1546938919.762 * [misc]progress: [Phase 1 of 3] Setting up. 1546938919.762 * * * [misc]progress: [1/2] Preparing points 1546938919.762 * * * * [misc]points: Sampling 256 additional inputs, on iter 0 have 0 / 256 1546938919.827 * * * * [misc]points: Filtering points with unrepresentable outputs 1546938919.827 * * * * [misc]points: Sampling 195 additional inputs, on iter 1 have 61 / 256 1546938919.884 * * * * [misc]points: Filtering points with unrepresentable outputs 1546938919.885 * * * * [misc]points: Sampling 149 additional inputs, on iter 2 have 107 / 256 1546938919.905 * * * * [misc]points: Filtering points with unrepresentable outputs 1546938919.905 * * * * [misc]points: Sampling 112 additional inputs, on iter 3 have 144 / 256 1546938919.935 * * * * [misc]points: Filtering points with unrepresentable outputs 1546938919.936 * * * * [misc]points: Sampling 76 additional inputs, on iter 4 have 180 / 256 1546938919.949 * * * * [misc]points: Filtering points with unrepresentable outputs 1546938919.949 * * * * [misc]points: Sampling 61 additional inputs, on iter 5 have 195 / 256 1546938919.960 * * * * [misc]points: Filtering points with unrepresentable outputs 1546938919.960 * * * * [misc]points: Sampling 49 additional inputs, on iter 6 have 207 / 256 1546938919.970 * * * * [misc]points: Filtering points with unrepresentable outputs 1546938919.970 * * * * [misc]points: Sampling 44 additional inputs, on iter 7 have 212 / 256 1546938919.985 * * * * [misc]points: Filtering points with unrepresentable outputs 1546938919.985 * * * * [misc]points: Sampling 31 additional inputs, on iter 8 have 225 / 256 1546938920.018 * * * * [misc]points: Filtering points with unrepresentable outputs 1546938920.018 * * * * [misc]points: Sampling 20 additional inputs, on iter 9 have 236 / 256 1546938920.023 * * * * [misc]points: Filtering points with unrepresentable outputs 1546938920.023 * * * * [misc]points: Sampling 16 additional inputs, on iter 10 have 240 / 256 1546938920.031 * * * * [misc]points: Filtering points with unrepresentable outputs 1546938920.031 * * * * [misc]points: Sampling 14 additional inputs, on iter 11 have 242 / 256 1546938920.041 * * * * [misc]points: Filtering points with unrepresentable outputs 1546938920.041 * * * * [misc]points: Sampling 13 additional inputs, on iter 12 have 243 / 256 1546938920.050 * * * * [misc]points: Filtering points with unrepresentable outputs 1546938920.051 * * * * [misc]points: Sampling 9 additional inputs, on iter 13 have 247 / 256 1546938920.059 * * * * [misc]points: Filtering points with unrepresentable outputs 1546938920.059 * * * * [misc]points: Sampling 5 additional inputs, on iter 14 have 251 / 256 1546938920.065 * * * * [misc]points: Filtering points with unrepresentable outputs 1546938920.065 * * * * [misc]points: Sampling 5 additional inputs, on iter 15 have 251 / 256 1546938920.069 * * * * [misc]points: Filtering points with unrepresentable outputs 1546938920.069 * * * * [misc]points: Sampling 4 additional inputs, on iter 16 have 253 / 256 1546938920.073 * * * * [misc]points: Filtering points with unrepresentable outputs 1546938920.073 * * * * [misc]points: Sampling 4 additional inputs, on iter 17 have 254 / 256 1546938920.076 * * * * [misc]points: Filtering points with unrepresentable outputs 1546938920.076 * * * * [misc]points: Sampling 4 additional inputs, on iter 18 have 254 / 256 1546938920.080 * * * * [misc]points: Filtering points with unrepresentable outputs 1546938920.080 * * * * [misc]points: Sampling 4 additional inputs, on iter 19 have 254 / 256 1546938920.084 * * * * [misc]points: Filtering points with unrepresentable outputs 1546938920.084 * * * * [exit]points: Sampled 257 points with exact outputs 1546938920.084 * * * [misc]progress: [2/2] Setting up program. 1546938920.087 * [misc]progress: [Phase 2 of 3] Improving. 1546938920.088 * * * * [misc]progress: [ 1 / 1 ] simplifiying candidate # 1546938920.088 * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) 1546938920.088 * * [misc]simplify: iters left: 6 (13 enodes) 1546938920.091 * * [misc]simplify: iters left: 5 (28 enodes) 1546938920.097 * * [misc]simplify: iters left: 4 (44 enodes) 1546938920.108 * * [misc]simplify: iters left: 3 (54 enodes) 1546938920.119 * * [misc]simplify: iters left: 2 (57 enodes) 1546938920.129 * * [misc]simplify: iters left: 1 (65 enodes) 1546938920.160 * [exit]simplify: Simplified to (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)) 1546938920.160 * [misc]simplify: Simplified (2) to (λ (k n) (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) 1546938920.167 * * [misc]progress: iteration 1 / 4 1546938920.169 * * * [misc]progress: picking best candidate 1546938920.175 * * * * [misc]pick: Picked # 1546938920.175 * * * [misc]progress: localizing error 1546938920.196 * * * [misc]progress: generating rewritten candidates 1546938920.196 * * * * [misc]progress: [ 1 / 3 ] rewriting at (2 1) 1546938920.198 * * * * [misc]progress: [ 2 / 3 ] rewriting at (2 1 1) 1546938920.199 * * * * [misc]progress: [ 3 / 3 ] rewriting at (2) 1546938920.205 * * * [misc]progress: generating series expansions 1546938920.205 * * * * [misc]progress: [ 1 / 3 ] generating series at (2 1) 1546938920.205 * [misc]backup-simplify: Simplify (pow (* PI (* n 2)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 1546938920.205 * [misc]approximate: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 1546938920.205 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1546938920.205 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1546938920.205 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1546938920.206 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546938920.206 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938920.206 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938920.206 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546938920.206 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938920.206 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938920.206 * [misc]taylor: Taking taylor expansion of k in k 1546938920.206 * [misc]backup-simplify: Simplify 0 into 0 1546938920.206 * [misc]backup-simplify: Simplify 1 into 1 1546938920.206 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1546938920.206 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1546938920.206 * [misc]taylor: Taking taylor expansion of 2 in k 1546938920.206 * [misc]backup-simplify: Simplify 2 into 2 1546938920.206 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1546938920.206 * [misc]taylor: Taking taylor expansion of n in k 1546938920.206 * [misc]backup-simplify: Simplify n into n 1546938920.206 * [misc]taylor: Taking taylor expansion of PI in k 1546938920.206 * [misc]backup-simplify: Simplify PI into PI 1546938920.206 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1546938920.206 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1546938920.206 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1546938920.206 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546938920.206 * [misc]backup-simplify: Simplify (- 0) into 0 1546938920.206 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546938920.206 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1546938920.206 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1546938920.206 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546938920.207 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546938920.207 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546938920.207 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546938920.207 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938920.207 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938920.207 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546938920.207 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938920.207 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938920.207 * [misc]taylor: Taking taylor expansion of k in n 1546938920.207 * [misc]backup-simplify: Simplify k into k 1546938920.207 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546938920.207 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546938920.207 * [misc]taylor: Taking taylor expansion of 2 in n 1546938920.207 * [misc]backup-simplify: Simplify 2 into 2 1546938920.207 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546938920.207 * [misc]taylor: Taking taylor expansion of n in n 1546938920.207 * [misc]backup-simplify: Simplify 0 into 0 1546938920.207 * [misc]backup-simplify: Simplify 1 into 1 1546938920.207 * [misc]taylor: Taking taylor expansion of PI in n 1546938920.207 * [misc]backup-simplify: Simplify PI into PI 1546938920.207 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546938920.207 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546938920.208 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546938920.208 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546938920.209 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546938920.209 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546938920.209 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546938920.209 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546938920.209 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546938920.210 * [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)))) 1546938920.210 * [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))))) 1546938920.210 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546938920.210 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546938920.210 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546938920.210 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546938920.210 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938920.210 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938920.210 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546938920.210 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938920.210 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938920.210 * [misc]taylor: Taking taylor expansion of k in n 1546938920.210 * [misc]backup-simplify: Simplify k into k 1546938920.210 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546938920.210 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546938920.210 * [misc]taylor: Taking taylor expansion of 2 in n 1546938920.210 * [misc]backup-simplify: Simplify 2 into 2 1546938920.210 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546938920.210 * [misc]taylor: Taking taylor expansion of n in n 1546938920.210 * [misc]backup-simplify: Simplify 0 into 0 1546938920.210 * [misc]backup-simplify: Simplify 1 into 1 1546938920.210 * [misc]taylor: Taking taylor expansion of PI in n 1546938920.210 * [misc]backup-simplify: Simplify PI into PI 1546938920.211 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546938920.211 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546938920.211 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546938920.211 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546938920.212 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546938920.212 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546938920.212 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546938920.212 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546938920.212 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546938920.213 * [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)))) 1546938920.213 * [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))))) 1546938920.213 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1546938920.213 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1546938920.213 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546938920.213 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938920.213 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938920.213 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546938920.213 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938920.213 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938920.213 * [misc]taylor: Taking taylor expansion of k in k 1546938920.213 * [misc]backup-simplify: Simplify 0 into 0 1546938920.213 * [misc]backup-simplify: Simplify 1 into 1 1546938920.213 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1546938920.213 * [misc]taylor: Taking taylor expansion of (log n) in k 1546938920.213 * [misc]taylor: Taking taylor expansion of n in k 1546938920.213 * [misc]backup-simplify: Simplify n into n 1546938920.213 * [misc]backup-simplify: Simplify (log n) into (log n) 1546938920.213 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1546938920.214 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1546938920.214 * [misc]taylor: Taking taylor expansion of 2 in k 1546938920.214 * [misc]backup-simplify: Simplify 2 into 2 1546938920.214 * [misc]taylor: Taking taylor expansion of PI in k 1546938920.214 * [misc]backup-simplify: Simplify PI into PI 1546938920.214 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546938920.214 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546938920.215 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546938920.215 * [misc]backup-simplify: Simplify (- 0) into 0 1546938920.215 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546938920.215 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546938920.216 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1546938920.216 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1546938920.216 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1546938920.217 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546938920.218 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1546938920.219 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546938920.220 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1546938920.220 * [misc]backup-simplify: Simplify (- 0) into 0 1546938920.220 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938920.220 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546938920.221 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1546938920.222 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1546938920.222 * [misc]taylor: Taking taylor expansion of 0 in k 1546938920.222 * [misc]backup-simplify: Simplify 0 into 0 1546938920.222 * [misc]backup-simplify: Simplify 0 into 0 1546938920.222 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1546938920.223 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546938920.224 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546938920.225 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938920.225 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1546938920.225 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546938920.225 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546938920.225 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1546938920.226 * [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))))))) 1546938920.227 * [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))))))) 1546938920.228 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1546938920.229 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1546938920.232 * [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 1546938920.232 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1546938920.232 * [misc]backup-simplify: Simplify (- 0) into 0 1546938920.232 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938920.233 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546938920.233 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1546938920.235 * [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 1546938920.235 * [misc]taylor: Taking taylor expansion of 0 in k 1546938920.235 * [misc]backup-simplify: Simplify 0 into 0 1546938920.235 * [misc]backup-simplify: Simplify 0 into 0 1546938920.235 * [misc]backup-simplify: Simplify 0 into 0 1546938920.236 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1546938920.236 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546938920.239 * [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 1546938920.239 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938920.239 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1546938920.240 * [misc]backup-simplify: Simplify (- 0) into 0 1546938920.240 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938920.240 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1546938920.246 * [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))))) 1546938920.248 * [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))))) 1546938920.251 * [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))))) 1546938920.252 * [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)))) 1546938920.252 * [misc]approximate: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 1546938920.252 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1546938920.252 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1546938920.252 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1546938920.252 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546938920.252 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938920.252 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938920.252 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546938920.252 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938920.252 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938920.252 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546938920.252 * [misc]taylor: Taking taylor expansion of k in k 1546938920.252 * [misc]backup-simplify: Simplify 0 into 0 1546938920.252 * [misc]backup-simplify: Simplify 1 into 1 1546938920.252 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546938920.252 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1546938920.252 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1546938920.252 * [misc]taylor: Taking taylor expansion of 2 in k 1546938920.252 * [misc]backup-simplify: Simplify 2 into 2 1546938920.252 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546938920.252 * [misc]taylor: Taking taylor expansion of PI in k 1546938920.252 * [misc]backup-simplify: Simplify PI into PI 1546938920.252 * [misc]taylor: Taking taylor expansion of n in k 1546938920.252 * [misc]backup-simplify: Simplify n into n 1546938920.252 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546938920.252 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1546938920.252 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1546938920.252 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546938920.253 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546938920.253 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546938920.253 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1546938920.253 * [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)))) 1546938920.253 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546938920.253 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546938920.253 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546938920.253 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546938920.253 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938920.253 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938920.253 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546938920.253 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938920.253 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938920.253 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938920.253 * [misc]taylor: Taking taylor expansion of k in n 1546938920.253 * [misc]backup-simplify: Simplify k into k 1546938920.253 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938920.253 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546938920.253 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546938920.253 * [misc]taylor: Taking taylor expansion of 2 in n 1546938920.253 * [misc]backup-simplify: Simplify 2 into 2 1546938920.253 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546938920.253 * [misc]taylor: Taking taylor expansion of PI in n 1546938920.253 * [misc]backup-simplify: Simplify PI into PI 1546938920.253 * [misc]taylor: Taking taylor expansion of n in n 1546938920.253 * [misc]backup-simplify: Simplify 0 into 0 1546938920.253 * [misc]backup-simplify: Simplify 1 into 1 1546938920.254 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546938920.254 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546938920.254 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546938920.254 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546938920.254 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546938920.254 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546938920.255 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546938920.255 * [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))) 1546938920.256 * [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)))) 1546938920.256 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546938920.256 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546938920.256 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546938920.256 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546938920.256 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938920.256 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938920.256 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546938920.256 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938920.256 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938920.256 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938920.256 * [misc]taylor: Taking taylor expansion of k in n 1546938920.256 * [misc]backup-simplify: Simplify k into k 1546938920.256 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938920.256 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546938920.256 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546938920.256 * [misc]taylor: Taking taylor expansion of 2 in n 1546938920.256 * [misc]backup-simplify: Simplify 2 into 2 1546938920.256 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546938920.256 * [misc]taylor: Taking taylor expansion of PI in n 1546938920.256 * [misc]backup-simplify: Simplify PI into PI 1546938920.256 * [misc]taylor: Taking taylor expansion of n in n 1546938920.256 * [misc]backup-simplify: Simplify 0 into 0 1546938920.256 * [misc]backup-simplify: Simplify 1 into 1 1546938920.256 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546938920.256 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546938920.257 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546938920.257 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546938920.257 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546938920.257 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546938920.257 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546938920.258 * [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))) 1546938920.258 * [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)))) 1546938920.258 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1546938920.258 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1546938920.258 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546938920.258 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938920.258 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938920.258 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546938920.258 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938920.258 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938920.258 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546938920.258 * [misc]taylor: Taking taylor expansion of k in k 1546938920.258 * [misc]backup-simplify: Simplify 0 into 0 1546938920.258 * [misc]backup-simplify: Simplify 1 into 1 1546938920.258 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546938920.258 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1546938920.258 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1546938920.258 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1546938920.258 * [misc]taylor: Taking taylor expansion of 2 in k 1546938920.258 * [misc]backup-simplify: Simplify 2 into 2 1546938920.258 * [misc]taylor: Taking taylor expansion of PI in k 1546938920.258 * [misc]backup-simplify: Simplify PI into PI 1546938920.259 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546938920.259 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546938920.259 * [misc]taylor: Taking taylor expansion of (log n) in k 1546938920.259 * [misc]taylor: Taking taylor expansion of n in k 1546938920.259 * [misc]backup-simplify: Simplify n into n 1546938920.259 * [misc]backup-simplify: Simplify (log n) into (log n) 1546938920.259 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546938920.259 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546938920.259 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546938920.259 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1546938920.260 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1546938920.260 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1546938920.260 * [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)))) 1546938920.261 * [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)))) 1546938920.262 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546938920.262 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546938920.266 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546938920.266 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546938920.266 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546938920.266 * [misc]backup-simplify: Simplify (- 0) into 0 1546938920.266 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938920.267 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546938920.267 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1546938920.268 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546938920.268 * [misc]taylor: Taking taylor expansion of 0 in k 1546938920.268 * [misc]backup-simplify: Simplify 0 into 0 1546938920.268 * [misc]backup-simplify: Simplify 0 into 0 1546938920.268 * [misc]backup-simplify: Simplify 0 into 0 1546938920.269 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938920.270 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546938920.273 * [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 1546938920.273 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546938920.273 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1546938920.273 * [misc]backup-simplify: Simplify (- 0) into 0 1546938920.273 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938920.274 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546938920.274 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1546938920.276 * [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 1546938920.276 * [misc]taylor: Taking taylor expansion of 0 in k 1546938920.276 * [misc]backup-simplify: Simplify 0 into 0 1546938920.276 * [misc]backup-simplify: Simplify 0 into 0 1546938920.276 * [misc]backup-simplify: Simplify 0 into 0 1546938920.276 * [misc]backup-simplify: Simplify 0 into 0 1546938920.277 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938920.278 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546938920.283 * [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 1546938920.283 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546938920.284 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1546938920.284 * [misc]backup-simplify: Simplify (- 0) into 0 1546938920.284 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938920.284 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546938920.285 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1546938920.287 * [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 1546938920.287 * [misc]taylor: Taking taylor expansion of 0 in k 1546938920.287 * [misc]backup-simplify: Simplify 0 into 0 1546938920.287 * [misc]backup-simplify: Simplify 0 into 0 1546938920.288 * [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))))) 1546938920.288 * [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)) 1546938920.288 * [misc]approximate: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 1546938920.288 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1546938920.288 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1546938920.288 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1546938920.288 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546938920.288 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546938920.288 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938920.288 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938920.288 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546938920.288 * [misc]taylor: Taking taylor expansion of k in k 1546938920.288 * [misc]backup-simplify: Simplify 0 into 0 1546938920.288 * [misc]backup-simplify: Simplify 1 into 1 1546938920.288 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546938920.288 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938920.288 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938920.288 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1546938920.288 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1546938920.288 * [misc]taylor: Taking taylor expansion of -2 in k 1546938920.288 * [misc]backup-simplify: Simplify -2 into -2 1546938920.288 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546938920.288 * [misc]taylor: Taking taylor expansion of PI in k 1546938920.288 * [misc]backup-simplify: Simplify PI into PI 1546938920.288 * [misc]taylor: Taking taylor expansion of n in k 1546938920.288 * [misc]backup-simplify: Simplify n into n 1546938920.288 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546938920.289 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1546938920.289 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1546938920.289 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546938920.289 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546938920.289 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1546938920.289 * [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))) 1546938920.289 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546938920.289 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546938920.289 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546938920.289 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546938920.289 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546938920.289 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938920.289 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938920.289 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938920.289 * [misc]taylor: Taking taylor expansion of k in n 1546938920.289 * [misc]backup-simplify: Simplify k into k 1546938920.289 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938920.289 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938920.289 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938920.289 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546938920.289 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546938920.289 * [misc]taylor: Taking taylor expansion of -2 in n 1546938920.289 * [misc]backup-simplify: Simplify -2 into -2 1546938920.289 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546938920.289 * [misc]taylor: Taking taylor expansion of PI in n 1546938920.289 * [misc]backup-simplify: Simplify PI into PI 1546938920.289 * [misc]taylor: Taking taylor expansion of n in n 1546938920.289 * [misc]backup-simplify: Simplify 0 into 0 1546938920.289 * [misc]backup-simplify: Simplify 1 into 1 1546938920.290 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546938920.290 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546938920.290 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546938920.290 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546938920.290 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546938920.291 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546938920.291 * [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))) 1546938920.291 * [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)))) 1546938920.291 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546938920.291 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546938920.292 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546938920.292 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546938920.292 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546938920.292 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938920.292 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938920.292 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938920.292 * [misc]taylor: Taking taylor expansion of k in n 1546938920.292 * [misc]backup-simplify: Simplify k into k 1546938920.292 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938920.292 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938920.292 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938920.292 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546938920.292 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546938920.292 * [misc]taylor: Taking taylor expansion of -2 in n 1546938920.292 * [misc]backup-simplify: Simplify -2 into -2 1546938920.292 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546938920.292 * [misc]taylor: Taking taylor expansion of PI in n 1546938920.292 * [misc]backup-simplify: Simplify PI into PI 1546938920.292 * [misc]taylor: Taking taylor expansion of n in n 1546938920.292 * [misc]backup-simplify: Simplify 0 into 0 1546938920.292 * [misc]backup-simplify: Simplify 1 into 1 1546938920.292 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546938920.292 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546938920.293 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546938920.293 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546938920.293 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546938920.293 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546938920.293 * [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))) 1546938920.294 * [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)))) 1546938920.294 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1546938920.294 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1546938920.294 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546938920.294 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546938920.294 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938920.294 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938920.294 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546938920.294 * [misc]taylor: Taking taylor expansion of k in k 1546938920.294 * [misc]backup-simplify: Simplify 0 into 0 1546938920.294 * [misc]backup-simplify: Simplify 1 into 1 1546938920.294 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546938920.294 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938920.294 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938920.294 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1546938920.294 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1546938920.294 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1546938920.294 * [misc]taylor: Taking taylor expansion of -2 in k 1546938920.294 * [misc]backup-simplify: Simplify -2 into -2 1546938920.294 * [misc]taylor: Taking taylor expansion of PI in k 1546938920.294 * [misc]backup-simplify: Simplify PI into PI 1546938920.294 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546938920.295 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546938920.295 * [misc]taylor: Taking taylor expansion of (log n) in k 1546938920.295 * [misc]taylor: Taking taylor expansion of n in k 1546938920.295 * [misc]backup-simplify: Simplify n into n 1546938920.295 * [misc]backup-simplify: Simplify (log n) into (log n) 1546938920.295 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546938920.295 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546938920.295 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1546938920.296 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1546938920.296 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1546938920.296 * [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)))) 1546938920.297 * [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)))) 1546938920.297 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546938920.298 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1546938920.299 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1546938920.299 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546938920.300 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546938920.300 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938920.300 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546938920.301 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1546938920.302 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546938920.302 * [misc]taylor: Taking taylor expansion of 0 in k 1546938920.302 * [misc]backup-simplify: Simplify 0 into 0 1546938920.302 * [misc]backup-simplify: Simplify 0 into 0 1546938920.302 * [misc]backup-simplify: Simplify 0 into 0 1546938920.303 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938920.303 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1546938920.306 * [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 1546938920.306 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546938920.307 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1546938920.307 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938920.307 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546938920.308 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1546938920.310 * [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 1546938920.310 * [misc]taylor: Taking taylor expansion of 0 in k 1546938920.310 * [misc]backup-simplify: Simplify 0 into 0 1546938920.310 * [misc]backup-simplify: Simplify 0 into 0 1546938920.310 * [misc]backup-simplify: Simplify 0 into 0 1546938920.310 * [misc]backup-simplify: Simplify 0 into 0 1546938920.312 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938920.314 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546938920.322 * [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 1546938920.322 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546938920.323 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1546938920.323 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938920.324 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546938920.324 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 1546938920.328 * [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 1546938920.328 * [misc]taylor: Taking taylor expansion of 0 in k 1546938920.328 * [misc]backup-simplify: Simplify 0 into 0 1546938920.328 * [misc]backup-simplify: Simplify 0 into 0 1546938920.329 * [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))))) 1546938920.329 * * * * [misc]progress: [ 2 / 3 ] generating series at (2 1 1) 1546938920.329 * [misc]backup-simplify: Simplify (* PI (* n 2)) into (* 2 (* n PI)) 1546938920.329 * [misc]approximate: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1546938920.329 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546938920.329 * [misc]taylor: Taking taylor expansion of 2 in n 1546938920.329 * [misc]backup-simplify: Simplify 2 into 2 1546938920.329 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546938920.329 * [misc]taylor: Taking taylor expansion of n in n 1546938920.330 * [misc]backup-simplify: Simplify 0 into 0 1546938920.330 * [misc]backup-simplify: Simplify 1 into 1 1546938920.330 * [misc]taylor: Taking taylor expansion of PI in n 1546938920.330 * [misc]backup-simplify: Simplify PI into PI 1546938920.330 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546938920.330 * [misc]taylor: Taking taylor expansion of 2 in n 1546938920.330 * [misc]backup-simplify: Simplify 2 into 2 1546938920.330 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546938920.330 * [misc]taylor: Taking taylor expansion of n in n 1546938920.330 * [misc]backup-simplify: Simplify 0 into 0 1546938920.330 * [misc]backup-simplify: Simplify 1 into 1 1546938920.330 * [misc]taylor: Taking taylor expansion of PI in n 1546938920.330 * [misc]backup-simplify: Simplify PI into PI 1546938920.330 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546938920.331 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546938920.331 * [misc]backup-simplify: Simplify 0 into 0 1546938920.331 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546938920.332 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546938920.332 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546938920.333 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546938920.334 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1546938920.334 * [misc]backup-simplify: Simplify 0 into 0 1546938920.336 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1546938920.337 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1546938920.337 * [misc]backup-simplify: Simplify 0 into 0 1546938920.339 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1546938920.341 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1546938920.341 * [misc]backup-simplify: Simplify 0 into 0 1546938920.342 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1546938920.344 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1546938920.344 * [misc]backup-simplify: Simplify 0 into 0 1546938920.346 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1546938920.348 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1546938920.348 * [misc]backup-simplify: Simplify 0 into 0 1546938920.350 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1546938920.353 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1546938920.353 * [misc]backup-simplify: Simplify 0 into 0 1546938920.353 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1546938920.353 * [misc]backup-simplify: Simplify (* PI (* (/ 1 n) 2)) into (* 2 (/ PI n)) 1546938920.353 * [misc]approximate: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1546938920.353 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546938920.353 * [misc]taylor: Taking taylor expansion of 2 in n 1546938920.353 * [misc]backup-simplify: Simplify 2 into 2 1546938920.353 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546938920.353 * [misc]taylor: Taking taylor expansion of PI in n 1546938920.353 * [misc]backup-simplify: Simplify PI into PI 1546938920.353 * [misc]taylor: Taking taylor expansion of n in n 1546938920.353 * [misc]backup-simplify: Simplify 0 into 0 1546938920.353 * [misc]backup-simplify: Simplify 1 into 1 1546938920.354 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546938920.354 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546938920.354 * [misc]taylor: Taking taylor expansion of 2 in n 1546938920.354 * [misc]backup-simplify: Simplify 2 into 2 1546938920.354 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546938920.354 * [misc]taylor: Taking taylor expansion of PI in n 1546938920.354 * [misc]backup-simplify: Simplify PI into PI 1546938920.354 * [misc]taylor: Taking taylor expansion of n in n 1546938920.354 * [misc]backup-simplify: Simplify 0 into 0 1546938920.354 * [misc]backup-simplify: Simplify 1 into 1 1546938920.354 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546938920.354 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546938920.354 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546938920.355 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546938920.355 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546938920.355 * [misc]backup-simplify: Simplify 0 into 0 1546938920.356 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938920.357 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546938920.357 * [misc]backup-simplify: Simplify 0 into 0 1546938920.358 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938920.359 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546938920.359 * [misc]backup-simplify: Simplify 0 into 0 1546938920.360 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938920.363 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1546938920.363 * [misc]backup-simplify: Simplify 0 into 0 1546938920.364 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938920.365 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1546938920.366 * [misc]backup-simplify: Simplify 0 into 0 1546938920.367 * [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 1546938920.369 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1546938920.369 * [misc]backup-simplify: Simplify 0 into 0 1546938920.369 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 1546938920.369 * [misc]backup-simplify: Simplify (* PI (* (/ 1 (- n)) 2)) into (* -2 (/ PI n)) 1546938920.370 * [misc]approximate: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1546938920.370 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546938920.370 * [misc]taylor: Taking taylor expansion of -2 in n 1546938920.370 * [misc]backup-simplify: Simplify -2 into -2 1546938920.370 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546938920.370 * [misc]taylor: Taking taylor expansion of PI in n 1546938920.370 * [misc]backup-simplify: Simplify PI into PI 1546938920.370 * [misc]taylor: Taking taylor expansion of n in n 1546938920.370 * [misc]backup-simplify: Simplify 0 into 0 1546938920.370 * [misc]backup-simplify: Simplify 1 into 1 1546938920.370 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546938920.370 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546938920.370 * [misc]taylor: Taking taylor expansion of -2 in n 1546938920.370 * [misc]backup-simplify: Simplify -2 into -2 1546938920.370 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546938920.370 * [misc]taylor: Taking taylor expansion of PI in n 1546938920.370 * [misc]backup-simplify: Simplify PI into PI 1546938920.370 * [misc]taylor: Taking taylor expansion of n in n 1546938920.370 * [misc]backup-simplify: Simplify 0 into 0 1546938920.370 * [misc]backup-simplify: Simplify 1 into 1 1546938920.370 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546938920.370 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546938920.371 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546938920.371 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546938920.372 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1546938920.372 * [misc]backup-simplify: Simplify 0 into 0 1546938920.372 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938920.373 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1546938920.373 * [misc]backup-simplify: Simplify 0 into 0 1546938920.374 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938920.375 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546938920.375 * [misc]backup-simplify: Simplify 0 into 0 1546938920.376 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938920.377 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1546938920.377 * [misc]backup-simplify: Simplify 0 into 0 1546938920.379 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938920.381 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1546938920.381 * [misc]backup-simplify: Simplify 0 into 0 1546938920.383 * [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 1546938920.387 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1546938920.387 * [misc]backup-simplify: Simplify 0 into 0 1546938920.387 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 1546938920.387 * * * * [misc]progress: [ 3 / 3 ] generating series at (2) 1546938920.387 * [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)))) 1546938920.387 * [misc]approximate: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (n k) around 0 1546938920.388 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 1546938920.388 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1546938920.388 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546938920.388 * [misc]taylor: Taking taylor expansion of k in k 1546938920.388 * [misc]backup-simplify: Simplify 0 into 0 1546938920.388 * [misc]backup-simplify: Simplify 1 into 1 1546938920.388 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546938920.388 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546938920.389 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546938920.389 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1546938920.389 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1546938920.389 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1546938920.389 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546938920.389 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938920.389 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938920.389 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546938920.389 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938920.389 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938920.389 * [misc]taylor: Taking taylor expansion of k in k 1546938920.389 * [misc]backup-simplify: Simplify 0 into 0 1546938920.389 * [misc]backup-simplify: Simplify 1 into 1 1546938920.389 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1546938920.389 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1546938920.389 * [misc]taylor: Taking taylor expansion of 2 in k 1546938920.389 * [misc]backup-simplify: Simplify 2 into 2 1546938920.389 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1546938920.389 * [misc]taylor: Taking taylor expansion of n in k 1546938920.389 * [misc]backup-simplify: Simplify n into n 1546938920.389 * [misc]taylor: Taking taylor expansion of PI in k 1546938920.389 * [misc]backup-simplify: Simplify PI into PI 1546938920.389 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1546938920.389 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1546938920.390 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1546938920.390 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546938920.390 * [misc]backup-simplify: Simplify (- 0) into 0 1546938920.390 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546938920.390 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1546938920.390 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1546938920.390 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 1546938920.390 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1546938920.390 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938920.390 * [misc]taylor: Taking taylor expansion of k in n 1546938920.390 * [misc]backup-simplify: Simplify k into k 1546938920.390 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938920.391 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1546938920.391 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546938920.391 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1546938920.391 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546938920.391 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546938920.391 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546938920.391 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546938920.391 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938920.391 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938920.391 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546938920.391 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938920.391 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938920.391 * [misc]taylor: Taking taylor expansion of k in n 1546938920.391 * [misc]backup-simplify: Simplify k into k 1546938920.391 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546938920.391 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546938920.391 * [misc]taylor: Taking taylor expansion of 2 in n 1546938920.391 * [misc]backup-simplify: Simplify 2 into 2 1546938920.391 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546938920.391 * [misc]taylor: Taking taylor expansion of n in n 1546938920.391 * [misc]backup-simplify: Simplify 0 into 0 1546938920.391 * [misc]backup-simplify: Simplify 1 into 1 1546938920.391 * [misc]taylor: Taking taylor expansion of PI in n 1546938920.391 * [misc]backup-simplify: Simplify PI into PI 1546938920.392 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546938920.392 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546938920.392 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546938920.393 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546938920.394 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546938920.394 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546938920.394 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546938920.394 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546938920.394 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546938920.395 * [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)))) 1546938920.395 * [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))))) 1546938920.396 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 1546938920.396 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1546938920.396 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938920.396 * [misc]taylor: Taking taylor expansion of k in n 1546938920.396 * [misc]backup-simplify: Simplify k into k 1546938920.396 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938920.396 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1546938920.396 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546938920.396 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1546938920.396 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546938920.396 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546938920.396 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546938920.396 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546938920.396 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938920.396 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938920.396 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546938920.396 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938920.396 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938920.396 * [misc]taylor: Taking taylor expansion of k in n 1546938920.396 * [misc]backup-simplify: Simplify k into k 1546938920.396 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546938920.396 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546938920.396 * [misc]taylor: Taking taylor expansion of 2 in n 1546938920.396 * [misc]backup-simplify: Simplify 2 into 2 1546938920.396 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546938920.396 * [misc]taylor: Taking taylor expansion of n in n 1546938920.396 * [misc]backup-simplify: Simplify 0 into 0 1546938920.396 * [misc]backup-simplify: Simplify 1 into 1 1546938920.396 * [misc]taylor: Taking taylor expansion of PI in n 1546938920.396 * [misc]backup-simplify: Simplify PI into PI 1546938920.396 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546938920.396 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546938920.397 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546938920.397 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546938920.398 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546938920.398 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546938920.398 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546938920.398 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546938920.398 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546938920.398 * [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)))) 1546938920.399 * [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))))) 1546938920.399 * [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))) 1546938920.399 * [misc]taylor: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k))) in k 1546938920.399 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1546938920.399 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1546938920.399 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546938920.399 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938920.399 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938920.399 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546938920.399 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938920.399 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938920.400 * [misc]taylor: Taking taylor expansion of k in k 1546938920.400 * [misc]backup-simplify: Simplify 0 into 0 1546938920.400 * [misc]backup-simplify: Simplify 1 into 1 1546938920.400 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1546938920.400 * [misc]taylor: Taking taylor expansion of (log n) in k 1546938920.400 * [misc]taylor: Taking taylor expansion of n in k 1546938920.400 * [misc]backup-simplify: Simplify n into n 1546938920.400 * [misc]backup-simplify: Simplify (log n) into (log n) 1546938920.400 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1546938920.400 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1546938920.400 * [misc]taylor: Taking taylor expansion of 2 in k 1546938920.400 * [misc]backup-simplify: Simplify 2 into 2 1546938920.400 * [misc]taylor: Taking taylor expansion of PI in k 1546938920.400 * [misc]backup-simplify: Simplify PI into PI 1546938920.400 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546938920.400 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546938920.400 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546938920.400 * [misc]backup-simplify: Simplify (- 0) into 0 1546938920.401 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546938920.401 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546938920.401 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1546938920.402 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1546938920.402 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1546938920.402 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546938920.402 * [misc]taylor: Taking taylor expansion of k in k 1546938920.402 * [misc]backup-simplify: Simplify 0 into 0 1546938920.402 * [misc]backup-simplify: Simplify 1 into 1 1546938920.402 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546938920.402 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546938920.402 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546938920.402 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) into 0 1546938920.402 * [misc]backup-simplify: Simplify 0 into 0 1546938920.403 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546938920.404 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1546938920.405 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546938920.405 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1546938920.406 * [misc]backup-simplify: Simplify (- 0) into 0 1546938920.406 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938920.406 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546938920.406 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1546938920.407 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1546938920.408 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 k)) 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))) into 0 1546938920.408 * [misc]taylor: Taking taylor expansion of 0 in k 1546938920.408 * [misc]backup-simplify: Simplify 0 into 0 1546938920.409 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1546938920.409 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546938920.411 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546938920.411 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938920.411 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1546938920.411 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546938920.411 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546938920.411 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1546938920.412 * [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))))))) 1546938920.413 * [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))))))) 1546938920.414 * [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))))))) 1546938920.415 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1546938920.416 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1546938920.419 * [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 1546938920.419 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1546938920.419 * [misc]backup-simplify: Simplify (- 0) into 0 1546938920.419 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938920.420 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546938920.420 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1546938920.422 * [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 1546938920.422 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546938920.422 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 1546938920.423 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))))) into 0 1546938920.423 * [misc]taylor: Taking taylor expansion of 0 in k 1546938920.423 * [misc]backup-simplify: Simplify 0 into 0 1546938920.423 * [misc]backup-simplify: Simplify 0 into 0 1546938920.423 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1546938920.424 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1546938920.425 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1546938920.425 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546938920.428 * [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 1546938920.428 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938920.429 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1546938920.429 * [misc]backup-simplify: Simplify (- 0) into 0 1546938920.429 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938920.429 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1546938920.431 * [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))))) 1546938920.435 * [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)))))))) 1546938920.438 * [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)))))))) 1546938920.440 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1546938920.442 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1546938920.450 * [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 1546938920.450 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 1546938920.451 * [misc]backup-simplify: Simplify (- 0) into 0 1546938920.451 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938920.451 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546938920.452 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 1546938920.456 * [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 1546938920.456 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546938920.456 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 1546938920.457 * [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 1546938920.457 * [misc]taylor: Taking taylor expansion of 0 in k 1546938920.458 * [misc]backup-simplify: Simplify 0 into 0 1546938920.458 * [misc]backup-simplify: Simplify 0 into 0 1546938920.458 * [misc]backup-simplify: Simplify 0 into 0 1546938920.458 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938920.459 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1546938920.461 * [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 1546938920.462 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546938920.466 * [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 1546938920.466 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938920.466 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1546938920.467 * [misc]backup-simplify: Simplify (- 0) into 0 1546938920.467 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938920.467 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 1546938920.470 * [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))))))) 1546938920.474 * [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)))))))))))))) 1546938920.479 * [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)))))))))))))) 1546938920.486 * [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)))))))))))))))))))))) 1546938920.486 * [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))))) 1546938920.486 * [misc]approximate: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0 1546938920.486 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 1546938920.486 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1546938920.486 * [misc]taylor: Taking taylor expansion of k in k 1546938920.486 * [misc]backup-simplify: Simplify 0 into 0 1546938920.486 * [misc]backup-simplify: Simplify 1 into 1 1546938920.486 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546938920.487 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546938920.487 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1546938920.487 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1546938920.487 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1546938920.487 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546938920.487 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938920.487 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938920.487 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546938920.487 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938920.487 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938920.487 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546938920.487 * [misc]taylor: Taking taylor expansion of k in k 1546938920.487 * [misc]backup-simplify: Simplify 0 into 0 1546938920.487 * [misc]backup-simplify: Simplify 1 into 1 1546938920.487 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546938920.487 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1546938920.487 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1546938920.487 * [misc]taylor: Taking taylor expansion of 2 in k 1546938920.487 * [misc]backup-simplify: Simplify 2 into 2 1546938920.487 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546938920.487 * [misc]taylor: Taking taylor expansion of PI in k 1546938920.487 * [misc]backup-simplify: Simplify PI into PI 1546938920.487 * [misc]taylor: Taking taylor expansion of n in k 1546938920.487 * [misc]backup-simplify: Simplify n into n 1546938920.487 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546938920.487 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1546938920.487 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1546938920.487 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546938920.487 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546938920.488 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546938920.488 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1546938920.488 * [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)))) 1546938920.488 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1546938920.488 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1546938920.488 * [misc]taylor: Taking taylor expansion of k in n 1546938920.488 * [misc]backup-simplify: Simplify k into k 1546938920.488 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1546938920.488 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1546938920.488 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546938920.488 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546938920.488 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546938920.488 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546938920.488 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938920.488 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938920.488 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546938920.488 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938920.488 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938920.488 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938920.488 * [misc]taylor: Taking taylor expansion of k in n 1546938920.488 * [misc]backup-simplify: Simplify k into k 1546938920.488 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938920.488 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546938920.488 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546938920.488 * [misc]taylor: Taking taylor expansion of 2 in n 1546938920.488 * [misc]backup-simplify: Simplify 2 into 2 1546938920.488 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546938920.488 * [misc]taylor: Taking taylor expansion of PI in n 1546938920.488 * [misc]backup-simplify: Simplify PI into PI 1546938920.488 * [misc]taylor: Taking taylor expansion of n in n 1546938920.488 * [misc]backup-simplify: Simplify 0 into 0 1546938920.488 * [misc]backup-simplify: Simplify 1 into 1 1546938920.489 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546938920.489 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546938920.489 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546938920.489 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546938920.489 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546938920.489 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546938920.490 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546938920.490 * [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))) 1546938920.490 * [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)))) 1546938920.490 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1546938920.490 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1546938920.490 * [misc]taylor: Taking taylor expansion of k in n 1546938920.490 * [misc]backup-simplify: Simplify k into k 1546938920.490 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1546938920.490 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1546938920.491 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546938920.491 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546938920.491 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546938920.491 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546938920.491 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938920.491 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938920.491 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546938920.491 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938920.491 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938920.491 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938920.491 * [misc]taylor: Taking taylor expansion of k in n 1546938920.491 * [misc]backup-simplify: Simplify k into k 1546938920.491 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938920.491 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546938920.491 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546938920.491 * [misc]taylor: Taking taylor expansion of 2 in n 1546938920.491 * [misc]backup-simplify: Simplify 2 into 2 1546938920.491 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546938920.491 * [misc]taylor: Taking taylor expansion of PI in n 1546938920.491 * [misc]backup-simplify: Simplify PI into PI 1546938920.491 * [misc]taylor: Taking taylor expansion of n in n 1546938920.491 * [misc]backup-simplify: Simplify 0 into 0 1546938920.491 * [misc]backup-simplify: Simplify 1 into 1 1546938920.491 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546938920.491 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546938920.492 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546938920.492 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546938920.492 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546938920.492 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546938920.493 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546938920.493 * [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))) 1546938920.494 * [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)))) 1546938920.495 * [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)) 1546938920.495 * [misc]taylor: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) in k 1546938920.495 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1546938920.495 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1546938920.495 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546938920.495 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938920.495 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938920.495 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546938920.495 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938920.495 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938920.495 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546938920.495 * [misc]taylor: Taking taylor expansion of k in k 1546938920.495 * [misc]backup-simplify: Simplify 0 into 0 1546938920.495 * [misc]backup-simplify: Simplify 1 into 1 1546938920.495 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546938920.495 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1546938920.495 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1546938920.495 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1546938920.495 * [misc]taylor: Taking taylor expansion of 2 in k 1546938920.495 * [misc]backup-simplify: Simplify 2 into 2 1546938920.495 * [misc]taylor: Taking taylor expansion of PI in k 1546938920.495 * [misc]backup-simplify: Simplify PI into PI 1546938920.496 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546938920.496 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546938920.496 * [misc]taylor: Taking taylor expansion of (log n) in k 1546938920.496 * [misc]taylor: Taking taylor expansion of n in k 1546938920.496 * [misc]backup-simplify: Simplify n into n 1546938920.496 * [misc]backup-simplify: Simplify (log n) into (log n) 1546938920.497 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546938920.497 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546938920.497 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546938920.497 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1546938920.497 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1546938920.498 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1546938920.499 * [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)))) 1546938920.499 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1546938920.499 * [misc]taylor: Taking taylor expansion of k in k 1546938920.499 * [misc]backup-simplify: Simplify 0 into 0 1546938920.499 * [misc]backup-simplify: Simplify 1 into 1 1546938920.499 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546938920.499 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546938920.500 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) into 0 1546938920.500 * [misc]backup-simplify: Simplify 0 into 0 1546938920.501 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546938920.502 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546938920.505 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546938920.505 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546938920.505 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546938920.505 * [misc]backup-simplify: Simplify (- 0) into 0 1546938920.505 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938920.506 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546938920.507 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1546938920.508 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546938920.509 * [misc]backup-simplify: Simplify (+ (* (sqrt k) 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0 1546938920.509 * [misc]taylor: Taking taylor expansion of 0 in k 1546938920.509 * [misc]backup-simplify: Simplify 0 into 0 1546938920.509 * [misc]backup-simplify: Simplify 0 into 0 1546938920.510 * [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)))))) 1546938920.511 * [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)))))) 1546938920.512 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938920.513 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546938920.518 * [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 1546938920.519 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546938920.519 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1546938920.519 * [misc]backup-simplify: Simplify (- 0) into 0 1546938920.519 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938920.520 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546938920.521 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1546938920.523 * [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 1546938920.524 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 1546938920.524 * [misc]backup-simplify: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0 1546938920.524 * [misc]taylor: Taking taylor expansion of 0 in k 1546938920.524 * [misc]backup-simplify: Simplify 0 into 0 1546938920.524 * [misc]backup-simplify: Simplify 0 into 0 1546938920.524 * [misc]backup-simplify: Simplify 0 into 0 1546938920.525 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1546938920.525 * [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)))))) 1546938920.526 * [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)))))) 1546938920.527 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938920.528 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546938920.532 * [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 1546938920.533 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546938920.533 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1546938920.533 * [misc]backup-simplify: Simplify (- 0) into 0 1546938920.533 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938920.533 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546938920.534 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1546938920.536 * [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 1546938920.536 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 1546938920.537 * [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 1546938920.537 * [misc]taylor: Taking taylor expansion of 0 in k 1546938920.537 * [misc]backup-simplify: Simplify 0 into 0 1546938920.537 * [misc]backup-simplify: Simplify 0 into 0 1546938920.537 * [misc]backup-simplify: Simplify 0 into 0 1546938920.537 * [misc]backup-simplify: Simplify 0 into 0 1546938920.538 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1546938920.539 * [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)))))) 1546938920.539 * [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)))))) 1546938920.541 * [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)))))))) 1546938920.541 * [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))) 1546938920.541 * [misc]approximate: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (n k) around 0 1546938920.541 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 1546938920.541 