390555.248 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) in k 1545390555.248 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) in k 1545390555.248 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390555.248 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390555.248 * [misc]taylor: Taking taylor expansion of (* (- 1 k) (+ (log n) (log (* 2 PI)))) in k 1545390555.248 * [misc]taylor: Taking taylor expansion of (- 1 k) in k 1545390555.248 * [misc]taylor: Taking taylor expansion of 1 in k 1545390555.249 * [misc]backup-simplify: Simplify 1 into 1 1545390555.249 * [misc]taylor: Taking taylor expansion of k in k 1545390555.249 * [misc]backup-simplify: Simplify 0 into 0 1545390555.249 * [misc]backup-simplify: Simplify 1 into 1 1545390555.249 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1545390555.249 * [misc]taylor: Taking taylor expansion of (log n) in k 1545390555.249 * [misc]taylor: Taking taylor expansion of n in k 1545390555.249 * [misc]backup-simplify: Simplify n into n 1545390555.249 * [misc]backup-simplify: Simplify (log n) into (log n) 1545390555.249 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1545390555.249 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1545390555.249 * [misc]taylor: Taking taylor expansion of 2 in k 1545390555.249 * [misc]backup-simplify: Simplify 2 into 2 1545390555.249 * [misc]taylor: Taking taylor expansion of PI in k 1545390555.249 * [misc]backup-simplify: Simplify PI into PI 1545390555.249 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545390555.249 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545390555.249 * [misc]backup-simplify: Simplify (- 0) into 0 1545390555.249 * [misc]backup-simplify: Simplify (+ 1 0) into 1 1545390555.250 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545390555.250 * [misc]backup-simplify: Simplify (* 1 (+ (log n) (log (* 2 PI)))) into (+ (log n) (log (* 2 PI))) 1545390555.250 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1545390555.251 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1545390555.251 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1545390555.252 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1545390555.252 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1545390555.254 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1545390555.256 * [misc]backup-simplify: Simplify (- 0) into 0 1545390555.256 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390555.256 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- 1 k))) into 0 1545390555.257 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545390555.257 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1545390555.258 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0 1545390555.258 * [misc]taylor: Taking taylor expansion of 0 in k 1545390555.258 * [misc]backup-simplify: Simplify 0 into 0 1545390555.258 * [misc]backup-simplify: Simplify 0 into 0 1545390555.259 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1545390555.259 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1545390555.261 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1545390555.261 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390555.261 * [misc]backup-simplify: Simplify (- 1) into -1 1545390555.261 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 1545390555.261 * [misc]backup-simplify: Simplify (+ (* 1 0) (* -1 (+ (log n) (log (* 2 PI))))) into (- (+ (log (* 2 PI)) (log n))) 1545390555.262 * [misc]backup-simplify: Simplify (+ (* 1/2 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1545390555.263 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 1545390555.264 * [misc]backup-simplify: Simplify (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 1545390555.265 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1545390555.265 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1545390555.268 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1545390555.268 * [misc]backup-simplify: Simplify (- 0) into 0 1545390555.268 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390555.269 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0 1545390555.269 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545390555.269 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1545390555.271 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1545390555.271 * [misc]taylor: Taking taylor expansion of 0 in k 1545390555.271 * [misc]backup-simplify: Simplify 0 into 0 1545390555.271 * [misc]backup-simplify: Simplify 0 into 0 1545390555.271 * [misc]backup-simplify: Simplify 0 into 0 1545390555.272 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1545390555.272 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1545390555.275 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1545390555.275 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390555.276 * [misc]backup-simplify: Simplify (- 0) into 0 1545390555.276 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390555.277 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1545390555.278 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1545390555.280 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 1545390555.282 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 1545390555.287 * [misc]backup-simplify: Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) 1545390555.288 * [misc]backup-simplify: Simplify (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) into (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) 1545390555.288 * [misc]approximate: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in (n k) around 0 1545390555.288 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k 1545390555.288 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1545390555.288 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1545390555.288 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k 1545390555.288 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390555.288 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390555.288 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k 1545390555.288 * [misc]taylor: Taking taylor expansion of 1 in k 1545390555.288 * [misc]backup-simplify: Simplify 1 into 1 1545390555.288 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545390555.288 * [misc]taylor: Taking taylor expansion of k in k 1545390555.288 * [misc]backup-simplify: Simplify 0 into 0 1545390555.288 * [misc]backup-simplify: Simplify 1 into 1 1545390555.288 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545390555.288 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1545390555.288 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1545390555.288 * [misc]taylor: Taking taylor expansion of 2 in k 1545390555.289 * [misc]backup-simplify: Simplify 2 into 2 1545390555.289 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1545390555.289 * [misc]taylor: Taking taylor expansion of PI in k 1545390555.289 * [misc]backup-simplify: Simplify PI into PI 1545390555.289 * [misc]taylor: Taking taylor expansion of n in k 1545390555.289 * [misc]backup-simplify: Simplify n into n 1545390555.289 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1545390555.289 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1545390555.289 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1545390555.289 * [misc]backup-simplify: Simplify (- 1) into -1 1545390555.289 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 1545390555.289 * [misc]backup-simplify: Simplify (* 1/2 -1) into -1/2 1545390555.289 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1545390555.290 * [misc]backup-simplify: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 1545390555.290 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n 1545390555.290 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1545390555.290 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1545390555.290 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n 1545390555.290 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390555.290 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390555.290 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n 1545390555.290 * [misc]taylor: Taking taylor expansion of 1 in n 1545390555.290 * [misc]backup-simplify: Simplify 1 into 1 1545390555.290 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545390555.290 * [misc]taylor: Taking taylor expansion of k in n 1545390555.290 * [misc]backup-simplify: Simplify k into k 1545390555.290 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545390555.290 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1545390555.290 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1545390555.290 * [misc]taylor: Taking taylor expansion of 2 in n 1545390555.290 * [misc]backup-simplify: Simplify 2 into 2 1545390555.290 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390555.290 * [misc]taylor: Taking taylor expansion of PI in n 1545390555.290 * [misc]backup-simplify: Simplify PI into PI 1545390555.290 * [misc]taylor: Taking taylor expansion of n in n 1545390555.290 * [misc]backup-simplify: Simplify 0 into 0 1545390555.290 * [misc]backup-simplify: Simplify 1 into 1 1545390555.291 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390555.291 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545390555.291 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545390555.291 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1545390555.292 * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 1545390555.292 * [misc]backup-simplify: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k))) 1545390555.292 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545390555.293 * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 1545390555.294 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 1545390555.294 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n 1545390555.294 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1545390555.294 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1545390555.294 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n 1545390555.294 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390555.294 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390555.294 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n 1545390555.294 * [misc]taylor: Taking taylor expansion of 1 in n 1545390555.294 * [misc]backup-simplify: Simplify 1 into 1 1545390555.294 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545390555.294 * [misc]taylor: Taking taylor expansion of k in n 1545390555.294 * [misc]backup-simplify: Simplify k into k 1545390555.294 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545390555.294 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1545390555.294 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1545390555.295 * [misc]taylor: Taking taylor expansion of 2 in n 1545390555.295 * [misc]backup-simplify: Simplify 2 into 2 1545390555.295 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390555.295 * [misc]taylor: Taking taylor expansion of PI in n 1545390555.295 * [misc]backup-simplify: Simplify PI into PI 1545390555.295 * [misc]taylor: Taking taylor expansion of n in n 1545390555.295 * [misc]backup-simplify: Simplify 0 into 0 1545390555.295 * [misc]backup-simplify: Simplify 1 into 1 1545390555.295 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390555.295 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545390555.296 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545390555.296 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1545390555.296 * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 1545390555.296 * [misc]backup-simplify: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k))) 1545390555.297 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545390555.297 * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 1545390555.298 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 1545390555.298 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k 1545390555.298 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k 1545390555.298 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390555.298 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390555.298 * [misc]taylor: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k 1545390555.298 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k 1545390555.298 * [misc]taylor: Taking taylor expansion of 1 in k 1545390555.298 * [misc]backup-simplify: Simplify 1 into 1 1545390555.298 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545390555.298 * [misc]taylor: Taking taylor expansion of k in k 1545390555.298 * [misc]backup-simplify: Simplify 0 into 0 1545390555.298 * [misc]backup-simplify: Simplify 1 into 1 1545390555.298 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545390555.298 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1545390555.298 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1545390555.298 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1545390555.298 * [misc]taylor: Taking taylor expansion of 2 in k 1545390555.298 * [misc]backup-simplify: Simplify 2 into 2 1545390555.299 * [misc]taylor: Taking taylor expansion of PI in k 1545390555.299 * [misc]backup-simplify: Simplify PI into PI 1545390555.299 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545390555.299 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545390555.299 * [misc]taylor: Taking taylor expansion of (log n) in k 1545390555.299 * [misc]taylor: Taking taylor expansion of n in k 1545390555.299 * [misc]backup-simplify: Simplify n into n 1545390555.299 * [misc]backup-simplify: Simplify (log n) into (log n) 1545390555.300 * [misc]backup-simplify: Simplify (- 1) into -1 1545390555.300 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 1545390555.300 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1545390555.300 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1545390555.301 * [misc]backup-simplify: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n))) 1545390555.301 * [misc]backup-simplify: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1545390555.302 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 1545390555.303 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 1545390555.304 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1545390555.304 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1545390555.307 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1545390555.307 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1545390555.307 * [misc]backup-simplify: Simplify (- 0) into 0 1545390555.308 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390555.308 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- 1 (/ 1 k)))) into 0 1545390555.308 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545390555.309 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1545390555.311 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1545390555.311 * [misc]taylor: Taking taylor expansion of 0 in k 1545390555.311 * [misc]backup-simplify: Simplify 0 into 0 1545390555.311 * [misc]backup-simplify: Simplify 0 into 0 1545390555.311 * [misc]backup-simplify: Simplify 0 into 0 1545390555.312 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390555.313 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1545390555.318 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1545390555.318 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545390555.319 * [misc]backup-simplify: Simplify (- 0) into 0 1545390555.319 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390555.319 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0 1545390555.320 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545390555.320 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1545390555.323 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1545390555.323 * [misc]taylor: Taking taylor expansion of 0 in k 1545390555.323 * [misc]backup-simplify: Simplify 0 into 0 1545390555.323 * [misc]backup-simplify: Simplify 0 into 0 1545390555.323 * [misc]backup-simplify: Simplify 0 into 0 1545390555.323 * [misc]backup-simplify: Simplify 0 into 0 1545390555.325 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390555.326 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1545390555.334 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 1545390555.334 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545390555.334 * [misc]backup-simplify: Simplify (- 0) into 0 1545390555.334 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390555.335 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0 1545390555.335 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545390555.336 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1545390555.338 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1545390555.338 * [misc]taylor: Taking taylor expansion of 0 in k 1545390555.338 * [misc]backup-simplify: Simplify 0 into 0 1545390555.338 * [misc]backup-simplify: Simplify 0 into 0 1545390555.338 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) 1545390555.339 * [misc]backup-simplify: Simplify (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) into (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) 1545390555.339 * [misc]approximate: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in (n k) around 0 1545390555.339 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k 1545390555.339 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k 1545390555.339 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k 1545390555.339 * [misc]taylor: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k 1545390555.339 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390555.339 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390555.339 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in k 1545390555.339 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545390555.339 * [misc]taylor: Taking taylor expansion of k in k 1545390555.339 * [misc]backup-simplify: Simplify 0 into 0 1545390555.339 * [misc]backup-simplify: Simplify 1 into 1 1545390555.339 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545390555.339 * [misc]taylor: Taking taylor expansion of 1 in k 1545390555.339 * [misc]backup-simplify: Simplify 1 into 1 1545390555.339 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1545390555.339 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1545390555.339 * [misc]taylor: Taking taylor expansion of -2 in k 1545390555.339 * [misc]backup-simplify: Simplify -2 into -2 1545390555.339 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1545390555.339 * [misc]taylor: Taking taylor expansion of PI in k 1545390555.339 * [misc]backup-simplify: Simplify PI into PI 1545390555.339 * [misc]taylor: Taking taylor expansion of n in k 1545390555.339 * [misc]backup-simplify: Simplify n into n 1545390555.339 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1545390555.339 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1545390555.339 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1545390555.339 * [misc]backup-simplify: Simplify (+ 1 0) into 1 1545390555.340 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545390555.340 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1545390555.340 * [misc]backup-simplify: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) 1545390555.340 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n 1545390555.340 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n 1545390555.340 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n 1545390555.340 * [misc]taylor: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n 1545390555.340 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390555.340 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390555.340 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in n 1545390555.340 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545390555.340 * [misc]taylor: Taking taylor expansion of k in n 1545390555.340 * [misc]backup-simplify: Simplify k into k 1545390555.340 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545390555.340 * [misc]taylor: Taking taylor expansion of 1 in n 1545390555.340 * [misc]backup-simplify: Simplify 1 into 1 1545390555.340 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1545390555.340 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1545390555.340 * [misc]taylor: Taking taylor expansion of -2 in n 1545390555.340 * [misc]backup-simplify: Simplify -2 into -2 1545390555.340 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390555.340 * [misc]taylor: Taking taylor expansion of PI in n 1545390555.340 * [misc]backup-simplify: Simplify PI into PI 1545390555.340 * [misc]taylor: Taking taylor expansion of n in n 1545390555.340 * [misc]backup-simplify: Simplify 0 into 0 1545390555.340 * [misc]backup-simplify: Simplify 1 into 1 1545390555.340 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390555.340 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1545390555.341 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1545390555.341 * [misc]backup-simplify: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 1545390555.341 * [misc]backup-simplify: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1)) 1545390555.341 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545390555.342 * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 1545390555.342 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 1545390555.342 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n 1545390555.342 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n 1545390555.342 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n 1545390555.342 * [misc]taylor: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n 1545390555.342 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390555.342 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390555.342 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in n 1545390555.342 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545390555.342 * [misc]taylor: Taking taylor expansion of k in n 1545390555.342 * [misc]backup-simplify: Simplify k into k 1545390555.342 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545390555.342 * [misc]taylor: Taking taylor expansion of 1 in n 1545390555.342 * [misc]backup-simplify: Simplify 1 into 1 1545390555.342 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1545390555.342 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1545390555.342 * [misc]taylor: Taking taylor expansion of -2 in n 1545390555.342 * [misc]backup-simplify: Simplify -2 into -2 1545390555.342 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390555.342 * [misc]taylor: Taking taylor expansion of PI in n 1545390555.342 * [misc]backup-simplify: Simplify PI into PI 1545390555.342 * [misc]taylor: Taking taylor expansion of n in n 1545390555.342 * [misc]backup-simplify: Simplify 0 into 0 1545390555.342 * [misc]backup-simplify: Simplify 1 into 1 1545390555.343 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390555.343 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1545390555.343 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1545390555.343 * [misc]backup-simplify: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 1545390555.343 * [misc]backup-simplify: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1)) 1545390555.344 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545390555.344 * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 1545390555.345 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 1545390555.345 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k 1545390555.345 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) in k 1545390555.345 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390555.345 