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1546938920.541 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1546938920.541 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1546938920.541 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546938920.541 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546938920.541 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938920.541 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938920.541 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546938920.541 * [misc]taylor: Taking taylor expansion of k in k 1546938920.541 * [misc]backup-simplify: Simplify 0 into 0 1546938920.541 * [misc]backup-simplify: Simplify 1 into 1 1546938920.541 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546938920.541 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938920.541 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938920.541 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1546938920.541 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1546938920.541 * [misc]taylor: Taking taylor expansion of -2 in k 1546938920.541 * [misc]backup-simplify: Simplify -2 into -2 1546938920.541 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546938920.541 * [misc]taylor: Taking taylor expansion of PI in k 1546938920.541 * [misc]backup-simplify: Simplify PI into PI 1546938920.541 * [misc]taylor: Taking taylor expansion of n in k 1546938920.541 * [misc]backup-simplify: Simplify n into n 1546938920.541 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546938920.542 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1546938920.542 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1546938920.542 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546938920.542 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546938920.542 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1546938920.542 * [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))) 1546938920.542 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1546938920.542 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1546938920.542 * [misc]taylor: Taking taylor expansion of -1 in k 1546938920.542 * [misc]backup-simplify: Simplify -1 into -1 1546938920.542 * [misc]taylor: Taking taylor expansion of k in k 1546938920.542 * [misc]backup-simplify: Simplify 0 into 0 1546938920.542 * [misc]backup-simplify: Simplify 1 into 1 1546938920.542 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1546938920.542 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546938920.543 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1546938920.543 * [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)))) 1546938920.543 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 1546938920.543 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546938920.543 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546938920.543 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546938920.543 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546938920.543 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546938920.543 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938920.543 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938920.543 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938920.543 * [misc]taylor: Taking taylor expansion of k in n 1546938920.543 * [misc]backup-simplify: Simplify k into k 1546938920.543 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938920.543 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938920.543 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938920.543 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546938920.543 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546938920.543 * [misc]taylor: Taking taylor expansion of -2 in n 1546938920.543 * [misc]backup-simplify: Simplify -2 into -2 1546938920.543 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546938920.543 * [misc]taylor: Taking taylor expansion of PI in n 1546938920.543 * [misc]backup-simplify: Simplify PI into PI 1546938920.543 * [misc]taylor: Taking taylor expansion of n in n 1546938920.543 * [misc]backup-simplify: Simplify 0 into 0 1546938920.543 * [misc]backup-simplify: Simplify 1 into 1 1546938920.543 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546938920.544 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546938920.544 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546938920.544 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546938920.544 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546938920.544 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546938920.545 * [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))) 1546938920.545 * [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)))) 1546938920.545 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1546938920.545 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1546938920.545 * [misc]taylor: Taking taylor expansion of -1 in n 1546938920.545 * [misc]backup-simplify: Simplify -1 into -1 1546938920.545 * [misc]taylor: Taking taylor expansion of k in n 1546938920.545 * [misc]backup-simplify: Simplify k into k 1546938920.545 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1546938920.545 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1546938920.546 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1546938920.546 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1546938920.546 * [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))) 1546938920.546 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 1546938920.546 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546938920.546 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546938920.546 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546938920.546 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546938920.546 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546938920.546 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938920.546 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938920.546 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938920.546 * [misc]taylor: Taking taylor expansion of k in n 1546938920.546 * [misc]backup-simplify: Simplify k into k 1546938920.546 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938920.546 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938920.546 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938920.546 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546938920.546 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546938920.546 * [misc]taylor: Taking taylor expansion of -2 in n 1546938920.546 * [misc]backup-simplify: Simplify -2 into -2 1546938920.546 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546938920.546 * [misc]taylor: Taking taylor expansion of PI in n 1546938920.546 * [misc]backup-simplify: Simplify PI into PI 1546938920.546 * [misc]taylor: Taking taylor expansion of n in n 1546938920.546 * [misc]backup-simplify: Simplify 0 into 0 1546938920.546 * [misc]backup-simplify: Simplify 1 into 1 1546938920.547 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546938920.547 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546938920.547 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546938920.547 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546938920.547 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546938920.548 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546938920.548 * [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))) 1546938920.548 * [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)))) 1546938920.548 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1546938920.548 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1546938920.548 * [misc]taylor: Taking taylor expansion of -1 in n 1546938920.549 * [misc]backup-simplify: Simplify -1 into -1 1546938920.549 * [misc]taylor: Taking taylor expansion of k in n 1546938920.549 * [misc]backup-simplify: Simplify k into k 1546938920.549 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1546938920.549 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1546938920.549 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1546938920.549 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1546938920.549 * [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))) 1546938920.549 * [misc]taylor: Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) in k 1546938920.549 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1546938920.549 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1546938920.549 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546938920.549 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546938920.549 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938920.549 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938920.549 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546938920.549 * [misc]taylor: Taking taylor expansion of k in k 1546938920.549 * [misc]backup-simplify: Simplify 0 into 0 1546938920.550 * [misc]backup-simplify: Simplify 1 into 1 1546938920.550 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546938920.550 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938920.550 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938920.550 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1546938920.550 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1546938920.550 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1546938920.550 * [misc]taylor: Taking taylor expansion of -2 in k 1546938920.550 * [misc]backup-simplify: Simplify -2 into -2 1546938920.550 * [misc]taylor: Taking taylor expansion of PI in k 1546938920.550 * [misc]backup-simplify: Simplify PI into PI 1546938920.550 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546938920.550 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546938920.550 * [misc]taylor: Taking taylor expansion of (log n) in k 1546938920.550 * [misc]taylor: Taking taylor expansion of n in k 1546938920.550 * [misc]backup-simplify: Simplify n into n 1546938920.550 * [misc]backup-simplify: Simplify (log n) into (log n) 1546938920.551 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546938920.551 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546938920.551 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1546938920.551 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1546938920.552 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1546938920.552 * [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)))) 1546938920.552 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1546938920.552 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1546938920.552 * [misc]taylor: Taking taylor expansion of -1 in k 1546938920.552 * [misc]backup-simplify: Simplify -1 into -1 1546938920.552 * [misc]taylor: Taking taylor expansion of k in k 1546938920.552 * [misc]backup-simplify: Simplify 0 into 0 1546938920.552 * [misc]backup-simplify: Simplify 1 into 1 1546938920.553 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1546938920.553 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546938920.553 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1546938920.554 * [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))))) 1546938920.554 * [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))))) 1546938920.556 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546938920.556 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1546938920.559 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1546938920.559 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546938920.559 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546938920.559 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938920.560 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546938920.561 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1546938920.562 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546938920.563 * [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 1546938920.563 * [misc]taylor: Taking taylor expansion of 0 in k 1546938920.563 * [misc]backup-simplify: Simplify 0 into 0 1546938920.563 * [misc]backup-simplify: Simplify 0 into 0 1546938920.564 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1546938920.565 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1546938920.566 * [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)))))) 1546938920.566 * [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)))))) 1546938920.568 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938920.569 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1546938920.574 * [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 1546938920.575 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546938920.575 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1546938920.575 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938920.576 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546938920.577 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1546938920.579 * [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 1546938920.579 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546938920.580 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 1546938920.581 * [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 1546938920.581 * [misc]taylor: Taking taylor expansion of 0 in k 1546938920.581 * [misc]backup-simplify: Simplify 0 into 0 1546938920.581 * [misc]backup-simplify: Simplify 0 into 0 1546938920.581 * [misc]backup-simplify: Simplify 0 into 0 1546938920.582 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938920.583 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1546938920.585 * [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)))))) 1546938920.586 * [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)))))) 1546938920.589 * [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))))))))))) 1546938920.589 * * * [misc]progress: simplifying candidates 1546938920.589 * * * * [misc]progress: [ 1 / 77 ] simplifiying candidate # 1546938920.589 * [enter]simplify: Simplifying (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) 1546938920.589 * * [misc]simplify: iters left: 6 (11 enodes) 1546938920.592 * * [misc]simplify: iters left: 5 (21 enodes) 1546938920.596 * * [misc]simplify: iters left: 4 (47 enodes) 1546938920.605 * * [misc]simplify: iters left: 3 (109 enodes) 1546938920.632 * * [misc]simplify: iters left: 2 (300 enodes) 1546938920.838 * [exit]simplify: Simplified to (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) 1546938920.838 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (exp (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI)))) (sqrt k))) 1546938920.838 * * * * [misc]progress: [ 2 / 77 ] simplifiying candidate # 1546938920.838 * * * * [misc]progress: [ 3 / 77 ] simplifiying candidate # 1546938920.838 * [enter]simplify: Simplifying (* PI (* n 2)) 1546938920.838 * * [misc]simplify: iters left: 4 (5 enodes) 1546938920.840 * * [misc]simplify: iters left: 3 (9 enodes) 1546938920.843 * * [misc]simplify: iters left: 2 (15 enodes) 1546938920.846 * * [misc]simplify: iters left: 1 (17 enodes) 1546938920.850 * [exit]simplify: Simplified to (* (* 2 n) PI) 1546938920.851 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* 2 n) PI) (* 1 (- 1/2 (/ k 2)))) (sqrt k))) 1546938920.851 * * * * [misc]progress: [ 4 / 77 ] simplifiying candidate # 1546938920.851 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (/ k 2)) 1546938920.851 * * [misc]simplify: iters left: 5 (8 enodes) 1546938920.854 * * [misc]simplify: iters left: 4 (12 enodes) 1546938920.857 * * [misc]simplify: iters left: 3 (18 enodes) 1546938920.862 * * [misc]simplify: iters left: 2 (20 enodes) 1546938920.867 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ k 2)) 1546938920.867 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (/ (pow (* PI (* n 2)) 1/2) (pow (* (* 2 n) PI) (/ k 2))) (sqrt k))) 1546938920.867 * * * * [misc]progress: [ 5 / 77 ] simplifiying candidate # 1546938920.868 * [enter]simplify: Simplifying (cbrt (- 1/2 (/ k 2))) 1546938920.868 * * [misc]simplify: iters left: 5 (6 enodes) 1546938920.869 * * [misc]simplify: iters left: 4 (8 enodes) 1546938920.875 * * [misc]simplify: iters left: 3 (11 enodes) 1546938920.878 * [exit]simplify: Simplified to (cbrt (- 1/2 (/ k 2))) 1546938920.878 * [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))) 1546938920.878 * * * * [misc]progress: [ 6 / 77 ] simplifiying candidate # 1546938920.878 * [enter]simplify: Simplifying (sqrt (- 1/2 (/ k 2))) 1546938920.878 * * [misc]simplify: iters left: 5 (6 enodes) 1546938920.881 * * [misc]simplify: iters left: 4 (8 enodes) 1546938920.883 * * [misc]simplify: iters left: 3 (11 enodes) 1546938920.886 * [exit]simplify: Simplified to (sqrt (- 1/2 (/ k 2))) 1546938920.886 * [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))) 1546938920.886 * * * * [misc]progress: [ 7 / 77 ] simplifiying candidate # 1546938920.887 * [enter]simplify: Simplifying (- 1/2 (/ k 2)) 1546938920.887 * * [misc]simplify: iters left: 4 (5 enodes) 1546938920.888 * * [misc]simplify: iters left: 3 (7 enodes) 1546938920.890 * * [misc]simplify: iters left: 2 (10 enodes) 1546938920.893 * [exit]simplify: Simplified to (- 1/2 (/ k 2)) 1546938920.893 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (pow (pow (* PI (* n 2)) 1) (- 1/2 (/ k 2))) (sqrt k))) 1546938920.893 * * * * [misc]progress: [ 8 / 77 ] simplifiying candidate # 1546938920.893 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1546938920.893 * * [misc]simplify: iters left: 5 (9 enodes) 1546938920.896 * * [misc]simplify: iters left: 4 (15 enodes) 1546938920.901 * * [misc]simplify: iters left: 3 (21 enodes) 1546938920.906 * * [misc]simplify: iters left: 2 (22 enodes) 1546938920.909 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1546938920.909 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2)))) (sqrt k))) 1546938920.910 * * * * [misc]progress: [ 9 / 77 ] simplifiying candidate # 1546938920.910 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1546938920.910 * * [misc]simplify: iters left: 5 (9 enodes) 1546938920.911 * * [misc]simplify: iters left: 4 (15 enodes) 1546938920.913 * * [misc]simplify: iters left: 3 (21 enodes) 1546938920.916 * * [misc]simplify: iters left: 2 (22 enodes) 1546938920.918 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1546938920.918 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2)))) (sqrt k))) 1546938920.918 * * * * [misc]progress: [ 10 / 77 ] simplifiying candidate # 1546938920.919 * [enter]simplify: Simplifying (pow PI (- 1/2 (/ k 2))) 1546938920.919 * * [misc]simplify: iters left: 5 (7 enodes) 1546938920.920 * * [misc]simplify: iters left: 4 (9 enodes) 1546938920.921 * * [misc]simplify: iters left: 3 (12 enodes) 1546938920.923 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1546938920.923 * [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))) 1546938920.923 * * * * [misc]progress: [ 11 / 77 ] simplifiying candidate # 1546938920.923 * * * * [misc]progress: [ 12 / 77 ] simplifiying candidate # 1546938920.923 * * * * [misc]progress: [ 13 / 77 ] simplifiying candidate # 1546938920.923 * * * * [misc]progress: [ 14 / 77 ] simplifiying candidate # 1546938920.923 * * * * [misc]progress: [ 15 / 77 ] simplifiying candidate # 1546938920.923 * * * * [misc]progress: [ 16 / 77 ] simplifiying candidate # 1546938920.923 * * * * [misc]progress: [ 17 / 77 ] simplifiying candidate # 1546938920.923 * * * * [misc]progress: [ 18 / 77 ] simplifiying candidate # 1546938920.923 * * * * [misc]progress: [ 19 / 77 ] simplifiying candidate # 1546938920.923 * * * * [misc]progress: [ 20 / 77 ] simplifiying candidate # 1546938920.923 * * * * [misc]progress: [ 21 / 77 ] simplifiying candidate # 1546938920.923 * * * * [misc]progress: [ 22 / 77 ] simplifiying candidate # 1546938920.924 * * * * [misc]progress: [ 23 / 77 ] simplifiying candidate # 1546938920.924 * * * * [misc]progress: [ 24 / 77 ] simplifiying candidate # 1546938920.924 * * * * [misc]progress: [ 25 / 77 ] simplifiying candidate # 1546938920.924 * * * * [misc]progress: [ 26 / 77 ] simplifiying candidate # 1546938920.924 * * * * [misc]progress: [ 27 / 77 ] simplifiying candidate # 1546938920.924 * * * * [misc]progress: [ 28 / 77 ] simplifiying candidate # 1546938920.924 * [enter]simplify: Simplifying (- (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) (log (sqrt k))) 1546938920.924 * * [misc]simplify: iters left: 6 (14 enodes) 1546938920.926 * * [misc]simplify: iters left: 5 (26 enodes) 1546938920.930 * * [misc]simplify: iters left: 4 (53 enodes) 1546938920.942 * * [misc]simplify: iters left: 3 (137 enodes) 1546938921.022 * * [misc]simplify: iters left: 2 (487 enodes) 1546938921.531 * [exit]simplify: Simplified to (- (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) (log (sqrt k))) 1546938921.531 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) (log (sqrt k))))) 1546938921.531 * * * * [misc]progress: [ 29 / 77 ] simplifiying candidate # 1546938921.531 * [enter]simplify: Simplifying (- (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) (log (sqrt k))) 1546938921.531 * * [misc]simplify: iters left: 6 (14 enodes) 1546938921.536 * * [misc]simplify: iters left: 5 (26 enodes) 1546938921.544 * * [misc]simplify: iters left: 4 (53 enodes) 1546938921.564 * * [misc]simplify: iters left: 3 (137 enodes) 1546938921.633 * * [misc]simplify: iters left: 2 (487 enodes) 1546938922.097 * [exit]simplify: Simplified to (- (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) (log (sqrt k))) 1546938922.097 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) (log (sqrt k))))) 1546938922.097 * * * * [misc]progress: [ 30 / 77 ] simplifiying candidate # 1546938922.097 * [enter]simplify: Simplifying (- (log (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (log (sqrt k))) 1546938922.097 * * [misc]simplify: iters left: 6 (14 enodes) 1546938922.099 * * [misc]simplify: iters left: 5 (24 enodes) 1546938922.103 * * [misc]simplify: iters left: 4 (42 enodes) 1546938922.109 * * [misc]simplify: iters left: 3 (71 enodes) 1546938922.124 * * [misc]simplify: iters left: 2 (208 enodes) 1546938922.290 * [exit]simplify: Simplified to (- (* (log (* (* 2 n) PI)) (- 1/2 (/ k 2))) (log (sqrt k))) 1546938922.290 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (log (* (* 2 n) PI)) (- 1/2 (/ k 2))) (log (sqrt k))))) 1546938922.290 * * * * [misc]progress: [ 31 / 77 ] simplifiying candidate # 1546938922.290 * * * * [misc]progress: [ 32 / 77 ] simplifiying candidate # 1546938922.290 * * * * [misc]progress: [ 33 / 77 ] simplifiying candidate # 1546938922.290 * [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))) 1546938922.290 * * [misc]simplify: iters left: 6 (16 enodes) 1546938922.293 * * [misc]simplify: iters left: 5 (31 enodes) 1546938922.299 * * [misc]simplify: iters left: 4 (67 enodes) 1546938922.316 * * [misc]simplify: iters left: 3 (124 enodes) 1546938922.337 * * [misc]simplify: iters left: 2 (195 enodes) 1546938922.410 * * [misc]simplify: iters left: 1 (309 enodes) 1546938922.550 * [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)))) 1546938922.550 * [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)))))) 1546938922.550 * * * * [misc]progress: [ 34 / 77 ] simplifiying candidate # 1546938922.550 * * * * [misc]progress: [ 35 / 77 ] simplifiying candidate # 1546938922.550 * * * * [misc]progress: [ 36 / 77 ] simplifiying candidate # 1546938922.550 * * * * [misc]progress: [ 37 / 77 ] simplifiying candidate # 1546938922.550 * * * * [misc]progress: [ 38 / 77 ] simplifiying candidate # 1546938922.551 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1546938922.551 * * [misc]simplify: iters left: 6 (12 enodes) 1546938922.554 * * [misc]simplify: iters left: 5 (19 enodes) 1546938922.560 * * [misc]simplify: iters left: 4 (25 enodes) 1546938922.566 * * [misc]simplify: iters left: 3 (26 enodes) 1546938922.573 * [exit]simplify: Simplified to (/ (sqrt (* (* 2 n) PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1546938922.573 * [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))))) 1546938922.573 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (sqrt k))) 1546938922.573 * * [misc]simplify: iters left: 6 (12 enodes) 1546938922.577 * * [misc]simplify: iters left: 5 (18 enodes) 1546938922.582 * * [misc]simplify: iters left: 4 (24 enodes) 1546938922.590 * * [misc]simplify: iters left: 3 (25 enodes) 1546938922.596 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt k))) 1546938922.596 * [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))))) 1546938922.596 * * * * [misc]progress: [ 39 / 77 ] simplifiying candidate # 1546938922.597 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (sqrt (sqrt k))) 1546938922.597 * * [misc]simplify: iters left: 6 (11 enodes) 1546938922.600 * * [misc]simplify: iters left: 5 (16 enodes) 1546938922.604 * * [misc]simplify: iters left: 4 (22 enodes) 1546938922.610 * * [misc]simplify: iters left: 3 (24 enodes) 1546938922.616 * [exit]simplify: Simplified to (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) 1546938922.616 * [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))))) 1546938922.616 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k))) 1546938922.616 * * [misc]simplify: iters left: 6 (12 enodes) 1546938922.620 * * [misc]simplify: iters left: 5 (18 enodes) 1546938922.625 * * [misc]simplify: iters left: 4 (24 enodes) 1546938922.631 * * [misc]simplify: iters left: 3 (25 enodes) 1546938922.638 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k))) 1546938922.638 * [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))))) 1546938922.638 * * * * [misc]progress: [ 40 / 77 ] simplifiying candidate # 1546938922.638 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) 1) 1546938922.638 * * [misc]simplify: iters left: 6 (9 enodes) 1546938922.641 * * [misc]simplify: iters left: 5 (16 enodes) 1546938922.646 * * [misc]simplify: iters left: 4 (24 enodes) 1546938922.651 * * [misc]simplify: iters left: 3 (26 enodes) 1546938922.656 * [exit]simplify: Simplified to (sqrt (* (* PI 2) n)) 1546938922.656 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) 1546938922.656 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)) 1546938922.657 * * [misc]simplify: iters left: 6 (11 enodes) 1546938922.660 * * [misc]simplify: iters left: 5 (17 enodes) 1546938922.664 * * [misc]simplify: iters left: 4 (23 enodes) 1546938922.670 * * [misc]simplify: iters left: 3 (24 enodes) 1546938922.676 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)) 1546938922.676 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)))) 1546938922.676 * * * * [misc]progress: [ 41 / 77 ] simplifiying candidate # 1546938922.677 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1546938922.677 * * [misc]simplify: iters left: 6 (12 enodes) 1546938922.680 * * [misc]simplify: iters left: 5 (19 enodes) 1546938922.682 * * [misc]simplify: iters left: 4 (25 enodes) 1546938922.686 * * [misc]simplify: iters left: 3 (26 enodes) 1546938922.689 * [exit]simplify: Simplified to (/ (sqrt (* (* 2 n) PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1546938922.689 * [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))))) 1546938922.689 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (sqrt k))) 1546938922.689 * * [misc]simplify: iters left: 6 (12 enodes) 1546938922.691 * * [misc]simplify: iters left: 5 (18 enodes) 1546938922.693 * * [misc]simplify: iters left: 4 (24 enodes) 1546938922.696 * * [misc]simplify: iters left: 3 (25 enodes) 1546938922.699 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt k))) 1546938922.699 * [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))))) 1546938922.699 * * * * [misc]progress: [ 42 / 77 ] simplifiying candidate # 1546938922.699 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (sqrt (sqrt k))) 1546938922.699 * * [misc]simplify: iters left: 6 (11 enodes) 1546938922.701 * * [misc]simplify: iters left: 5 (16 enodes) 1546938922.703 * * [misc]simplify: iters left: 4 (22 enodes) 1546938922.707 * * [misc]simplify: iters left: 3 (24 enodes) 1546938922.709 * [exit]simplify: Simplified to (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) 1546938922.709 * [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))))) 1546938922.710 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k))) 1546938922.710 * * [misc]simplify: iters left: 6 (12 enodes) 1546938922.711 * * [misc]simplify: iters left: 5 (18 enodes) 1546938922.714 * * [misc]simplify: iters left: 4 (24 enodes) 1546938922.717 * * [misc]simplify: iters left: 3 (25 enodes) 1546938922.720 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k))) 1546938922.720 * [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))))) 1546938922.720 * * * * [misc]progress: [ 43 / 77 ] simplifiying candidate # 1546938922.720 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) 1) 1546938922.720 * * [misc]simplify: iters left: 6 (9 enodes) 1546938922.723 * * [misc]simplify: iters left: 5 (16 enodes) 1546938922.728 * * [misc]simplify: iters left: 4 (24 enodes) 1546938922.733 * * [misc]simplify: iters left: 3 (26 enodes) 1546938922.739 * [exit]simplify: Simplified to (sqrt (* (* PI 2) n)) 1546938922.739 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) 1546938922.739 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)) 1546938922.739 * * [misc]simplify: iters left: 6 (11 enodes) 1546938922.743 * * [misc]simplify: iters left: 5 (17 enodes) 1546938922.748 * * [misc]simplify: iters left: 4 (23 enodes) 1546938922.754 * * [misc]simplify: iters left: 3 (24 enodes) 1546938922.757 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)) 1546938922.758 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)))) 1546938922.758 * * * * [misc]progress: [ 44 / 77 ] simplifiying candidate # 1546938922.758 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1546938922.758 * * [misc]simplify: iters left: 6 (11 enodes) 1546938922.759 * * [misc]simplify: iters left: 5 (15 enodes) 1546938922.761 * * [misc]simplify: iters left: 4 (18 enodes) 1546938922.764 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1546938922.764 * [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))))) 1546938922.764 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1546938922.764 * * [misc]simplify: iters left: 6 (11 enodes) 1546938922.765 * * [misc]simplify: iters left: 5 (14 enodes) 1546938922.767 * * [misc]simplify: iters left: 4 (17 enodes) 1546938922.770 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1546938922.770 * [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))))) 1546938922.770 * * * * [misc]progress: [ 45 / 77 ] simplifiying candidate # 1546938922.770 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1546938922.770 * * [misc]simplify: iters left: 6 (10 enodes) 1546938922.771 * * [misc]simplify: iters left: 5 (12 enodes) 1546938922.773 * * [misc]simplify: iters left: 4 (15 enodes) 1546938922.775 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1546938922.775 * [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))))) 1546938922.775 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1546938922.775 * * [misc]simplify: iters left: 6 (11 enodes) 1546938922.778 * * [misc]simplify: iters left: 5 (14 enodes) 1546938922.782 * * [misc]simplify: iters left: 4 (17 enodes) 1546938922.785 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1546938922.785 * [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))))) 1546938922.785 * * * * [misc]progress: [ 46 / 77 ] simplifiying candidate # 1546938922.785 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) 1) 1546938922.785 * * [misc]simplify: iters left: 6 (9 enodes) 1546938922.786 * * [misc]simplify: iters left: 5 (13 enodes) 1546938922.788 * * [misc]simplify: iters left: 4 (18 enodes) 1546938922.790 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1546938922.790 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1546938922.790 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)) 1546938922.791 * * [misc]simplify: iters left: 6 (10 enodes) 1546938922.792 * * [misc]simplify: iters left: 5 (13 enodes) 1546938922.794 * * [misc]simplify: iters left: 4 (16 enodes) 1546938922.796 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)) 1546938922.796 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1546938922.796 * * * * [misc]progress: [ 47 / 77 ] simplifiying candidate # 1546938922.796 * [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)))) 1546938922.796 * * [misc]simplify: iters left: 6 (16 enodes) 1546938922.799 * * [misc]simplify: iters left: 5 (28 enodes) 1546938922.804 * * [misc]simplify: iters left: 4 (46 enodes) 1546938922.810 * * [misc]simplify: iters left: 3 (50 enodes) 1546938922.816 * * [misc]simplify: iters left: 2 (53 enodes) 1546938922.822 * [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)))) 1546938922.822 * [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))))) 1546938922.823 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1546938922.823 * * [misc]simplify: iters left: 6 (14 enodes) 1546938922.825 * * [misc]simplify: iters left: 5 (20 enodes) 1546938922.827 * * [misc]simplify: iters left: 4 (29 enodes) 1546938922.831 * * [misc]simplify: iters left: 3 (30 enodes) 1546938922.838 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1546938922.838 * [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))))) 1546938922.838 * * * * [misc]progress: [ 48 / 77 ] simplifiying candidate # 1546938922.838 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) 1546938922.838 * * [misc]simplify: iters left: 6 (15 enodes) 1546938922.843 * * [misc]simplify: iters left: 5 (23 enodes) 1546938922.850 * * [misc]simplify: iters left: 4 (34 enodes) 1546938922.859 * * [misc]simplify: iters left: 3 (37 enodes) 1546938922.868 * [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)))))) 1546938922.868 * [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))))) 1546938922.869 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1546938922.869 * * [misc]simplify: iters left: 6 (14 enodes) 1546938922.873 * * [misc]simplify: iters left: 5 (20 enodes) 1546938922.878 * * [misc]simplify: iters left: 4 (29 enodes) 1546938922.885 * * [misc]simplify: iters left: 3 (30 enodes) 1546938922.890 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1546938922.890 * [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))))) 1546938922.890 * * * * [misc]progress: [ 49 / 77 ] simplifiying candidate # 1546938922.890 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1) 1546938922.890 * * [misc]simplify: iters left: 6 (14 enodes) 1546938922.892 * * [misc]simplify: iters left: 5 (24 enodes) 1546938922.896 * * [misc]simplify: iters left: 4 (39 enodes) 1546938922.901 * * [misc]simplify: iters left: 3 (54 enodes) 1546938922.909 * * [misc]simplify: iters left: 2 (80 enodes) 1546938922.918 * [exit]simplify: Simplified to (* (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))) 1546938922.918 * [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)))) 1546938922.919 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt k)) 1546938922.919 * * [misc]simplify: iters left: 6 (13 enodes) 1546938922.921 * * [misc]simplify: iters left: 5 (19 enodes) 1546938922.923 * * [misc]simplify: iters left: 4 (28 enodes) 1546938922.927 * * [misc]simplify: iters left: 3 (30 enodes) 1546938922.930 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt k)) 1546938922.930 * [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)))) 1546938922.930 * * * * [misc]progress: [ 50 / 77 ] simplifiying candidate # 1546938922.931 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1546938922.931 * * [misc]simplify: iters left: 6 (15 enodes) 1546938922.933 * * [misc]simplify: iters left: 5 (23 enodes) 1546938922.937 * * [misc]simplify: iters left: 4 (32 enodes) 1546938922.945 * * [misc]simplify: iters left: 3 (34 enodes) 1546938922.954 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1546938922.954 * [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))))) 1546938922.954 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1546938922.955 * * [misc]simplify: iters left: 6 (14 enodes) 1546938922.959 * * [misc]simplify: iters left: 5 (20 enodes) 1546938922.964 * * [misc]simplify: iters left: 4 (29 enodes) 1546938922.972 * * [misc]simplify: iters left: 3 (30 enodes) 1546938922.977 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1546938922.977 * [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))))) 1546938922.977 * * * * [misc]progress: [ 51 / 77 ] simplifiying candidate # 1546938922.977 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1546938922.978 * * [misc]simplify: iters left: 6 (14 enodes) 1546938922.979 * * [misc]simplify: iters left: 5 (20 enodes) 1546938922.982 * * [misc]simplify: iters left: 4 (29 enodes) 1546938922.986 * * [misc]simplify: iters left: 3 (30 enodes) 1546938922.989 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1546938922.989 * [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))))) 1546938922.990 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1546938922.990 * * [misc]simplify: iters left: 6 (14 enodes) 1546938922.992 * * [misc]simplify: iters left: 5 (20 enodes) 1546938922.994 * * [misc]simplify: iters left: 4 (29 enodes) 1546938922.999 * * [misc]simplify: iters left: 3 (30 enodes) 1546938923.002 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1546938923.002 * [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))))) 1546938923.002 * * * * [misc]progress: [ 52 / 77 ] simplifiying candidate # 1546938923.002 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1) 1546938923.002 * * [misc]simplify: iters left: 6 (13 enodes) 1546938923.004 * * [misc]simplify: iters left: 5 (21 enodes) 1546938923.008 * * [misc]simplify: iters left: 4 (32 enodes) 1546938923.011 * * [misc]simplify: iters left: 3 (33 enodes) 1546938923.019 * [exit]simplify: Simplified to (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) 1546938923.019 * [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)))) 1546938923.019 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt k)) 1546938923.020 * * [misc]simplify: iters left: 6 (13 enodes) 1546938923.024 * * [misc]simplify: iters left: 5 (19 enodes) 1546938923.029 * * [misc]simplify: iters left: 4 (28 enodes) 1546938923.036 * * [misc]simplify: iters left: 3 (30 enodes) 1546938923.044 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt k)) 1546938923.044 * [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)))) 1546938923.044 * * * * [misc]progress: [ 53 / 77 ] simplifiying candidate # 1546938923.044 * [enter]simplify: Simplifying (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1546938923.044 * * [misc]simplify: iters left: 6 (6 enodes) 1546938923.046 * * [misc]simplify: iters left: 5 (10 enodes) 1546938923.049 * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) 1546938923.049 * [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))))) 1546938923.049 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1546938923.049 * * [misc]simplify: iters left: 6 (13 enodes) 1546938923.053 * * [misc]simplify: iters left: 5 (19 enodes) 1546938923.059 * * [misc]simplify: iters left: 4 (28 enodes) 1546938923.066 * * [misc]simplify: iters left: 3 (30 enodes) 1546938923.073 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1546938923.073 * [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))))) 1546938923.073 * * * * [misc]progress: [ 54 / 77 ] simplifiying candidate # 1546938923.074 * [enter]simplify: Simplifying (/ 1 (sqrt (sqrt k))) 1546938923.074 * * [misc]simplify: iters left: 4 (5 enodes) 1546938923.076 * * [misc]simplify: iters left: 3 (7 enodes) 1546938923.077 * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt k))) 1546938923.077 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) 1546938923.078 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1546938923.078 * * [misc]simplify: iters left: 6 (13 enodes) 1546938923.082 * * [misc]simplify: iters left: 5 (19 enodes) 1546938923.087 * * [misc]simplify: iters left: 4 (28 enodes) 1546938923.094 * * [misc]simplify: iters left: 3 (30 enodes) 1546938923.102 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1546938923.102 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) 1546938923.102 * * * * [misc]progress: [ 55 / 77 ] simplifiying candidate # 1546938923.102 * [enter]simplify: Simplifying (/ 1 1) 1546938923.102 * * [misc]simplify: iters left: 2 (2 enodes) 1546938923.103 * * [misc]simplify: iters left: 1 (4 enodes) 1546938923.104 * [exit]simplify: Simplified to 1 1546938923.104 * [misc]simplify: Simplified (2 1) to (λ (k n) (* 1 (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))) 1546938923.104 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)) 1546938923.104 * * [misc]simplify: iters left: 6 (12 enodes) 1546938923.108 * * [misc]simplify: iters left: 5 (18 enodes) 1546938923.110 * * [misc]simplify: iters left: 4 (27 enodes) 1546938923.114 * * [misc]simplify: iters left: 3 (29 enodes) 1546938923.117 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k)) 1546938923.117 * [misc]simplify: Simplified (2 2) to (λ (k n) (* 1 (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k)))) 1546938923.117 * * * * [misc]progress: [ 56 / 77 ] simplifiying candidate # 1546938923.117 * * * * [misc]progress: [ 57 / 77 ] simplifiying candidate # 1546938923.117 * * * * [misc]progress: [ 58 / 77 ] simplifiying candidate # 1546938923.117 * * * * [misc]progress: [ 59 / 77 ] simplifiying candidate # 1546938923.117 * [enter]simplify: Simplifying (cbrt (sqrt k)) 1546938923.117 * * [misc]simplify: iters left: 2 (3 enodes) 1546938923.119 * [exit]simplify: Simplified to (cbrt (sqrt k)) 1546938923.119 * [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)))) 1546938923.119 * * * * [misc]progress: [ 60 / 77 ] simplifiying candidate # 1546938923.119 * [enter]simplify: Simplifying (sqrt (sqrt k)) 1546938923.119 * * [misc]simplify: iters left: 2 (3 enodes) 1546938923.119 * [exit]simplify: Simplified to (sqrt (sqrt k)) 1546938923.119 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k)))) 1546938923.119 * * * * [misc]progress: [ 61 / 77 ] simplifiying candidate # 1546938923.119 * [enter]simplify: Simplifying (sqrt k) 1546938923.120 * * [misc]simplify: iters left: 1 (2 enodes) 1546938923.120 * [exit]simplify: Simplified to (sqrt k) 1546938923.120 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) 1) (sqrt k))) 1546938923.120 * * * * [misc]progress: [ 62 / 77 ] simplifiying candidate # 1546938923.120 * [enter]simplify: Simplifying (pow (* PI (* n 2)) 1/2) 1546938923.120 * * [misc]simplify: iters left: 5 (7 enodes) 1546938923.121 * * [misc]simplify: iters left: 4 (12 enodes) 1546938923.123 * * [misc]simplify: iters left: 3 (18 enodes) 1546938923.125 * * [misc]simplify: iters left: 2 (20 enodes) 1546938923.128 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1546938923.128 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2)))))) 1546938923.128 * * * * [misc]progress: [ 63 / 77 ] simplifiying candidate # 1546938923.128 * [enter]simplify: Simplifying (pow (* PI (* n 2)) 1/2) 1546938923.128 * * [misc]simplify: iters left: 5 (7 enodes) 1546938923.129 * * [misc]simplify: iters left: 4 (12 enodes) 1546938923.131 * * [misc]simplify: iters left: 3 (18 enodes) 1546938923.133 * * [misc]simplify: iters left: 2 (20 enodes) 1546938923.135 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1546938923.135 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2)))))) 1546938923.135 * * * * [misc]progress: [ 64 / 77 ] simplifiying candidate # 1546938923.135 * [enter]simplify: Simplifying (pow PI (- 1/2 (/ k 2))) 1546938923.135 * * [misc]simplify: iters left: 5 (7 enodes) 1546938923.136 * * [misc]simplify: iters left: 4 (9 enodes) 1546938923.138 * * [misc]simplify: iters left: 3 (12 enodes) 1546938923.139 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1546938923.139 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (pow PI (- 1/2 (/ k 2))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2)))))) 1546938923.139 * * * * [misc]progress: [ 65 / 77 ] simplifiying candidate # 1546938923.140 * [enter]simplify: Simplifying (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546938923.140 * * [misc]simplify: iters left: 6 (12 enodes) 1546938923.144 * * [misc]simplify: iters left: 5 (18 enodes) 1546938923.149 * * [misc]simplify: iters left: 4 (27 enodes) 1546938923.156 * * [misc]simplify: iters left: 3 (29 enodes) 1546938923.163 * [exit]simplify: Simplified to (* (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) 1546938923.163 * [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))))))) 1546938923.163 * * * * [misc]progress: [ 66 / 77 ] simplifiying candidate # 1546938923.164 * [enter]simplify: Simplifying (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1546938923.164 * * [misc]simplify: iters left: 6 (11 enodes) 1546938923.167 * * [misc]simplify: iters left: 5 (17 enodes) 1546938923.172 * * [misc]simplify: iters left: 4 (26 enodes) 1546938923.178 * * [misc]simplify: iters left: 3 (27 enodes) 1546938923.185 * [exit]simplify: Simplified to (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) 1546938923.185 * [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))))))) 1546938923.185 * * * * [misc]progress: [ 67 / 77 ] simplifiying candidate # 1546938923.185 * * * * [misc]progress: [ 68 / 77 ] simplifiying candidate # 1546938923.186 * [enter]simplify: Simplifying (pow (* PI (* n 2)) 1/2) 1546938923.186 * * [misc]simplify: iters left: 5 (7 enodes) 1546938923.188 * * [misc]simplify: iters left: 4 (12 enodes) 1546938923.191 * * [misc]simplify: iters left: 3 (18 enodes) 1546938923.196 * * [misc]simplify: iters left: 2 (20 enodes) 1546938923.201 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1546938923.201 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2))))) 1546938923.201 * * * * [misc]progress: [ 69 / 77 ] simplifiying candidate # 1546938923.202 * [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))))) 1546938923.202 * * [misc]simplify: iters left: 6 (37 enodes) 1546938923.217 * * [misc]simplify: iters left: 5 (105 enodes) 1546938923.241 * * [misc]simplify: iters left: 4 (339 enodes) 1546938923.435 * [exit]simplify: Simplified to (+ (+ (* (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) -1/2) (+ (* (* (* k (log n)) (* k (log n))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (pow (* PI 2) 1/2) (pow n 1/2)))) (* (* k k) (+ (* (* (log (* PI 2)) (log (* PI 2))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (* (* (log n) (pow n 1/2)) (pow (* PI 2) 1/2)) (* (log (* PI 2)) 1/4))))) 1546938923.435 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (+ (+ (* (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) -1/2) (+ (* (* (* k (log n)) (* k (log n))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (pow (* PI 2) 1/2) (pow n 1/2)))) (* (* k k) (+ (* (* (log (* PI 2)) (log (* PI 2))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (* (* (log n) (pow n 1/2)) (pow (* PI 2) 1/2)) (* (log (* PI 2)) 1/4))))) (sqrt k))) 1546938923.435 * * * * [misc]progress: [ 70 / 77 ] simplifiying candidate # 1546938923.436 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 1546938923.436 * * [misc]simplify: iters left: 6 (15 enodes) 1546938923.439 * * [misc]simplify: iters left: 5 (33 enodes) 1546938923.444 * * [misc]simplify: iters left: 4 (64 enodes) 1546938923.456 * * [misc]simplify: iters left: 3 (171 enodes) 1546938923.560 * [exit]simplify: Simplified to (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow n (- 1/2 (* 1/2 k)))) 1546938923.560 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow n (- 1/2 (* 1/2 k)))) (sqrt k))) 1546938923.560 * * * * [misc]progress: [ 71 / 77 ] simplifiying candidate # 1546938923.560 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 1546938923.560 * * [misc]simplify: iters left: 6 (15 enodes) 1546938923.566 * * [misc]simplify: iters left: 5 (30 enodes) 1546938923.577 * * [misc]simplify: iters left: 4 (65 enodes) 1546938923.603 * * [misc]simplify: iters left: 3 (200 enodes) 1546938923.735 * [exit]simplify: Simplified to (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))) 1546938923.735 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))) (sqrt k))) 1546938923.735 * * * * [misc]progress: [ 72 / 77 ] simplifiying candidate # 1546938923.736 * [enter]simplify: Simplifying (* 2 (* n PI)) 1546938923.736 * * [misc]simplify: iters left: 4 (5 enodes) 1546938923.737 * * [misc]simplify: iters left: 3 (9 enodes) 1546938923.738 * * [misc]simplify: iters left: 2 (15 enodes) 1546938923.740 * * [misc]simplify: iters left: 1 (17 enodes) 1546938923.742 * [exit]simplify: Simplified to (* (* PI n) 2) 1546938923.742 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt k))) 1546938923.742 * * * * [misc]progress: [ 73 / 77 ] simplifiying candidate # 1546938923.742 * [enter]simplify: Simplifying (* 2 (* n PI)) 1546938923.742 * * [misc]simplify: iters left: 4 (5 enodes) 1546938923.743 * * [misc]simplify: iters left: 3 (9 enodes) 1546938923.744 * * [misc]simplify: iters left: 2 (15 enodes) 1546938923.746 * * [misc]simplify: iters left: 1 (17 enodes) 1546938923.748 * [exit]simplify: Simplified to (* (* PI n) 2) 1546938923.748 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt k))) 1546938923.748 * * * * [misc]progress: [ 74 / 77 ] simplifiying candidate # 1546938923.748 * [enter]simplify: Simplifying (* 2 (* n PI)) 1546938923.749 * * [misc]simplify: iters left: 4 (5 enodes) 1546938923.749 * * [misc]simplify: iters left: 3 (9 enodes) 1546938923.751 * * [misc]simplify: iters left: 2 (15 enodes) 1546938923.752 * * [misc]simplify: iters left: 1 (17 enodes) 1546938923.758 * [exit]simplify: Simplified to (* (* PI n) 2) 1546938923.758 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt k))) 1546938923.758 * * * * [misc]progress: [ 75 / 77 ] simplifiying candidate # 1546938923.759 * [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)))))))))))))))))))))) 1546938923.759 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1546938923.759 * * * * [misc]progress: [ 76 / 77 ] simplifiying candidate # 1546938923.759 * [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)))))))) 1546938923.759 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1546938923.759 * * * * [misc]progress: [ 77 / 77 ] simplifiying candidate # 1546938923.759 * [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))))))))))) 1546938923.759 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1546938923.760 * * * [misc]progress: adding candidates to table 1546938924.510 * * [misc]progress: iteration 2 / 4 1546938924.510 * * * [misc]progress: picking best candidate 1546938924.547 * * * * [misc]pick: Picked # 1546938924.547 * * * [misc]progress: localizing error 1546938924.562 * * * [misc]progress: generating rewritten candidates 1546938924.562 * * * * [misc]progress: [ 1 / 4 ] rewriting at (2 1 2 1) 1546938924.566 * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 1 1 1) 1546938924.569 * * * * [misc]progress: [ 3 / 4 ] rewriting at (2 1) 1546938924.581 * * * * [misc]progress: [ 4 / 4 ] rewriting at (2 1 2 1 1) 1546938924.583 * * * [misc]progress: generating series expansions 1546938924.583 * * * * [misc]progress: [ 1 / 4 ] generating series at (2 1 2 1) 1546938924.583 * [misc]backup-simplify: Simplify (pow (* PI (* n 2)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 1546938924.583 * [misc]approximate: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 1546938924.583 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1546938924.583 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1546938924.583 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1546938924.583 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546938924.583 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938924.583 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.583 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546938924.583 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938924.583 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.583 * [misc]taylor: Taking taylor expansion of k in k 1546938924.583 * [misc]backup-simplify: Simplify 0 into 0 1546938924.584 * [misc]backup-simplify: Simplify 1 into 1 1546938924.584 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1546938924.584 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1546938924.584 * [misc]taylor: Taking taylor expansion of 2 in k 1546938924.584 * [misc]backup-simplify: Simplify 2 into 2 1546938924.584 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1546938924.584 * [misc]taylor: Taking taylor expansion of n in k 1546938924.584 * [misc]backup-simplify: Simplify n into n 1546938924.584 * [misc]taylor: Taking taylor expansion of PI in k 1546938924.584 * [misc]backup-simplify: Simplify PI into PI 1546938924.584 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1546938924.584 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1546938924.584 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1546938924.584 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546938924.584 * [misc]backup-simplify: Simplify (- 0) into 0 1546938924.584 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546938924.584 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1546938924.584 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1546938924.584 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546938924.584 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546938924.585 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546938924.585 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546938924.585 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938924.585 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.585 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546938924.585 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938924.585 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.585 * [misc]taylor: Taking taylor expansion of k in n 1546938924.585 * [misc]backup-simplify: Simplify k into k 1546938924.585 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546938924.585 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546938924.585 * [misc]taylor: Taking taylor expansion of 2 in n 1546938924.585 * [misc]backup-simplify: Simplify 2 into 2 1546938924.585 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546938924.585 * [misc]taylor: Taking taylor expansion of n in n 1546938924.585 * [misc]backup-simplify: Simplify 0 into 0 1546938924.585 * [misc]backup-simplify: Simplify 1 into 1 1546938924.585 * [misc]taylor: Taking taylor expansion of PI in n 1546938924.585 * [misc]backup-simplify: Simplify PI into PI 1546938924.585 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546938924.585 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546938924.586 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546938924.586 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546938924.586 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546938924.586 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546938924.587 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546938924.587 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546938924.587 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546938924.587 * [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)))) 1546938924.588 * [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))))) 1546938924.588 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546938924.588 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546938924.588 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546938924.588 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546938924.588 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938924.588 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.588 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546938924.588 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938924.588 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.588 * [misc]taylor: Taking taylor expansion of k in n 1546938924.588 * [misc]backup-simplify: Simplify k into k 1546938924.588 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546938924.588 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546938924.588 * [misc]taylor: Taking taylor expansion of 2 in n 1546938924.588 * [misc]backup-simplify: Simplify 2 into 2 1546938924.588 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546938924.588 * [misc]taylor: Taking taylor expansion of n in n 1546938924.588 * [misc]backup-simplify: Simplify 0 into 0 1546938924.588 * [misc]backup-simplify: Simplify 1 into 1 1546938924.588 * [misc]taylor: Taking taylor expansion of PI in n 1546938924.588 * [misc]backup-simplify: Simplify PI into PI 1546938924.588 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546938924.588 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546938924.589 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546938924.589 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546938924.589 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546938924.590 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546938924.590 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546938924.590 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546938924.590 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546938924.593 * [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)))) 1546938924.593 * [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))))) 1546938924.593 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1546938924.594 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1546938924.594 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546938924.594 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938924.594 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.594 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546938924.594 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938924.594 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.594 * [misc]taylor: Taking taylor expansion of k in k 1546938924.594 * [misc]backup-simplify: Simplify 0 into 0 1546938924.594 * [misc]backup-simplify: Simplify 1 into 1 1546938924.594 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1546938924.594 * [misc]taylor: Taking taylor expansion of (log n) in k 1546938924.594 * [misc]taylor: Taking taylor expansion of n in k 1546938924.594 * [misc]backup-simplify: Simplify n into n 1546938924.594 * [misc]backup-simplify: Simplify (log n) into (log n) 1546938924.594 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1546938924.594 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1546938924.594 * [misc]taylor: Taking taylor expansion of 2 in k 1546938924.594 * [misc]backup-simplify: Simplify 2 into 2 1546938924.594 * [misc]taylor: Taking taylor expansion of PI in k 1546938924.594 * [misc]backup-simplify: Simplify PI into PI 1546938924.594 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546938924.594 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546938924.594 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546938924.595 * [misc]backup-simplify: Simplify (- 0) into 0 1546938924.595 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546938924.595 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546938924.595 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1546938924.596 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1546938924.596 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1546938924.597 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546938924.597 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1546938924.599 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546938924.599 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1546938924.599 * [misc]backup-simplify: Simplify (- 0) into 0 1546938924.599 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938924.600 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546938924.600 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1546938924.601 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1546938924.601 * [misc]taylor: Taking taylor expansion of 0 in k 1546938924.601 * [misc]backup-simplify: Simplify 0 into 0 1546938924.601 * [misc]backup-simplify: Simplify 0 into 0 1546938924.602 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1546938924.602 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546938924.604 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546938924.604 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938924.604 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1546938924.604 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546938924.604 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546938924.605 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1546938924.605 * [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))))))) 1546938924.606 * [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))))))) 1546938924.607 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1546938924.608 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1546938924.611 * [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 1546938924.611 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1546938924.612 * [misc]backup-simplify: Simplify (- 0) into 0 1546938924.612 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938924.612 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546938924.613 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1546938924.614 * [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 1546938924.614 * [misc]taylor: Taking taylor expansion of 0 in k 1546938924.614 * [misc]backup-simplify: Simplify 0 into 0 1546938924.614 * [misc]backup-simplify: Simplify 0 into 0 1546938924.614 * [misc]backup-simplify: Simplify 0 into 0 1546938924.615 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1546938924.616 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546938924.619 * [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 1546938924.619 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938924.619 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1546938924.619 * [misc]backup-simplify: Simplify (- 0) into 0 1546938924.619 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938924.620 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1546938924.621 * [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))))) 1546938924.623 * [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))))) 1546938924.626 * [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))))) 1546938924.626 * [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)))) 1546938924.626 * [misc]approximate: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 1546938924.626 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1546938924.626 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1546938924.626 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1546938924.626 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546938924.626 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938924.626 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.626 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546938924.626 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938924.626 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.626 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546938924.626 * [misc]taylor: Taking taylor expansion of k in k 1546938924.626 * [misc]backup-simplify: Simplify 0 into 0 1546938924.626 * [misc]backup-simplify: Simplify 1 into 1 1546938924.627 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546938924.627 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1546938924.627 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1546938924.627 * [misc]taylor: Taking taylor expansion of 2 in k 1546938924.627 * [misc]backup-simplify: Simplify 2 into 2 1546938924.627 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546938924.627 * [misc]taylor: Taking taylor expansion of PI in k 1546938924.627 * [misc]backup-simplify: Simplify PI into PI 1546938924.627 * [misc]taylor: Taking taylor expansion of n in k 1546938924.627 * [misc]backup-simplify: Simplify n into n 1546938924.627 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546938924.627 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1546938924.627 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1546938924.627 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546938924.627 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546938924.627 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546938924.627 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1546938924.627 * [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)))) 1546938924.627 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546938924.627 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546938924.627 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546938924.627 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546938924.628 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938924.628 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.628 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546938924.628 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938924.628 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.628 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938924.628 * [misc]taylor: Taking taylor expansion of k in n 1546938924.628 * [misc]backup-simplify: Simplify k into k 1546938924.628 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938924.628 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546938924.628 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546938924.628 * [misc]taylor: Taking taylor expansion of 2 in n 1546938924.628 * [misc]backup-simplify: Simplify 2 into 2 1546938924.628 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546938924.628 * [misc]taylor: Taking taylor expansion of PI in n 1546938924.628 * [misc]backup-simplify: Simplify PI into PI 1546938924.628 * [misc]taylor: Taking taylor expansion of n in n 1546938924.628 * [misc]backup-simplify: Simplify 0 into 0 1546938924.628 * [misc]backup-simplify: Simplify 1 into 1 1546938924.628 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546938924.628 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546938924.629 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546938924.629 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546938924.629 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546938924.629 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546938924.629 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546938924.630 * [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))) 1546938924.630 * [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)))) 1546938924.630 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546938924.630 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546938924.630 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546938924.630 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546938924.630 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938924.630 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.630 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546938924.630 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938924.630 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.630 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938924.630 * [misc]taylor: Taking taylor expansion of k in n 1546938924.630 * [misc]backup-simplify: Simplify k into k 1546938924.630 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938924.630 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546938924.630 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546938924.630 * [misc]taylor: Taking taylor expansion of 2 in n 1546938924.630 * [misc]backup-simplify: Simplify 2 into 2 1546938924.630 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546938924.630 * [misc]taylor: Taking taylor expansion of PI in n 1546938924.630 * [misc]backup-simplify: Simplify PI into PI 1546938924.630 * [misc]taylor: Taking taylor expansion of n in n 1546938924.630 * [misc]backup-simplify: Simplify 0 into 0 1546938924.630 * [misc]backup-simplify: Simplify 1 into 1 1546938924.631 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546938924.631 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546938924.631 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546938924.631 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546938924.631 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546938924.631 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546938924.632 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546938924.632 * [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))) 1546938924.632 * [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)))) 1546938924.633 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1546938924.633 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1546938924.633 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546938924.633 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938924.633 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.633 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546938924.633 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938924.633 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.633 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546938924.633 * [misc]taylor: Taking taylor expansion of k in k 1546938924.633 * [misc]backup-simplify: Simplify 0 into 0 1546938924.633 * [misc]backup-simplify: Simplify 1 into 1 1546938924.633 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546938924.633 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1546938924.633 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1546938924.633 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1546938924.633 * [misc]taylor: Taking taylor expansion of 2 in k 1546938924.633 * [misc]backup-simplify: Simplify 2 into 2 1546938924.633 * [misc]taylor: Taking taylor expansion of PI in k 1546938924.633 * [misc]backup-simplify: Simplify PI into PI 1546938924.633 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546938924.633 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546938924.633 * [misc]taylor: Taking taylor expansion of (log n) in k 1546938924.633 * [misc]taylor: Taking taylor expansion of n in k 1546938924.633 * [misc]backup-simplify: Simplify n into n 1546938924.634 * [misc]backup-simplify: Simplify (log n) into (log n) 1546938924.634 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546938924.634 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546938924.634 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546938924.634 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1546938924.634 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1546938924.635 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1546938924.635 * [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)))) 1546938924.635 * [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)))) 1546938924.636 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546938924.637 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546938924.638 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546938924.638 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546938924.638 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546938924.638 * [misc]backup-simplify: Simplify (- 0) into 0 1546938924.639 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938924.639 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546938924.639 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1546938924.640 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546938924.640 * [misc]taylor: Taking taylor expansion of 0 in k 1546938924.640 * [misc]backup-simplify: Simplify 0 into 0 1546938924.640 * [misc]backup-simplify: Simplify 0 into 0 1546938924.640 * [misc]backup-simplify: Simplify 0 into 0 1546938924.641 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938924.642 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546938924.645 * [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 1546938924.645 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546938924.645 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1546938924.645 * [misc]backup-simplify: Simplify (- 0) into 0 1546938924.645 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938924.646 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546938924.646 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1546938924.648 * [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 1546938924.648 * [misc]taylor: Taking taylor expansion of 0 in k 1546938924.648 * [misc]backup-simplify: Simplify 0 into 0 1546938924.648 * [misc]backup-simplify: Simplify 0 into 0 1546938924.648 * [misc]backup-simplify: Simplify 0 into 0 1546938924.648 * [misc]backup-simplify: Simplify 0 into 0 1546938924.649 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938924.650 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546938924.654 * [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 1546938924.654 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546938924.655 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1546938924.655 * [misc]backup-simplify: Simplify (- 0) into 0 1546938924.655 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938924.656 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546938924.657 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1546938924.660 * [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 1546938924.660 * [misc]taylor: Taking taylor expansion of 0 in k 1546938924.660 * [misc]backup-simplify: Simplify 0 into 0 1546938924.660 * [misc]backup-simplify: Simplify 0 into 0 1546938924.661 * [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))))) 1546938924.661 * [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)) 1546938924.661 * [misc]approximate: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 1546938924.661 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1546938924.661 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1546938924.661 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1546938924.662 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546938924.662 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546938924.662 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938924.662 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.662 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546938924.662 * [misc]taylor: Taking taylor expansion of k in k 1546938924.662 * [misc]backup-simplify: Simplify 0 into 0 1546938924.662 * [misc]backup-simplify: Simplify 1 into 1 1546938924.662 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546938924.662 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938924.662 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.662 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1546938924.662 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1546938924.662 * [misc]taylor: Taking taylor expansion of -2 in k 1546938924.662 * [misc]backup-simplify: Simplify -2 into -2 1546938924.662 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546938924.662 * [misc]taylor: Taking taylor expansion of PI in k 1546938924.662 * [misc]backup-simplify: Simplify PI into PI 1546938924.662 * [misc]taylor: Taking taylor expansion of n in k 1546938924.662 * [misc]backup-simplify: Simplify n into n 1546938924.662 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546938924.662 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1546938924.662 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1546938924.663 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546938924.663 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546938924.663 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1546938924.663 * [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))) 1546938924.663 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546938924.663 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546938924.663 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546938924.663 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546938924.663 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546938924.663 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938924.663 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.663 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938924.663 * [misc]taylor: Taking taylor expansion of k in n 1546938924.663 * [misc]backup-simplify: Simplify k into k 1546938924.663 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938924.663 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938924.664 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.664 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546938924.664 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546938924.664 * [misc]taylor: Taking taylor expansion of -2 in n 1546938924.664 * [misc]backup-simplify: Simplify -2 into -2 1546938924.664 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546938924.664 * [misc]taylor: Taking taylor expansion of PI in n 1546938924.664 * [misc]backup-simplify: Simplify PI into PI 1546938924.664 * [misc]taylor: Taking taylor expansion of n in n 1546938924.664 * [misc]backup-simplify: Simplify 0 into 0 1546938924.664 * [misc]backup-simplify: Simplify 1 into 1 1546938924.664 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546938924.664 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546938924.665 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546938924.665 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546938924.665 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546938924.666 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546938924.666 * [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))) 1546938924.667 * [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)))) 1546938924.667 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546938924.667 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546938924.667 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546938924.667 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546938924.667 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546938924.667 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938924.667 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.667 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938924.667 * [misc]taylor: Taking taylor expansion