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390555.345 * [misc]taylor: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) in k 1545390555.345 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in k 1545390555.345 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545390555.345 * [misc]taylor: Taking taylor expansion of k in k 1545390555.345 * [misc]backup-simplify: Simplify 0 into 0 1545390555.345 * [misc]backup-simplify: Simplify 1 into 1 1545390555.345 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545390555.345 * [misc]taylor: Taking taylor expansion of 1 in k 1545390555.345 * [misc]backup-simplify: Simplify 1 into 1 1545390555.345 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1545390555.345 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1545390555.345 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1545390555.345 * [misc]taylor: Taking taylor expansion of -2 in k 1545390555.345 * [misc]backup-simplify: Simplify -2 into -2 1545390555.345 * [misc]taylor: Taking taylor expansion of PI in k 1545390555.345 * [misc]backup-simplify: Simplify PI into PI 1545390555.345 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1545390555.345 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1545390555.345 * [misc]taylor: Taking taylor expansion of (log n) in k 1545390555.345 * [misc]taylor: Taking taylor expansion of n in k 1545390555.346 * [misc]backup-simplify: Simplify n into n 1545390555.346 * [misc]backup-simplify: Simplify (log n) into (log n) 1545390555.346 * [misc]backup-simplify: Simplify (+ 1 0) into 1 1545390555.346 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1545390555.346 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1545390555.346 * [misc]backup-simplify: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n)) 1545390555.347 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1545390555.347 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 1545390555.347 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 1545390555.348 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1545390555.349 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1545390555.350 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1545390555.350 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1545390555.350 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390555.350 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (+ (/ 1 k) 1))) into 0 1545390555.351 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545390555.351 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1545390555.352 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1545390555.352 * [misc]taylor: Taking taylor expansion of 0 in k 1545390555.352 * [misc]backup-simplify: Simplify 0 into 0 1545390555.352 * [misc]backup-simplify: Simplify 0 into 0 1545390555.352 * [misc]backup-simplify: Simplify 0 into 0 1545390555.353 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390555.354 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1545390555.356 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 1545390555.357 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545390555.357 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390555.357 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0 1545390555.357 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545390555.358 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1545390555.359 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1545390555.359 * [misc]taylor: Taking taylor expansion of 0 in k 1545390555.359 * [misc]backup-simplify: Simplify 0 into 0 1545390555.359 * [misc]backup-simplify: Simplify 0 into 0 1545390555.359 * [misc]backup-simplify: Simplify 0 into 0 1545390555.359 * [misc]backup-simplify: Simplify 0 into 0 1545390555.361 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390555.363 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1545390555.370 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0 1545390555.371 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545390555.371 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390555.371 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1))))) into 0 1545390555.372 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545390555.373 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 1545390555.377 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1545390555.377 * [misc]taylor: Taking taylor expansion of 0 in k 1545390555.377 * [misc]backup-simplify: Simplify 0 into 0 1545390555.377 * [misc]backup-simplify: Simplify 0 into 0 1545390555.377 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) 1545390555.378 * * * * [misc]progress: [ 2 / 4 ] generating series at (2 1 1 2) 1545390555.378 * [misc]backup-simplify: Simplify (pow (* (* 2 PI) n) (/ (- 1 k) 2)) into (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) 1545390555.378 * [misc]approximate: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in (n k) around 0 1545390555.378 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k 1545390555.378 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k 1545390555.378 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k 1545390555.378 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 k)) in k 1545390555.378 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390555.378 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390555.378 * [misc]taylor: Taking taylor expansion of (- 1 k) in k 1545390555.378 * [misc]taylor: Taking taylor expansion of 1 in k 1545390555.378 * [misc]backup-simplify: Simplify 1 into 1 1545390555.378 * [misc]taylor: Taking taylor expansion of k in k 1545390555.378 * [misc]backup-simplify: Simplify 0 into 0 1545390555.379 * [misc]backup-simplify: Simplify 1 into 1 1545390555.379 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1545390555.379 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1545390555.379 * [misc]taylor: Taking taylor expansion of 2 in k 1545390555.379 * [misc]backup-simplify: Simplify 2 into 2 1545390555.379 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1545390555.379 * [misc]taylor: Taking taylor expansion of n in k 1545390555.379 * [misc]backup-simplify: Simplify n into n 1545390555.379 * [misc]taylor: Taking taylor expansion of PI in k 1545390555.379 * [misc]backup-simplify: Simplify PI into PI 1545390555.379 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1545390555.379 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1545390555.379 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1545390555.379 * [misc]backup-simplify: Simplify (- 0) into 0 1545390555.379 * [misc]backup-simplify: Simplify (+ 1 0) into 1 1545390555.380 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545390555.380 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1545390555.380 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1545390555.380 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n 1545390555.380 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n 1545390555.380 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n 1545390555.380 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 k)) in n 1545390555.380 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390555.380 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390555.380 * [misc]taylor: Taking taylor expansion of (- 1 k) in n 1545390555.380 * [misc]taylor: Taking taylor expansion of 1 in n 1545390555.380 * [misc]backup-simplify: Simplify 1 into 1 1545390555.380 * [misc]taylor: Taking taylor expansion of k in n 1545390555.380 * [misc]backup-simplify: Simplify k into k 1545390555.380 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1545390555.380 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1545390555.380 * [misc]taylor: Taking taylor expansion of 2 in n 1545390555.380 * [misc]backup-simplify: Simplify 2 into 2 1545390555.380 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545390555.380 * [misc]taylor: Taking taylor expansion of n in n 1545390555.380 * [misc]backup-simplify: Simplify 0 into 0 1545390555.380 * [misc]backup-simplify: Simplify 1 into 1 1545390555.380 * [misc]taylor: Taking taylor expansion of PI in n 1545390555.380 * [misc]backup-simplify: Simplify PI into PI 1545390555.381 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1545390555.381 * [misc]backup-simplify: Simplify (* 2 0) into 0 1545390555.381 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1545390555.382 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1545390555.383 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545390555.383 * [misc]backup-simplify: Simplify (- k) into (- k) 1545390555.383 * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) 1545390555.383 * [misc]backup-simplify: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k)) 1545390555.383 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545390555.384 * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) 1545390555.385 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 1545390555.385 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n 1545390555.385 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n 1545390555.385 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n 1545390555.385 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 k)) in n 1545390555.385 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390555.385 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390555.385 * [misc]taylor: Taking taylor expansion of (- 1 k) in n 1545390555.385 * [misc]taylor: Taking taylor expansion of 1 in n 1545390555.385 * [misc]backup-simplify: Simplify 1 into 1 1545390555.385 * [misc]taylor: Taking taylor expansion of k in n 1545390555.385 * [misc]backup-simplify: Simplify k into k 1545390555.385 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1545390555.385 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1545390555.385 * [misc]taylor: Taking taylor expansion of 2 in n 1545390555.385 * [misc]backup-simplify: Simplify 2 into 2 1545390555.385 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545390555.385 * [misc]taylor: Taking taylor expansion of n in n 1545390555.385 * [misc]backup-simplify: Simplify 0 into 0 1545390555.385 * [misc]backup-simplify: Simplify 1 into 1 1545390555.385 * [misc]taylor: Taking taylor expansion of PI in n 1545390555.385 * [misc]backup-simplify: Simplify PI into PI 1545390555.385 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1545390555.386 * [misc]backup-simplify: Simplify (* 2 0) into 0 1545390555.386 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1545390555.387 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1545390555.387 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545390555.387 * [misc]backup-simplify: Simplify (- k) into (- k) 1545390555.387 * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) 1545390555.387 * [misc]backup-simplify: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k)) 1545390555.388 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545390555.389 * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) 1545390555.389 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 1545390555.389 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) in k 1545390555.389 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) in k 1545390555.389 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390555.390 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390555.390 * [misc]taylor: Taking taylor expansion of (* (- 1 k) (+ (log n) (log (* 2 PI)))) in k 1545390555.390 * [misc]taylor: Taking taylor expansion of (- 1 k) in k 1545390555.390 * [misc]taylor: Taking taylor expansion of 1 in k 1545390555.390 * [misc]backup-simplify: Simplify 1 into 1 1545390555.390 * [misc]taylor: Taking taylor expansion of k in k 1545390555.390 * [misc]backup-simplify: Simplify 0 into 0 1545390555.390 * [misc]backup-simplify: Simplify 1 into 1 1545390555.390 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1545390555.390 * [misc]taylor: Taking taylor expansion of (log n) in k 1545390555.390 * [misc]taylor: Taking taylor expansion of n in k 1545390555.390 * [misc]backup-simplify: Simplify n into n 1545390555.390 * [misc]backup-simplify: Simplify (log n) into (log n) 1545390555.390 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1545390555.390 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1545390555.390 * [misc]taylor: Taking taylor expansion of 2 in k 1545390555.390 * [misc]backup-simplify: Simplify 2 into 2 1545390555.390 * [misc]taylor: Taking taylor expansion of PI in k 1545390555.390 * [misc]backup-simplify: Simplify PI into PI 1545390555.390 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545390555.392 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545390555.392 * [misc]backup-simplify: Simplify (- 0) into 0 1545390555.392 * [misc]backup-simplify: Simplify (+ 1 0) into 1 1545390555.393 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545390555.393 * [misc]backup-simplify: Simplify (* 1 (+ (log n) (log (* 2 PI)))) into (+ (log n) (log (* 2 PI))) 1545390555.394 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1545390555.395 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1545390555.395 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1545390555.396 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1545390555.397 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1545390555.400 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1545390555.400 * [misc]backup-simplify: Simplify (- 0) into 0 1545390555.401 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390555.401 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- 1 k))) into 0 1545390555.401 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545390555.402 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1545390555.403 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0 1545390555.404 * [misc]taylor: Taking taylor expansion of 0 in k 1545390555.404 * [misc]backup-simplify: Simplify 0 into 0 1545390555.404 * [misc]backup-simplify: Simplify 0 into 0 1545390555.404 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1545390555.405 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1545390555.408 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1545390555.408 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390555.408 * [misc]backup-simplify: Simplify (- 1) into -1 1545390555.408 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 1545390555.409 * [misc]backup-simplify: Simplify (+ (* 1 0) (* -1 (+ (log n) (log (* 2 PI))))) into (- (+ (log (* 2 PI)) (log n))) 1545390555.410 * [misc]backup-simplify: Simplify (+ (* 1/2 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1545390555.411 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 1545390555.413 * [misc]backup-simplify: Simplify (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 1545390555.414 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1545390555.416 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1545390555.421 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1545390555.421 * [misc]backup-simplify: Simplify (- 0) into 0 1545390555.421 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390555.422 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0 1545390555.422 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545390555.423 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1545390555.425 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1545390555.425 * [misc]taylor: Taking taylor expansion of 0 in k 1545390555.425 * [misc]backup-simplify: Simplify 0 into 0 1545390555.425 * [misc]backup-simplify: Simplify 0 into 0 1545390555.425 * [misc]backup-simplify: Simplify 0 into 0 1545390555.427 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1545390555.428 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1545390555.433 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1545390555.433 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390555.433 * [misc]backup-simplify: Simplify (- 0) into 0 1545390555.433 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390555.434 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1545390555.435 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1545390555.437 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 1545390555.440 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 1545390555.445 * [misc]backup-simplify: Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) 1545390555.446 * [misc]backup-simplify: Simplify (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) into (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) 1545390555.446 * [misc]approximate: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in (n k) around 0 1545390555.446 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k 1545390555.446 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1545390555.446 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1545390555.446 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k 1545390555.446 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390555.446 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390555.446 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k 1545390555.446 * [misc]taylor: Taking taylor expansion of 1 in k 1545390555.446 * [misc]backup-simplify: Simplify 1 into 1 1545390555.446 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545390555.446 * [misc]taylor: Taking taylor expansion of k in k 1545390555.446 * [misc]backup-simplify: Simplify 0 into 0 1545390555.446 * [misc]backup-simplify: Simplify 1 into 1 1545390555.447 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545390555.447 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1545390555.447 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1545390555.447 * [misc]taylor: Taking taylor expansion of 2 in k 1545390555.447 * [misc]backup-simplify: Simplify 2 into 2 1545390555.447 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1545390555.447 * [misc]taylor: Taking taylor expansion of PI in k 1545390555.447 * [misc]backup-simplify: Simplify PI into PI 1545390555.447 * [misc]taylor: Taking taylor expansion of n in k 1545390555.447 * [misc]backup-simplify: Simplify n into n 1545390555.447 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1545390555.447 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1545390555.447 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1545390555.447 * [misc]backup-simplify: Simplify (- 1) into -1 1545390555.447 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 1545390555.448 * [misc]backup-simplify: Simplify (* 1/2 -1) into -1/2 1545390555.448 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1545390555.448 * [misc]backup-simplify: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 1545390555.448 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n 1545390555.448 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1545390555.448 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1545390555.448 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n 1545390555.448 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390555.448 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390555.448 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n 1545390555.448 * [misc]taylor: Taking taylor expansion of 1 in n 1545390555.448 * [misc]backup-simplify: Simplify 1 into 1 1545390555.448 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545390555.448 * [misc]taylor: Taking taylor expansion of k in n 1545390555.448 * [misc]backup-simplify: Simplify k into k 1545390555.448 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545390555.448 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1545390555.448 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1545390555.448 * [misc]taylor: Taking taylor expansion of 2 in n 1545390555.448 * [misc]backup-simplify: Simplify 2 into 2 1545390555.448 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390555.449 * [misc]taylor: Taking taylor expansion of PI in n 1545390555.449 * [misc]backup-simplify: Simplify PI into PI 1545390555.449 * [misc]taylor: Taking taylor expansion of n in n 1545390555.449 * [misc]backup-simplify: Simplify 0 into 0 1545390555.449 * [misc]backup-simplify: Simplify 1 into 1 1545390555.449 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390555.449 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545390555.450 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545390555.450 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1545390555.450 * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 1545390555.450 * [misc]backup-simplify: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k))) 1545390555.451 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545390555.451 * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 1545390555.452 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 1545390555.452 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n 1545390555.452 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1545390555.452 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1545390555.452 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n 1545390555.452 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390555.452 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390555.452 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n 1545390555.452 * [misc]taylor: Taking taylor expansion of 1 in n 1545390555.452 * [misc]backup-simplify: Simplify 1 into 1 1545390555.452 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545390555.452 * [misc]taylor: Taking taylor expansion of k in n 1545390555.452 * [misc]backup-simplify: Simplify k into k 1545390555.452 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545390555.452 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1545390555.452 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1545390555.452 * [misc]taylor: Taking taylor expansion of 2 in n 1545390555.452 * [misc]backup-simplify: Simplify 2 into 2 1545390555.452 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390555.452 * [misc]taylor: Taking taylor expansion of PI in n 1545390555.453 * [misc]backup-simplify: Simplify PI into PI 1545390555.453 * [misc]taylor: Taking taylor expansion of n in n 1545390555.453 * [misc]backup-simplify: Simplify 0 into 0 1545390555.453 * [misc]backup-simplify: Simplify 1 into 1 1545390555.453 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390555.453 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545390555.454 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545390555.454 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1545390555.454 * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 1545390555.454 * [misc]backup-simplify: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k))) 1545390555.454 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545390555.455 * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 1545390555.456 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 1545390555.456 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k 1545390555.456 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k 1545390555.456 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390555.456 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390555.456 * [misc]taylor: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k 1545390555.456 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k 1545390555.456 * [misc]taylor: Taking taylor expansion of 1 in k 1545390555.456 * [misc]backup-simplify: Simplify 1 into 1 1545390555.456 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545390555.456 * [misc]taylor: Taking taylor expansion of k in k 1545390555.456 * [misc]backup-simplify: Simplify 0 into 0 1545390555.456 * [misc]backup-simplify: Simplify 1 into 1 1545390555.456 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545390555.456 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1545390555.456 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1545390555.456 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1545390555.456 * [misc]taylor: Taking taylor expansion of 2 in k 1545390555.456 * [misc]backup-simplify: Simplify 2 into 2 1545390555.457 * [misc]taylor: Taking taylor expansion of PI in k 1545390555.457 * [misc]backup-simplify: Simplify PI into PI 1545390555.457 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545390555.457 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545390555.457 * [misc]taylor: Taking taylor expansion of (log n) in k 1545390555.457 * [misc]taylor: Taking taylor expansion of n in k 1545390555.457 * [misc]backup-simplify: Simplify n into n 1545390555.457 * [misc]backup-simplify: Simplify (log n) into (log n) 1545390555.458 * [misc]backup-simplify: Simplify (- 1) into -1 1545390555.458 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 1545390555.458 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1545390555.458 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1545390555.459 * [misc]backup-simplify: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n))) 1545390555.459 * [misc]backup-simplify: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1545390555.460 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 1545390555.461 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 1545390555.462 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1545390555.462 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1545390555.465 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1545390555.465 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1545390555.465 * [misc]backup-simplify: Simplify (- 0) into 0 1545390555.465 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390555.466 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- 1 (/ 1 k)))) into 0 1545390555.466 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545390555.467 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1545390555.468 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1545390555.468 * [misc]taylor: Taking taylor expansion of 0 in k 1545390555.468 * [misc]backup-simplify: Simplify 0 into 0 1545390555.468 * [misc]backup-simplify: Simplify 0 into 0 1545390555.468 * [misc]backup-simplify: Simplify 0 into 0 1545390555.468 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390555.469 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1545390555.472 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1545390555.472 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545390555.472 * [misc]backup-simplify: Simplify (- 0) into 0 1545390555.472 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390555.472 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0 1545390555.473 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545390555.473 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1545390555.475 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1545390555.475 * [misc]taylor: Taking taylor expansion of 0 in k 1545390555.475 * [misc]backup-simplify: Simplify 0 into 0 1545390555.475 * [misc]backup-simplify: Simplify 0 into 0 1545390555.475 * [misc]backup-simplify: Simplify 0 into 0 1545390555.475 * [misc]backup-simplify: Simplify 0 into 0 1545390555.476 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390555.477 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1545390555.481 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 1545390555.481 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545390555.481 * [misc]backup-simplify: Simplify (- 0) into 0 1545390555.481 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390555.482 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0 1545390555.482 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545390555.483 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1545390555.485 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1545390555.485 * [misc]taylor: Taking taylor expansion of 0 in k 1545390555.485 * [misc]backup-simplify: Simplify 0 into 0 1545390555.485 * [misc]backup-simplify: Simplify 0 into 0 1545390555.485 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) 1545390555.486 * [misc]backup-simplify: Simplify (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) into (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) 1545390555.486 * [misc]approximate: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in (n k) around 0 1545390555.486 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k 1545390555.486 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k 1545390555.486 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k 1545390555.486 * [misc]taylor: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k 1545390555.486 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390555.486 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390555.486 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in k 1545390555.486 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545390555.486 * [misc]taylor: Taking taylor expansion of k in k 1545390555.486 * [misc]backup-simplify: Simplify 0 into 0 1545390555.486 * [misc]backup-simplify: Simplify 1 into 1 1545390555.486 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545390555.486 * [misc]taylor: Taking taylor expansion of 1 in k 1545390555.486 * [misc]backup-simplify: Simplify 1 into 1 1545390555.486 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1545390555.486 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1545390555.486 * [misc]taylor: Taking taylor expansion of -2 in k 1545390555.486 * [misc]backup-simplify: Simplify -2 into -2 1545390555.486 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1545390555.486 * [misc]taylor: Taking taylor expansion of PI in k 1545390555.486 * [misc]backup-simplify: Simplify PI into PI 1545390555.486 * [misc]taylor: Taking taylor expansion of n in k 1545390555.486 * [misc]backup-simplify: Simplify n into n 1545390555.486 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1545390555.486 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1545390555.486 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1545390555.487 * [misc]backup-simplify: Simplify (+ 1 0) into 1 1545390555.487 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545390555.487 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1545390555.487 * [misc]backup-simplify: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) 1545390555.487 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n 1545390555.487 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n 1545390555.487 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n 1545390555.487 * [misc]taylor: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n 1545390555.487 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390555.487 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390555.487 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in n 1545390555.487 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545390555.487 * [misc]taylor: Taking taylor expansion of k in n 1545390555.487 * [misc]backup-simplify: Simplify k into k 1545390555.487 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545390555.487 * [misc]taylor: Taking taylor expansion of 1 in n 1545390555.487 * [misc]backup-simplify: Simplify 1 into 1 1545390555.487 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1545390555.487 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1545390555.487 * [misc]taylor: Taking taylor expansion of -2 in n 1545390555.487 * [misc]backup-simplify: Simplify -2 into -2 1545390555.487 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390555.487 * [misc]taylor: Taking taylor expansion of PI in n 1545390555.487 * [misc]backup-simplify: Simplify PI into PI 1545390555.487 * [misc]taylor: Taking taylor expansion of n in n 1545390555.487 * [misc]backup-simplify: Simplify 0 into 0 1545390555.487 * [misc]backup-simplify: Simplify 1 into 1 1545390555.487 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390555.488 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1545390555.488 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1545390555.488 * [misc]backup-simplify: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 1545390555.488 * [misc]backup-simplify: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1)) 1545390555.488 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545390555.489 * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 1545390555.489 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 1545390555.489 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n 1545390555.489 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n 1545390555.489 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n 1545390555.489 * [misc]taylor: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n 1545390555.489 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390555.489 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390555.489 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in n 1545390555.489 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545390555.489 * [misc]taylor: Taking taylor expansion of k in n 1545390555.489 * [misc]backup-simplify: Simplify k into k 1545390555.489 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545390555.489 * [misc]taylor: Taking taylor expansion of 1 in n 1545390555.489 * [misc]backup-simplify: Simplify 1 into 1 1545390555.489 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1545390555.489 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1545390555.489 * [misc]taylor: Taking taylor expansion of -2 in n 1545390555.489 * [misc]backup-simplify: Simplify -2 into -2 1545390555.489 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390555.490 * [misc]taylor: Taking taylor expansion of PI in n 1545390555.490 * [misc]backup-simplify: Simplify PI into PI 1545390555.490 * [misc]taylor: Taking taylor expansion of n in n 1545390555.490 * [misc]backup-simplify: Simplify 0 into 0 1545390555.490 * [misc]backup-simplify: Simplify 1 into 1 1545390555.490 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390555.490 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1545390555.490 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1545390555.490 * [misc]backup-simplify: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 1545390555.490 * [misc]backup-simplify: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1)) 1545390555.491 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545390555.491 * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 1545390555.492 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 1545390555.492 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k 1545390555.492 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) in k 1545390555.492 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390555.492 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390555.492 * [misc]taylor: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) in k 1545390555.492 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in k 1545390555.492 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545390555.492 * [misc]taylor: Taking taylor expansion of k in k 1545390555.492 * [misc]backup-simplify: Simplify 0 into 0 1545390555.492 * [misc]backup-simplify: Simplify 1 into 1 1545390555.492 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545390555.492 * [misc]taylor: Taking taylor expansion of 1 in k 1545390555.492 * [misc]backup-simplify: Simplify 1 into 1 1545390555.492 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1545390555.492 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1545390555.492 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1545390555.492 * [misc]taylor: Taking taylor expansion of -2 in k 1545390555.492 * [misc]backup-simplify: Simplify -2 into -2 1545390555.492 * [misc]taylor: Taking taylor expansion of PI in k 1545390555.492 * [misc]backup-simplify: Simplify PI into PI 1545390555.493 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1545390555.493 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1545390555.493 * [misc]taylor: Taking taylor expansion of (log n) in k 1545390555.493 * [misc]taylor: Taking taylor expansion of n in k 1545390555.493 * [misc]backup-simplify: Simplify n into n 1545390555.493 * [misc]backup-simplify: Simplify (log n) into (log n) 1545390555.493 * [misc]backup-simplify: Simplify (+ 1 0) into 1 1545390555.494 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1545390555.494 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1545390555.495 * [misc]backup-simplify: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n)) 1545390555.496 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1545390555.496 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 1545390555.497 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 1545390555.498 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1545390555.499 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1545390555.501 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1545390555.501 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1545390555.502 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390555.502 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (+ (/ 1 k) 1))) into 0 1545390555.503 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545390555.503 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1545390555.505 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1545390555.505 * [misc]taylor: Taking taylor expansion of 0 in k 1545390555.505 * [misc]backup-simplify: Simplify 0 into 0 1545390555.505 * [misc]backup-simplify: Simplify 0 into 0 1545390555.505 * [misc]backup-simplify: Simplify 0 into 0 1545390555.506 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390555.507 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1545390555.512 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 1545390555.513 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545390555.513 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390555.513 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0 1545390555.514 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545390555.515 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1545390555.517 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1545390555.517 * [misc]taylor: Taking taylor expansion of 0 in k 1545390555.517 * [misc]backup-simplify: Simplify 0 into 0 1545390555.517 * [misc]backup-simplify: Simplify 0 into 0 1545390555.517 * [misc]backup-simplify: Simplify 0 into 0 1545390555.517 * [misc]backup-simplify: Simplify 0 into 0 1545390555.519 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390555.520 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1545390555.528 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0 1545390555.528 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545390555.529 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390555.529 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1))))) into 0 1545390555.530 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545390555.531 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 1545390555.534 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1545390555.534 * [misc]taylor: Taking taylor expansion of 0 in k 1545390555.534 * [misc]backup-simplify: Simplify 0 into 0 1545390555.534 * [misc]backup-simplify: Simplify 0 into 0 1545390555.535 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) 1545390555.535 * * * * [misc]progress: [ 3 / 4 ] generating series at (2) 1545390555.536 * [misc]backup-simplify: Simplify (* (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) into (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) 1545390555.536 * [misc]approximate: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in (k n) around 0 1545390555.536 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in n 1545390555.536 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n 1545390555.536 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n 1545390555.536 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n 1545390555.536 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 k)) in n 1545390555.536 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390555.536 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390555.536 * [misc]taylor: Taking taylor expansion of (- 1 k) in n 1545390555.536 * [misc]taylor: Taking taylor expansion of 1 in n 1545390555.537 * [misc]backup-simplify: Simplify 1 into 1 1545390555.537 * [misc]taylor: Taking taylor expansion of k in n 1545390555.537 * [misc]backup-simplify: Simplify k into k 1545390555.537 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1545390555.537 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1545390555.537 * [misc]taylor: Taking taylor expansion of 2 in n 1545390555.537 * [misc]backup-simplify: Simplify 2 into 2 1545390555.537 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545390555.537 * [misc]taylor: Taking taylor expansion of n in n 1545390555.537 * [misc]backup-simplify: Simplify 0 into 0 1545390555.537 * [misc]backup-simplify: Simplify 1 into 1 1545390555.537 * [misc]taylor: Taking taylor expansion of PI in n 1545390555.537 * [misc]backup-simplify: Simplify PI into PI 1545390555.537 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1545390555.537 * [misc]backup-simplify: Simplify (* 2 0) into 0 1545390555.538 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1545390555.539 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1545390555.540 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545390555.540 * [misc]backup-simplify: Simplify (- k) into (- k) 1545390555.540 * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) 1545390555.540 * [misc]backup-simplify: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k)) 1545390555.541 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545390555.541 * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) 1545390555.542 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 1545390555.542 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1545390555.542 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545390555.542 * [misc]taylor: Taking taylor expansion of k in n 1545390555.542 * [misc]backup-simplify: Simplify k into k 1545390555.542 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545390555.542 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1545390555.542 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1545390555.542 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1545390555.542 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k 1545390555.542 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k 1545390555.542 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k 1545390555.542 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k 1545390555.542 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 k)) in k 1545390555.542 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390555.543 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390555.543 * [misc]taylor: Taking taylor expansion of (- 1 k) in k 1545390555.543 * [misc]taylor: Taking taylor expansion of 1 in k 1545390555.543 * [misc]backup-simplify: Simplify 1 into 1 1545390555.543 * [misc]taylor: Taking taylor expansion of k in k 1545390555.543 * [misc]backup-simplify: Simplify 0 into 0 1545390555.543 * [misc]backup-simplify: Simplify 1 into 1 1545390555.543 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1545390555.543 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1545390555.543 * [misc]taylor: Taking taylor expansion of 2 in k 1545390555.543 * [misc]backup-simplify: Simplify 2 into 2 1545390555.543 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1545390555.543 * [misc]taylor: Taking taylor expansion of n in k 1545390555.543 * [misc]backup-simplify: Simplify n into n 1545390555.543 * [misc]taylor: Taking taylor expansion of PI in k 1545390555.543 * [misc]backup-simplify: Simplify PI into PI 1545390555.543 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1545390555.543 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1545390555.543 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1545390555.543 * [misc]backup-simplify: Simplify (- 0) into 0 1545390555.543 * [misc]backup-simplify: Simplify (+ 1 0) into 1 1545390555.543 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545390555.544 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1545390555.544 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1545390555.544 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1545390555.544 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545390555.544 * [misc]taylor: Taking taylor expansion of k in k 1545390555.544 * [misc]backup-simplify: Simplify 0 into 0 1545390555.544 * [misc]backup-simplify: Simplify 1 into 1 1545390555.544 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545390555.544 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545390555.544 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1545390555.544 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k 1545390555.544 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k 1545390555.544 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k 1545390555.544 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k 1545390555.544 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 k)) in k 1545390555.544 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390555.544 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390555.544 * [misc]taylor: Taking taylor expansion of (- 1 k) in k 1545390555.544 * [misc]taylor: Taking taylor expansion of 1 in k 1545390555.544 * [misc]backup-simplify: Simplify 1 into 1 1545390555.544 * [misc]taylor: Taking taylor expansion of k in k 1545390555.544 * [misc]backup-simplify: Simplify 0 into 0 1545390555.544 * [misc]backup-simplify: Simplify 1 into 1 1545390555.544 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1545390555.544 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1545390555.544 * [misc]taylor: Taking taylor expansion of 2 in k 1545390555.545 * [misc]backup-simplify: Simplify 2 into 2 1545390555.545 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1545390555.545 * [misc]taylor: Taking taylor expansion of n in k 1545390555.545 * [misc]backup-simplify: Simplify n into n 1545390555.545 * [misc]taylor: Taking taylor expansion of PI in k 1545390555.545 * [misc]backup-simplify: Simplify PI into PI 1545390555.545 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1545390555.545 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1545390555.545 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1545390555.545 * [misc]backup-simplify: Simplify (- 0) into 0 1545390555.545 * [misc]backup-simplify: Simplify (+ 1 0) into 1 1545390555.545 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545390555.545 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1545390555.545 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1545390555.545 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1545390555.545 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545390555.545 * [misc]taylor: Taking taylor expansion of k in k 1545390555.545 * [misc]backup-simplify: Simplify 0 into 0 1545390555.545 * [misc]backup-simplify: Simplify 1 into 1 1545390555.546 