of k in n 1546938924.668 * [misc]backup-simplify: Simplify k into k 1546938924.668 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938924.668 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938924.668 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.668 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546938924.668 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546938924.668 * [misc]taylor: Taking taylor expansion of -2 in n 1546938924.668 * [misc]backup-simplify: Simplify -2 into -2 1546938924.668 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546938924.668 * [misc]taylor: Taking taylor expansion of PI in n 1546938924.668 * [misc]backup-simplify: Simplify PI into PI 1546938924.668 * [misc]taylor: Taking taylor expansion of n in n 1546938924.668 * [misc]backup-simplify: Simplify 0 into 0 1546938924.668 * [misc]backup-simplify: Simplify 1 into 1 1546938924.668 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546938924.669 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546938924.669 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546938924.669 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546938924.669 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546938924.670 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546938924.670 * [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))) 1546938924.671 * [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)))) 1546938924.671 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1546938924.671 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1546938924.671 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546938924.671 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546938924.671 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938924.671 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.671 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546938924.671 * [misc]taylor: Taking taylor expansion of k in k 1546938924.671 * [misc]backup-simplify: Simplify 0 into 0 1546938924.671 * [misc]backup-simplify: Simplify 1 into 1 1546938924.672 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546938924.672 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938924.672 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.672 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1546938924.672 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1546938924.672 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1546938924.672 * [misc]taylor: Taking taylor expansion of -2 in k 1546938924.672 * [misc]backup-simplify: Simplify -2 into -2 1546938924.672 * [misc]taylor: Taking taylor expansion of PI in k 1546938924.672 * [misc]backup-simplify: Simplify PI into PI 1546938924.672 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546938924.673 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546938924.673 * [misc]taylor: Taking taylor expansion of (log n) in k 1546938924.673 * [misc]taylor: Taking taylor expansion of n in k 1546938924.673 * [misc]backup-simplify: Simplify n into n 1546938924.673 * [misc]backup-simplify: Simplify (log n) into (log n) 1546938924.673 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546938924.673 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546938924.673 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1546938924.674 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1546938924.674 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1546938924.675 * [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)))) 1546938924.675 * [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)))) 1546938924.677 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546938924.677 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1546938924.680 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1546938924.680 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546938924.680 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546938924.680 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938924.681 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546938924.682 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1546938924.683 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546938924.683 * [misc]taylor: Taking taylor expansion of 0 in k 1546938924.683 * [misc]backup-simplify: Simplify 0 into 0 1546938924.683 * [misc]backup-simplify: Simplify 0 into 0 1546938924.683 * [misc]backup-simplify: Simplify 0 into 0 1546938924.685 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938924.686 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1546938924.690 * [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 1546938924.691 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546938924.691 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1546938924.691 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938924.692 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546938924.693 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1546938924.695 * [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 1546938924.695 * [misc]taylor: Taking taylor expansion of 0 in k 1546938924.695 * [misc]backup-simplify: Simplify 0 into 0 1546938924.695 * [misc]backup-simplify: Simplify 0 into 0 1546938924.695 * [misc]backup-simplify: Simplify 0 into 0 1546938924.695 * [misc]backup-simplify: Simplify 0 into 0 1546938924.697 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938924.698 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546938924.703 * [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 1546938924.703 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546938924.704 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1546938924.704 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938924.704 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546938924.705 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 1546938924.707 * [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 1546938924.707 * [misc]taylor: Taking taylor expansion of 0 in k 1546938924.707 * [misc]backup-simplify: Simplify 0 into 0 1546938924.707 * [misc]backup-simplify: Simplify 0 into 0 1546938924.708 * [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))))) 1546938924.708 * * * * [misc]progress: [ 2 / 4 ] generating series at (2 1 1 1) 1546938924.708 * [misc]backup-simplify: Simplify (pow (* PI (* n 2)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 1546938924.708 * [misc]approximate: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 1546938924.708 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1546938924.708 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1546938924.708 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1546938924.708 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546938924.708 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938924.708 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.708 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546938924.708 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938924.708 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.708 * [misc]taylor: Taking taylor expansion of k in k 1546938924.708 * [misc]backup-simplify: Simplify 0 into 0 1546938924.708 * [misc]backup-simplify: Simplify 1 into 1 1546938924.708 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1546938924.708 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1546938924.708 * [misc]taylor: Taking taylor expansion of 2 in k 1546938924.708 * [misc]backup-simplify: Simplify 2 into 2 1546938924.708 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1546938924.708 * [misc]taylor: Taking taylor expansion of n in k 1546938924.708 * [misc]backup-simplify: Simplify n into n 1546938924.708 * [misc]taylor: Taking taylor expansion of PI in k 1546938924.708 * [misc]backup-simplify: Simplify PI into PI 1546938924.708 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1546938924.708 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1546938924.708 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1546938924.708 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546938924.708 * [misc]backup-simplify: Simplify (- 0) into 0 1546938924.709 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546938924.709 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1546938924.709 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1546938924.709 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546938924.709 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546938924.709 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546938924.709 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546938924.709 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938924.709 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.709 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546938924.709 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938924.709 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.709 * [misc]taylor: Taking taylor expansion of k in n 1546938924.709 * [misc]backup-simplify: Simplify k into k 1546938924.709 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546938924.709 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546938924.709 * [misc]taylor: Taking taylor expansion of 2 in n 1546938924.709 * [misc]backup-simplify: Simplify 2 into 2 1546938924.709 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546938924.709 * [misc]taylor: Taking taylor expansion of n in n 1546938924.709 * [misc]backup-simplify: Simplify 0 into 0 1546938924.709 * [misc]backup-simplify: Simplify 1 into 1 1546938924.709 * [misc]taylor: Taking taylor expansion of PI in n 1546938924.709 * [misc]backup-simplify: Simplify PI into PI 1546938924.709 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546938924.709 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546938924.710 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546938924.710 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546938924.711 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546938924.711 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546938924.711 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546938924.711 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546938924.712 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546938924.713 * [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)))) 1546938924.713 * [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))))) 1546938924.713 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546938924.713 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546938924.713 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546938924.713 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546938924.713 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938924.713 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.713 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546938924.713 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938924.713 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.713 * [misc]taylor: Taking taylor expansion of k in n 1546938924.713 * [misc]backup-simplify: Simplify k into k 1546938924.713 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546938924.713 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546938924.713 * [misc]taylor: Taking taylor expansion of 2 in n 1546938924.713 * [misc]backup-simplify: Simplify 2 into 2 1546938924.713 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546938924.713 * [misc]taylor: Taking taylor expansion of n in n 1546938924.713 * [misc]backup-simplify: Simplify 0 into 0 1546938924.713 * [misc]backup-simplify: Simplify 1 into 1 1546938924.713 * [misc]taylor: Taking taylor expansion of PI in n 1546938924.713 * [misc]backup-simplify: Simplify PI into PI 1546938924.714 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546938924.714 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546938924.714 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546938924.714 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546938924.715 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546938924.715 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546938924.715 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546938924.715 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546938924.715 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546938924.716 * [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)))) 1546938924.716 * [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))))) 1546938924.716 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1546938924.716 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1546938924.716 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546938924.716 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938924.716 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.716 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546938924.716 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938924.716 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.716 * [misc]taylor: Taking taylor expansion of k in k 1546938924.716 * [misc]backup-simplify: Simplify 0 into 0 1546938924.716 * [misc]backup-simplify: Simplify 1 into 1 1546938924.716 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1546938924.716 * [misc]taylor: Taking taylor expansion of (log n) in k 1546938924.716 * [misc]taylor: Taking taylor expansion of n in k 1546938924.716 * [misc]backup-simplify: Simplify n into n 1546938924.716 * [misc]backup-simplify: Simplify (log n) into (log n) 1546938924.716 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1546938924.716 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1546938924.716 * [misc]taylor: Taking taylor expansion of 2 in k 1546938924.716 * [misc]backup-simplify: Simplify 2 into 2 1546938924.716 * [misc]taylor: Taking taylor expansion of PI in k 1546938924.716 * [misc]backup-simplify: Simplify PI into PI 1546938924.717 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546938924.717 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546938924.717 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546938924.717 * [misc]backup-simplify: Simplify (- 0) into 0 1546938924.717 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546938924.718 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546938924.718 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1546938924.718 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1546938924.719 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1546938924.719 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546938924.720 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1546938924.722 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546938924.722 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1546938924.722 * [misc]backup-simplify: Simplify (- 0) into 0 1546938924.722 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938924.723 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546938924.723 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1546938924.724 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1546938924.724 * [misc]taylor: Taking taylor expansion of 0 in k 1546938924.724 * [misc]backup-simplify: Simplify 0 into 0 1546938924.724 * [misc]backup-simplify: Simplify 0 into 0 1546938924.725 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1546938924.725 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546938924.727 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546938924.727 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938924.727 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1546938924.727 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546938924.727 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546938924.728 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1546938924.729 * [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))))))) 1546938924.729 * [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))))))) 1546938924.730 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1546938924.731 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1546938924.734 * [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 1546938924.735 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1546938924.735 * [misc]backup-simplify: Simplify (- 0) into 0 1546938924.735 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938924.735 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546938924.736 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1546938924.737 * [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 1546938924.737 * [misc]taylor: Taking taylor expansion of 0 in k 1546938924.737 * [misc]backup-simplify: Simplify 0 into 0 1546938924.737 * [misc]backup-simplify: Simplify 0 into 0 1546938924.737 * [misc]backup-simplify: Simplify 0 into 0 1546938924.738 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1546938924.739 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546938924.742 * [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 1546938924.742 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938924.742 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1546938924.742 * [misc]backup-simplify: Simplify (- 0) into 0 1546938924.742 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938924.743 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1546938924.744 * [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))))) 1546938924.746 * [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))))) 1546938924.749 * [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))))) 1546938924.749 * [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)))) 1546938924.749 * [misc]approximate: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 1546938924.749 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1546938924.749 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1546938924.749 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1546938924.749 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546938924.749 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938924.749 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.749 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546938924.749 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938924.749 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.749 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546938924.749 * [misc]taylor: Taking taylor expansion of k in k 1546938924.749 * [misc]backup-simplify: Simplify 0 into 0 1546938924.749 * [misc]backup-simplify: Simplify 1 into 1 1546938924.749 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546938924.749 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1546938924.749 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1546938924.749 * [misc]taylor: Taking taylor expansion of 2 in k 1546938924.750 * [misc]backup-simplify: Simplify 2 into 2 1546938924.750 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546938924.750 * [misc]taylor: Taking taylor expansion of PI in k 1546938924.750 * [misc]backup-simplify: Simplify PI into PI 1546938924.750 * [misc]taylor: Taking taylor expansion of n in k 1546938924.750 * [misc]backup-simplify: Simplify n into n 1546938924.750 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546938924.750 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1546938924.750 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1546938924.750 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546938924.750 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546938924.750 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546938924.750 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1546938924.750 * [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)))) 1546938924.750 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546938924.750 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546938924.750 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546938924.750 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546938924.750 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938924.750 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.750 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546938924.750 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938924.750 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.750 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938924.750 * [misc]taylor: Taking taylor expansion of k in n 1546938924.750 * [misc]backup-simplify: Simplify k into k 1546938924.751 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938924.751 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546938924.751 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546938924.751 * [misc]taylor: Taking taylor expansion of 2 in n 1546938924.751 * [misc]backup-simplify: Simplify 2 into 2 1546938924.751 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546938924.751 * [misc]taylor: Taking taylor expansion of PI in n 1546938924.751 * [misc]backup-simplify: Simplify PI into PI 1546938924.751 * [misc]taylor: Taking taylor expansion of n in n 1546938924.751 * [misc]backup-simplify: Simplify 0 into 0 1546938924.751 * [misc]backup-simplify: Simplify 1 into 1 1546938924.751 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546938924.751 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546938924.751 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546938924.752 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546938924.752 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546938924.752 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546938924.752 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546938924.752 * [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))) 1546938924.753 * [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)))) 1546938924.753 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546938924.753 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546938924.753 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546938924.753 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546938924.753 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938924.753 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.753 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546938924.753 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938924.753 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.753 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938924.753 * [misc]taylor: Taking taylor expansion of k in n 1546938924.753 * [misc]backup-simplify: Simplify k into k 1546938924.753 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938924.753 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546938924.753 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546938924.753 * [misc]taylor: Taking taylor expansion of 2 in n 1546938924.753 * [misc]backup-simplify: Simplify 2 into 2 1546938924.753 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546938924.753 * [misc]taylor: Taking taylor expansion of PI in n 1546938924.753 * [misc]backup-simplify: Simplify PI into PI 1546938924.753 * [misc]taylor: Taking taylor expansion of n in n 1546938924.753 * [misc]backup-simplify: Simplify 0 into 0 1546938924.753 * [misc]backup-simplify: Simplify 1 into 1 1546938924.753 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546938924.754 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546938924.754 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546938924.754 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546938924.754 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546938924.754 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546938924.755 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546938924.755 * [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))) 1546938924.755 * [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)))) 1546938924.755 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1546938924.755 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1546938924.755 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546938924.755 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938924.755 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.755 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546938924.755 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938924.756 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.756 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546938924.756 * [misc]taylor: Taking taylor expansion of k in k 1546938924.756 * [misc]backup-simplify: Simplify 0 into 0 1546938924.756 * [misc]backup-simplify: Simplify 1 into 1 1546938924.756 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546938924.756 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1546938924.756 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1546938924.756 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1546938924.756 * [misc]taylor: Taking taylor expansion of 2 in k 1546938924.756 * [misc]backup-simplify: Simplify 2 into 2 1546938924.756 * [misc]taylor: Taking taylor expansion of PI in k 1546938924.756 * [misc]backup-simplify: Simplify PI into PI 1546938924.756 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546938924.756 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546938924.756 * [misc]taylor: Taking taylor expansion of (log n) in k 1546938924.756 * [misc]taylor: Taking taylor expansion of n in k 1546938924.756 * [misc]backup-simplify: Simplify n into n 1546938924.756 * [misc]backup-simplify: Simplify (log n) into (log n) 1546938924.756 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546938924.757 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546938924.757 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546938924.757 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1546938924.757 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1546938924.757 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1546938924.758 * [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)))) 1546938924.758 * [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)))) 1546938924.759 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546938924.759 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546938924.761 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546938924.761 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546938924.761 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546938924.761 * [misc]backup-simplify: Simplify (- 0) into 0 1546938924.761 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938924.762 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546938924.762 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1546938924.763 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546938924.763 * [misc]taylor: Taking taylor expansion of 0 in k 1546938924.763 * [misc]backup-simplify: Simplify 0 into 0 1546938924.763 * [misc]backup-simplify: Simplify 0 into 0 1546938924.763 * [misc]backup-simplify: Simplify 0 into 0 1546938924.764 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938924.765 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546938924.767 * [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 1546938924.768 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546938924.768 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1546938924.768 * [misc]backup-simplify: Simplify (- 0) into 0 1546938924.768 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938924.769 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546938924.769 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1546938924.770 * [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 1546938924.771 * [misc]taylor: Taking taylor expansion of 0 in k 1546938924.771 * [misc]backup-simplify: Simplify 0 into 0 1546938924.771 * [misc]backup-simplify: Simplify 0 into 0 1546938924.771 * [misc]backup-simplify: Simplify 0 into 0 1546938924.771 * [misc]backup-simplify: Simplify 0 into 0 1546938924.772 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938924.773 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546938924.777 * [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 1546938924.778 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546938924.778 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1546938924.778 * [misc]backup-simplify: Simplify (- 0) into 0 1546938924.778 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938924.778 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546938924.779 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1546938924.781 * [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 1546938924.781 * [misc]taylor: Taking taylor expansion of 0 in k 1546938924.781 * [misc]backup-simplify: Simplify 0 into 0 1546938924.781 * [misc]backup-simplify: Simplify 0 into 0 1546938924.782 * [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))))) 1546938924.782 * [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)) 1546938924.782 * [misc]approximate: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 1546938924.782 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1546938924.782 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1546938924.782 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1546938924.782 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546938924.782 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546938924.782 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938924.782 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.782 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546938924.782 * [misc]taylor: Taking taylor expansion of k in k 1546938924.782 * [misc]backup-simplify: Simplify 0 into 0 1546938924.782 * [misc]backup-simplify: Simplify 1 into 1 1546938924.782 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546938924.782 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938924.782 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.782 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1546938924.782 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1546938924.782 * [misc]taylor: Taking taylor expansion of -2 in k 1546938924.782 * [misc]backup-simplify: Simplify -2 into -2 1546938924.782 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546938924.782 * [misc]taylor: Taking taylor expansion of PI in k 1546938924.782 * [misc]backup-simplify: Simplify PI into PI 1546938924.782 * [misc]taylor: Taking taylor expansion of n in k 1546938924.782 * [misc]backup-simplify: Simplify n into n 1546938924.783 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546938924.783 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1546938924.783 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1546938924.783 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546938924.783 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546938924.783 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1546938924.783 * [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))) 1546938924.783 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546938924.783 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546938924.783 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546938924.783 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546938924.783 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546938924.783 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938924.783 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.783 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938924.783 * [misc]taylor: Taking taylor expansion of k in n 1546938924.783 * [misc]backup-simplify: Simplify k into k 1546938924.783 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938924.783 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938924.783 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.783 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546938924.783 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546938924.783 * [misc]taylor: Taking taylor expansion of -2 in n 1546938924.783 * [misc]backup-simplify: Simplify -2 into -2 1546938924.783 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546938924.783 * [misc]taylor: Taking taylor expansion of PI in n 1546938924.783 * [misc]backup-simplify: Simplify PI into PI 1546938924.783 * [misc]taylor: Taking taylor expansion of n in n 1546938924.783 * [misc]backup-simplify: Simplify 0 into 0 1546938924.783 * [misc]backup-simplify: Simplify 1 into 1 1546938924.784 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546938924.784 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546938924.784 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546938924.784 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546938924.784 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546938924.785 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546938924.785 * [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))) 1546938924.786 * [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)))) 1546938924.786 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546938924.786 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546938924.786 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546938924.786 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546938924.786 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546938924.786 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938924.786 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.786 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938924.786 * [misc]taylor: Taking taylor expansion of k in n 1546938924.786 * [misc]backup-simplify: Simplify k into k 1546938924.786 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938924.786 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938924.786 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.786 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546938924.786 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546938924.786 * [misc]taylor: Taking taylor expansion of -2 in n 1546938924.786 * [misc]backup-simplify: Simplify -2 into -2 1546938924.786 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546938924.786 * [misc]taylor: Taking taylor expansion of PI in n 1546938924.786 * [misc]backup-simplify: Simplify PI into PI 1546938924.786 * [misc]taylor: Taking taylor expansion of n in n 1546938924.786 * [misc]backup-simplify: Simplify 0 into 0 1546938924.786 * [misc]backup-simplify: Simplify 1 into 1 1546938924.786 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546938924.786 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546938924.787 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546938924.787 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546938924.787 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546938924.787 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546938924.788 * [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))) 1546938924.788 * [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)))) 1546938924.788 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1546938924.788 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1546938924.788 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546938924.788 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546938924.788 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938924.788 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.788 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546938924.788 * [misc]taylor: Taking taylor expansion of k in k 1546938924.788 * [misc]backup-simplify: Simplify 0 into 0 1546938924.788 * [misc]backup-simplify: Simplify 1 into 1 1546938924.788 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546938924.788 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938924.788 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.788 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1546938924.789 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1546938924.789 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1546938924.789 * [misc]taylor: Taking taylor expansion of -2 in k 1546938924.789 * [misc]backup-simplify: Simplify -2 into -2 1546938924.789 * [misc]taylor: Taking taylor expansion of PI in k 1546938924.789 * [misc]backup-simplify: Simplify PI into PI 1546938924.789 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546938924.789 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546938924.789 * [misc]taylor: Taking taylor expansion of (log n) in k 1546938924.789 * [misc]taylor: Taking taylor expansion of n in k 1546938924.789 * [misc]backup-simplify: Simplify n into n 1546938924.789 * [misc]backup-simplify: Simplify (log n) into (log n) 1546938924.789 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546938924.789 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546938924.789 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1546938924.790 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1546938924.790 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1546938924.790 * [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)))) 1546938924.791 * [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)))) 1546938924.792 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546938924.792 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1546938924.793 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1546938924.794 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546938924.794 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546938924.794 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938924.794 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546938924.795 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1546938924.796 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546938924.796 * [misc]taylor: Taking taylor expansion of 0 in k 1546938924.796 * [misc]backup-simplify: Simplify 0 into 0 1546938924.796 * [misc]backup-simplify: Simplify 0 into 0 1546938924.796 * [misc]backup-simplify: Simplify 0 into 0 1546938924.797 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938924.797 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1546938924.800 * [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 1546938924.800 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546938924.800 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1546938924.801 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938924.801 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546938924.801 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1546938924.803 * [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 1546938924.803 * [misc]taylor: Taking taylor expansion of 0 in k 1546938924.803 * [misc]backup-simplify: Simplify 0 into 0 1546938924.803 * [misc]backup-simplify: Simplify 0 into 0 1546938924.803 * [misc]backup-simplify: Simplify 0 into 0 1546938924.803 * [misc]backup-simplify: Simplify 0 into 0 1546938924.804 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938924.805 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546938924.812 * [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 1546938924.812 