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545390555.546 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545390555.546 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1545390555.546 * [misc]backup-simplify: Simplify (* (pow (* 2 (* n PI)) 1/2) 0) into 0 1545390555.546 * [misc]taylor: Taking taylor expansion of 0 in n 1545390555.546 * [misc]backup-simplify: Simplify 0 into 0 1545390555.546 * [misc]backup-simplify: Simplify 0 into 0 1545390555.546 * [misc]backup-simplify: Simplify (+ (* n 0) (* 0 PI)) into 0 1545390555.547 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0 1545390555.547 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 1545390555.547 * [misc]backup-simplify: Simplify (- 1) into -1 1545390555.547 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 1545390555.547 * [misc]backup-simplify: Simplify (+ (* 1/2 -1) (* 0 1)) into -1/2 1545390555.548 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI))))) 1545390555.548 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1)))) into (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) 1545390555.548 * [misc]backup-simplify: Simplify (+ (* (pow (* 2 (* n PI)) 1/2) +nan.0) (* (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) 0)) into (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) 1545390555.548 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 1545390555.548 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 1545390555.548 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1545390555.548 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545390555.548 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1545390555.548 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1545390555.548 * [misc]taylor: Taking taylor expansion of 2 in n 1545390555.548 * [misc]backup-simplify: Simplify 2 into 2 1545390555.548 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1545390555.548 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1545390555.548 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1545390555.548 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545390555.548 * [misc]taylor: Taking taylor expansion of n in n 1545390555.548 * [misc]backup-simplify: Simplify 0 into 0 1545390555.548 * [misc]backup-simplify: Simplify 1 into 1 1545390555.548 * [misc]taylor: Taking taylor expansion of PI in n 1545390555.548 * [misc]backup-simplify: Simplify PI into PI 1545390555.549 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1545390555.549 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1545390555.549 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545390555.549 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1545390555.550 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1545390555.550 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1545390555.550 * [misc]backup-simplify: Simplify (- 0) into 0 1545390555.550 * [misc]backup-simplify: Simplify 0 into 0 1545390555.550 * [misc]backup-simplify: Simplify 0 into 0 1545390555.550 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1545390555.551 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1545390555.551 * [misc]backup-simplify: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 1545390555.551 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 1545390555.552 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 1)))) 2) into 0 1545390555.552 * [misc]backup-simplify: Simplify (- 0) into 0 1545390555.552 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390555.552 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 -1) (* 0 1))) into 0 1545390555.553 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0 1545390555.553 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) 1545390555.554 * [misc]backup-simplify: Simplify (+ (* (pow (* 2 (* n PI)) 1/2) +nan.0) (+ (* (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) +nan.0) (* (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) 0))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) 1545390555.554 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) in n 1545390555.554 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))) in n 1545390555.554 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n 1545390555.554 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1545390555.554 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545390555.554 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n 1545390555.554 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n 1545390555.554 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1545390555.554 * [misc]taylor: Taking taylor expansion of 2 in n 1545390555.554 * [misc]backup-simplify: Simplify 2 into 2 1545390555.554 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1545390555.554 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1545390555.554 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1545390555.554 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1545390555.554 * [misc]taylor: Taking taylor expansion of 2 in n 1545390555.554 * [misc]backup-simplify: Simplify 2 into 2 1545390555.554 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545390555.554 * [misc]taylor: Taking taylor expansion of n in n 1545390555.554 * [misc]backup-simplify: Simplify 0 into 0 1545390555.554 * [misc]backup-simplify: Simplify 1 into 1 1545390555.554 * [misc]taylor: Taking taylor expansion of PI in n 1545390555.554 * [misc]backup-simplify: Simplify PI into PI 1545390555.555 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1545390555.555 * [misc]backup-simplify: Simplify (* 2 0) into 0 1545390555.555 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1545390555.556 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1545390555.556 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545390555.556 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1545390555.556 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545390555.556 * [misc]taylor: Taking taylor expansion of n in n 1545390555.556 * [misc]backup-simplify: Simplify 0 into 0 1545390555.556 * [misc]backup-simplify: Simplify 1 into 1 1545390555.556 * [misc]taylor: Taking taylor expansion of PI in n 1545390555.556 * [misc]backup-simplify: Simplify PI into PI 1545390555.556 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1545390555.556 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1545390555.557 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545390555.557 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1545390555.557 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 1545390555.557 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 1545390555.557 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1545390555.557 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545390555.557 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1545390555.557 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1545390555.557 * [misc]taylor: Taking taylor expansion of 2 in n 1545390555.557 * [misc]backup-simplify: Simplify 2 into 2 1545390555.557 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1545390555.557 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1545390555.557 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1545390555.557 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545390555.557 * [misc]taylor: Taking taylor expansion of n in n 1545390555.557 * [misc]backup-simplify: Simplify 0 into 0 1545390555.557 * [misc]backup-simplify: Simplify 1 into 1 1545390555.557 * [misc]taylor: Taking taylor expansion of PI in n 1545390555.557 * [misc]backup-simplify: Simplify PI into PI 1545390555.557 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1545390555.558 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1545390555.558 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545390555.558 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1545390555.559 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545390555.559 * [misc]backup-simplify: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 1545390555.559 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0 1545390555.560 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1545390555.560 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1545390555.560 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1545390555.560 * [misc]backup-simplify: Simplify (- 0) into 0 1545390555.560 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390555.560 * [misc]backup-simplify: Simplify (- 0) into 0 1545390555.560 * [misc]backup-simplify: Simplify 0 into 0 1545390555.561 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1545390555.562 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1545390555.563 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 1545390555.563 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI))) 1545390555.563 * [misc]backup-simplify: Simplify 0 into 0 1545390555.563 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390555.564 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1545390555.565 * [misc]backup-simplify: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1545390555.565 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 1545390555.567 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 (* n PI)) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 (* n PI)) 1)))) 6) into 0 1545390555.567 * [misc]backup-simplify: Simplify (- 0) into 0 1545390555.567 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390555.567 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1)))) into 0 1545390555.567 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log (* 2 (* n PI))))))) into 0 1545390555.568 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 3) 6)) (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 3))) 1545390555.569 * [misc]backup-simplify: Simplify (+ (* (pow (* 2 (* n PI)) 1/2) +nan.0) (+ (* (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) +nan.0) (+ (* (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) +nan.0) (* (* -1/48 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 3))) 0)))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))))))) 1545390555.569 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))))))) in n 1545390555.569 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))))))) in n 1545390555.569 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n 1545390555.569 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1545390555.569 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545390555.569 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n 1545390555.569 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n 1545390555.569 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1545390555.569 * [misc]taylor: Taking taylor expansion of 2 in n 1545390555.569 * [misc]backup-simplify: Simplify 2 into 2 1545390555.569 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1545390555.570 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1545390555.570 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1545390555.570 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1545390555.570 * [misc]taylor: Taking taylor expansion of 2 in n 1545390555.570 * [misc]backup-simplify: Simplify 2 into 2 1545390555.570 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545390555.570 * [misc]taylor: Taking taylor expansion of n in n 1545390555.570 * [misc]backup-simplify: Simplify 0 into 0 1545390555.570 * [misc]backup-simplify: Simplify 1 into 1 1545390555.570 * [misc]taylor: Taking taylor expansion of PI in n 1545390555.570 * [misc]backup-simplify: Simplify PI into PI 1545390555.570 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1545390555.570 * [misc]backup-simplify: Simplify (* 2 0) into 0 1545390555.570 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1545390555.571 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1545390555.571 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545390555.571 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1545390555.571 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545390555.571 * [misc]taylor: Taking taylor expansion of n in n 1545390555.571 * [misc]backup-simplify: Simplify 0 into 0 1545390555.571 * [misc]backup-simplify: Simplify 1 into 1 1545390555.571 * [misc]taylor: Taking taylor expansion of PI in n 1545390555.571 * [misc]backup-simplify: Simplify PI into PI 1545390555.571 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1545390555.572 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1545390555.572 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545390555.572 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1545390555.572 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))))) in n 1545390555.572 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))))) in n 1545390555.572 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 1545390555.572 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1545390555.572 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545390555.572 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1545390555.572 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1545390555.572 * [misc]taylor: Taking taylor expansion of 2 in n 1545390555.572 * [misc]backup-simplify: Simplify 2 into 2 1545390555.573 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1545390555.573 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1545390555.573 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1545390555.573 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545390555.573 * [misc]taylor: Taking taylor expansion of n in n 1545390555.573 * [misc]backup-simplify: Simplify 0 into 0 1545390555.573 * [misc]backup-simplify: Simplify 1 into 1 1545390555.573 * [misc]taylor: Taking taylor expansion of PI in n 1545390555.573 * [misc]backup-simplify: Simplify PI into PI 1545390555.573 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1545390555.573 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1545390555.573 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545390555.574 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1545390555.574 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))) in n 1545390555.574 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) in n 1545390555.574 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1545390555.574 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545390555.574 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))) in n 1545390555.574 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) in n 1545390555.574 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1545390555.574 * [misc]taylor: Taking taylor expansion of 2 in n 1545390555.574 * [misc]backup-simplify: Simplify 2 into 2 1545390555.574 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1545390555.574 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1545390555.574 * [misc]taylor: Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n 1545390555.574 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1545390555.574 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1545390555.574 * [misc]taylor: Taking taylor expansion of 2 in n 1545390555.574 * [misc]backup-simplify: Simplify 2 into 2 1545390555.574 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545390555.574 * [misc]taylor: Taking taylor expansion of n in n 1545390555.574 * [misc]backup-simplify: Simplify 0 into 0 1545390555.574 * [misc]backup-simplify: Simplify 1 into 1 1545390555.574 * [misc]taylor: Taking taylor expansion of PI in n 1545390555.574 * [misc]backup-simplify: Simplify PI into PI 1545390555.574 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1545390555.574 * [misc]backup-simplify: Simplify (* 2 0) into 0 1545390555.575 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1545390555.575 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1545390555.576 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545390555.576 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545390555.576 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1545390555.576 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545390555.576 * [misc]taylor: Taking taylor expansion of n in n 1545390555.576 * [misc]backup-simplify: Simplify 0 into 0 1545390555.576 * [misc]backup-simplify: Simplify 1 into 1 1545390555.576 * [misc]taylor: Taking taylor expansion of PI in n 1545390555.576 * [misc]backup-simplify: Simplify PI into PI 1545390555.576 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1545390555.577 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1545390555.577 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545390555.577 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1545390555.577 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545390555.578 * [misc]backup-simplify: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 1545390555.578 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0 1545390555.578 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1545390555.578 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1545390555.579 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1545390555.579 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545390555.579 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545390555.580 * [misc]backup-simplify: Simplify (* (+ (log n) (log (* 2 PI))) (+ (log n) (log (* 2 PI)))) into (pow (+ (log n) (log (* 2 PI))) 2) 1545390555.580 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) into (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 1545390555.581 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 0) into 0 1545390555.581 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1545390555.581 * [misc]backup-simplify: Simplify (- 0) into 0 1545390555.581 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390555.581 * [misc]backup-simplify: Simplify (- 0) into 0 1545390555.581 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390555.581 * [misc]backup-simplify: Simplify (- 0) into 0 1545390555.581 * [misc]backup-simplify: Simplify 0 into 0 1545390555.582 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1545390555.583 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1545390555.584 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1545390555.585 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545390555.585 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1545390555.586 * [misc]backup-simplify: Simplify (+ (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) (* +nan.0 PI)) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) 1545390555.587 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) 1545390555.588 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1545390555.590 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1545390555.592 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 1545390555.595 * [misc]backup-simplify: Simplify (+ (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) (- (* +nan.0 (* (sqrt 2) PI)))) into (- (+ (* +nan.0 (* (sqrt 2) PI)) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))))) 1545390555.599 * [misc]backup-simplify: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) PI)) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) 1545390555.602 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) 1545390555.603 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1545390555.604 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 1545390555.606 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1545390555.608 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 (pow PI 2))) (+ (* 0 (* +nan.0 PI)) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 1545390555.612 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) (+ (* 0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 1545390555.613 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 1545390555.614 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 1545390555.617 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) (pow (* n 1) 2)) (+ (* (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) (* n k)) (* (- (* +nan.0 (* (sqrt 2) PI))) (* n 1)))) into (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))))))) 1545390555.618 * [misc]backup-simplify: Simplify (* (sqrt (* (/ 1 (sqrt (/ 1 k))) (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)))) (sqrt (* (/ 1 (sqrt (/ 1 k))) (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2))))) into (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) 1545390555.618 * [misc]approximate: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in (k n) around 0 1545390555.618 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in n 1545390555.618 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n 1545390555.618 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1545390555.618 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1545390555.618 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n 1545390555.618 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390555.618 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390555.618 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n 1545390555.618 * [misc]taylor: Taking taylor expansion of 1 in n 1545390555.618 * [misc]backup-simplify: Simplify 1 into 1 1545390555.618 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545390555.618 * [misc]taylor: Taking taylor expansion of k in n 1545390555.618 * [misc]backup-simplify: Simplify k into k 1545390555.618 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545390555.618 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1545390555.618 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1545390555.618 * [misc]taylor: Taking taylor expansion of 2 in n 1545390555.618 * [misc]backup-simplify: Simplify 2 into 2 1545390555.618 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390555.618 * [misc]taylor: Taking taylor expansion of PI in n 1545390555.618 * [misc]backup-simplify: Simplify PI into PI 1545390555.618 * [misc]taylor: Taking taylor expansion of n in n 1545390555.618 * [misc]backup-simplify: Simplify 0 into 0 1545390555.618 * [misc]backup-simplify: Simplify 1 into 1 1545390555.618 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390555.619 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545390555.619 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545390555.619 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1545390555.619 * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 1545390555.619 * [misc]backup-simplify: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k))) 1545390555.619 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545390555.620 * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 1545390555.620 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 1545390555.620 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1545390555.620 * [misc]taylor: Taking taylor expansion of k in n 1545390555.620 * [misc]backup-simplify: Simplify k into k 1545390555.620 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1545390555.620 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1545390555.620 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k 1545390555.620 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k 1545390555.620 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1545390555.620 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1545390555.620 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k 1545390555.620 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390555.620 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390555.620 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k 1545390555.621 * [misc]taylor: Taking taylor expansion of 1 in k 1545390555.621 * [misc]backup-simplify: Simplify 1 into 1 1545390555.621 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545390555.621 * [misc]taylor: Taking taylor expansion of k in k 1545390555.621 * [misc]backup-simplify: Simplify 0 into 0 1545390555.621 * [misc]backup-simplify: Simplify 1 into 1 1545390555.621 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545390555.621 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1545390555.621 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1545390555.621 * [misc]taylor: Taking taylor expansion of 2 in k 1545390555.621 * [misc]backup-simplify: Simplify 2 into 2 1545390555.621 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1545390555.621 * [misc]taylor: Taking taylor expansion of PI in k 1545390555.621 * [misc]backup-simplify: Simplify PI into PI 1545390555.621 * [misc]taylor: Taking taylor expansion of n in k 1545390555.621 * [misc]backup-simplify: Simplify n into n 1545390555.621 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1545390555.621 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1545390555.621 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1545390555.621 * [misc]backup-simplify: Simplify (- 1) into -1 1545390555.621 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 1545390555.621 * [misc]backup-simplify: Simplify (* 1/2 -1) into -1/2 1545390555.621 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1545390555.621 * [misc]backup-simplify: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 1545390555.621 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1545390555.621 * [misc]taylor: Taking taylor expansion of k in k 1545390555.622 * [misc]backup-simplify: Simplify 0 into 0 1545390555.622 * [misc]backup-simplify: Simplify 1 into 1 1545390555.622 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545390555.622 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1545390555.622 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k 1545390555.622 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k 1545390555.622 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1545390555.622 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1545390555.622 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k 1545390555.622 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390555.622 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390555.622 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k 1545390555.622 * [misc]taylor: Taking taylor expansion of 1 in k 1545390555.622 * [misc]backup-simplify: Simplify 1 into 1 1545390555.622 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545390555.622 * [misc]taylor: Taking taylor expansion of k in k 1545390555.622 * [misc]backup-simplify: Simplify 0 into 0 1545390555.622 * [misc]backup-simplify: Simplify 1 into 1 1545390555.622 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545390555.622 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1545390555.622 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1545390555.622 * [misc]taylor: Taking taylor expansion of 2 in k 1545390555.622 * [misc]backup-simplify: Simplify 2 into 2 1545390555.622 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1545390555.622 * [misc]taylor: Taking taylor expansion of PI in k 1545390555.622 * [misc]backup-simplify: Simplify PI into PI 1545390555.622 * [misc]taylor: Taking taylor expansion of n in k 1545390555.622 * [misc]backup-simplify: Simplify n into n 1545390555.622 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1545390555.622 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1545390555.622 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1545390555.623 * [misc]backup-simplify: Simplify (- 1) into -1 1545390555.623 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 1545390555.623 * [misc]backup-simplify: Simplify (* 1/2 -1) into -1/2 1545390555.623 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1545390555.623 * [misc]backup-simplify: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 1545390555.623 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1545390555.623 * [misc]taylor: Taking taylor expansion of k in k 1545390555.623 * [misc]backup-simplify: Simplify 0 into 0 1545390555.623 * [misc]backup-simplify: Simplify 1 into 1 1545390555.623 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545390555.623 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1545390555.624 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 0) into 0 1545390555.624 * [misc]taylor: Taking taylor expansion of 0 in n 1545390555.624 * [misc]backup-simplify: Simplify 0 into 0 1545390555.624 * [misc]backup-simplify: Simplify 0 into 0 1545390555.624 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) 1545390555.624 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n 1545390555.624 * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n 1545390555.624 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1545390555.624 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545390555.624 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n 1545390555.624 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n 1545390555.624 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390555.624 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390555.624 * [misc]taylor: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n 1545390555.624 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n 1545390555.624 * [misc]taylor: Taking taylor expansion of 1 in n 1545390555.624 * [misc]backup-simplify: Simplify 1 into 1 1545390555.624 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545390555.624 * [misc]taylor: Taking taylor expansion of k in n 1545390555.624 * [misc]backup-simplify: Simplify k into k 1545390555.624 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545390555.624 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1545390555.624 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1545390555.624 * [misc]taylor: Taking taylor expansion of 2 in n 1545390555.624 * [misc]backup-simplify: Simplify 2 into 2 1545390555.624 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390555.624 * [misc]taylor: Taking taylor expansion of PI in n 1545390555.624 * [misc]backup-simplify: Simplify PI into PI 1545390555.624 * [misc]taylor: Taking taylor expansion of n in n 1545390555.624 * [misc]backup-simplify: Simplify 0 into 0 1545390555.624 * [misc]backup-simplify: Simplify 1 into 1 1545390555.625 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390555.625 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545390555.625 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545390555.625 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1545390555.625 * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 1545390555.625 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545390555.626 * [misc]backup-simplify: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) 1545390555.626 * [misc]backup-simplify: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 1545390555.627 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 1545390555.627 * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) 1545390555.627 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 1545390555.628 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 1545390555.628 * [misc]backup-simplify: Simplify 0 into 0 1545390555.629 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1545390555.629 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) 1545390555.629 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n 1545390555.629 * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n 1545390555.629 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1545390555.629 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545390555.629 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n 1545390555.629 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n 1545390555.629 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390555.629 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390555.629 * [misc]taylor: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n 1545390555.629 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n 1545390555.629 * [misc]taylor: Taking taylor expansion of 1 in n 1545390555.629 * [misc]backup-simplify: Simplify 1 into 1 1545390555.629 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545390555.629 * [misc]taylor: Taking taylor expansion of k in n 1545390555.629 * [misc]backup-simplify: Simplify k into k 1545390555.629 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545390555.629 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1545390555.629 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1545390555.629 * [misc]taylor: Taking taylor expansion of 2 in n 1545390555.629 * [misc]backup-simplify: Simplify 2 into 2 1545390555.629 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390555.629 * [misc]taylor: Taking taylor expansion of PI in n 1545390555.629 * [misc]backup-simplify: Simplify PI into PI 1545390555.629 * [misc]taylor: Taking taylor expansion of n in n 1545390555.629 * [misc]backup-simplify: Simplify 0 into 0 1545390555.629 * [misc]backup-simplify: Simplify 1 into 1 1545390555.629 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390555.630 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545390555.630 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545390555.630 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1545390555.630 * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 1545390555.630 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545390555.631 * [misc]backup-simplify: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) 1545390555.631 * [misc]backup-simplify: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 1545390555.632 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 1545390555.632 * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) 1545390555.632 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 1545390555.633 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 1545390555.633 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1545390555.634 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1545390555.635 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1545390555.636 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1545390555.636 * [misc]backup-simplify: Simplify (- 0) into 0 1545390555.636 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390555.636 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545390555.636 * [misc]backup-simplify: Simplify (+ (* (- 1 (/ 1 k)) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1545390555.637 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into 0 1545390555.638 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1545390555.638 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into 0 1545390555.638 * [misc]backup-simplify: Simplify (- 0) into 0 1545390555.638 * [misc]backup-simplify: Simplify 0 into 0 1545390555.639 * [misc]backup-simplify: Simplify 0 into 0 1545390555.639 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1545390555.640 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) 1545390555.640 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n 1545390555.640 * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n 1545390555.640 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1545390555.640 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545390555.640 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n 1545390555.640 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n 1545390555.640 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390555.640 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390555.640 * [misc]taylor: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n 1545390555.640 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n 1545390555.640 * [misc]taylor: Taking taylor expansion of 1 in n 1545390555.640 * [misc]backup-simplify: Simplify 1 into 1 1545390555.640 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545390555.640 * [misc]taylor: Taking taylor expansion of k in n 1545390555.640 * [misc]backup-simplify: Simplify k into k 1545390555.640 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545390555.640 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1545390555.640 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1545390555.640 * [misc]taylor: Taking taylor expansion of 2 in n 1545390555.640 * [misc]backup-simplify: Simplify 2 into 2 1545390555.640 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390555.641 * [misc]taylor: Taking taylor expansion of PI in n 1545390555.641 * [misc]backup-simplify: Simplify PI into PI 1545390555.641 * [misc]taylor: Taking taylor expansion of n in n 1545390555.641 * [misc]backup-simplify: Simplify 0 into 0 1545390555.641 * [misc]backup-simplify: Simplify 1 into 1 1545390555.641 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390555.641 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545390555.642 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545390555.642 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1545390555.642 * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 1545390555.642 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545390555.643 * [misc]backup-simplify: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) 1545390555.644 * [misc]backup-simplify: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 1545390555.644 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 1545390555.645 * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) 1545390555.646 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 1545390555.647 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 1545390555.649 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3)))))))) 1545390555.651 * [misc]backup-simplify: Simplify (* (sqrt (* (/ 1 (sqrt (/ 1 (- k)))) (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)))) (sqrt (* (/ 1 (sqrt (/ 1 (- k)))) (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2))))) into (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) 1545390555.651 * [misc]approximate: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in (k n) around 0 1545390555.651 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in n 1545390555.651 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n 1545390555.651 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n 1545390555.651 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n 1545390555.651 * [misc]taylor: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n 1545390555.651 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390555.651 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390555.651 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in n 1545390555.651 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545390555.651 * [misc]taylor: Taking taylor expansion of k in n 1545390555.651 * [misc]backup-simplify: Simplify k into k 1545390555.651 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545390555.651 * [misc]taylor: Taking taylor expansion of 1 in n 1545390555.651 * [misc]backup-simplify: Simplify 1 into 1 1545390555.651 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1545390555.651 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1545390555.651 * [misc]taylor: Taking taylor expansion of -2 in n 1545390555.651 * [misc]backup-simplify: Simplify -2 into -2 1545390555.651 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390555.651 * [misc]taylor: Taking taylor expansion of PI in n 1545390555.652 * [misc]backup-simplify: Simplify PI into PI 1545390555.652 * [misc]taylor: Taking taylor expansion of n in n 1545390555.652 * [misc]backup-simplify: Simplify 0 into 0 1545390555.652 * [misc]backup-simplify: Simplify 1 into 1 1545390555.652 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390555.652 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1545390555.653 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1545390555.653 * [misc]backup-simplify: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 1545390555.653 * [misc]backup-simplify: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1)) 1545390555.653 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545390555.654 * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 1545390555.656 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 1545390555.656 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1545390555.656 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1545390555.656 * [misc]taylor: Taking taylor expansion of -1 in n 1545390555.656 * [misc]backup-simplify: Simplify -1 into -1 1545390555.656 * [misc]taylor: Taking taylor expansion of k in n 1545390555.656 * [misc]backup-simplify: Simplify k into k 1545390555.656 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1545390555.656 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1545390555.656 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1545390555.656 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1545390555.657 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) 1545390555.657 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in k 1545390555.657 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k 1545390555.657 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k 1545390555.657 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k 1545390555.657 * [misc]taylor: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k 1545390555.657 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390555.657 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390555.657 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in k 1545390555.657 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545390555.657 * [misc]taylor: Taking taylor expansion of k in k 1545390555.657 * [misc]backup-simplify: Simplify 0 into 0 1545390555.657 * [misc]backup-simplify: Simplify 1 into 1 1545390555.657 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545390555.658 * [misc]taylor: Taking taylor expansion of 1 in k 1545390555.658 * [misc]backup-simplify: Simplify 1 into 1 1545390555.658 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1545390555.658 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1545390555.658 * [misc]taylor: Taking taylor expansion of -2 in k 1545390555.658 * [misc]backup-simplify: Simplify -2 into -2 1545390555.658 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1545390555.658 * [misc]taylor: Taking taylor expansion of PI in k 1545390555.658 * [misc]backup-simplify: Simplify PI into PI 1545390555.658 * [misc]taylor: Taking taylor expansion of n in k 1545390555.658 * [misc]backup-simplify: Simplify n into n 1545390555.658 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1545390555.658 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1545390555.658 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1545390555.658 * [misc]backup-simplify: Simplify (+ 1 0) into 1 1545390555.658 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545390555.658 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1545390555.659 * [misc]backup-simplify: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) 1545390555.659 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1545390555.659 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1545390555.659 * [misc]taylor: Taking taylor expansion of -1 in k 1545390555.659 * [misc]backup-simplify: Simplify -1 into -1 1545390555.659 * [misc]taylor: Taking taylor expansion of k in k 1545390555.659 * [misc]backup-simplify: Simplify 0 into 0 1545390555.659 * [misc]backup-simplify: Simplify 1 into 1 1545390555.659 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1545390555.659 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545390555.660 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1545390555.660 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) 1545390555.660 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in k 1545390555.660 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k 1545390555.660 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k 1545390555.660 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k 1545390555.660 * [misc]taylor: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k 1545390555.660 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545390555.660 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390555.660 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in k 1545390555.660 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545390555.660 * [misc]taylor: Taking taylor expansion of k in k 1545390555.660 * [misc]backup-simplify: Simplify 0 into 0 1545390555.660 * [misc]backup-simplify: Simplify 1 into 1 1545390555.660 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545390555.661 * [misc]taylor: Taking taylor expansion of 1 in k 1545390555.661 * [misc]backup-simplify: Simplify 1 into 1 1545390555.661 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1545390555.661 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1545390555.661 * [misc]taylor: Taking taylor expansion of -2 in k 1545390555.661 * [misc]backup-simplify: Simplify -2 into -2 1545390555.661 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1545390555.661 * [misc]taylor: Taking taylor expansion of PI in k 1545390555.661 * [misc]backup-simplify: Simplify PI into PI 1545390555.661 * [misc]taylor: Taking taylor expansion of n in k 1545390555.661 * [misc]backup-simplify: Simplify n into n 1545390555.661 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1545390555.661 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1545390555.661 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1545390555.661 * [misc]backup-simplify: Simplify (+ 1 0) into 1 1545390555.661 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545390555.661 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1545390555.662 * [misc]backup-simplify: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) 1545390555.662 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1545390555.662 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1545390555.662 * [misc]taylor: Taking taylor expansion of -1 in k 1545390555.662 * [misc]backup-simplify: Simplify -1 into -1 1545390555.662 * [misc]taylor: Taking taylor expansion of k in k 1545390555.662 * [misc]backup-simplify: Simplify 0 into 0 1545390555.662 * [misc]backup-simplify: Simplify 1 into 1 1545390555.662 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1545390555.662 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545390555.663 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1545390555.663 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) 1545390555.663 * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n 1545390555.663 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1545390555.663 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545390555.663 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n 1545390555.663 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n 1545390555.663 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390555.663 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390555.663 * [misc]taylor: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n 1545390555.663 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1545390555.663 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1545390555.663 * [misc]taylor: Taking taylor expansion of -2 in n 1545390555.663 * [misc]backup-simplify: Simplify -2 into -2 1545390555.663 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390555.663 * [misc]taylor: Taking taylor expansion of PI in n 1545390555.663 * [misc]backup-simplify: Simplify PI into PI 1545390555.663 * [misc]taylor: Taking taylor expansion of n in n 1545390555.663 * [misc]backup-simplify: Simplify 0 into 0 1545390555.663 * [misc]backup-simplify: Simplify 1 into 1 1545390555.664 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390555.664 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1545390555.664 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1545390555.665 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in n 1545390555.665 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545390555.665 * [misc]taylor: Taking taylor expansion of k in n 1545390555.665 * [misc]backup-simplify: Simplify k into k 1545390555.665 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545390555.665 * [misc]taylor: Taking taylor expansion of 1 in n 1545390555.665 * [misc]backup-simplify: Simplify 1 into 1 1545390555.665 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545390555.666 * [misc]backup-simplify: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 1545390555.666 * [misc]backup-simplify: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) 1545390555.667 * [misc]backup-simplify: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 1545390555.667 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 1545390555.668 * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) 1545390555.669 * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) 1545390555.669 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1545390555.670 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1545390555.671 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) 1545390555.671 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n 1545390555.671 * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n 1545390555.671 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1545390555.671 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545390555.671 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n 1545390555.671 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n 1545390555.671 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390555.671 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390555.671 * [misc]taylor: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n 1545390555.671 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1545390555.671 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1545390555.671 * [misc]taylor: Taking taylor expansion of -2 in n 1545390555.671 * [misc]backup-simplify: Simplify -2 into -2 1545390555.671 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390555.671 * [misc]taylor: Taking taylor expansion of PI in n 1545390555.671 * [misc]backup-simplify: Simplify PI into PI 1545390555.671 * [misc]taylor: Taking taylor expansion of n in n 1545390555.671 * [misc]backup-simplify: Simplify 0 into 0 1545390555.671 * [misc]backup-simplify: Simplify 1 into 1 1545390555.671 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390555.672 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1545390555.672 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1545390555.672 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in n 1545390555.672 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545390555.672 * [misc]taylor: Taking taylor expansion of k in n 1545390555.672 * [misc]backup-simplify: Simplify k into k 1545390555.672 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545390555.672 * [misc]taylor: Taking taylor expansion of 1 in n 1545390555.672 * [misc]backup-simplify: Simplify 1 into 1 1545390555.673 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545390555.673 * [misc]backup-simplify: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 1545390555.674 * [misc]backup-simplify: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) 1545390555.674 * [misc]backup-simplify: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 1545390555.675 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 1545390555.675 * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) 1545390555.676 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) 1545390555.676 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) 1545390555.677 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545390555.677 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1545390555.677 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545390555.678 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1545390555.678 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1545390555.680 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1545390555.680 * [misc]backup-simplify: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (/ 1 k) 1))) into 0 1545390555.680 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into 0 1545390555.681 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1545390555.682 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into 0 1545390555.682 * [misc]backup-simplify: Simplify 0 into 0 1545390555.682 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390555.683 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1545390555.683 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) 1545390555.683 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n 1545390555.683 * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n 1545390555.683 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1545390555.683 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545390555.683 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n 1545390555.683 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n 1545390555.683 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545390555.683 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545390555.683 * [misc]taylor: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n 1545390555.683 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1545390555.683 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1545390555.683 * [misc]taylor: Taking taylor expansion of -2 in n 1545390555.684 * [misc]backup-simplify: Simplify -2 into -2 1545390555.684 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390555.684 * [misc]taylor: Taking taylor expansion of PI in n 1545390555.684 * [misc]backup-simplify: Simplify PI into PI 1545390555.684 * [misc]taylor: Taking taylor expansion of n in n 1545390555.684 * [misc]backup-simplify: Simplify 0 into 0 1545390555.684 * [misc]backup-simplify: Simplify 1 into 1 1545390555.684 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390555.684 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1545390555.684 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1545390555.684 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in n 1545390555.684 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545390555.684 * [misc]taylor: Taking taylor expansion of k in n 1545390555.684 * [misc]backup-simplify: Simplify k into k 1545390555.684 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545390555.684 * [misc]taylor: Taking taylor expansion of 1 in n 1545390555.684 * [misc]backup-simplify: Simplify 1 into 1 1545390555.685 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545390555.685 * [misc]backup-simplify: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 1545390555.685 * [misc]backup-simplify: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) 1545390555.686 * [misc]backup-simplify: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 1545390555.686 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 1545390555.686 * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) 1545390555.687 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) 1545390555.687 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) 1545390555.689 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (* 1 (/ 1 (- k)))) (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))))))))) 1545390555.689 * * * * [misc]progress: [ 4 / 4 ] generating series at (2 2 1 2 1) 1545390555.689 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1545390555.689 * [misc]approximate: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1545390555.689 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1545390555.689 * [misc]taylor: Taking taylor expansion of 2 in n 1545390555.689 * [misc]backup-simplify: Simplify 2 into 2 1545390555.689 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545390555.689 * [misc]taylor: Taking taylor expansion of n in n 1545390555.689 * [misc]backup-simplify: Simplify 0 into 0 1545390555.689 * [misc]backup-simplify: Simplify 1 into 1 1545390555.689 * [misc]taylor: Taking taylor expansion of PI in n 1545390555.689 * [misc]backup-simplify: Simplify PI into PI 1545390555.689 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1545390555.689 * [misc]taylor: Taking taylor expansion of 2 in n 1545390555.689 * [misc]backup-simplify: Simplify 2 into 2 1545390555.689 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545390555.689 * [misc]taylor: Taking taylor expansion of n in n 1545390555.689 * [misc]backup-simplify: Simplify 0 into 0 1545390555.689 * [misc]backup-simplify: Simplify 1 into 1 1545390555.689 * [misc]taylor: Taking taylor expansion of PI in n 1545390555.689 * [misc]backup-simplify: Simplify PI into PI 1545390555.690 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1545390555.690 * [misc]backup-simplify: Simplify (* 2 0) into 0 1545390555.690 * [misc]backup-simplify: Simplify 0 into 0 1545390555.690 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1545390555.691 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1545390555.691 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545390555.691 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1545390555.692 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1545390555.692 * [misc]backup-simplify: Simplify 0 into 0 1545390555.693 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1545390555.694 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1545390555.694 * [misc]backup-simplify: Simplify 0 into 0 1545390555.695 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1545390555.696 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1545390555.696 * [misc]backup-simplify: Simplify 0 into 0 1545390555.698 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1545390555.699 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1545390555.699 * [misc]backup-simplify: Simplify 0 into 0 1545390555.701 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1545390555.703 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1545390555.703 * [misc]backup-simplify: Simplify 0 into 0 1545390555.707 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1545390555.711 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1545390555.711 * [misc]backup-simplify: Simplify 0 into 0 1545390555.711 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1545390555.712 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 n)) into (* 2 (/ PI n)) 1545390555.712 * [misc]approximate: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1545390555.712 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1545390555.712 * [misc]taylor: Taking taylor expansion of 2 in n 1545390555.712 * [misc]backup-simplify: Simplify 2 into 2 1545390555.712 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390555.712 * [misc]taylor: Taking taylor expansion of PI in n 1545390555.712 * [misc]backup-simplify: Simplify PI into PI 1545390555.712 * [misc]taylor: Taking taylor expansion of n in n 1545390555.712 * [misc]backup-simplify: Simplify 0 into 0 1545390555.712 * [misc]backup-simplify: Simplify 1 into 1 1545390555.712 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390555.712 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1545390555.712 * [misc]taylor: Taking taylor expansion of 2 in n 1545390555.712 * [misc]backup-simplify: Simplify 2 into 2 1545390555.713 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390555.713 * [misc]taylor: Taking taylor expansion of PI in n 1545390555.713 * [misc]backup-simplify: Simplify PI into PI 1545390555.713 * [misc]taylor: Taking taylor expansion of n in n 1545390555.713 * [misc]backup-simplify: Simplify 0 into 0 1545390555.713 * [misc]backup-simplify: Simplify 1 into 1 1545390555.713 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390555.713 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545390555.713 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545390555.715 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1545390555.715 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1545390555.715 * [misc]backup-simplify: Simplify 0 into 0 1545390555.717 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390555.718 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1545390555.718 * [misc]backup-simplify: Simplify 0 into 0 1545390555.719 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390555.721 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1545390555.721 * [misc]backup-simplify: Simplify 0 into 0 1545390555.723 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390555.725 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1545390555.725 * [misc]backup-simplify: Simplify 0 into 0 1545390555.727 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390555.730 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1545390555.730 * [misc]backup-simplify: Simplify 0 into 0 1545390555.732 * [misc]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 1545390555.736 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1545390555.736 * [misc]backup-simplify: Simplify 0 into 0 1545390555.736 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 1545390555.736 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (- n))) into (* -2 (/ PI n)) 1545390555.736 * [misc]approximate: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1545390555.736 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1545390555.737 * [misc]taylor: Taking taylor expansion of -2 in n 1545390555.737 * [misc]backup-simplify: Simplify -2 into -2 1545390555.737 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390555.737 * [misc]taylor: Taking taylor expansion of PI in n 1545390555.737 * [misc]backup-simplify: Simplify PI into PI 1545390555.737 * [misc]taylor: Taking taylor expansion of n in n 1545390555.737 * [misc]backup-simplify: Simplify 0 into 0 1545390555.737 * [misc]backup-simplify: Simplify 1 into 1 1545390555.737 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390555.737 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1545390555.737 * [misc]taylor: Taking taylor expansion of -2 in n 1545390555.737 * [misc]backup-simplify: Simplify -2 into -2 1545390555.737 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545390555.737 * [misc]taylor: Taking taylor expansion of PI in n 1545390555.737 * [misc]backup-simplify: Simplify PI into PI 1545390555.737 * [misc]taylor: Taking taylor expansion of n in n 1545390555.737 * [misc]backup-simplify: Simplify 0 into 0 1545390555.737 * [misc]backup-simplify: Simplify 1 into 1 1545390555.737 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545390555.738 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1545390555.738 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1545390555.739 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1545390555.740 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1545390555.740 * [misc]backup-simplify: Simplify 0 into 0 1545390555.741 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390555.742 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1545390555.742 * [misc]backup-simplify: Simplify 0 into 0 1545390555.744 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390555.745 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1545390555.745 * [misc]backup-simplify: Simplify 0 into 0 1545390555.747 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390555.749 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1545390555.749 * [misc]backup-simplify: Simplify 0 into 0 1545390555.751 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545390555.754 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1545390555.754 * [misc]backup-simplify: Simplify 0 into 0 1545390555.756 * [misc]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 1545390555.758 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1545390555.758 * [misc]backup-simplify: Simplify 0 into 0 1545390555.759 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 1545390555.759 * * * [misc]progress: simplifying candidates 1545390555.759 * * * * [misc]progress: [ 1 / 102 ] simplifiying candidate # 1545390555.759 * * * * [misc]progress: [ 2 / 102 ] simplifiying candidate # 1545390555.759 * * * * [misc]progress: [ 3 / 102 ] simplifiying candidate # 1545390555.759 * [enter]simplify: Simplifying (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)) 1545390555.759 * * [misc]simplify: iters left: 6 (11 enodes) 1545390555.762 * * [misc]simplify: iters left: 5 (29 enodes) 1545390555.766 * * [misc]simplify: iters left: 4 (59 enodes) 1545390555.778 * * [misc]simplify: iters left: 3 (146 enodes) 1545390555.866 * [exit]simplify: Simplified to (* (- 1/2 (/ k 2)) (log (* (* 2 PI) n))) 1545390555.866 * [misc]simplify: Simplified (2 2 1 2 1) to (λ (k n) (* (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (* (/ 1 (sqrt k)) (exp (* (- 1/2 (/ k 2)) (log (* (* 2 PI) n)))))))) 1545390555.866 * * * * [misc]progress: [ 4 / 102 ] simplifiying candidate # 1545390555.866 * * * * [misc]progress: [ 5 / 102 ] simplifiying candidate # 1545390555.867 * [enter]simplify: Simplifying (* (* 2 PI) n) 1545390555.867 * * [misc]simplify: iters left: 4 (5 enodes) 1545390555.868 * * [misc]simplify: iters left: 3 (9 enodes) 1545390555.871 * * [misc]simplify: iters left: 2 (15 enodes) 1545390555.875 * * [misc]simplify: iters left: 1 (17 enodes) 1545390555.879 * [exit]simplify: Simplified to (* (* 2 PI) n) 1545390555.879 * [misc]simplify: Simplified (2 2 1 2 1) to (λ (k n) (* (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (* 1 (/ (- 1 k) 2))))))) 1545390555.879 * * * * [misc]progress: [ 6 / 102 ] simplifiying candidate # 1545390555.879 * [enter]simplify: Simplifying (pow (* (* 2 PI) n) (/ k 2)) 1545390555.879 * * [misc]simplify: iters left: 5 (8 enodes) 1545390555.884 * * [misc]simplify: iters left: 4 (12 enodes) 1545390555.888 * * [misc]simplify: iters left: 3 (18 enodes) 1545390555.893 * * [misc]simplify: iters left: 2 (20 enodes) 1545390555.898 * [exit]simplify: Simplified to (pow (* 2 (* n PI)) (/ k 2)) 1545390555.898 * [misc]simplify: Simplified (2 2 1 2 2) to (λ (k n) (* (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (* (/ 1 (sqrt k)) (/ (pow (* (* 2 PI) n) (/ 1 2)) (pow (* 2 (* n PI)) (/ k 2))))))) 1545390555.898 * * * * [misc]progress: [ 7 / 102 ] simplifiying candidate # 1545390555.898 * [enter]simplify: Simplifying (cbrt (/ (- 1 k) 2)) 1545390555.898 * * [misc]simplify: iters left: 5 (6 enodes) 1545390555.901 * * [misc]simplify: iters left: 4 (14 enodes) 1545390555.905 * * [misc]simplify: iters left: 3 (17 enodes) 1545390555.909 * * [misc]simplify: iters left: 2 (19 enodes) 1545390555.913 * [exit]simplify: Simplified to (cbrt (/ (- 1 k) 2)) 1545390555.913 * [misc]simplify: Simplified (2 2 1 2 2) to (λ (k n) (* (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) (cbrt (/ (- 1 k) 2))))))) 1545390555.914 * * * * [misc]progress: [ 8 / 102 ] simplifiying candidate # 1545390555.914 * [enter]simplify: Simplifying (sqrt (/ (- 1 k) 2)) 1545390555.914 * * [misc]simplify: iters left: 5 (6 enodes) 1545390555.917 * * [misc]simplify: iters left: 4 (14 enodes) 1545390555.920 * * [misc]simplify: iters left: 3 (17 enodes) 1545390555.924 * * [misc]simplify: iters left: 2 (19 enodes) 1545390555.928 * [exit]simplify: Simplified to (sqrt (/ (- 1 k) 2)) 1545390555.929 * [misc]simplify: Simplified (2 2 1 2 2) to (λ (k n) (* (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (sqrt (/ (- 1 k) 2))) (sqrt (/ (- 1 k) 2))))))) 1545390555.929 * * * * [misc]progress: [ 9 / 102 ] simplifiying candidate # 1545390555.929 * [enter]simplify: Simplifying (/ (- 1 k) 2) 1545390555.929 * * [misc]simplify: iters left: 4 (5 enodes) 1545390555.931 * * [misc]simplify: iters left: 3 (13 enodes) 1545390555.935 * * [misc]simplify: iters left: 2 (16 enodes) 1545390555.938 * * [misc]simplify: iters left: 1 (18 enodes) 1545390555.942 * [exit]simplify: Simplified to (/ (- 1 k) 2) 1545390555.943 * [misc]simplify: Simplified (2 2 1 2 2) to (λ (k n) (* (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) 1) (/ (- 1 k) 2)))))) 1545390555.943 * * * * [misc]progress: [ 10 / 102 ] simplifiying candidate # 1545390555.943 * [enter]simplify: Simplifying (/ 1 2) 1545390555.943 * * [misc]simplify: iters left: 2 (3 enodes) 1545390555.945 * * [misc]simplify: iters left: 1 (6 enodes) 1545390555.946 * [exit]simplify: Simplified to 1/2 1545390555.946 * [misc]simplify: Simplified (2 2 1 2 2) to (λ (k n) (* (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (- 1 k)) 1/2))))) 1545390555.946 * * * * [misc]progress: [ 11 / 102 ] simplifiying candidate # 1545390555.946 * [enter]simplify: Simplifying (pow (* 2 PI) (/ (- 1 k) 2)) 1545390555.946 * * [misc]simplify: iters left: 5 (8 enodes) 1545390555.950 * * [misc]simplify: iters left: 4 (17 enodes) 1545390555.954 * * [misc]simplify: iters left: 3 (20 enodes) 1545390555.959 * * [misc]simplify: iters left: 2 (22 enodes) 1545390555.964 * [exit]simplify: Simplified to (pow (* 2 PI) (- 1/2 (/ k 2))) 1545390555.964 * [misc]simplify: Simplified (2 2 1 2 1) to (λ (k n) (* (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (* (/ 1 (sqrt k)) (* (pow (* 2 PI) (- 1/2 (/ k 2))) (pow n (/ (- 1 k) 2))))))) 1545390555.964 * * * * [misc]progress: [ 12 / 102 ] simplifiying candidate # 1545390555.964 * * * * [misc]progress: [ 13 / 102 ] simplifiying candidate # 1545390555.964 * * * * [misc]progress: [ 14 / 102 ] simplifiying candidate # 1545390555.964 * * * * [misc]progress: [ 15 / 102 ] simplifiying candidate # 1545390555.964 * * * * [misc]progress: [ 16 / 102 ] simplifiying candidate # 1545390555.964 * * * * [misc]progress: [ 17 / 102 ] simplifiying candidate # 1545390555.965 * * * * [misc]progress: [ 18 / 102 ] simplifiying candidate # 1545390555.965 * * * * [misc]progress: [ 19 / 102 ] simplifiying candidate # 1545390555.965 * * * * [misc]progress: [ 20 / 102 ] simplifiying candidate # 1545390555.965 * * * * [misc]progress: [ 21 / 102 ] simplifiying candidate # 1545390555.965 * [enter]simplify: Simplifying (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)) 1545390555.965 * * [misc]simplify: iters left: 6 (11 enodes) 1545390555.970 * * [misc]simplify: iters left: 5 (29 enodes) 1545390555.979 * * [misc]simplify: iters left: 4 (59 enodes) 1545390555.990 * * [misc]simplify: iters left: 3 (146 enodes) 1545390556.090 * [exit]simplify: Simplified to (* (- 1/2 (/ k 2)) (log (* (* 2 PI) n))) 1545390556.090 * [misc]simplify: Simplified (2 1 1 2 1) to (λ (k n) (* (sqrt (* (/ 1 (sqrt k)) (exp (* (- 1/2 (/ k 2)) (log (* (* 2 PI) n)))))) (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))) 1545390556.090 * * * * [misc]progress: [ 22 / 102 ] simplifiying candidate # 1545390556.090 * * * * [misc]progress: [ 23 / 102 ] simplifiying candidate # 1545390556.091 * [enter]simplify: Simplifying (* (* 2 PI) n) 1545390556.091 * * [misc]simplify: iters left: 4 (5 enodes) 1545390556.092 * * [misc]simplify: iters left: 3 (9 enodes) 1545390556.093 * * [misc]simplify: iters left: 2 (15 enodes) 1545390556.095 * * [misc]simplify: iters left: 1 (17 enodes) 1545390556.097 * [exit]simplify: Simplified to (* (* 2 PI) n) 1545390556.097 * [misc]simplify: Simplified (2 1 1 2 1) to (λ (k n) (* (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (* 1 (/ (- 1 k) 2))))) (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))) 1545390556.097 * * * * [misc]progress: [ 24 / 102 ] simplifiying candidate # 1545390556.097 * [enter]simplify: Simplifying (pow (* (* 2 PI) n) (/ k 2)) 1545390556.097 * * [misc]simplify: iters left: 5 (8 enodes) 1545390556.099 * * [misc]simplify: iters left: 4 (12 enodes) 1545390556.100 * * [misc]simplify: iters left: 3 (18 enodes) 1545390556.103 * * [misc]simplify: iters left: 2 (20 enodes) 1545390556.105 * [exit]simplify: Simplified to (pow (* 2 (* n PI)) (/ k 2)) 1545390556.105 * [misc]simplify: Simplified (2 1 1 2 2) to (λ (k n) (* (sqrt (* (/ 1 (sqrt k)) (/ (pow (* (* 2 PI) n) (/ 1 2)) (pow (* 2 (* n PI)) (/ k 2))))) (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))) 1545390556.105 * * * * [misc]progress: [ 25 / 102 ] simplifiying candidate # 1545390556.106 * [enter]simplify: Simplifying (cbrt (/ (- 1 k) 2)) 1545390556.106 * * [misc]simplify: iters left: 5 (6 enodes) 1545390556.107 * * [misc]simplify: iters left: 4 (14 enodes) 1545390556.109 * * [misc]simplify: iters left: 3 (17 enodes) 1545390556.111 * * [misc]simplify: iters left: 2 (19 enodes) 1545390556.113 * [exit]simplify: Simplified to (cbrt (/ (- 1 k) 2)) 1545390556.113 * [misc]simplify: Simplified (2 1 1 2 2) to (λ (k n) (* (sqrt (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) (cbrt (/ (- 1 k) 2))))) (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))) 1545390556.113 * * * * [misc]progress: [ 26 / 102 ] simplifiying candidate # 1545390556.113 * [enter]simplify: Simplifying (sqrt (/ (- 1 k) 2)) 1545390556.113 * * [misc]simplify: iters left: 5 (6 enodes) 1545390556.114 * * [misc]simplify: iters left: 4 (14 enodes) 1545390556.116 * * [misc]simplify: iters left: 3 (17 enodes) 1545390556.120 * * [misc]simplify: iters left: 2 (19 enodes) 1545390556.122 * [exit]simplify: Simplified to (sqrt (/ (- 1 k) 2)) 1545390556.123 * [misc]simplify: Simplified (2 1 1 2 2) to (λ (k n) (* (sqrt (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (sqrt (/ (- 1 k) 2))) (sqrt (/ (- 1 k) 2))))) (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))) 1545390556.123 * * * * [misc]progress: [ 27 / 102 ] simplifiying candidate # 1545390556.123 * [enter]simplify: Simplifying (/ (- 1 k) 2) 1545390556.123 * * [misc]simplify: iters left: 4 (5 enodes) 1545390556.124 * * [misc]simplify: iters left: 3 (13 enodes) 1545390556.126 * * [misc]simplify: iters left: 2 (16 enodes) 1545390556.128 * * [misc]simplify: iters left: 1 (18 enodes) 1545390556.130 * [exit]simplify: Simplified to (/ (- 1 k) 2) 1545390556.130 * [misc]simplify: Simplified (2 1 1 2 2) to (λ (k n) (* (sqrt (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) 1) (/ (- 1 k) 2)))) (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))) 1545390556.130 * * * * [misc]progress: [ 28 / 102 ] simplifiying candidate # 1545390556.130 * [enter]simplify: Simplifying (/ 1 2) 1545390556.130 * * [misc]simplify: iters left: 2 (3 enodes) 1545390556.131 * * [misc]simplify: iters left: 1 (6 enodes) 1545390556.132 * [exit]simplify: Simplified to 1/2 1545390556.132 * [misc]simplify: Simplified (2 1 1 2 2) to (λ (k n) (* (sqrt (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (- 1 k)) 1/2))) (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))) 1545390556.132 * * * * [misc]progress: [ 29 / 102 ] simplifiying candidate # 1545390556.132 * [enter]simplify: Simplifying (pow (* 2 PI) (/ (- 1 k) 2)) 1545390556.132 * * [misc]simplify: iters left: 5 (8 enodes) 1545390556.134 * * [misc]simplify: iters left: 4 (17 enodes) 1545390556.136 * * [misc]simplify: iters left: 3 (20 enodes) 1545390556.138 * * [misc]simplify: iters left: 2 (22 enodes) 1545390556.140 * [exit]simplify: Simplified to (pow (* 2 PI) (- 1/2 (/ k 2))) 1545390556.140 * [misc]simplify: Simplified (2 1 1 2 1) to (λ (k n) (* (sqrt (* (/ 1 (sqrt k)) (* (pow (* 2 PI) (- 1/2 (/ k 2))) (pow n (/ (- 1 k) 2))))) (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))) 1545390556.140 * * * * [misc]progress: [ 30 / 102 ] simplifiying candidate # 1545390556.140 * * * * [misc]progress: [ 31 / 102 ] simplifiying candidate # 1545390556.141 * * * * [misc]progress: [ 32 / 102 ] simplifiying candidate # 1545390556.141 * * * * [misc]progress: [ 33 / 102 ] simplifiying candidate # 1545390556.141 * * * * [misc]progress: [ 34 / 102 ] simplifiying candidate # 1545390556.141 * * * * [misc]progress: [ 35 / 102 ] simplifiying candidate # 1545390556.141 * * * * [misc]progress: [ 36 / 102 ] simplifiying candidate # 1545390556.141 * * * * [misc]progress: [ 37 / 102 ] simplifiying candidate # 1545390556.141 * * * * [misc]progress: [ 38 / 102 ] simplifiying candidate # 1545390556.141 * * * * [misc]progress: [ 39 / 102 ] simplifiying candidate # 1545390556.141 * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) 1545390556.141 * * [misc]simplify: iters left: 6 (13 enodes) 1545390556.144 * * [misc]simplify: iters left: 5 (28 enodes) 1545390556.152 * * [misc]simplify: iters left: 4 (44 enodes) 1545390556.164 * * [misc]simplify: iters left: 3 (54 enodes) 1545390556.173 * * [misc]simplify: iters left: 2 (57 enodes) 1545390556.180 * * [misc]simplify: iters left: 1 (65 enodes) 1545390556.187 * [exit]simplify: Simplified to (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)) 1545390556.187 * [misc]simplify: Simplified (2 1) to (λ (k n) (pow (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)) (+ 1/2 1/2))) 1545390556.188 * [enter]simplify: Simplifying (+ 1/2 1/2) 1545390556.188 * * [misc]simplify: iters left: 2 (2 enodes) 1545390556.188 * * [misc]simplify: iters left: 1 (3 enodes) 1545390556.189 * [exit]simplify: Simplified to 1 1545390556.189 * [misc]simplify: Simplified (2 2) to (λ (k n) (pow (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)) 1)) 1545390556.189 * * * * [misc]progress: [ 40 / 102 ] simplifiying candidate # 1545390556.189 * [enter]simplify: Simplifying (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) 1545390556.189 * * [misc]simplify: iters left: 6 (14 enodes) 1545390556.192 * * [misc]simplify: iters left: 5 (29 enodes) 1545390556.196 * * [misc]simplify: iters left: 4 (45 enodes) 1545390556.205 * * [misc]simplify: iters left: 3 (54 enodes) 1545390556.216 * * [misc]simplify: iters left: 2 (57 enodes) 1545390556.224 * * [misc]simplify: iters left: 1 (65 enodes) 1545390556.232 * [exit]simplify: Simplified to (sqrt (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k))) 1545390556.232 * [misc]simplify: Simplified (2 1) to (λ (k n) (pow (sqrt (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k))) (+ 1 1))) 1545390556.232 * [enter]simplify: Simplifying (+ 1 1) 1545390556.232 * * [misc]simplify: iters left: 2 (2 enodes) 1545390556.233 * * [misc]simplify: iters left: 1 (5 enodes) 1545390556.234 * [exit]simplify: Simplified to 2 1545390556.234 * [misc]simplify: Simplified (2 2) to (λ (k n) (pow (sqrt (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k))) 2)) 1545390556.234 * * * * [misc]progress: [ 41 / 102 ] simplifiying candidate # 1545390556.234 * [enter]simplify: Simplifying (* (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) 1545390556.234 * * [misc]simplify: iters left: 6 (14 enodes) 1545390556.237 * * [misc]simplify: iters left: 5 (33 enodes) 1545390556.242 * * [misc]simplify: iters left: 4 (73 enodes) 1545390556.260 * * [misc]simplify: iters left: 3 (130 enodes) 1545390556.280 * * [misc]simplify: iters left: 2 (214 enodes) 1545390556.359 * * [misc]simplify: iters left: 1 (370 enodes) 1545390556.539 * [exit]simplify: Simplified to (* (/ (pow (* (* n PI) 2) (- 1/2 (/ k 2))) k) (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) 1545390556.539 * [misc]simplify: Simplified (2 1) to (λ (k n) (pow (* (/ (pow (* (* n PI) 2) (- 1/2 (/ k 2))) k) (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) 1/2)) 1545390556.540 * * * * [misc]progress: [ 42 / 102 ] simplifiying candidate # 1545390556.540 * [enter]simplify: Simplifying (* (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) 1545390556.540 * * [misc]simplify: iters left: 6 (15 enodes) 1545390556.546 * * [misc]simplify: iters left: 5 (30 enodes) 1545390556.555 * * [misc]simplify: iters left: 4 (47 enodes) 1545390556.568 * * [misc]simplify: iters left: 3 (56 enodes) 1545390556.580 * * [misc]simplify: iters left: 2 (59 enodes) 1545390556.594 * * [misc]simplify: iters left: 1 (69 enodes) 1545390556.612 * [exit]simplify: Simplified to (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)) 1545390556.612 * [misc]simplify: Simplified (2 1) to (λ (k n) (pow (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)) 1)) 1545390556.612 * * * * [misc]progress: [ 43 / 102 ] simplifiying candidate # 1545390556.612 * * * * [misc]progress: [ 44 / 102 ] simplifiying candidate # 1545390556.612 * [enter]simplify: Simplifying (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) 1545390556.612 * * [misc]simplify: iters left: 6 (14 enodes) 1545390556.618 * * [misc]simplify: iters left: 5 (29 enodes) 1545390556.627 * * [misc]simplify: iters left: 4 (45 enodes) 1545390556.640 * * [misc]simplify: iters left: 3 (54 enodes) 1545390556.651 * * [misc]simplify: iters left: 2 (57 enodes) 1545390556.657 * * [misc]simplify: iters left: 1 (65 enodes) 1545390556.665 * [exit]simplify: Simplified to (sqrt (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k))) 1545390556.665 * [misc]simplify: Simplified (2 1) to (λ (k n) (pow (sqrt (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k))) (+ 1 1))) 1545390556.665 * * * * [misc]progress: [ 45 / 102 ] simplifiying candidate # 1545390556.665 * * * * [misc]progress: [ 46 / 102 ] simplifiying candidate # 1545390556.665 * [enter]simplify: Simplifying (+ (log (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) (log (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))) 1545390556.665 * * [misc]simplify: iters left: 6 (16 enodes) 1545390556.669 * * [misc]simplify: iters left: 5 (31 enodes) 1545390556.675 * * [misc]simplify: iters left: 4 (47 enodes) 1545390556.688 * * [misc]simplify: iters left: 3 (56 enodes) 1545390556.701 * * [misc]simplify: iters left: 2 (59 enodes) 1545390556.715 * * [misc]simplify: iters left: 1 (67 enodes) 1545390556.733 * [exit]simplify: Simplified to (+ (log (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (log (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))) 1545390556.733 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (+ (log (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (log (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))) 1545390556.733 * * * * [misc]progress: [ 47 / 102 ] simplifiying candidate # 1545390556.733 * * * * [misc]progress: [ 48 / 102 ] simplifiying candidate # 1545390556.733 * * * * [misc]progress: [ 49 / 102 ] simplifiying candidate # 1545390556.733 * [enter]simplify: Simplifying (* (* (* (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) (* (* (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))) 1545390556.734 * * [misc]simplify: iters left: 6 (17 enodes) 1545390556.738 * * [misc]simplify: iters left: 5 (37 enodes) 1545390556.744 * * [misc]simplify: iters left: 4 (76 enodes) 1545390556.759 * * [misc]simplify: iters left: 3 (175 enodes) 1545390556.825 * * [misc]simplify: iters left: 2 (462 enodes) 1545390557.188 * [exit]simplify: Simplified to (pow (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k)) 3) 1545390557.188 * [misc]simplify: Simplified (2 1) to (λ (k n) (cbrt (pow (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k)) 3))) 1545390557.188 * * * * [misc]progress: [ 50 / 102 ] simplifiying candidate # 1545390557.188 * * * * [misc]progress: [ 51 / 102 ] simplifiying candidate # 1545390557.188 * * * * [misc]progress: [ 52 / 102 ] simplifiying candidate # 1545390557.188 * [enter]simplify: Simplifying (* (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) 1545390557.189 * * [misc]simplify: iters left: 6 (14 enodes) 1545390557.194 * * [misc]simplify: iters left: 5 (33 enodes) 1545390557.205 * * [misc]simplify: iters left: 4 (73 enodes) 1545390557.238 * * [misc]simplify: iters left: 3 (130 enodes) 1545390557.259 * * [misc]simplify: iters left: 2 (214 enodes) 1545390557.355 * * [misc]simplify: iters left: 1 (370 enodes) 1545390557.509 * [exit]simplify: Simplified to (* (/ (pow (* (* n PI) 2) (- 1/2 (/ k 2))) k) (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) 1545390557.509 * [misc]simplify: Simplified (2 1) to (λ (k n) (sqrt (* (/ (pow (* (* n PI) 2) (- 1/2 (/ k 2))) k) (pow (* (* n PI) 2) (- 1/2 (/ k 2)))))) 1545390557.509 * * * * [misc]progress: [ 53 / 102 ] simplifiying candidate # 1545390557.509 * * * * [misc]progress: [ 54 / 102 ] simplifiying candidate # 1545390557.509 * [enter]simplify: Simplifying (/ 1 (sqrt k)) 1545390557.509 * * [misc]simplify: iters left: 3 (4 enodes) 1545390557.510 * * [misc]simplify: iters left: 2 (6 enodes) 1545390557.510 * [exit]simplify: Simplified to (/ 1 (sqrt k)) 1545390557.510 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) 1545390557.510 * [enter]simplify: Simplifying (pow (* (* 2 PI) n) (/ (- 1 k) 2)) 1545390557.511 * * [misc]simplify: iters left: 5 (10 enodes) 1545390557.513 * * [misc]simplify: iters left: 4 (22 enodes) 1545390557.516 * * [misc]simplify: iters left: 3 (31 enodes) 1545390557.520 * * [misc]simplify: iters left: 2 (34 enodes) 1545390557.523 * [exit]simplify: Simplified to (pow (* (* n 2) PI) (/ (- 1 k) 2)) 1545390557.523 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* n 2) PI) (/ (- 1 k) 2)))) 1545390557.523 * * * * [misc]progress: [ 55 / 102 ] simplifiying candidate # 1545390557.524 * [enter]simplify: Simplifying (* (sqrt (* 1 (pow (* (* 2 PI) n) (/ 1 2)))) (sqrt (* 1 (pow (* (* 2 PI) n) (/ 1 2))))) 1545390557.524 * * [misc]simplify: iters left: 6 (11 enodes) 1545390557.526 * * [misc]simplify: iters left: 5 (19 enodes) 1545390557.529 * * [misc]simplify: iters left: 4 (34 enodes) 1545390557.533 * * [misc]simplify: iters left: 3 (35 enodes) 1545390557.536 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1545390557.536 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (* (sqrt (* (sqrt k) (pow (* (* 2 PI) n) (/ k 2)))) (sqrt (* (sqrt k) (pow (* (* 2 PI) n) (/ k 2))))))) 1545390557.536 * [enter]simplify: Simplifying (* (sqrt (* (sqrt k) (pow (* (* 2 PI) n) (/ k 2)))) (sqrt (* (sqrt k) (pow (* (* 2 PI) n) (/ k 2))))) 1545390557.536 * * [misc]simplify: iters left: 6 (12 enodes) 1545390557.538 * * [misc]simplify: iters left: 5 (17 enodes) 1545390557.540 * * [misc]simplify: iters left: 4 (24 enodes) 1545390557.543 * * [misc]simplify: iters left: 3 (26 enodes) 1545390557.547 * [exit]simplify: Simplified to (* (pow (* (* 2 n) PI) (/ k 2)) (sqrt k)) 1545390557.547 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (* (pow (* (* 2 n) PI) (/ k 2)) (sqrt k)))) 1545390557.547 * * * * [misc]progress: [ 56 / 102 ] simplifiying candidate # 1545390557.547 * [enter]simplify: Simplifying (* (sqrt (* 1 (pow (* (* 2 PI) n) (/ 1 2)))) (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ 1 2))))) 1545390557.547 * * [misc]simplify: iters left: 6 (16 enodes) 1545390557.550 * * [misc]simplify: iters left: 5 (28 enodes) 1545390557.554 * * [misc]simplify: iters left: 4 (42 enodes) 1545390557.567 * * [misc]simplify: iters left: 3 (50 enodes) 1545390557.575 * * [misc]simplify: iters left: 2 (51 enodes) 1545390557.579 * * [misc]simplify: iters left: 1 (54 enodes) 1545390557.584 * [exit]simplify: Simplified to (* (sqrt (/ (sqrt (* 2 (* n PI))) (sqrt k))) (sqrt (sqrt (* 2 (* n PI))))) 1545390557.585 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (* (sqrt (/ (sqrt (* 2 (* n PI))) (sqrt k))) (sqrt (sqrt (* 2 (* n PI))))) (* (sqrt (* (sqrt k) (pow (* (* 2 PI) n) (/ k 2)))) (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) 1545390557.585 * [enter]simplify: Simplifying (* (sqrt (* (sqrt k) (pow (* (* 2 PI) n) (/ k 2)))) (sqrt (pow (* (* 2 PI) n) (/ k 2)))) 1545390557.585 * * [misc]simplify: iters left: 6 (13 enodes) 1545390557.587 * * [misc]simplify: iters left: 5 (19 enodes) 1545390557.589 * * [misc]simplify: iters left: 4 (25 enodes) 1545390557.593 * * [misc]simplify: iters left: 3 (27 enodes) 1545390557.596 * [exit]simplify: Simplified to (* (sqrt (* (pow (* PI (* 2 n)) (/ k 2)) (sqrt k))) (sqrt (pow (* PI (* 2 n)) (/ k 2)))) 1545390557.596 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (* (sqrt (/ (sqrt (* 2 (* n PI))) (sqrt k))) (sqrt (sqrt (* 2 (* n PI))))) (* (sqrt (* (pow (* PI (* 2 n)) (/ k 2)) (sqrt k))) (sqrt (pow (* PI (* 2 n)) (/ k 2)))))) 1545390557.596 * * * * [misc]progress: [ 57 / 102 ] simplifiying candidate # 1545390557.596 * [enter]simplify: Simplifying (* (sqrt (* 1 (pow (* (* 2 PI) n) (/ 1 2)))) (sqrt (* 1 (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) 1545390557.596 * * [misc]simplify: iters left: 6 (17 enodes) 1545390557.600 * * [misc]simplify: iters left: 5 (31 enodes) 1545390557.605 * * [misc]simplify: iters left: 4 (44 enodes) 1545390557.612 * * [misc]simplify: iters left: 3 (48 enodes) 1545390557.622 * [exit]simplify: Simplified to (* (sqrt (sqrt (* (* n PI) 2))) (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2))))) 1545390557.622 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (* (sqrt (sqrt (* (* n PI) 2))) (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2))))) (* (sqrt (* (sqrt k) (pow (* (* 2 PI) n) (/ k 2)))) (sqrt (sqrt k))))) 1545390557.623 * [enter]simplify: Simplifying (* (sqrt (* (sqrt k) (pow (* (* 2 PI) n) (/ k 2)))) (sqrt (sqrt k))) 1545390557.623 * * [misc]simplify: iters left: 6 (13 enodes) 1545390557.627 * * [misc]simplify: iters left: 5 (19 enodes) 1545390557.632 * * [misc]simplify: iters left: 4 (25 enodes) 1545390557.639 * * [misc]simplify: iters left: 3 (27 enodes) 1545390557.646 * [exit]simplify: Simplified to (* (sqrt (* (pow (* PI (* 2 n)) (/ k 2)) (sqrt k))) (sqrt (sqrt k))) 1545390557.646 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (* (sqrt (sqrt (* (* n PI) 2))) (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2))))) (* (sqrt (* (pow (* PI (* 2 n)) (/ k 2)) (sqrt k))) (sqrt (sqrt k))))) 1545390557.646 * * * * [misc]progress: [ 58 / 102 ] simplifiying candidate # 1545390557.646 * [enter]simplify: Simplifying (* (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ 1 2)))) (sqrt (* 1 (pow (* (* 2 PI) n) (/ 1 2))))) 1545390557.647 * * [misc]simplify: iters left: 6 (16 enodes) 1545390557.653 * * [misc]simplify: iters left: 5 (28 enodes) 1545390557.661 * * [misc]simplify: iters left: 4 (42 enodes) 1545390557.671 * * [misc]simplify: iters left: 3 (50 enodes) 1545390557.684 * * [misc]simplify: iters left: 2 (51 enodes) 1545390557.693 * * [misc]simplify: iters left: 1 (54 enodes) 1545390557.699 * [exit]simplify: Simplified to (* (sqrt (/ (sqrt (* (* n 2) PI)) (sqrt k))) (sqrt (sqrt (* (* n 2) PI)))) 1545390557.699 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (* (sqrt (/ (sqrt (* (* n 2) PI)) (sqrt k))) (sqrt (sqrt (* (* n 2) PI)))) (* (sqrt (pow (* (* 2 PI) n) (/ k 2))) (sqrt (* (sqrt k) (pow (* (* 2 PI) n) (/ k 2))))))) 1545390557.700 * [enter]simplify: Simplifying (* (sqrt (pow (* (* 2 PI) n) (/ k 2))) (sqrt (* (sqrt k) (pow (* (* 2 PI) n) (/ k 2))))) 1545390557.700 * * [misc]simplify: iters left: 6 (13 enodes) 1545390557.702 * * [misc]simplify: iters left: 5 (19 enodes) 1545390557.704 * * [misc]simplify: iters left: 4 (25 enodes) 1545390557.708 * * [misc]simplify: iters left: 3 (26 enodes) 1545390557.711 * [exit]simplify: Simplified to (* (sqrt (* (sqrt k) (pow (* (* 2 PI) n) (/ k 2)))) (sqrt (pow (* (* 2 PI) n) (/ k 2)))) 1545390557.711 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (* (sqrt (/ (sqrt (* (* n 2) PI)) (sqrt k))) (sqrt (sqrt (* (* n 2) PI)))) (* (sqrt (* (sqrt k) (pow (* (* 2 PI) n) (/ k 2)))) (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) 1545390557.711 * * * * [misc]progress: [ 59 / 102 ] simplifiying candidate # 1545390557.711 * [enter]simplify: Simplifying (* (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ 1 2)))) (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ 1 2))))) 1545390557.711 * * [misc]simplify: iters left: 6 (14 enodes) 1545390557.714 * * [misc]simplify: iters left: 5 (24 enodes) 1545390557.717 * * [misc]simplify: iters left: 4 (36 enodes) 1545390557.722 * * [misc]simplify: iters left: 3 (49 enodes) 1545390557.732 * * [misc]simplify: iters left: 2 (57 enodes) 1545390557.740 * * [misc]simplify: iters left: 1 (64 enodes) 1545390557.746 * [exit]simplify: Simplified to (/ (sqrt (* (* n 2) PI)) (sqrt k)) 1545390557.747 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (/ (sqrt (* (* n 2) PI)) (sqrt k)) (* (sqrt (pow (* (* 2 PI) n) (/ k 2))) (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) 1545390557.747 * [enter]simplify: Simplifying (* (sqrt (pow (* (* 2 PI) n) (/ k 2))) (sqrt (pow (* (* 2 PI) n) (/ k 2)))) 1545390557.747 * * [misc]simplify: iters left: 6 (10 enodes) 1545390557.748 * * [misc]simplify: iters left: 5 (14 enodes) 1545390557.750 * * [misc]simplify: iters left: 4 (21 enodes) 1545390557.753 * * [misc]simplify: iters left: 3 (22 enodes) 1545390557.755 * [exit]simplify: Simplified to (pow (* 2 (* n PI)) (/ k 2)) 1545390557.755 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (sqrt (* (* n 2) PI)) (sqrt k)) (pow (* 2 (* n PI)) (/ k 2)))) 1545390557.756 * * * * [misc]progress: [ 60 / 102 ] simplifiying candidate # 1545390557.756 * [enter]simplify: Simplifying (* (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ 1 2)))) (sqrt (* 1 (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) 1545390557.756 * * [misc]simplify: iters left: 6 (19 enodes) 1545390557.759 * * [misc]simplify: iters left: 5 (35 enodes) 1545390557.767 * * [misc]simplify: iters left: 4 (51 enodes) 1545390557.781 * * [misc]simplify: iters left: 3 (63 enodes) 1545390557.796 * * [misc]simplify: iters left: 2 (69 enodes) 1545390557.810 * * [misc]simplify: iters left: 1 (74 enodes) 1545390557.827 * [exit]simplify: Simplified to (* (sqrt (/ (sqrt (* (* n PI) 2)) (sqrt k))) (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))) 1545390557.827 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (* (sqrt (/ (sqrt (* (* n PI) 2)) (sqrt k))) (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))) (* (sqrt (pow (* (* 2 PI) n) (/ k 2))) (sqrt (sqrt k))))) 1545390557.828 * [enter]simplify: Simplifying (* (sqrt (pow (* (* 2 PI) n) (/ k 2))) (sqrt (sqrt k))) 1545390557.828 * * [misc]simplify: iters left: 6 (12 enodes) 1545390557.831 * * [misc]simplify: iters left: 5 (17 enodes) 1545390557.836 * * [misc]simplify: iters left: 4 (23 enodes) 1545390557.843 * * [misc]simplify: iters left: 3 (24 enodes) 1545390557.849 * [exit]simplify: Simplified to (* (sqrt (pow (* (* n PI) 2) (/ k 2))) (sqrt (sqrt k))) 1545390557.849 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (* (sqrt (/ (sqrt (* (* n PI) 2)) (sqrt k))) (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))) (* (sqrt (pow (* (* n PI) 2) (/ k 2))) (sqrt (sqrt k))))) 1545390557.849 * * * * [misc]progress: [ 61 / 102 ] simplifiying candidate # 1545390557.850 * [enter]simplify: Simplifying (* (sqrt (* 1 (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (* 1 (pow (* (* 2 PI) n) (/ 1 2))))) 1545390557.850 * * [misc]simplify: iters left: 6 (17 enodes) 1545390557.856 * * [misc]simplify: iters left: 5 (31 enodes) 1545390557.866 * * [misc]simplify: iters left: 4 (44 enodes) 1545390557.876 * * [misc]simplify: iters left: 3 (48 enodes) 1545390557.886 * [exit]simplify: Simplified to (* (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (sqrt (sqrt (* (* n PI) 2)))) 1545390557.886 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (* (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (sqrt (sqrt (* (* n PI) 2)))) (* (sqrt (sqrt k)) (sqrt (* (sqrt k) (pow (* (* 2 PI) n) (/ k 2))))))) 1545390557.887 * [enter]simplify: Simplifying (* (sqrt (sqrt k)) (sqrt (* (sqrt k) (pow (* (* 2 PI) n) (/ k 2))))) 1545390557.887 * * [misc]simplify: iters left: 6 (13 enodes) 1545390557.891 * * [misc]simplify: iters left: 5 (19 enodes) 1545390557.896 * * [misc]simplify: iters left: 4 (25 enodes) 1545390557.903 * * [misc]simplify: iters left: 3 (26 enodes) 1545390557.910 * [exit]simplify: Simplified to (* (sqrt (* (sqrt k) (pow (* PI (* 2 n)) (/ k 2)))) (sqrt (sqrt k))) 1545390557.910 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (* (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (sqrt (sqrt (* (* n PI) 2)))) (* (sqrt (* (sqrt k) (pow (* PI (* 2 n)) (/ k 2)))) (sqrt (sqrt k))))) 1545390557.910 * * * * [misc]progress: [ 62 / 102 ] simplifiying candidate # 1545390557.910 * [enter]simplify: Simplifying (* (sqrt (* 1 (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ 1 2))))) 1545390557.911 * * [misc]simplify: iters left: 6 (19 enodes) 1545390557.919 * * [misc]simplify: iters left: 5 (35 enodes) 1545390557.930 * * [misc]simplify: iters left: 4 (51 enodes) 1545390557.943 * * [misc]simplify: iters left: 3 (64 enodes) 1545390557.958 * * [misc]simplify: iters left: 2 (70 enodes) 1545390557.973 * * [misc]simplify: iters left: 1 (75 enodes) 1545390557.990 * [exit]simplify: Simplified to (* (sqrt (pow (* PI (* 2 n)) (/ (- 1 k) 2))) (sqrt (/ (sqrt (* PI (* 2 n))) (sqrt k)))) 1545390557.990 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (* (sqrt (pow (* PI (* 2 n)) (/ (- 1 k) 2))) (sqrt (/ (sqrt (* PI (* 2 n))) (sqrt k)))) (* (sqrt (sqrt k)) (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) 1545390557.990 * [enter]simplify: Simplifying (* (sqrt (sqrt k)) (sqrt (pow (* (* 2 PI) n) (/ k 2)))) 1545390557.990 * * [misc]simplify: iters left: 6 (12 enodes) 1545390557.994 * * [misc]simplify: iters left: 5 (17 enodes) 1545390557.999 * * [misc]simplify: iters left: 4 (23 enodes) 1545390558.005 * * [misc]simplify: iters left: 3 (24 enodes) 1545390558.011 * [exit]simplify: Simplified to (* (sqrt (sqrt k)) (sqrt (pow (* PI (* 2 n)) (/ k 2)))) 1545390558.011 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (* (sqrt (pow (* PI (* 2 n)) (/ (- 1 k) 2))) (sqrt (/ (sqrt (* PI (* 2 n))) (sqrt k)))) (* (sqrt (sqrt k)) (sqrt (pow (* PI (* 2 n)) (/ k 2)))))) 1545390558.012 * * * * [misc]progress: [ 63 / 102 ] simplifiying candidate # 1545390558.012 * [enter]simplify: Simplifying (* (sqrt (* 1 (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (* 1 (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) 1545390558.012 * * [misc]simplify: iters left: 6 (13 enodes) 1545390558.017 * * [misc]simplify: iters left: 5 (26 enodes) 1545390558.025 * * [misc]simplify: iters left: 4 (43 enodes) 1545390558.035 * * [misc]simplify: iters left: 3 (46 enodes) 1545390558.045 * [exit]simplify: Simplified to (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) 1545390558.045 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (* (sqrt (sqrt k)) (sqrt (sqrt k))))) 1545390558.045 * [enter]simplify: Simplifying (* (sqrt (sqrt k)) (sqrt (sqrt k))) 1545390558.045 * * [misc]simplify: iters left: 4 (4 enodes) 1545390558.046 * [exit]simplify: Simplified to (sqrt k) 1545390558.047 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k))) 1545390558.047 * * * * [misc]progress: [ 64 / 102 ] simplifiying candidate # 1545390558.047 * * * * [misc]progress: [ 65 / 102 ] simplifiying candidate # 1545390558.047 * [enter]simplify: Simplifying (cbrt (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) 1545390558.047 * * [misc]simplify: iters left: 6 (15 enodes) 1545390558.053 * * [misc]simplify: iters left: 5 (30 enodes) 1545390558.062 * * [misc]simplify: iters left: 4 (46 enodes) 1545390558.076 * * [misc]simplify: iters left: 3 (55 enodes) 1545390558.088 * * [misc]simplify: iters left: 2 (58 enodes) 1545390558.100 * * [misc]simplify: iters left: 1 (66 enodes) 1545390558.112 * [exit]simplify: Simplified to (cbrt (sqrt (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))) 1545390558.112 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (cbrt (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) (cbrt (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))) (cbrt (sqrt (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))))) 1545390558.112 * * * * [misc]progress: [ 66 / 102 ] simplifiying candidate # 1545390558.112 * [enter]simplify: Simplifying (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) 1545390558.112 * * [misc]simplify: iters left: 6 (11 enodes) 1545390558.115 * * [misc]simplify: iters left: 5 (23 enodes) 1545390558.118 * * [misc]simplify: iters left: 4 (32 enodes) 1545390558.122 * * [misc]simplify: iters left: 3 (35 enodes) 1545390558.126 * [exit]simplify: Simplified to (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) 1545390558.126 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (/ 1 (sqrt k)))) (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))))) 1545390558.126 * * * * [misc]progress: [ 67 / 102 ] simplifiying candidate # 1545390558.126 * [enter]simplify: Simplifying (sqrt (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) 1545390558.126 * * [misc]simplify: iters left: 6 (15 enodes) 1545390558.129 * * [misc]simplify: iters left: 5 (30 enodes) 1545390558.133 * * [misc]simplify: iters left: 4 (46 enodes) 1545390558.139 * * [misc]simplify: iters left: 3 (55 enodes) 1545390558.147 * * [misc]simplify: iters left: 2 (58 enodes) 1545390558.159 * * [misc]simplify: iters left: 1 (66 enodes) 1545390558.176 * [exit]simplify: Simplified to (sqrt (sqrt (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))) 1545390558.177 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))) (sqrt (sqrt (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))))) 1545390558.177 * * * * [misc]progress: [ 68 / 102 ] simplifiying candidate # 1545390558.177 * [enter]simplify: Simplifying (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) 1545390558.177 * * [misc]simplify: iters left: 6 (14 enodes) 1545390558.182 * * [misc]simplify: iters left: 5 (29 enodes) 1545390558.186 * * [misc]simplify: iters left: 4 (45 enodes) 1545390558.192 * * [misc]simplify: iters left: 3 (54 enodes) 1545390558.198 * * [misc]simplify: iters left: 2 (57 enodes) 1545390558.203 * * [misc]simplify: iters left: 1 (65 enodes) 1545390558.216 * [exit]simplify: Simplified to (sqrt (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k))) 1545390558.216 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) 1) (sqrt (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k))))) 1545390558.216 * * * * [misc]progress: [ 69 / 102 ] simplifiying candidate # 1545390558.216 * [enter]simplify: Simplifying (* (cbrt (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) (cbrt (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))) 1545390558.216 * * [misc]simplify: iters left: 6 (16 enodes) 1545390558.222 * * [misc]simplify: iters left: 5 (31 enodes) 1545390558.231 * * [misc]simplify: iters left: 4 (47 enodes) 1545390558.244 * * [misc]simplify: iters left: 3 (56 enodes) 1545390558.256 * * [misc]simplify: iters left: 2 (59 enodes) 1545390558.268 * * [misc]simplify: iters left: 1 (67 enodes) 1545390558.284 * [exit]simplify: Simplified to (* (cbrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (cbrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))) 1545390558.285 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (* (cbrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (cbrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))) (* (cbrt (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))) 1545390558.285 * * * * [misc]progress: [ 70 / 102 ] simplifiying candidate # 1545390558.285 * [enter]simplify: Simplifying (sqrt (/ 1 (sqrt k))) 1545390558.285 * * [misc]simplify: iters left: 4 (5 enodes) 1545390558.286 * * [misc]simplify: iters left: 3 (7 enodes) 1545390558.288 * [exit]simplify: Simplified to (sqrt (/ 1 (sqrt k))) 1545390558.288 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (/ 1 (sqrt k))) (* (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))) 1545390558.288 * * * * [misc]progress: [ 71 / 102 ] simplifiying candidate # 1545390558.288 * [enter]simplify: Simplifying (sqrt (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) 1545390558.289 * * [misc]simplify: iters left: 6 (15 enodes) 1545390558.294 * * [misc]simplify: iters left: 5 (30 enodes) 1545390558.302 * * [misc]simplify: iters left: 4 (46 enodes) 1545390558.308 * * [misc]simplify: iters left: 3 (55 enodes) 1545390558.314 * * [misc]simplify: iters left: 2 (58 enodes) 1545390558.321 * * [misc]simplify: iters left: 1 (66 enodes) 1545390558.328 * [exit]simplify: Simplified to (sqrt (sqrt (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))) 1545390558.329 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (sqrt (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))) (* (sqrt (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))) 1545390558.329 * * * * [misc]progress: [ 72 / 102 ] simplifiying candidate # 1545390558.329 * * * * [misc]progress: [ 73 / 102 ] simplifiying candidate # 1545390558.329 * [enter]simplify: Simplifying (sqrt (* (sqrt k) (pow (* (* 2 PI) n) (/ k 2)))) 1545390558.329 * * [misc]simplify: iters left: 6 (11 enodes) 1545390558.331 * * [misc]simplify: iters left: 5 (16 enodes) 1545390558.334 * * [misc]simplify: iters left: 4 (22 enodes) 1545390558.340 * * [misc]simplify: iters left: 3 (24 enodes) 1545390558.346 * [exit]simplify: Simplified to (sqrt (* (pow (* (* PI n) 2) (/ k 2)) (sqrt k))) 1545390558.346 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (* (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (* 1 (pow (* (* 2 PI) n) (/ 1 2))))) (sqrt (* (pow (* (* PI n) 2) (/ k 2)) (sqrt k))))) 1545390558.347 * * * * [misc]progress: [ 74 / 102 ] simplifiying candidate # 1545390558.347 * [enter]simplify: Simplifying (sqrt (pow (* (* 2 PI) n) (/ k 2))) 1545390558.347 * * [misc]simplify: iters left: 6 (9 enodes) 1545390558.350 * * [misc]simplify: iters left: 5 (13 enodes) 1545390558.353 * * [misc]simplify: iters left: 4 (19 enodes) 1545390558.358 * * [misc]simplify: iters left: 3 (20 enodes) 1545390558.363 * [exit]simplify: Simplified to (sqrt (pow (* (* 2 PI) n) (/ k 2))) 1545390558.363 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (* (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ 1 2))))) (sqrt (pow (* (* 2 PI) n) (/ k 2))))) 1545390558.363 * * * * [misc]progress: [ 75 / 102 ] simplifiying candidate # 1545390558.364 * [enter]simplify: Simplifying (sqrt (sqrt k)) 1545390558.364 * * [misc]simplify: iters left: 2 (3 enodes) 1545390558.364 * [exit]simplify: Simplified to (sqrt (sqrt k)) 1545390558.365 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (* (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (* 1 (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) (sqrt (sqrt k)))) 1545390558.365 * * * * [misc]progress: [ 76 / 102 ] simplifiying candidate # 1545390558.365 * [enter]simplify: Simplifying (* (sqrt (* 1 (pow (* (* 2 PI) n) (/ 1 2)))) (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) 1545390558.365 * * [misc]simplify: iters left: 6 (19 enodes) 1545390558.372 * * [misc]simplify: iters left: 5 (35 enodes) 1545390558.383 * * [misc]simplify: iters left: 4 (54 enodes) 1545390558.397 * * [misc]simplify: iters left: 3 (62 enodes) 1545390558.410 * * [misc]simplify: iters left: 2 (65 enodes) 1545390558.425 * * [misc]simplify: iters left: 1 (73 enodes) 1545390558.439 * [exit]simplify: Simplified to (* (sqrt (/ (pow (* PI (* 2 n)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (sqrt (* PI (* 2 n))))) 1545390558.439 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (* (sqrt (/ (pow (* PI (* 2 n)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (sqrt (* PI (* 2 n))))) (sqrt (* (sqrt k) (pow (* (* 2 PI) n) (/ k 2)))))) 1545390558.439 * * * * [misc]progress: [ 77 / 102 ] simplifiying candidate # 1545390558.439 * [enter]simplify: Simplifying (* (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ 1 2)))) (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) 1545390558.440 * * [misc]simplify: iters left: 6 (19 enodes) 1545390558.443 * * [misc]simplify: iters left: 5 (37 enodes) 1545390558.448 * * [misc]simplify: iters left: 4 (58 enodes) 1545390558.457 * * [misc]simplify: iters left: 3 (77 enodes) 1545390558.465 * * [misc]simplify: iters left: 2 (88 enodes) 1545390558.482 * * [misc]simplify: iters left: 1 (99 enodes) 1545390558.504 * [exit]simplify: Simplified to (* (sqrt (/ (sqrt (* (* n PI) 2)) (sqrt k))) (sqrt (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k)))) 1545390558.504 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (* (sqrt (/ (sqrt (* (* n PI) 2)) (sqrt k))) (sqrt (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (pow (* (* 2 PI) n) (/ k 2))))) 1545390558.504 * * * * [misc]progress: [ 78 / 102 ] simplifiying candidate # 1545390558.504 * [enter]simplify: Simplifying (* (sqrt (* 1 (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) 1545390558.504 * * [misc]simplify: iters left: 6 (17 enodes) 1545390558.511 * * [misc]simplify: iters left: 5 (34 enodes) 1545390558.521 * * [misc]simplify: iters left: 4 (50 enodes) 1545390558.537 * * [misc]simplify: iters left: 3 (61 enodes) 1545390558.547 * * [misc]simplify: iters left: 2 (62 enodes) 1545390558.553 * * [misc]simplify: iters left: 1 (65 enodes) 1545390558.559 * [exit]simplify: Simplified to (* (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k)))) 1545390558.559 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (* (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (sqrt k)))) 1545390558.559 * * * * [misc]progress: [ 79 / 102 ] simplifiying candidate # 1545390558.560 * * * * [misc]progress: [ 80 / 102 ] simplifiying candidate # 1545390558.560 * * * * [misc]progress: [ 81 / 102 ] simplifiying candidate # 1545390558.560 * * * * [misc]progress: [ 82 / 102 ] simplifiying candidate # 1545390558.560 * * * * [misc]progress: [ 83 / 102 ] simplifiying candidate # 1545390558.560 * * * * [misc]progress: [ 84 / 102 ] simplifiying candidate # 1545390558.560 * * * * [misc]progress: [ 85 / 102 ] simplifiying candidate # 1545390558.560 * * * * [misc]progress: [ 86 / 102 ] simplifiying candidate # 1545390558.560 * * * * [misc]progress: [ 87 / 102 ] simplifiying candidate # 1545390558.560 * * * * [misc]progress: [ 88 / 102 ] simplifiying candidate # 1545390558.560 * * * * [misc]progress: [ 89 / 102 ] simplifiying candidate # 1545390558.560 * * * * [misc]progress: [ 90 / 102 ] simplifiying candidate # 1545390558.560 * * * * [misc]progress: [ 91 / 102 ] simplifiying candidate # 1545390558.560 * [enter]simplify: Simplifying (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) 1545390558.560 * * [misc]simplify: iters left: 6 (37 enodes) 1545390558.568 * * [misc]simplify: iters left: 5 (108 enodes) 1545390558.596 * * [misc]simplify: iters left: 4 (368 enodes) 1545390558.826 * [exit]simplify: Simplified to (fma -1/2 (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) (fma (* (* (* k k) (log n)) (* (log (* PI 2)) 1/4)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (fma (* (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (log (* PI 2)) (log (* PI 2)))) (* (* k k) 1/8) (fma (* (* (* k k) (log n)) (* (log n) 1/8)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (pow n 1/2) (pow (* PI 2) 1/2)))))) 1545390558.826 * [misc]simplify: Simplified (2 2 1 2) to (λ (k n) (* (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (* (/ 1 (sqrt k)) (fma -1/2 (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) (fma (* (* (* k k) (log n)) (* (log (* PI 2)) 1/4)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (fma (* (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (log (* PI 2)) (log (* PI 2)))) (* (* k k) 1/8) (fma (* (* (* k k) (log n)) (* (log n) 1/8)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (pow n 1/2) (pow (* PI 2) 1/2)))))))))) 1545390558.826 * * * * [misc]progress: [ 92 / 102 ] simplifiying candidate # 1545390558.827 * [enter]simplify: Simplifying (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) 1545390558.827 * * [misc]simplify: iters left: 6 (15 enodes) 1545390558.834 * * [misc]simplify: iters left: 5 (35 enodes) 1545390558.850 * * [misc]simplify: iters left: 4 (72 enodes) 1545390558.883 * * [misc]simplify: iters left: 3 (240 enodes) 1545390559.087 * [exit]simplify: Simplified to (pow (exp (- 1/2 (* 1/2 k))) (+ (log (* 2 PI)) (log n))) 1545390559.087 * [misc]simplify: Simplified (2 2 1 2) to (λ (k n) (* (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (* (/ 1 (sqrt k)) (pow (exp (- 1/2 (* 1/2 k))) (+ (log (* 2 PI)) (log n))))))) 1545390559.087 * * * * [misc]progress: [ 93 / 102 ] simplifiying candidate # 1545390559.088 * [enter]simplify: Simplifying (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) 1545390559.088 * * [misc]simplify: iters left: 6 (16 enodes) 1545390559.094 * * [misc]simplify: iters left: 5 (35 enodes) 1545390559.110 * * [misc]simplify: iters left: 4 (76 enodes) 1545390559.149 * * [misc]simplify: iters left: 3 (278 enodes) 1545390559.311 * [exit]simplify: Simplified to (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))) 1545390559.311 * [misc]simplify: Simplified (2 2 1 2) to (λ (k n) (* (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (* (/ 1 (sqrt k)) (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))))))) 1545390559.311 * * * * [misc]progress: [ 94 / 102 ] simplifiying candidate # 1545390559.311 * [enter]simplify: Simplifying (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) 1545390559.311 * * [misc]simplify: iters left: 6 (37 enodes) 1545390559.319 * * [misc]simplify: iters left: 5 (108 enodes) 1545390559.352 * * [misc]simplify: iters left: 4 (368 enodes) 1545390559.618 * [exit]simplify: Simplified to (fma -1/2 (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) (fma (* (* (* k k) (log n)) (* (log (* PI 2)) 1/4)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (fma (* (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (log (* PI 2)) (log (* PI 2)))) (* (* k k) 1/8) (fma (* (* (* k k) (log n)) (* (log n) 1/8)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (pow n 1/2) (pow (* PI 2) 1/2)))))) 1545390559.619 * [misc]simplify: Simplified (2 1 1 2) to (λ (k n) (* (sqrt (* (/ 1 (sqrt k)) (fma -1/2 (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) (fma (* (* (* k k) (log n)) (* (log (* PI 2)) 1/4)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (fma (* (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (log (* PI 2)) (log (* PI 2)))) (* (* k k) 1/8) (fma (* (* (* k k) (log n)) (* (log n) 1/8)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (pow n 1/2) (pow (* PI 2) 1/2)))))))) (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))) 1545390559.619 * * * * [misc]progress: [ 95 / 102 ] simplifiying candidate # 1545390559.619 * [enter]simplify: Simplifying (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) 1545390559.619 * * [misc]simplify: iters left: 6 (15 enodes) 1545390559.626 * * [misc]simplify: iters left: 5 (35 enodes) 1545390559.638 * * [misc]simplify: iters left: 4 (72 enodes) 1545390559.655 * * [misc]simplify: iters left: 3 (240 enodes) 1545390559.770 * [exit]simplify: Simplified to (pow (exp (- 1/2 (* 1/2 k))) (+ (log (* 2 PI)) (log n))) 1545390559.770 * [misc]simplify: Simplified (2 1 1 2) to (λ (k n) (* (sqrt (* (/ 1 (sqrt k)) (pow (exp (- 1/2 (* 1/2 k))) (+ (log (* 2 PI)) (log n))))) (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))) 1545390559.771 * * * * [misc]progress: [ 96 / 102 ] simplifiying candidate # 1545390559.771 * [enter]simplify: Simplifying (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) 1545390559.771 * * [misc]simplify: iters left: 6 (16 enodes) 1545390559.775 * * [misc]simplify: iters left: 5 (35 enodes) 1545390559.790 * * [misc]simplify: iters left: 4 (76 enodes) 1545390559.812 * * [misc]simplify: iters left: 3 (278 enodes) 1545390560.009 * [exit]simplify: Simplified to (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))) 1545390560.009 * [misc]simplify: Simplified (2 1 1 2) to (λ (k n) (* (sqrt (* (/ 1 (sqrt k)) (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))))) (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))) 1545390560.009 * * * * [misc]progress: [ 97 / 102 ] simplifiying candidate # 1545390560.010 * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))))))) 1545390560.010 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1545390560.010 * * * * [misc]progress: [ 98 / 102 ] simplifiying candidate # 1545390560.010 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3)))))))) 1545390560.010 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1545390560.010 * * * * [misc]progress: [ 99 / 102 ] simplifiying candidate # 1545390560.010 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))))))))) 1545390560.010 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1545390560.010 * * * * [misc]progress: [ 100 / 102 ] simplifiying candidate # 1545390560.010 * [enter]simplify: Simplifying (* 2 (* n PI)) 1545390560.010 * * [misc]simplify: iters left: 4 (5 enodes) 1545390560.011 * * [misc]simplify: iters left: 3 (9 enodes) 1545390560.012 * * [misc]simplify: iters left: 2 (15 enodes) 1545390560.014 * * [misc]simplify: iters left: 1 (17 enodes) 1545390560.016 * [exit]simplify: Simplified to (* (* PI n) 2) 1545390560.016 * [misc]simplify: Simplified (2 2 1 2 1) to (λ (k n) (* (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (* (/ 1 (sqrt k)) (pow (* (* PI n) 2) (/ (- 1 k) 2)))))) 1545390560.016 * * * * [misc]progress: [ 101 / 102 ] simplifiying candidate # 1545390560.016 * [enter]simplify: Simplifying (* 2 (* n PI)) 1545390560.017 * * [misc]simplify: iters left: 4 (5 enodes) 1545390560.017 * * [misc]simplify: iters left: 3 (9 enodes) 1545390560.019 * * [misc]simplify: iters left: 2 (15 enodes) 1545390560.021 * * [misc]simplify: iters left: 1 (17 enodes) 1545390560.027 * [exit]simplify: Simplified to (* (* PI n) 2) 1545390560.027 * [misc]simplify: Simplified (2 2 1 2 1) to (λ (k n) (* (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (* (/ 1 (sqrt k)) (pow (* (* PI n) 2) (/ (- 1 k) 2)))))) 1545390560.027 * * * * [misc]progress: [ 102 / 102 ] simplifiying candidate # 1545390560.027 * [enter]simplify: Simplifying (* 2 (* n PI)) 1545390560.027 * * [misc]simplify: iters left: 4 (5 enodes) 1545390560.029 * * [misc]simplify: iters left: 3 (9 enodes) 1545390560.032 * * [misc]simplify: iters left: 2 (15 enodes) 1545390560.036 * * [misc]simplify: iters left: 1 (17 enodes) 1545390560.040 * [exit]simplify: Simplified to (* (* PI n) 2) 1545390560.040 * [misc]simplify: Simplified (2 2 1 2 1) to (λ (k n) (* (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (* (/ 1 (sqrt k)) (pow (* (* PI n) 2) (/ (- 1 k) 2)))))) 1545390560.040 * * * [misc]progress: adding candidates to table 1545390561.607 * [misc]progress: [Phase 3 of 3] Extracting. 1545390561.607 * * [misc]regime: Finding splitpoints for: (# # # # # # #) 1545390561.609 * * * [misc]regime-changes: Trying 4 branch expressions: (n (* (* 2 PI) n) k (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) 1545390561.609 * * * * [misc]regimes: Trying to branch on n from (# # # # # # #) 1545390561.653 * * * * [misc]regimes: Trying to branch on (* (* 2 PI) n) from (# # # # # # #) 1545390561.703 * * * * [misc]regimes: Trying to branch on k from (# # # # # # #) 1545390561.747 * * * * [misc]regimes: Trying to branch on (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) from (# # # # # # #) 1545390561.806 * * * [misc]regime: Found split indices: #