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546938924.812 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1546938924.813 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938924.813 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546938924.814 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 1546938924.818 * [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 1546938924.818 * [misc]taylor: Taking taylor expansion of 0 in k 1546938924.818 * [misc]backup-simplify: Simplify 0 into 0 1546938924.818 * [misc]backup-simplify: Simplify 0 into 0 1546938924.820 * [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))))) 1546938924.820 * * * * [misc]progress: [ 3 / 4 ] generating series at (2 1) 1546938924.820 * [misc]backup-simplify: Simplify (* (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 1546938924.820 * [misc]approximate: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 1546938924.820 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1546938924.820 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1546938924.820 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1546938924.820 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546938924.820 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938924.820 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.820 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546938924.820 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938924.821 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.821 * [misc]taylor: Taking taylor expansion of k in k 1546938924.821 * [misc]backup-simplify: Simplify 0 into 0 1546938924.821 * [misc]backup-simplify: Simplify 1 into 1 1546938924.821 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1546938924.821 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1546938924.821 * [misc]taylor: Taking taylor expansion of 2 in k 1546938924.821 * [misc]backup-simplify: Simplify 2 into 2 1546938924.821 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1546938924.821 * [misc]taylor: Taking taylor expansion of n in k 1546938924.821 * [misc]backup-simplify: Simplify n into n 1546938924.821 * [misc]taylor: Taking taylor expansion of PI in k 1546938924.821 * [misc]backup-simplify: Simplify PI into PI 1546938924.821 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1546938924.821 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1546938924.821 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1546938924.821 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546938924.821 * [misc]backup-simplify: Simplify (- 0) into 0 1546938924.822 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546938924.822 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1546938924.822 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1546938924.822 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546938924.822 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546938924.822 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546938924.822 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546938924.822 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938924.822 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.822 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546938924.822 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938924.822 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.822 * [misc]taylor: Taking taylor expansion of k in n 1546938924.822 * [misc]backup-simplify: Simplify k into k 1546938924.822 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546938924.822 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546938924.822 * [misc]taylor: Taking taylor expansion of 2 in n 1546938924.822 * [misc]backup-simplify: Simplify 2 into 2 1546938924.822 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546938924.822 * [misc]taylor: Taking taylor expansion of n in n 1546938924.822 * [misc]backup-simplify: Simplify 0 into 0 1546938924.822 * [misc]backup-simplify: Simplify 1 into 1 1546938924.823 * [misc]taylor: Taking taylor expansion of PI in n 1546938924.823 * [misc]backup-simplify: Simplify PI into PI 1546938924.823 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546938924.823 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546938924.824 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546938924.825 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546938924.825 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546938924.826 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546938924.826 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546938924.826 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546938924.827 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546938924.827 * [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)))) 1546938924.828 * [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))))) 1546938924.828 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546938924.828 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546938924.828 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546938924.828 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546938924.828 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938924.828 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.828 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546938924.828 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938924.828 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.828 * [misc]taylor: Taking taylor expansion of k in n 1546938924.828 * [misc]backup-simplify: Simplify k into k 1546938924.828 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546938924.828 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546938924.828 * [misc]taylor: Taking taylor expansion of 2 in n 1546938924.828 * [misc]backup-simplify: Simplify 2 into 2 1546938924.828 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546938924.828 * [misc]taylor: Taking taylor expansion of n in n 1546938924.828 * [misc]backup-simplify: Simplify 0 into 0 1546938924.828 * [misc]backup-simplify: Simplify 1 into 1 1546938924.828 * [misc]taylor: Taking taylor expansion of PI in n 1546938924.828 * [misc]backup-simplify: Simplify PI into PI 1546938924.829 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546938924.829 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546938924.829 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546938924.830 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546938924.831 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546938924.831 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546938924.831 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546938924.831 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546938924.832 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546938924.832 * [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)))) 1546938924.833 * [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))))) 1546938924.833 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1546938924.833 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1546938924.833 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546938924.833 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938924.833 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.833 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546938924.833 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938924.833 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.833 * [misc]taylor: Taking taylor expansion of k in k 1546938924.833 * [misc]backup-simplify: Simplify 0 into 0 1546938924.833 * [misc]backup-simplify: Simplify 1 into 1 1546938924.833 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1546938924.833 * [misc]taylor: Taking taylor expansion of (log n) in k 1546938924.833 * [misc]taylor: Taking taylor expansion of n in k 1546938924.833 * [misc]backup-simplify: Simplify n into n 1546938924.833 * [misc]backup-simplify: Simplify (log n) into (log n) 1546938924.833 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1546938924.833 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1546938924.833 * [misc]taylor: Taking taylor expansion of 2 in k 1546938924.833 * [misc]backup-simplify: Simplify 2 into 2 1546938924.834 * [misc]taylor: Taking taylor expansion of PI in k 1546938924.834 * [misc]backup-simplify: Simplify PI into PI 1546938924.834 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546938924.834 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546938924.834 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546938924.835 * [misc]backup-simplify: Simplify (- 0) into 0 1546938924.835 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546938924.835 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546938924.836 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1546938924.836 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1546938924.837 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1546938924.838 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546938924.839 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1546938924.842 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546938924.842 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1546938924.842 * [misc]backup-simplify: Simplify (- 0) into 0 1546938924.843 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938924.843 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546938924.844 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1546938924.846 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1546938924.846 * [misc]taylor: Taking taylor expansion of 0 in k 1546938924.846 * [misc]backup-simplify: Simplify 0 into 0 1546938924.846 * [misc]backup-simplify: Simplify 0 into 0 1546938924.847 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1546938924.847 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546938924.850 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546938924.850 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938924.850 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1546938924.851 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546938924.851 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546938924.851 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1546938924.853 * [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))))))) 1546938924.854 * [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))))))) 1546938924.856 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1546938924.857 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1546938924.860 * [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 1546938924.860 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1546938924.860 * [misc]backup-simplify: Simplify (- 0) into 0 1546938924.860 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938924.861 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546938924.861 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1546938924.862 * [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 1546938924.862 * [misc]taylor: Taking taylor expansion of 0 in k 1546938924.863 * [misc]backup-simplify: Simplify 0 into 0 1546938924.863 * [misc]backup-simplify: Simplify 0 into 0 1546938924.863 * [misc]backup-simplify: Simplify 0 into 0 1546938924.864 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1546938924.864 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546938924.867 * [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 1546938924.867 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938924.867 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1546938924.867 * [misc]backup-simplify: Simplify (- 0) into 0 1546938924.868 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938924.868 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1546938924.869 * [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))))) 1546938924.871 * [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))))) 1546938924.874 * [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))))) 1546938924.874 * [misc]backup-simplify: Simplify (* (sqrt (pow (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2)))) (sqrt (pow (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 1546938924.874 * [misc]approximate: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 1546938924.874 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1546938924.874 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1546938924.874 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1546938924.874 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546938924.874 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938924.874 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.874 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546938924.874 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938924.874 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.874 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546938924.874 * [misc]taylor: Taking taylor expansion of k in k 1546938924.874 * [misc]backup-simplify: Simplify 0 into 0 1546938924.874 * [misc]backup-simplify: Simplify 1 into 1 1546938924.874 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546938924.874 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1546938924.875 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1546938924.875 * [misc]taylor: Taking taylor expansion of 2 in k 1546938924.875 * [misc]backup-simplify: Simplify 2 into 2 1546938924.875 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546938924.875 * [misc]taylor: Taking taylor expansion of PI in k 1546938924.875 * [misc]backup-simplify: Simplify PI into PI 1546938924.875 * [misc]taylor: Taking taylor expansion of n in k 1546938924.875 * [misc]backup-simplify: Simplify n into n 1546938924.875 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546938924.875 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1546938924.875 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1546938924.875 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546938924.875 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546938924.875 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546938924.875 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1546938924.875 * [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)))) 1546938924.875 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546938924.875 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546938924.875 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546938924.875 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546938924.875 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938924.875 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.875 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546938924.875 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938924.875 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.875 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938924.875 * [misc]taylor: Taking taylor expansion of k in n 1546938924.876 * [misc]backup-simplify: Simplify k into k 1546938924.876 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938924.876 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546938924.876 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546938924.876 * [misc]taylor: Taking taylor expansion of 2 in n 1546938924.876 * [misc]backup-simplify: Simplify 2 into 2 1546938924.876 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546938924.876 * [misc]taylor: Taking taylor expansion of PI in n 1546938924.876 * [misc]backup-simplify: Simplify PI into PI 1546938924.876 * [misc]taylor: Taking taylor expansion of n in n 1546938924.876 * [misc]backup-simplify: Simplify 0 into 0 1546938924.876 * [misc]backup-simplify: Simplify 1 into 1 1546938924.876 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546938924.876 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546938924.876 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546938924.877 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546938924.877 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546938924.877 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546938924.877 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546938924.877 * [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))) 1546938924.878 * [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)))) 1546938924.878 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546938924.878 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546938924.878 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546938924.878 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546938924.878 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938924.878 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.878 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546938924.878 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938924.878 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.878 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938924.878 * [misc]taylor: Taking taylor expansion of k in n 1546938924.878 * [misc]backup-simplify: Simplify k into k 1546938924.878 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938924.878 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546938924.878 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546938924.878 * [misc]taylor: Taking taylor expansion of 2 in n 1546938924.878 * [misc]backup-simplify: Simplify 2 into 2 1546938924.878 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546938924.878 * [misc]taylor: Taking taylor expansion of PI in n 1546938924.878 * [misc]backup-simplify: Simplify PI into PI 1546938924.878 * [misc]taylor: Taking taylor expansion of n in n 1546938924.878 * [misc]backup-simplify: Simplify 0 into 0 1546938924.878 * [misc]backup-simplify: Simplify 1 into 1 1546938924.878 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546938924.879 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546938924.879 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546938924.879 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546938924.879 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546938924.879 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546938924.880 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546938924.880 * [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))) 1546938924.880 * [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)))) 1546938924.881 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1546938924.881 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1546938924.881 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546938924.881 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938924.881 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.881 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546938924.881 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938924.881 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.881 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546938924.881 * [misc]taylor: Taking taylor expansion of k in k 1546938924.881 * [misc]backup-simplify: Simplify 0 into 0 1546938924.881 * [misc]backup-simplify: Simplify 1 into 1 1546938924.881 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546938924.881 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1546938924.881 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1546938924.881 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1546938924.881 * [misc]taylor: Taking taylor expansion of 2 in k 1546938924.881 * [misc]backup-simplify: Simplify 2 into 2 1546938924.881 * [misc]taylor: Taking taylor expansion of PI in k 1546938924.881 * [misc]backup-simplify: Simplify PI into PI 1546938924.881 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546938924.881 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546938924.881 * [misc]taylor: Taking taylor expansion of (log n) in k 1546938924.882 * [misc]taylor: Taking taylor expansion of n in k 1546938924.882 * [misc]backup-simplify: Simplify n into n 1546938924.882 * [misc]backup-simplify: Simplify (log n) into (log n) 1546938924.882 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546938924.882 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546938924.882 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546938924.882 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1546938924.882 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1546938924.883 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1546938924.883 * [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)))) 1546938924.883 * [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)))) 1546938924.884 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546938924.884 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546938924.886 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546938924.886 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546938924.886 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546938924.886 * [misc]backup-simplify: Simplify (- 0) into 0 1546938924.886 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938924.887 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546938924.887 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1546938924.888 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546938924.888 * [misc]taylor: Taking taylor expansion of 0 in k 1546938924.888 * [misc]backup-simplify: Simplify 0 into 0 1546938924.888 * [misc]backup-simplify: Simplify 0 into 0 1546938924.888 * [misc]backup-simplify: Simplify 0 into 0 1546938924.889 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938924.890 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546938924.893 * [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 1546938924.893 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546938924.893 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1546938924.893 * [misc]backup-simplify: Simplify (- 0) into 0 1546938924.894 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938924.894 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546938924.894 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1546938924.896 * [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 1546938924.897 * [misc]taylor: Taking taylor expansion of 0 in k 1546938924.897 * [misc]backup-simplify: Simplify 0 into 0 1546938924.897 * [misc]backup-simplify: Simplify 0 into 0 1546938924.897 * [misc]backup-simplify: Simplify 0 into 0 1546938924.897 * [misc]backup-simplify: Simplify 0 into 0 1546938924.899 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938924.900 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546938924.904 * [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 1546938924.904 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546938924.905 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1546938924.905 * [misc]backup-simplify: Simplify (- 0) into 0 1546938924.905 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938924.905 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546938924.906 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1546938924.908 * [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 1546938924.908 * [misc]taylor: Taking taylor expansion of 0 in k 1546938924.908 * [misc]backup-simplify: Simplify 0 into 0 1546938924.908 * [misc]backup-simplify: Simplify 0 into 0 1546938924.909 * [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))))) 1546938924.909 * [misc]backup-simplify: Simplify (* (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2)))) (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2))))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 1546938924.909 * [misc]approximate: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 1546938924.909 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1546938924.909 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1546938924.909 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1546938924.909 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546938924.909 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546938924.909 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938924.909 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.909 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546938924.909 * [misc]taylor: Taking taylor expansion of k in k 1546938924.909 * [misc]backup-simplify: Simplify 0 into 0 1546938924.909 * [misc]backup-simplify: Simplify 1 into 1 1546938924.909 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546938924.909 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938924.909 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.909 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1546938924.909 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1546938924.909 * [misc]taylor: Taking taylor expansion of -2 in k 1546938924.909 * [misc]backup-simplify: Simplify -2 into -2 1546938924.909 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546938924.909 * [misc]taylor: Taking taylor expansion of PI in k 1546938924.909 * [misc]backup-simplify: Simplify PI into PI 1546938924.909 * [misc]taylor: Taking taylor expansion of n in k 1546938924.909 * [misc]backup-simplify: Simplify n into n 1546938924.909 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546938924.910 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1546938924.910 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1546938924.910 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546938924.910 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546938924.910 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1546938924.910 * [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))) 1546938924.910 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546938924.910 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546938924.910 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546938924.910 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546938924.910 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546938924.910 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938924.910 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.910 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938924.910 * [misc]taylor: Taking taylor expansion of k in n 1546938924.910 * [misc]backup-simplify: Simplify k into k 1546938924.910 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938924.910 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938924.910 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.910 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546938924.910 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546938924.910 * [misc]taylor: Taking taylor expansion of -2 in n 1546938924.910 * [misc]backup-simplify: Simplify -2 into -2 1546938924.910 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546938924.910 * [misc]taylor: Taking taylor expansion of PI in n 1546938924.910 * [misc]backup-simplify: Simplify PI into PI 1546938924.910 * [misc]taylor: Taking taylor expansion of n in n 1546938924.910 * [misc]backup-simplify: Simplify 0 into 0 1546938924.910 * [misc]backup-simplify: Simplify 1 into 1 1546938924.911 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546938924.911 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546938924.911 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546938924.911 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546938924.911 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546938924.912 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546938924.912 * [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))) 1546938924.913 * [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)))) 1546938924.913 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546938924.913 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546938924.913 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546938924.913 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546938924.913 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546938924.913 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938924.913 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.913 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938924.913 * [misc]taylor: Taking taylor expansion of k in n 1546938924.913 * [misc]backup-simplify: Simplify k into k 1546938924.913 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938924.913 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938924.913 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.913 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546938924.913 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546938924.913 * [misc]taylor: Taking taylor expansion of -2 in n 1546938924.913 * [misc]backup-simplify: Simplify -2 into -2 1546938924.913 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546938924.913 * [misc]taylor: Taking taylor expansion of PI in n 1546938924.913 * [misc]backup-simplify: Simplify PI into PI 1546938924.913 * [misc]taylor: Taking taylor expansion of n in n 1546938924.913 * [misc]backup-simplify: Simplify 0 into 0 1546938924.913 * [misc]backup-simplify: Simplify 1 into 1 1546938924.913 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546938924.913 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546938924.914 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546938924.914 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546938924.914 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546938924.914 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546938924.914 * [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))) 1546938924.915 * [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)))) 1546938924.915 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1546938924.915 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1546938924.915 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546938924.915 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546938924.915 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938924.915 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.915 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546938924.915 * [misc]taylor: Taking taylor expansion of k in k 1546938924.915 * [misc]backup-simplify: Simplify 0 into 0 1546938924.915 * [misc]backup-simplify: Simplify 1 into 1 1546938924.915 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546938924.915 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938924.915 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938924.915 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1546938924.915 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1546938924.915 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1546938924.915 * [misc]taylor: Taking taylor expansion of -2 in k 1546938924.915 * [misc]backup-simplify: Simplify -2 into -2 1546938924.915 * [misc]taylor: Taking taylor expansion of PI in k 1546938924.915 * [misc]backup-simplify: Simplify PI into PI 1546938924.916 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546938924.916 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546938924.916 * [misc]taylor: Taking taylor expansion of (log n) in k 1546938924.916 * [misc]taylor: Taking taylor expansion of n in k 1546938924.916 * [misc]backup-simplify: Simplify n into n 1546938924.916 * [misc]backup-simplify: Simplify (log n) into (log n) 1546938924.916 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546938924.916 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546938924.916 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1546938924.916 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1546938924.917 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1546938924.917 * [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)))) 1546938924.918 * [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)))) 1546938924.918 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546938924.919 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1546938924.920 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1546938924.920 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546938924.920 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546938924.921 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938924.921 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546938924.921 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1546938924.922 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546938924.922 * [misc]taylor: Taking taylor expansion of 0 in k 1546938924.922 * [misc]backup-simplify: Simplify 0 into 0 1546938924.922 * [misc]backup-simplify: Simplify 0 into 0 1546938924.922 * [misc]backup-simplify: Simplify 0 into 0 1546938924.923 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938924.924 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1546938924.927 * [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 1546938924.927 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546938924.928 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1546938924.928 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938924.928 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546938924.929 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1546938924.932 * [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 1546938924.932 * [misc]taylor: Taking taylor expansion of 0 in k 1546938924.932 * [misc]backup-simplify: Simplify 0 into 0 1546938924.932 * [misc]backup-simplify: Simplify 0 into 0 1546938924.932 * [misc]backup-simplify: Simplify 0 into 0 1546938924.932 * [misc]backup-simplify: Simplify 0 into 0 1546938924.934 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938924.935 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546938924.943 * [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 1546938924.944 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546938924.944 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1546938924.945 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938924.946 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546938924.947 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 1546938924.951 * [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 1546938924.951 * [misc]taylor: Taking taylor expansion of 0 in k 1546938924.951 * [misc]backup-simplify: Simplify 0 into 0 1546938924.951 * [misc]backup-simplify: Simplify 0 into 0 1546938924.952 * [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))))) 1546938924.952 * * * * [misc]progress: [ 4 / 4 ] generating series at (2 1 2 1 1) 1546938924.952 * [misc]backup-simplify: Simplify (* PI (* n 2)) into (* 2 (* n PI)) 1546938924.952 * [misc]approximate: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1546938924.952 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546938924.952 * [misc]taylor: Taking taylor expansion of 2 in n 1546938924.952 * [misc]backup-simplify: Simplify 2 into 2 1546938924.952 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546938924.952 * [misc]taylor: Taking taylor expansion of n in n 1546938924.952 * [misc]backup-simplify: Simplify 0 into 0 1546938924.952 * [misc]backup-simplify: Simplify 1 into 1 1546938924.952 * [misc]taylor: Taking taylor expansion of PI in n 1546938924.952 * [misc]backup-simplify: Simplify PI into PI 1546938924.952 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546938924.952 * [misc]taylor: Taking taylor expansion of 2 in n 1546938924.952 * [misc]backup-simplify: Simplify 2 into 2 1546938924.952 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546938924.952 * [misc]taylor: Taking taylor expansion of n in n 1546938924.952 * [misc]backup-simplify: Simplify 0 into 0 1546938924.952 * [misc]backup-simplify: Simplify 1 into 1 1546938924.952 * [misc]taylor: Taking taylor expansion of PI in n 1546938924.952 * [misc]backup-simplify: Simplify PI into PI 1546938924.953 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546938924.953 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546938924.953 * [misc]backup-simplify: Simplify 0 into 0 1546938924.954 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546938924.954 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546938924.955 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546938924.956 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546938924.957 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1546938924.957 * [misc]backup-simplify: Simplify 0 into 0 1546938924.958 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1546938924.960 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1546938924.960 * [misc]backup-simplify: Simplify 0 into 0 1546938924.962 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1546938924.964 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1546938924.964 * [misc]backup-simplify: Simplify 0 into 0 1546938924.967 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1546938924.970 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1546938924.970 * [misc]backup-simplify: Simplify 0 into 0 1546938924.973 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1546938924.976 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1546938924.977 * [misc]backup-simplify: Simplify 0 into 0 1546938924.980 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1546938924.985 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1546938924.985 * [misc]backup-simplify: Simplify 0 into 0 1546938924.985 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1546938924.985 * [misc]backup-simplify: Simplify (* PI (* (/ 1 n) 2)) into (* 2 (/ PI n)) 1546938924.985 * [misc]approximate: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1546938924.985 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546938924.985 * [misc]taylor: Taking taylor expansion of 2 in n 1546938924.985 * [misc]backup-simplify: Simplify 2 into 2 1546938924.985 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546938924.985 * [misc]taylor: Taking taylor expansion of PI in n 1546938924.985 * [misc]backup-simplify: Simplify PI into PI 1546938924.985 * [misc]taylor: Taking taylor expansion of n in n 1546938924.985 * [misc]backup-simplify: Simplify 0 into 0 1546938924.985 * [misc]backup-simplify: Simplify 1 into 1 1546938924.986 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546938924.986 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546938924.986 * [misc]taylor: Taking taylor expansion of 2 in n 1546938924.986 * [misc]backup-simplify: Simplify 2 into 2 1546938924.986 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546938924.986 * [misc]taylor: Taking taylor expansion of PI in n 1546938924.986 * [misc]backup-simplify: Simplify PI into PI 1546938924.986 * [misc]taylor: Taking taylor expansion of n in n 1546938924.986 * [misc]backup-simplify: Simplify 0 into 0 1546938924.986 * [misc]backup-simplify: Simplify 1 into 1 1546938924.986 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546938924.987 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546938924.987 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546938924.988 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546938924.989 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546938924.989 * [misc]backup-simplify: Simplify 0 into 0 1546938924.990 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938924.991 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546938924.991 * [misc]backup-simplify: Simplify 0 into 0 1546938924.993 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938924.995 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546938924.995 * [misc]backup-simplify: Simplify 0 into 0 1546938924.996 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938924.999 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1546938924.999 * [misc]backup-simplify: Simplify 0 into 0 1546938925.001 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938925.004 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1546938925.004 * [misc]backup-simplify: Simplify 0 into 0 1546938925.006 * [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 1546938925.009 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1546938925.009 * [misc]backup-simplify: Simplify 0 into 0 1546938925.010 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 1546938925.010 * [misc]backup-simplify: Simplify (* PI (* (/ 1 (- n)) 2)) into (* -2 (/ PI n)) 1546938925.010 * [misc]approximate: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1546938925.010 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546938925.010 * [misc]taylor: Taking taylor expansion of -2 in n 1546938925.010 * [misc]backup-simplify: Simplify -2 into -2 1546938925.010 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546938925.010 * [misc]taylor: Taking taylor expansion of PI in n 1546938925.010 * [misc]backup-simplify: Simplify PI into PI 1546938925.010 * [misc]taylor: Taking taylor expansion of n in n 1546938925.010 * [misc]backup-simplify: Simplify 0 into 0 1546938925.010 * [misc]backup-simplify: Simplify 1 into 1 1546938925.011 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546938925.011 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546938925.011 * [misc]taylor: Taking taylor expansion of -2 in n 1546938925.011 * [misc]backup-simplify: Simplify -2 into -2 1546938925.011 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546938925.011 * [misc]taylor: Taking taylor expansion of PI in n 1546938925.011 * [misc]backup-simplify: Simplify PI into PI 1546938925.011 * [misc]taylor: Taking taylor expansion of n in n 1546938925.011 * [misc]backup-simplify: Simplify 0 into 0 1546938925.011 * [misc]backup-simplify: Simplify 1 into 1 1546938925.011 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546938925.011 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546938925.012 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546938925.013 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546938925.013 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1546938925.013 * [misc]backup-simplify: Simplify 0 into 0 1546938925.015 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938925.016 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1546938925.016 * [misc]backup-simplify: Simplify 0 into 0 1546938925.017 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938925.019 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546938925.019 * [misc]backup-simplify: Simplify 0 into 0 1546938925.021 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938925.023 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1546938925.023 * [misc]backup-simplify: Simplify 0 into 0 1546938925.025 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938925.027 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1546938925.028 * [misc]backup-simplify: Simplify 0 into 0 1546938925.030 * [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 1546938925.033 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1546938925.033 * [misc]backup-simplify: Simplify 0 into 0 1546938925.034 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 1546938925.034 * * * [misc]progress: simplifying candidates 1546938925.034 * * * * [misc]progress: [ 1 / 94 ] simplifiying candidate # 1546938925.034 * [enter]simplify: Simplifying (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) 1546938925.034 * * [misc]simplify: iters left: 6 (11 enodes) 1546938925.038 * * [misc]simplify: iters left: 5 (21 enodes) 1546938925.045 * * [misc]simplify: iters left: 4 (47 enodes) 1546938925.061 * * [misc]simplify: iters left: 3 (109 enodes) 1546938925.111 * * [misc]simplify: iters left: 2 (300 enodes) 1546938925.309 * [exit]simplify: Simplified to (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) 1546938925.309 * [misc]simplify: Simplified (2 1 2 1 1) to (λ (k n) (/ (* (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (exp (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI)))))) (sqrt k))) 1546938925.310 * * * * [misc]progress: [ 2 / 94 ] simplifiying candidate # 1546938925.310 * * * * [misc]progress: [ 3 / 94 ] simplifiying candidate # 1546938925.310 * [enter]simplify: Simplifying (* PI (* n 2)) 1546938925.310 * * [misc]simplify: iters left: 4 (5 enodes) 1546938925.312 * * [misc]simplify: iters left: 3 (9 enodes) 1546938925.314 * * [misc]simplify: iters left: 2 (15 enodes) 1546938925.318 * * [misc]simplify: iters left: 1 (17 enodes) 1546938925.323 * [exit]simplify: Simplified to (* (* 2 n) PI) 1546938925.323 * [misc]simplify: Simplified (2 1 2 1 1) to (λ (k n) (/ (* (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (pow (* (* 2 n) PI) (* 1 (- 1/2 (/ k 2)))))) (sqrt k))) 1546938925.323 * * * * [misc]progress: [ 4 / 94 ] simplifiying candidate # 1546938925.323 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (/ k 2)) 1546938925.323 * * [misc]simplify: iters left: 5 (8 enodes) 1546938925.326 * * [misc]simplify: iters left: 4 (12 enodes) 1546938925.329 * * [misc]simplify: iters left: 3 (18 enodes) 1546938925.334 * * [misc]simplify: iters left: 2 (20 enodes) 1546938925.339 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ k 2)) 1546938925.339 * [misc]simplify: Simplified (2 1 2 1 2) to (λ (k n) (/ (* (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (/ (pow (* PI (* n 2)) 1/2) (pow (* (* 2 n) PI) (/ k 2))))) (sqrt k))) 1546938925.340 * * * * [misc]progress: [ 5 / 94 ] simplifiying candidate # 1546938925.340 * [enter]simplify: Simplifying (cbrt (- 1/2 (/ k 2))) 1546938925.340 * * [misc]simplify: iters left: 5 (6 enodes) 1546938925.342 * * [misc]simplify: iters left: 4 (8 enodes) 1546938925.345 * * [misc]simplify: iters left: 3 (11 enodes) 1546938925.348 * [exit]simplify: Simplified to (cbrt (- 1/2 (/ k 2))) 1546938925.348 * [misc]simplify: Simplified (2 1 2 1 2) to (λ (k n) (/ (* (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (pow (pow (* PI (* n 2)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))))) (sqrt k))) 1546938925.348 * * * * [misc]progress: [ 6 / 94 ] simplifiying candidate # 1546938925.348 * [enter]simplify: Simplifying (sqrt (- 1/2 (/ k 2))) 1546938925.348 * * [misc]simplify: iters left: 5 (6 enodes) 1546938925.350 * * [misc]simplify: iters left: 4 (8 enodes) 1546938925.352 * * [misc]simplify: iters left: 3 (11 enodes) 1546938925.356 * [exit]simplify: Simplified to (sqrt (- 1/2 (/ k 2))) 1546938925.356 * [misc]simplify: Simplified (2 1 2 1 2) to (λ (k n) (/ (* (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (pow (pow (* PI (* n 2)) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))))) (sqrt k))) 1546938925.356 * * * * [misc]progress: [ 7 / 94 ] simplifiying candidate # 1546938925.356 * [enter]simplify: Simplifying (- 1/2 (/ k 2)) 1546938925.356 * * [misc]simplify: iters left: 4 (5 enodes) 1546938925.358 * * [misc]simplify: iters left: 3 (7 enodes) 1546938925.360 * * [misc]simplify: iters left: 2 (10 enodes) 1546938925.363 * [exit]simplify: Simplified to (- 1/2 (/ k 2)) 1546938925.363 * [misc]simplify: Simplified (2 1 2 1 2) to (λ (k n) (/ (* (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (pow (pow (* PI (* n 2)) 1) (- 1/2 (/ k 2))))) (sqrt k))) 1546938925.363 * * * * [misc]progress: [ 8 / 94 ] simplifiying candidate # 1546938925.363 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1546938925.363 * * [misc]simplify: iters left: 5 (9 enodes) 1546938925.366 * * [misc]simplify: iters left: 4 (15 enodes) 1546938925.371 * * [misc]simplify: iters left: 3 (21 enodes) 1546938925.376 * * [misc]simplify: iters left: 2 (22 enodes) 1546938925.382 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1546938925.382 * [misc]simplify: Simplified (2 1 2 1 2) to (λ (k n) (/ (* (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2)))))) (sqrt k))) 1546938925.382 * * * * [misc]progress: [ 9 / 94 ] simplifiying candidate # 1546938925.382 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1546938925.382 * * [misc]simplify: iters left: 5 (9 enodes) 1546938925.385 * * [misc]simplify: iters left: 4 (15 enodes) 1546938925.391 * * [misc]simplify: iters left: 3 (21 enodes) 1546938925.393 * * [misc]simplify: iters left: 2 (22 enodes) 1546938925.396 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1546938925.396 * [misc]simplify: Simplified (2 1 2 1 2) to (λ (k n) (/ (* (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2)))))) (sqrt k))) 1546938925.396 * * * * [misc]progress: [ 10 / 94 ] simplifiying candidate # 1546938925.396 * [enter]simplify: Simplifying (pow PI (- 1/2 (/ k 2))) 1546938925.396 * * [misc]simplify: iters left: 5 (7 enodes) 1546938925.397 * * [misc]simplify: iters left: 4 (9 enodes) 1546938925.399 * * [misc]simplify: iters left: 3 (12 enodes) 1546938925.400 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1546938925.400 * [misc]simplify: Simplified (2 1 2 1 1) to (λ (k n) (/ (* (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (* (pow PI (- 1/2 (/ k 2))) (pow (* n 2) (- 1/2 (/ k 2)))))) (sqrt k))) 1546938925.400 * * * * [misc]progress: [ 11 / 94 ] simplifiying candidate # 1546938925.400 * * * * [misc]progress: [ 12 / 94 ] simplifiying candidate # 1546938925.400 * * * * [misc]progress: [ 13 / 94 ] simplifiying candidate # 1546938925.401 * * * * [misc]progress: [ 14 / 94 ] simplifiying candidate # 1546938925.401 * * * * [misc]progress: [ 15 / 94 ] simplifiying candidate # 1546938925.401 * * * * [misc]progress: [ 16 / 94 ] simplifiying candidate # 1546938925.401 * * * * [misc]progress: [ 17 / 94 ] simplifiying candidate # 1546938925.401 * * * * [misc]progress: [ 18 / 94 ] simplifiying candidate # 1546938925.401 * [enter]simplify: Simplifying (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) 1546938925.401 * * [misc]simplify: iters left: 6 (11 enodes) 1546938925.403 * * [misc]simplify: iters left: 5 (21 enodes) 1546938925.406 * * [misc]simplify: iters left: 4 (47 enodes) 1546938925.415 * * [misc]simplify: iters left: 3 (109 enodes) 1546938925.458 * * [misc]simplify: iters left: 2 (300 enodes) 1546938925.607 * [exit]simplify: Simplified to (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) 1546938925.607 * [misc]simplify: Simplified (2 1 1 1 1) to (λ (k n) (/ (* (sqrt (exp (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt k))) 1546938925.607 * * * * [misc]progress: [ 19 / 94 ] simplifiying candidate # 1546938925.607 * * * * [misc]progress: [ 20 / 94 ] simplifiying candidate # 1546938925.607 * [enter]simplify: Simplifying (* PI (* n 2)) 1546938925.607 * * [misc]simplify: iters left: 4 (5 enodes) 1546938925.608 * * [misc]simplify: iters left: 3 (9 enodes) 1546938925.609 * * [misc]simplify: iters left: 2 (15 enodes) 1546938925.611 * * [misc]simplify: iters left: 1 (17 enodes) 1546938925.613 * [exit]simplify: Simplified to (* (* 2 n) PI) 1546938925.613 * [misc]simplify: Simplified (2 1 1 1 1) to (λ (k n) (/ (* (sqrt (pow (* (* 2 n) PI) (* 1 (- 1/2 (/ k 2))))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt k))) 1546938925.613 * * * * [misc]progress: [ 21 / 94 ] simplifiying candidate # 1546938925.613 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (/ k 2)) 1546938925.613 * * [misc]simplify: iters left: 5 (8 enodes) 1546938925.614 * * [misc]simplify: iters left: 4 (12 enodes) 1546938925.616 * * [misc]simplify: iters left: 3 (18 enodes) 1546938925.618 * * [misc]simplify: iters left: 2 (20 enodes) 1546938925.620 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ k 2)) 1546938925.620 * [misc]simplify: Simplified (2 1 1 1 2) to (λ (k n) (/ (* (sqrt (/ (pow (* PI (* n 2)) 1/2) (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt k))) 1546938925.620 * * * * [misc]progress: [ 22 / 94 ] simplifiying candidate # 1546938925.621 * [enter]simplify: Simplifying (cbrt (- 1/2 (/ k 2))) 1546938925.621 * * [misc]simplify: iters left: 5 (6 enodes) 1546938925.622 * * [misc]simplify: iters left: 4 (8 enodes) 1546938925.623 * * [misc]simplify: iters left: 3 (11 enodes) 1546938925.625 * [exit]simplify: Simplified to (cbrt (- 1/2 (/ k 2))) 1546938925.625 * [misc]simplify: Simplified (2 1 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 (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt k))) 1546938925.625 * * * * [misc]progress: [ 23 / 94 ] simplifiying candidate # 1546938925.625 * [enter]simplify: Simplifying (sqrt (- 1/2 (/ k 2))) 1546938925.625 * * [misc]simplify: iters left: 5 (6 enodes) 1546938925.627 * * [misc]simplify: iters left: 4 (8 enodes) 1546938925.629 * * [misc]simplify: iters left: 3 (11 enodes) 1546938925.632 * [exit]simplify: Simplified to (sqrt (- 1/2 (/ k 2))) 1546938925.632 * [misc]simplify: Simplified (2 1 1 1 2) to (λ (k n) (/ (* (sqrt (pow (pow (* PI (* n 2)) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2))))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt k))) 1546938925.632 * * * * [misc]progress: [ 24 / 94 ] simplifiying candidate # 1546938925.633 * [enter]simplify: Simplifying (- 1/2 (/ k 2)) 1546938925.633 * * [misc]simplify: iters left: 4 (5 enodes) 1546938925.634 * * [misc]simplify: iters left: 3 (7 enodes) 1546938925.636 * * [misc]simplify: iters left: 2 (10 enodes) 1546938925.639 * [exit]simplify: Simplified to (- 1/2 (/ k 2)) 1546938925.639 * [misc]simplify: Simplified (2 1 1 1 2) to (λ (k n) (/ (* (sqrt (pow (pow (* PI (* n 2)) 1) (- 1/2 (/ k 2)))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt k))) 1546938925.639 * * * * [misc]progress: [ 25 / 94 ] simplifiying candidate # 1546938925.639 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1546938925.639 * * [misc]simplify: iters left: 5 (9 enodes) 1546938925.642 * * [misc]simplify: iters left: 4 (15 enodes) 1546938925.644 * * [misc]simplify: iters left: 3 (21 enodes) 1546938925.647 * * [misc]simplify: iters left: 2 (22 enodes) 1546938925.649 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1546938925.649 * [misc]simplify: Simplified (2 1 1 1 2) to (λ (k n) (/ (* (sqrt (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2))))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt k))) 1546938925.649 * * * * [misc]progress: [ 26 / 94 ] simplifiying candidate # 1546938925.650 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1546938925.650 * * [misc]simplify: iters left: 5 (9 enodes) 1546938925.651 * * [misc]simplify: iters left: 4 (15 enodes) 1546938925.653 * * [misc]simplify: iters left: 3 (21 enodes) 1546938925.656 * * [misc]simplify: iters left: 2 (22 enodes) 1546938925.658 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1546938925.658 * [misc]simplify: Simplified (2 1 1 1 2) to (λ (k n) (/ (* (sqrt (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2))))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt k))) 1546938925.658 * * * * [misc]progress: [ 27 / 94 ] simplifiying candidate # 1546938925.659 * [enter]simplify: Simplifying (pow PI (- 1/2 (/ k 2))) 1546938925.659 * * [misc]simplify: iters left: 5 (7 enodes) 1546938925.660 * * [misc]simplify: iters left: 4 (9 enodes) 1546938925.661 * * [misc]simplify: iters left: 3 (12 enodes) 1546938925.663 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1546938925.663 * [misc]simplify: Simplified (2 1 1 1 1) to (λ (k n) (/ (* (sqrt (* (pow PI (- 1/2 (/ k 2))) (pow (* n 2) (- 1/2 (/ k 2))))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt k))) 1546938925.663 * * * * [misc]progress: [ 28 / 94 ] simplifiying candidate # 1546938925.663 * * * * [misc]progress: [ 29 / 94 ] simplifiying candidate # 1546938925.663 * * * * [misc]progress: [ 30 / 94 ] simplifiying candidate # 1546938925.663 * * * * [misc]progress: [ 31 / 94 ] simplifiying candidate # 1546938925.663 * * * * [misc]progress: [ 32 / 94 ] simplifiying candidate # 1546938925.663 * * * * [misc]progress: [ 33 / 94 ] simplifiying candidate # 1546938925.663 * * * * [misc]progress: [ 34 / 94 ] simplifiying candidate # 1546938925.663 * * * * [misc]progress: [ 35 / 94 ] simplifiying candidate # 1546938925.663 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- 1/2 (/ k 2))) 1546938925.663 * * [misc]simplify: iters left: 5 (10 enodes) 1546938925.665 * * [misc]simplify: iters left: 4 (16 enodes) 1546938925.667 * * [misc]simplify: iters left: 3 (25 enodes) 1546938925.670 * * [misc]simplify: iters left: 2 (26 enodes) 1546938925.673 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) 1546938925.673 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (+ 1/2 1/2)) (sqrt k))) 1546938925.673 * [enter]simplify: Simplifying (+ 1/2 1/2) 1546938925.673 * * [misc]simplify: iters left: 2 (2 enodes) 1546938925.674 * * [misc]simplify: iters left: 1 (3 enodes) 1546938925.674 * [exit]simplify: Simplified to 1 1546938925.674 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (pow (pow (* PI (* n 2)) (- 1/2 (/ k 2))) 1) (sqrt k))) 1546938925.674 * * * * [misc]progress: [ 36 / 94 ] simplifiying candidate # 1546938925.674 * [enter]simplify: Simplifying (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1546938925.675 * * [misc]simplify: iters left: 6 (11 enodes) 1546938925.676 * * [misc]simplify: iters left: 5 (17 enodes) 1546938925.678 * * [misc]simplify: iters left: 4 (26 enodes) 1546938925.685 * * [misc]simplify: iters left: 3 (27 enodes) 1546938925.691 * [exit]simplify: Simplified to (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) 1546938925.691 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (+ 1 1)) (sqrt k))) 1546938925.691 * [enter]simplify: Simplifying (+ 1 1) 1546938925.691 * * [misc]simplify: iters left: 2 (2 enodes) 1546938925.694 * * [misc]simplify: iters left: 1 (5 enodes) 1546938925.695 * [exit]simplify: Simplified to 2 1546938925.695 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (pow (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 2) (sqrt k))) 1546938925.695 * * * * [misc]progress: [ 37 / 94 ] simplifiying candidate # 1546938925.695 * [enter]simplify: Simplifying (* (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1546938925.695 * * [misc]simplify: iters left: 6 (11 enodes) 1546938925.699 * * [misc]simplify: iters left: 5 (17 enodes) 1546938925.704 * * [misc]simplify: iters left: 4 (26 enodes) 1546938925.710 * * [misc]simplify: iters left: 3 (27 enodes) 1546938925.717 * [exit]simplify: Simplified to (* (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) 1546938925.717 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) 1/2) (sqrt k))) 1546938925.717 * * * * [misc]progress: [ 38 / 94 ] simplifiying candidate # 1546938925.718 * [enter]simplify: Simplifying (* (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546938925.718 * * [misc]simplify: iters left: 6 (12 enodes) 1546938925.721 * * [misc]simplify: iters left: 5 (18 enodes) 1546938925.727 * * [misc]simplify: iters left: 4 (28 enodes) 1546938925.734 * * [misc]simplify: iters left: 3 (30 enodes) 1546938925.741 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) 1546938925.742 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) 1) (sqrt k))) 1546938925.742 * * * * [misc]progress: [ 39 / 94 ] simplifiying candidate # 1546938925.742 * * * * [misc]progress: [ 40 / 94 ] simplifiying candidate # 1546938925.742 * [enter]simplify: Simplifying (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1546938925.742 * * [misc]simplify: iters left: 6 (11 enodes) 1546938925.744 * * [misc]simplify: iters left: 5 (17 enodes) 1546938925.747 * * [misc]simplify: iters left: 4 (26 enodes) 1546938925.750 * * [misc]simplify: iters left: 3 (27 enodes) 1546938925.753 * [exit]simplify: Simplified to (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) 1546938925.753 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (+ 1 1)) (sqrt k))) 1546938925.753 * * * * [misc]progress: [ 41 / 94 ] simplifiying candidate # 1546938925.753 * * * * [misc]progress: [ 42 / 94 ] simplifiying candidate # 1546938925.754 * [enter]simplify: Simplifying (+ (log (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (log (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) 1546938925.754 * * [misc]simplify: iters left: 6 (13 enodes) 1546938925.756 * * [misc]simplify: iters left: 5 (19 enodes) 1546938925.758 * * [misc]simplify: iters left: 4 (28 enodes) 1546938925.762 * * [misc]simplify: iters left: 3 (30 enodes) 1546938925.766 * [exit]simplify: Simplified to (+ (log (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) (log (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))))) 1546938925.766 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (exp (+ (log (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) (log (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))))) (sqrt k))) 1546938925.766 * * * * [misc]progress: [ 43 / 94 ] simplifiying candidate # 1546938925.766 * * * * [misc]progress: [ 44 / 94 ] simplifiying candidate # 1546938925.766 * * * * [misc]progress: [ 45 / 94 ] simplifiying candidate # 1546938925.766 * [enter]simplify: Simplifying (* (* (* (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (* (* (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) 1546938925.766 * * [misc]simplify: iters left: 6 (14 enodes) 1546938925.769 * * [misc]simplify: iters left: 5 (25 enodes) 1546938925.774 * * [misc]simplify: iters left: 4 (43 enodes) 1546938925.783 * * [misc]simplify: iters left: 3 (51 enodes) 1546938925.789 * * [misc]simplify: iters left: 2 (56 enodes) 1546938925.796 * * [misc]simplify: iters left: 1 (59 enodes) 1546938925.803 * [exit]simplify: Simplified to (pow (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) 3) 1546938925.803 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (cbrt (pow (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) 3)) (sqrt k))) 1546938925.803 * * * * [misc]progress: [ 46 / 94 ] simplifiying candidate # 1546938925.803 * * * * [misc]progress: [ 47 / 94 ] simplifiying candidate # 1546938925.803 * * * * [misc]progress: [ 48 / 94 ] simplifiying candidate # 1546938925.803 * [enter]simplify: Simplifying (* (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1546938925.803 * * [misc]simplify: iters left: 6 (11 enodes) 1546938925.805 * * [misc]simplify: iters left: 5 (17 enodes) 1546938925.807 * * [misc]simplify: iters left: 4 (26 enodes) 1546938925.811 * * [misc]simplify: iters left: 3 (27 enodes) 1546938925.817 * [exit]simplify: Simplified to (* (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) 1546938925.817 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (sqrt (* (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) (sqrt k))) 1546938925.817 * * * * [misc]progress: [ 49 / 94 ] simplifiying candidate # 1546938925.817 * * * * [misc]progress: [ 50 / 94 ] simplifiying candidate # 1546938925.817 * [enter]simplify: Simplifying (* PI (* n 2)) 1546938925.817 * * [misc]simplify: iters left: 4 (5 enodes) 1546938925.819 * * [misc]simplify: iters left: 3 (9 enodes) 1546938925.821 * * [misc]simplify: iters left: 2 (15 enodes) 1546938925.825 * * [misc]simplify: iters left: 1 (17 enodes) 1546938925.829 * [exit]simplify: Simplified to (* (* 2 n) PI) 1546938925.829 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k))) 1546938925.829 * [enter]simplify: Simplifying (- 1/2 (/ k 2)) 1546938925.829 * * [misc]simplify: iters left: 4 (5 enodes) 1546938925.831 * * [misc]simplify: iters left: 3 (7 enodes) 1546938925.833 * * [misc]simplify: iters left: 2 (10 enodes) 1546938925.836 * [exit]simplify: Simplified to (- 1/2 (/ k 2)) 1546938925.836 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) 1546938925.836 * * * * [misc]progress: [ 51 / 94 ] simplifiying candidate # 1546938925.836 * [enter]simplify: Simplifying (* (sqrt (pow (* PI (* n 2)) 1/2)) (sqrt (pow (* PI (* n 2)) 1/2))) 1546938925.836 * * [misc]simplify: iters left: 6 (9 enodes) 1546938925.839 * * [misc]simplify: iters left: 5 (14 enodes) 1546938925.843 * * [misc]simplify: iters left: 4 (21 enodes) 1546938925.848 * * [misc]simplify: iters left: 3 (22 enodes) 1546938925.850 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1546938925.850 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (/ (sqrt (* (* 2 n) PI)) (* (sqrt (pow (* PI (* n 2)) (/ k 2))) (sqrt (pow (* PI (* n 2)) (/ k 2))))) (sqrt k))) 1546938925.850 * [enter]simplify: Simplifying (* (sqrt (pow (* PI (* n 2)) (/ k 2))) (sqrt (pow (* PI (* n 2)) (/ k 2)))) 1546938925.850 * * [misc]simplify: iters left: 6 (10 enodes) 1546938925.852 * * [misc]simplify: iters left: 5 (14 enodes) 1546938925.854 * * [misc]simplify: iters left: 4 (21 enodes) 1546938925.857 * * [misc]simplify: iters left: 3 (22 enodes) 1546938925.859 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ k 2)) 1546938925.859 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (/ (sqrt (* (* 2 n) PI)) (pow (* (* 2 n) PI) (/ k 2))) (sqrt k))) 1546938925.859 * * * * [misc]progress: [ 52 / 94 ] simplifiying candidate # 1546938925.859 * * * * [misc]progress: [ 53 / 94 ] simplifiying candidate # 1546938925.859 * [enter]simplify: Simplifying (cbrt (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546938925.859 * * [misc]simplify: iters left: 6 (12 enodes) 1546938925.861 * * [misc]simplify: iters left: 5 (18 enodes) 1546938925.864 * * [misc]simplify: iters left: 4 (27 enodes) 1546938925.867 * * [misc]simplify: iters left: 3 (29 enodes) 1546938925.870 * [exit]simplify: Simplified to (cbrt (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) 1546938925.870 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (* (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (* (cbrt (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (cbrt (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))) (cbrt (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))))) (sqrt k))) 1546938925.870 * * * * [misc]progress: [ 54 / 94 ] simplifiying candidate # 1546938925.871 * [enter]simplify: Simplifying (sqrt (pow (* PI (* n 2)) (- (/ k 2)))) 1546938925.871 * * [misc]simplify: iters left: 6 (10 enodes) 1546938925.872 * * [misc]simplify: iters left: 5 (16 enodes) 1546938925.874 * * [misc]simplify: iters left: 4 (22 enodes) 1546938925.879 * * [misc]simplify: iters left: 3 (24 enodes) 1546938925.885 * [exit]simplify: Simplified to (sqrt (pow (* (* PI 2) n) (- (/ k 2)))) 1546938925.885 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (* (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (pow (* PI (* n 2)) 1/2))) (sqrt (pow (* (* PI 2) n) (- (/ k 2))))) (sqrt k))) 1546938925.885 * * * * [misc]progress: [ 55 / 94 ] simplifiying candidate # 1546938925.886 * [enter]simplify: Simplifying (sqrt (pow (* PI (* n 2)) (- (/ k 2)))) 1546938925.886 * * [misc]simplify: iters left: 6 (10 enodes) 1546938925.889 * * [misc]simplify: iters left: 5 (16 enodes) 1546938925.893 * * [misc]simplify: iters left: 4 (22 enodes) 1546938925.899 * * [misc]simplify: iters left: 3 (24 enodes) 1546938925.905 * [exit]simplify: Simplified to (sqrt (pow (* (* PI 2) n) (- (/ k 2)))) 1546938925.905 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (* (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (pow (* PI (* n 2)) 1/2))) (sqrt (pow (* (* PI 2) n) (- (/ k 2))))) (sqrt k))) 1546938925.906 * * * * [misc]progress: [ 56 / 94 ] simplifiying candidate # 1546938925.907 * [enter]simplify: Simplifying (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) 1546938925.907 * * [misc]simplify: iters left: 6 (9 enodes) 1546938925.910 * * [misc]simplify: iters left: 5 (12 enodes) 1546938925.913 * * [misc]simplify: iters left: 4 (15 enodes) 1546938925.917 * [exit]simplify: Simplified to (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) 1546938925.917 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (* (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (pow PI (- 1/2 (/ k 2))))) (sqrt (pow (* n 2) (- 1/2 (/ k 2))))) (sqrt k))) 1546938925.917 * * * * [misc]progress: [ 57 / 94 ] simplifiying candidate # 1546938925.918 * [enter]simplify: Simplifying (sqrt (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546938925.918 * * [misc]simplify: iters left: 6 (12 enodes) 1546938925.922 * * [misc]simplify: iters left: 5 (18 enodes) 1546938925.927 * * [misc]simplify: iters left: 4 (27 enodes) 1546938925.934 * * [misc]simplify: iters left: 3 (29 enodes) 1546938925.941 * [exit]simplify: Simplified to (sqrt (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) 1546938925.941 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (* (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))) (sqrt (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))))) (sqrt k))) 1546938925.942 * * * * [misc]progress: [ 58 / 94 ] simplifiying candidate # 1546938925.942 * [enter]simplify: Simplifying (sqrt (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546938925.942 * * [misc]simplify: iters left: 6 (12 enodes) 1546938925.944 * * [misc]simplify: iters left: 5 (18 enodes) 1546938925.947 * * [misc]simplify: iters left: 4 (27 enodes) 1546938925.950 * * [misc]simplify: iters left: 3 (29 enodes) 1546938925.954 * [exit]simplify: Simplified to (sqrt (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) 1546938925.954 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (* (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) (sqrt (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))))) (sqrt k))) 1546938925.954 * * * * [misc]progress: [ 59 / 94 ] simplifiying candidate # 1546938925.954 * [enter]simplify: Simplifying (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1546938925.954 * * [misc]simplify: iters left: 6 (11 enodes) 1546938925.956 * * [misc]simplify: iters left: 5 (17 enodes) 1546938925.958 * * [misc]simplify: iters left: 4 (26 enodes) 1546938925.961 * * [misc]simplify: iters left: 3 (27 enodes) 1546938925.964 * [exit]simplify: Simplified to (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) 1546938925.965 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (* (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt 1)) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) (sqrt k))) 1546938925.965 * * * * [misc]progress: [ 60 / 94 ] simplifiying candidate # 1546938925.965 * [enter]simplify: Simplifying (sqrt (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546938925.965 * * [misc]simplify: iters left: 6 (12 enodes) 1546938925.967 * * [misc]simplify: iters left: 5 (18 enodes) 1546938925.969 * * [misc]simplify: iters left: 4 (27 enodes) 1546938925.973 * * [misc]simplify: iters left: 3 (29 enodes) 1546938925.976 * [exit]simplify: Simplified to (sqrt (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) 1546938925.976 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (* (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) (sqrt (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))))) (sqrt k))) 1546938925.976 * * * * [misc]progress: [ 61 / 94 ] simplifiying candidate # 1546938925.977 * [enter]simplify: Simplifying (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1546938925.977 * * [misc]simplify: iters left: 6 (11 enodes) 1546938925.978 * * [misc]simplify: iters left: 5 (17 enodes) 1546938925.981 * * [misc]simplify: iters left: 4 (26 enodes) 1546938925.984 * * [misc]simplify: iters left: 3 (27 enodes) 1546938925.987 * [exit]simplify: Simplified to (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) 1546938925.987 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (* (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) (sqrt k))) 1546938925.987 * * * * [misc]progress: [ 62 / 94 ] simplifiying candidate # 1546938925.987 * [enter]simplify: Simplifying (* (cbrt (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (cbrt (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) 1546938925.988 * * [misc]simplify: iters left: 6 (13 enodes) 1546938925.990 * * [misc]simplify: iters left: 5 (19 enodes) 1546938925.992 * * [misc]simplify: iters left: 4 (28 enodes) 1546938925.996 * * [misc]simplify: iters left: 3 (30 enodes) 1546938926.005 * [exit]simplify: Simplified to (* (cbrt (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) (cbrt (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))))) 1546938926.005 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (* (* (cbrt (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) (cbrt (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))))) (* (cbrt (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) (sqrt k))) 1546938926.005 * * * * [misc]progress: [ 63 / 94 ] simplifiying candidate # 1546938926.005 * [enter]simplify: Simplifying (sqrt (pow (* PI (* n 2)) 1/2)) 1546938926.006 * * [misc]simplify: iters left: 6 (8 enodes) 1546938926.008 * * [misc]simplify: iters left: 5 (13 enodes) 1546938926.012 * * [misc]simplify: iters left: 4 (19 enodes) 1546938926.017 * * [misc]simplify: iters left: 3 (20 enodes) 1546938926.021 * [exit]simplify: Simplified to (sqrt (sqrt (* (* 2 n) PI))) 1546938926.021 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (* (sqrt (sqrt (* (* 2 n) PI))) (* (sqrt (pow (* PI (* n 2)) (- (/ k 2)))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) (sqrt k))) 1546938926.021 * * * * [misc]progress: [ 64 / 94 ] simplifiying candidate # 1546938926.022 * [enter]simplify: Simplifying (sqrt (pow (* PI (* n 2)) 1/2)) 1546938926.022 * * [misc]simplify: iters left: 6 (8 enodes) 1546938926.024 * * [misc]simplify: iters left: 5 (13 enodes) 1546938926.028 * * [misc]simplify: iters left: 4 (19 enodes) 1546938926.030 * * [misc]simplify: iters left: 3 (20 enodes) 1546938926.032 * [exit]simplify: Simplified to (sqrt (sqrt (* (* 2 n) PI))) 1546938926.032 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (* (sqrt (sqrt (* (* 2 n) PI))) (* (sqrt (pow (* PI (* n 2)) (- (/ k 2)))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) (sqrt k))) 1546938926.032 * * * * [misc]progress: [ 65 / 94 ] simplifiying candidate # 1546938926.032 * [enter]simplify: Simplifying (sqrt (pow PI (- 1/2 (/ k 2)))) 1546938926.033 * * [misc]simplify: iters left: 6 (8 enodes) 1546938926.034 * * [misc]simplify: iters left: 5 (10 enodes) 1546938926.035 * * [misc]simplify: iters left: 4 (13 enodes) 1546938926.037 * [exit]simplify: Simplified to (sqrt (pow PI (- 1/2 (/ k 2)))) 1546938926.037 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (* (sqrt (pow PI (- 1/2 (/ k 2)))) (* (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) (sqrt k))) 1546938926.037 * * * * [misc]progress: [ 66 / 94 ] simplifiying candidate # 1546938926.037 * [enter]simplify: Simplifying (sqrt (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) 1546938926.037 * * [misc]simplify: iters left: 6 (13 enodes) 1546938926.039 * * [misc]simplify: iters left: 5 (20 enodes) 1546938926.042 * * [misc]simplify: iters left: 4 (29 enodes) 1546938926.045 * * [misc]simplify: iters left: 3 (30 enodes) 1546938926.049 * [exit]simplify: Simplified to (fabs (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) 1546938926.049 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (* (fabs (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) (* (sqrt (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) (sqrt k))) 1546938926.049 * * * * [misc]progress: [ 67 / 94 ] simplifiying candidate # 1546938926.049 * [enter]simplify: Simplifying (sqrt (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546938926.049 * * [misc]simplify: iters left: 6 (12 enodes) 1546938926.051 * * [misc]simplify: iters left: 5 (18 enodes) 1546938926.053 * * [misc]simplify: iters left: 4 (27 enodes) 1546938926.057 * * [misc]simplify: iters left: 3 (29 enodes) 1546938926.060 * [exit]simplify: Simplified to (sqrt (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) 1546938926.060 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (* (sqrt (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) (* (sqrt (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) (sqrt k))) 1546938926.060 * * * * [misc]progress: [ 68 / 94 ] simplifiying candidate # 1546938926.060 * [enter]simplify: Simplifying (sqrt 1) 1546938926.061 * * [misc]simplify: iters left: 1 (2 enodes) 1546938926.061 * [exit]simplify: Simplified to 1 1546938926.061 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (* 1 (* (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) (sqrt k))) 1546938926.061 * * * * [misc]progress: [ 69 / 94 ] simplifiying candidate # 1546938926.062 * [enter]simplify: Simplifying (sqrt (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546938926.062 * * [misc]simplify: iters left: 6 (12 enodes) 1546938926.063 * * [misc]simplify: iters left: 5 (18 enodes) 1546938926.066 * * [misc]simplify: iters left: 4 (27 enodes) 1546938926.069 * * [misc]simplify: iters left: 3 (29 enodes) 1546938926.075 * [exit]simplify: Simplified to (sqrt (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) 1546938926.075 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (* (sqrt (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) (* (sqrt (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) (sqrt k))) 1546938926.075 * * * * [misc]progress: [ 70 / 94 ] simplifiying candidate # 1546938926.075 * * * * [misc]progress: [ 71 / 94 ] simplifiying candidate # 1546938926.075 * [enter]simplify: Simplifying (sqrt (pow (* PI (* n 2)) (/ k 2))) 1546938926.075 * * [misc]simplify: iters left: 6 (9 enodes) 1546938926.078 * * [misc]simplify: iters left: 5 (13 enodes) 1546938926.080 * * [misc]simplify: iters left: 4 (19 enodes) 1546938926.083 * * [misc]simplify: iters left: 3 (20 enodes) 1546938926.085 * [exit]simplify: Simplified to (sqrt (pow (* (* 2 n) PI) (/ k 2))) 1546938926.085 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (/ (* (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (pow (* PI (* n 2)) 1/2))) (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt k))) 1546938926.085 * * * * [misc]progress: [ 72 / 94 ] simplifiying candidate # 1546938926.086 * [enter]simplify: Simplifying (* (sqrt (pow (* PI (* n 2)) 1/2)) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546938926.086 * * [misc]simplify: iters left: 6 (14 enodes) 1546938926.088 * * [misc]simplify: iters left: 5 (22 enodes) 1546938926.091 * * [misc]simplify: iters left: 4 (31 enodes) 1546938926.095 * * [misc]simplify: iters left: 3 (33 enodes) 1546938926.099 * [exit]simplify: Simplified to (* (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt (* (* 2 n) PI)))) 1546938926.099 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (/ (* (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt (* (* 2 n) PI)))) (sqrt (pow (* PI (* n 2)) (/ k 2)))) (sqrt k))) 1546938926.099 * * * * [misc]progress: [ 73 / 94 ] simplifiying candidate # 1546938926.100 * * * * [misc]progress: [ 74 / 94 ] simplifiying candidate # 1546938926.100 * * * * [misc]progress: [ 75 / 94 ] simplifiying candidate # 1546938926.100 * * * * [misc]progress: [ 76 / 94 ] simplifiying candidate # 1546938926.100 * * * * [misc]progress: [ 77 / 94 ] simplifiying candidate # 1546938926.100 * * * * [misc]progress: [ 78 / 94 ] simplifiying candidate # 1546938926.100 * * * * [misc]progress: [ 79 / 94 ] simplifiying candidate # 1546938926.100 * * * * [misc]progress: [ 80 / 94 ] simplifiying candidate # 1546938926.100 * * * * [misc]progress: [ 81 / 94 ] simplifiying candidate # 1546938926.100 * * * * [misc]progress: [ 82 / 94 ] simplifiying candidate # 1546938926.100 * * * * [misc]progress: [ 83 / 94 ] simplifiying candidate # 1546938926.100 * [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))))) 1546938926.100 * * [misc]simplify: iters left: 6 (37 enodes) 1546938926.108 * * [misc]simplify: iters left: 5 (105 enodes) 1546938926.150 * * [misc]simplify: iters left: 4 (339 enodes) 1546938926.374 * [exit]simplify: Simplified to (+ (+ (* (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) -1/2) (+ (* (* (* k (log n)) (* k (log n))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (pow (* PI 2) 1/2) (pow n 1/2)))) (* (* k k) (+ (* (* (log (* PI 2)) (log (* PI 2))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (* (* (log n) (pow n 1/2)) (pow (* PI 2) 1/2)) (* (log (* PI 2)) 1/4))))) 1546938926.374 * [misc]simplify: Simplified (2 1 2 1) to (λ (k n) (/ (* (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (+ (+ (* (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) -1/2) (+ (* (* (* k (log n)) (* k (log n))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (pow (* PI 2) 1/2) (pow n 1/2)))) (* (* k k) (+ (* (* (log (* PI 2)) (log (* PI 2))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (* (* (log n) (pow n 1/2)) (pow (* PI 2) 1/2)) (* (log (* PI 2)) 1/4))))))) (sqrt k))) 1546938926.374 * * * * [misc]progress: [ 84 / 94 ] simplifiying candidate # 1546938926.374 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 1546938926.374 * * [misc]simplify: iters left: 6 (15 enodes) 1546938926.378 * * [misc]simplify: iters left: 5 (33 enodes) 1546938926.387 * * [misc]simplify: iters left: 4 (64 enodes) 1546938926.410 * * [misc]simplify: iters left: 3 (171 enodes) 1546938926.505 * [exit]simplify: Simplified to (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow n (- 1/2 (* 1/2 k)))) 1546938926.505 * [misc]simplify: Simplified (2 1 2 1) to (λ (k n) (/ (* (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow n (- 1/2 (* 1/2 k)))))) (sqrt k))) 1546938926.505 * * * * [misc]progress: [ 85 / 94 ] simplifiying candidate # 1546938926.505 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 1546938926.505 * * [misc]simplify: iters left: 6 (15 enodes) 1546938926.511 * * [misc]simplify: iters left: 5 (30 enodes) 1546938926.522 * * [misc]simplify: iters left: 4 (65 enodes) 1546938926.548 * * [misc]simplify: iters left: 3 (200 enodes) 1546938926.676 * [exit]simplify: Simplified to (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))) 1546938926.676 * [misc]simplify: Simplified (2 1 2 1) to (λ (k n) (/ (* (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))))) (sqrt k))) 1546938926.676 * * * * [misc]progress: [ 86 / 94 ] simplifiying candidate # 1546938926.677 * [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))))) 1546938926.677 * * [misc]simplify: iters left: 6 (37 enodes) 1546938926.692 * * [misc]simplify: iters left: 5 (105 enodes) 1546938926.733 * * [misc]simplify: iters left: 4 (339 enodes) 1546938926.899 * [exit]simplify: Simplified to (+ (+ (* (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) -1/2) (+ (* (* (* k (log n)) (* k (log n))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (pow (* PI 2) 1/2) (pow n 1/2)))) (* (* k k) (+ (* (* (log (* PI 2)) (log (* PI 2))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (* (* (log n) (pow n 1/2)) (pow (* PI 2) 1/2)) (* (log (* PI 2)) 1/4))))) 1546938926.899 * [misc]simplify: Simplified (2 1 1 1) to (λ (k n) (/ (* (sqrt (+ (+ (* (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) -1/2) (+ (* (* (* k (log n)) (* k (log n))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (pow (* PI 2) 1/2) (pow n 1/2)))) (* (* k k) (+ (* (* (log (* PI 2)) (log (* PI 2))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (* (* (log n) (pow n 1/2)) (pow (* PI 2) 1/2)) (* (log (* PI 2)) 1/4)))))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt k))) 1546938926.899 * * * * [misc]progress: [ 87 / 94 ] simplifiying candidate # 1546938926.900 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 1546938926.900 * * [misc]simplify: iters left: 6 (15 enodes) 1546938926.903 * * [misc]simplify: iters left: 5 (33 enodes) 1546938926.908 * * [misc]simplify: iters left: 4 (64 enodes) 1546938926.919 * * [misc]simplify: iters left: 3 (171 enodes) 1546938927.008 * [exit]simplify: Simplified to (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow n (- 1/2 (* 1/2 k)))) 1546938927.009 * [misc]simplify: Simplified (2 1 1 1) to (λ (k n) (/ (* (sqrt (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow n (- 1/2 (* 1/2 k))))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt k))) 1546938927.009 * * * * [misc]progress: [ 88 / 94 ] simplifiying candidate # 1546938927.009 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 1546938927.009 * * [misc]simplify: iters left: 6 (15 enodes) 1546938927.015 * * [misc]simplify: iters left: 5 (30 enodes) 1546938927.026 * * [misc]simplify: iters left: 4 (65 enodes) 1546938927.056 * * [misc]simplify: iters left: 3 (200 enodes) 1546938927.176 * [exit]simplify: Simplified to (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))) 1546938927.176 * [misc]simplify: Simplified (2 1 1 1) to (λ (k n) (/ (* (sqrt (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n))))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt k))) 1546938927.176 * * * * [misc]progress: [ 89 / 94 ] simplifiying candidate # 1546938927.176 * [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))))) 1546938927.177 * * [misc]simplify: iters left: 6 (37 enodes) 1546938927.192 * * [misc]simplify: iters left: 5 (105 enodes) 1546938927.233 * * [misc]simplify: iters left: 4 (339 enodes) 1546938927.470 * [exit]simplify: Simplified to (+ (+ (* (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) -1/2) (+ (* (* (* k (log n)) (* k (log n))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (pow (* PI 2) 1/2) (pow n 1/2)))) (* (* k k) (+ (* (* (log (* PI 2)) (log (* PI 2))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (* (* (log n) (pow n 1/2)) (pow (* PI 2) 1/2)) (* (log (* PI 2)) 1/4))))) 1546938927.470 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (+ (+ (* (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) -1/2) (+ (* (* (* k (log n)) (* k (log n))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (pow (* PI 2) 1/2) (pow n 1/2)))) (* (* k k) (+ (* (* (log (* PI 2)) (log (* PI 2))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (* (* (log n) (pow n 1/2)) (pow (* PI 2) 1/2)) (* (log (* PI 2)) 1/4))))) (sqrt k))) 1546938927.470 * * * * [misc]progress: [ 90 / 94 ] simplifiying candidate # 1546938927.470 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 1546938927.471 * * [misc]simplify: iters left: 6 (15 enodes) 1546938927.476 * * [misc]simplify: iters left: 5 (33 enodes) 1546938927.486 * * [misc]simplify: iters left: 4 (64 enodes) 1546938927.510 * * [misc]simplify: iters left: 3 (171 enodes) 1546938927.596 * [exit]simplify: Simplified to (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow n (- 1/2 (* 1/2 k)))) 1546938927.596 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow n (- 1/2 (* 1/2 k)))) (sqrt k))) 1546938927.596 * * * * [misc]progress: [ 91 / 94 ] simplifiying candidate # 1546938927.596 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 1546938927.596 * * [misc]simplify: iters left: 6 (15 enodes) 1546938927.599 * * [misc]simplify: iters left: 5 (30 enodes) 1546938927.604 * * [misc]simplify: iters left: 4 (65 enodes) 1546938927.619 * * [misc]simplify: iters left: 3 (200 enodes) 1546938927.724 * [exit]simplify: Simplified to (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))) 1546938927.724 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))) (sqrt k))) 1546938927.724 * * * * [misc]progress: [ 92 / 94 ] simplifiying candidate # 1546938927.724 * [enter]simplify: Simplifying (* 2 (* n PI)) 1546938927.724 * * [misc]simplify: iters left: 4 (5 enodes) 1546938927.726 * * [misc]simplify: iters left: 3 (9 enodes) 1546938927.729 * * [misc]simplify: iters left: 2 (15 enodes) 1546938927.732 * * [misc]simplify: iters left: 1 (17 enodes) 1546938927.736 * [exit]simplify: Simplified to (* (* PI n) 2) 1546938927.736 * [misc]simplify: Simplified (2 1 2 1 1) to (λ (k n) (/ (* (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) (sqrt k))) 1546938927.736 * * * * [misc]progress: [ 93 / 94 ] simplifiying candidate # 1546938927.737 * [enter]simplify: Simplifying (* 2 (* n PI)) 1546938927.737 * * [misc]simplify: iters left: 4 (5 enodes) 1546938927.738 * * [misc]simplify: iters left: 3 (9 enodes) 1546938927.741 * * [misc]simplify: iters left: 2 (15 enodes) 1546938927.745 * * [misc]simplify: iters left: 1 (17 enodes) 1546938927.749 * [exit]simplify: Simplified to (* (* PI n) 2) 1546938927.749 * [misc]simplify: Simplified (2 1 2 1 1) to (λ (k n) (/ (* (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) (sqrt k))) 1546938927.750 * * * * [misc]progress: [ 94 / 94 ] simplifiying candidate # 1546938927.750 * [enter]simplify: Simplifying (* 2 (* n PI)) 1546938927.750 * * [misc]simplify: iters left: 4 (5 enodes) 1546938927.752 * * [misc]simplify: iters left: 3 (9 enodes) 1546938927.754 * * [misc]simplify: iters left: 2 (15 enodes) 1546938927.758 * * [misc]simplify: iters left: 1 (17 enodes) 1546938927.762 * [exit]simplify: Simplified to (* (* PI n) 2) 1546938927.762 * [misc]simplify: Simplified (2 1 2 1 1) to (λ (k n) (/ (* (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) (sqrt k))) 1546938927.762 * * * [misc]progress: adding candidates to table 1546938929.079 * * [misc]progress: iteration 3 / 4 1546938929.079 * * * [misc]progress: picking best candidate 1546938929.117 * * * * [misc]pick: Picked # 1546938929.117 * * * [misc]progress: localizing error 1546938929.130 * * * [misc]progress: generating rewritten candidates 1546938929.130 * * * * [misc]progress: [ 1 / 4 ] rewriting at (2 2 1 1) 1546938929.133 * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 1 1 1) 1546938929.137 * * * * [misc]progress: [ 3 / 4 ] rewriting at (2) 1546938929.151 * * * * [misc]progress: [ 4 / 4 ] rewriting at (2 2 1 1 1) 1546938929.156 * * * [misc]progress: generating series expansions 1546938929.156 * * * * [misc]progress: [ 1 / 4 ] generating series at (2 2 1 1) 1546938929.157 * [misc]backup-simplify: Simplify (pow (* PI (* n 2)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 1546938929.157 * [misc]approximate: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 1546938929.157 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1546938929.157 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1546938929.157 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1546938929.157 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546938929.157 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938929.157 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.157 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546938929.157 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938929.157 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.157 * [misc]taylor: Taking taylor expansion of k in k 1546938929.157 * [misc]backup-simplify: Simplify 0 into 0 1546938929.157 * [misc]backup-simplify: Simplify 1 into 1 1546938929.157 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1546938929.157 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1546938929.157 * [misc]taylor: Taking taylor expansion of 2 in k 1546938929.157 * [misc]backup-simplify: Simplify 2 into 2 1546938929.157 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1546938929.157 * [misc]taylor: Taking taylor expansion of n in k 1546938929.157 * [misc]backup-simplify: Simplify n into n 1546938929.157 * [misc]taylor: Taking taylor expansion of PI in k 1546938929.157 * [misc]backup-simplify: Simplify PI into PI 1546938929.157 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1546938929.157 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1546938929.157 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1546938929.158 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546938929.158 * [misc]backup-simplify: Simplify (- 0) into 0 1546938929.158 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546938929.158 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1546938929.158 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1546938929.158 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546938929.158 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546938929.158 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546938929.158 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546938929.158 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938929.159 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.159 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546938929.159 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938929.159 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.159 * [misc]taylor: Taking taylor expansion of k in n 1546938929.159 * [misc]backup-simplify: Simplify k into k 1546938929.159 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546938929.159 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546938929.159 * [misc]taylor: Taking taylor expansion of 2 in n 1546938929.159 * [misc]backup-simplify: Simplify 2 into 2 1546938929.159 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546938929.159 * [misc]taylor: Taking taylor expansion of n in n 1546938929.159 * [misc]backup-simplify: Simplify 0 into 0 1546938929.159 * [misc]backup-simplify: Simplify 1 into 1 1546938929.159 * [misc]taylor: Taking taylor expansion of PI in n 1546938929.159 * [misc]backup-simplify: Simplify PI into PI 1546938929.159 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546938929.159 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546938929.160 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546938929.161 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546938929.161 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546938929.161 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546938929.161 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546938929.161 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546938929.162 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546938929.166 * [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)))) 1546938929.167 * [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))))) 1546938929.167 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546938929.167 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546938929.167 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546938929.167 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546938929.167 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938929.167 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.167 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546938929.167 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938929.168 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.168 * [misc]taylor: Taking taylor expansion of k in n 1546938929.168 * [misc]backup-simplify: Simplify k into k 1546938929.168 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546938929.168 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546938929.168 * [misc]taylor: Taking taylor expansion of 2 in n 1546938929.168 * [misc]backup-simplify: Simplify 2 into 2 1546938929.168 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546938929.168 * [misc]taylor: Taking taylor expansion of n in n 1546938929.168 * [misc]backup-simplify: Simplify 0 into 0 1546938929.168 * [misc]backup-simplify: Simplify 1 into 1 1546938929.168 * [misc]taylor: Taking taylor expansion of PI in n 1546938929.168 * [misc]backup-simplify: Simplify PI into PI 1546938929.168 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546938929.168 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546938929.169 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546938929.169 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546938929.170 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546938929.170 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546938929.170 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546938929.170 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546938929.171 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546938929.171 * [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)))) 1546938929.172 * [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))))) 1546938929.172 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1546938929.172 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1546938929.172 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546938929.172 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938929.172 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.172 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546938929.172 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938929.172 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.172 * [misc]taylor: Taking taylor expansion of k in k 1546938929.172 * [misc]backup-simplify: Simplify 0 into 0 1546938929.172 * [misc]backup-simplify: Simplify 1 into 1 1546938929.173 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1546938929.173 * [misc]taylor: Taking taylor expansion of (log n) in k 1546938929.173 * [misc]taylor: Taking taylor expansion of n in k 1546938929.173 * [misc]backup-simplify: Simplify n into n 1546938929.173 * [misc]backup-simplify: Simplify (log n) into (log n) 1546938929.173 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1546938929.173 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1546938929.173 * [misc]taylor: Taking taylor expansion of 2 in k 1546938929.173 * [misc]backup-simplify: Simplify 2 into 2 1546938929.173 * [misc]taylor: Taking taylor expansion of PI in k 1546938929.173 * [misc]backup-simplify: Simplify PI into PI 1546938929.173 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546938929.174 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546938929.174 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546938929.174 * [misc]backup-simplify: Simplify (- 0) into 0 1546938929.174 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546938929.175 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546938929.175 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1546938929.176 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1546938929.176 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1546938929.177 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546938929.178 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1546938929.181 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546938929.181 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1546938929.181 * [misc]backup-simplify: Simplify (- 0) into 0 1546938929.182 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938929.182 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546938929.183 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1546938929.184 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1546938929.184 * [misc]taylor: Taking taylor expansion of 0 in k 1546938929.184 * [misc]backup-simplify: Simplify 0 into 0 1546938929.184 * [misc]backup-simplify: Simplify 0 into 0 1546938929.185 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1546938929.186 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546938929.189 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546938929.189 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938929.189 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1546938929.189 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546938929.189 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546938929.190 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1546938929.191 * [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))))))) 1546938929.193 * [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))))))) 1546938929.194 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1546938929.196 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1546938929.201 * [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 1546938929.201 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1546938929.201 * [misc]backup-simplify: Simplify (- 0) into 0 1546938929.201 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938929.202 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546938929.203 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1546938929.205 * [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 1546938929.205 * [misc]taylor: Taking taylor expansion of 0 in k 1546938929.205 * [misc]backup-simplify: Simplify 0 into 0 1546938929.205 * [misc]backup-simplify: Simplify 0 into 0 1546938929.205 * [misc]backup-simplify: Simplify 0 into 0 1546938929.207 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1546938929.208 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546938929.214 * [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 1546938929.214 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938929.214 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1546938929.214 * [misc]backup-simplify: Simplify (- 0) into 0 1546938929.214 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938929.215 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1546938929.217 * [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))))) 1546938929.220 * [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))))) 1546938929.224 * [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))))) 1546938929.225 * [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)))) 1546938929.225 * [misc]approximate: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 1546938929.225 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1546938929.225 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1546938929.225 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1546938929.225 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546938929.225 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938929.225 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.225 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546938929.225 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938929.225 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.225 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546938929.225 * [misc]taylor: Taking taylor expansion of k in k 1546938929.225 * [misc]backup-simplify: Simplify 0 into 0 1546938929.225 * [misc]backup-simplify: Simplify 1 into 1 1546938929.225 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546938929.225 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1546938929.226 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1546938929.226 * [misc]taylor: Taking taylor expansion of 2 in k 1546938929.226 * [misc]backup-simplify: Simplify 2 into 2 1546938929.226 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546938929.226 * [misc]taylor: Taking taylor expansion of PI in k 1546938929.226 * [misc]backup-simplify: Simplify PI into PI 1546938929.226 * [misc]taylor: Taking taylor expansion of n in k 1546938929.226 * [misc]backup-simplify: Simplify n into n 1546938929.226 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546938929.226 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1546938929.226 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1546938929.226 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546938929.226 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546938929.226 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546938929.227 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1546938929.227 * [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)))) 1546938929.227 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546938929.227 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546938929.227 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546938929.227 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546938929.227 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938929.227 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.227 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546938929.227 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938929.227 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.227 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938929.227 * [misc]taylor: Taking taylor expansion of k in n 1546938929.227 * [misc]backup-simplify: Simplify k into k 1546938929.227 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938929.227 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546938929.227 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546938929.227 * [misc]taylor: Taking taylor expansion of 2 in n 1546938929.227 * [misc]backup-simplify: Simplify 2 into 2 1546938929.227 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546938929.227 * [misc]taylor: Taking taylor expansion of PI in n 1546938929.227 * [misc]backup-simplify: Simplify PI into PI 1546938929.227 * [misc]taylor: Taking taylor expansion of n in n 1546938929.227 * [misc]backup-simplify: Simplify 0 into 0 1546938929.227 * [misc]backup-simplify: Simplify 1 into 1 1546938929.228 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546938929.228 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546938929.229 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546938929.229 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546938929.229 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546938929.229 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546938929.230 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546938929.230 * [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))) 1546938929.231 * [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)))) 1546938929.231 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546938929.231 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546938929.231 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546938929.231 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546938929.231 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938929.231 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.231 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546938929.231 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938929.231 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.231 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938929.231 * [misc]taylor: Taking taylor expansion of k in n 1546938929.231 * [misc]backup-simplify: Simplify k into k 1546938929.231 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938929.231 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546938929.231 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546938929.231 * [misc]taylor: Taking taylor expansion of 2 in n 1546938929.231 * [misc]backup-simplify: Simplify 2 into 2 1546938929.231 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546938929.231 * [misc]taylor: Taking taylor expansion of PI in n 1546938929.231 * [misc]backup-simplify: Simplify PI into PI 1546938929.231 * [misc]taylor: Taking taylor expansion of n in n 1546938929.231 * [misc]backup-simplify: Simplify 0 into 0 1546938929.231 * [misc]backup-simplify: Simplify 1 into 1 1546938929.232 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546938929.232 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546938929.232 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546938929.232 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546938929.232 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546938929.233 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546938929.233 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546938929.234 * [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))) 1546938929.234 * [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)))) 1546938929.235 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1546938929.235 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1546938929.235 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546938929.235 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938929.235 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.235 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546938929.235 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938929.235 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.235 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546938929.235 * [misc]taylor: Taking taylor expansion of k in k 1546938929.235 * [misc]backup-simplify: Simplify 0 into 0 1546938929.235 * [misc]backup-simplify: Simplify 1 into 1 1546938929.235 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546938929.235 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1546938929.235 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1546938929.235 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1546938929.235 * [misc]taylor: Taking taylor expansion of 2 in k 1546938929.235 * [misc]backup-simplify: Simplify 2 into 2 1546938929.235 * [misc]taylor: Taking taylor expansion of PI in k 1546938929.235 * [misc]backup-simplify: Simplify PI into PI 1546938929.235 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546938929.236 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546938929.236 * [misc]taylor: Taking taylor expansion of (log n) in k 1546938929.236 * [misc]taylor: Taking taylor expansion of n in k 1546938929.236 * [misc]backup-simplify: Simplify n into n 1546938929.236 * [misc]backup-simplify: Simplify (log n) into (log n) 1546938929.236 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546938929.236 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546938929.236 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546938929.237 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1546938929.237 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1546938929.237 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1546938929.238 * [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)))) 1546938929.239 * [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)))) 1546938929.240 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546938929.240 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546938929.243 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546938929.243 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546938929.243 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546938929.244 * [misc]backup-simplify: Simplify (- 0) into 0 1546938929.244 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938929.244 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546938929.245 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1546938929.247 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546938929.247 * [misc]taylor: Taking taylor expansion of 0 in k 1546938929.247 * [misc]backup-simplify: Simplify 0 into 0 1546938929.247 * [misc]backup-simplify: Simplify 0 into 0 1546938929.247 * [misc]backup-simplify: Simplify 0 into 0 1546938929.248 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938929.249 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546938929.254 * [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 1546938929.254 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546938929.254 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1546938929.254 * [misc]backup-simplify: Simplify (- 0) into 0 1546938929.255 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938929.255 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546938929.256 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1546938929.258 * [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 1546938929.258 * [misc]taylor: Taking taylor expansion of 0 in k 1546938929.258 * [misc]backup-simplify: Simplify 0 into 0 1546938929.258 * [misc]backup-simplify: Simplify 0 into 0 1546938929.258 * [misc]backup-simplify: Simplify 0 into 0 1546938929.258 * [misc]backup-simplify: Simplify 0 into 0 1546938929.260 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938929.262 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546938929.273 * [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 1546938929.273 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546938929.274 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1546938929.274 * [misc]backup-simplify: Simplify (- 0) into 0 1546938929.274 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938929.275 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546938929.275 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1546938929.280 * [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 1546938929.280 * [misc]taylor: Taking taylor expansion of 0 in k 1546938929.280 * [misc]backup-simplify: Simplify 0 into 0 1546938929.280 * [misc]backup-simplify: Simplify 0 into 0 1546938929.281 * [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))))) 1546938929.281 * [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)) 1546938929.281 * [misc]approximate: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 1546938929.281 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1546938929.281 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1546938929.281 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1546938929.281 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546938929.281 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546938929.281 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938929.281 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.281 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546938929.281 * [misc]taylor: Taking taylor expansion of k in k 1546938929.281 * [misc]backup-simplify: Simplify 0 into 0 1546938929.281 * [misc]backup-simplify: Simplify 1 into 1 1546938929.281 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546938929.281 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938929.281 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.282 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1546938929.282 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1546938929.282 * [misc]taylor: Taking taylor expansion of -2 in k 1546938929.282 * [misc]backup-simplify: Simplify -2 into -2 1546938929.282 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546938929.282 * [misc]taylor: Taking taylor expansion of PI in k 1546938929.282 * [misc]backup-simplify: Simplify PI into PI 1546938929.282 * [misc]taylor: Taking taylor expansion of n in k 1546938929.282 * [misc]backup-simplify: Simplify n into n 1546938929.282 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546938929.282 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1546938929.282 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1546938929.282 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546938929.282 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546938929.282 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1546938929.283 * [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))) 1546938929.283 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546938929.283 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546938929.283 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546938929.283 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546938929.283 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546938929.283 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938929.283 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.283 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938929.283 * [misc]taylor: Taking taylor expansion of k in n 1546938929.283 * [misc]backup-simplify: Simplify k into k 1546938929.283 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938929.283 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938929.283 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.283 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546938929.283 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546938929.283 * [misc]taylor: Taking taylor expansion of -2 in n 1546938929.283 * [misc]backup-simplify: Simplify -2 into -2 1546938929.283 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546938929.283 * [misc]taylor: Taking taylor expansion of PI in n 1546938929.283 * [misc]backup-simplify: Simplify PI into PI 1546938929.283 * [misc]taylor: Taking taylor expansion of n in n 1546938929.283 * [misc]backup-simplify: Simplify 0 into 0 1546938929.283 * [misc]backup-simplify: Simplify 1 into 1 1546938929.284 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546938929.284 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546938929.284 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546938929.284 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546938929.284 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546938929.285 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546938929.286 * [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))) 1546938929.286 * [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)))) 1546938929.286 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546938929.286 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546938929.286 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546938929.286 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546938929.286 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546938929.287 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938929.287 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.287 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938929.287 * [misc]taylor: Taking taylor expansion of k in n 1546938929.287 * [misc]backup-simplify: Simplify k into k 1546938929.287 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938929.287 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938929.287 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.287 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546938929.287 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546938929.287 * [misc]taylor: Taking taylor expansion of -2 in n 1546938929.287 * [misc]backup-simplify: Simplify -2 into -2 1546938929.287 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546938929.287 * [misc]taylor: Taking taylor expansion of PI in n 1546938929.287 * [misc]backup-simplify: Simplify PI into PI 1546938929.287 * [misc]taylor: Taking taylor expansion of n in n 1546938929.287 * [misc]backup-simplify: Simplify 0 into 0 1546938929.287 * [misc]backup-simplify: Simplify 1 into 1 1546938929.287 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546938929.288 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546938929.288 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546938929.288 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546938929.288 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546938929.289 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546938929.289 * [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))) 1546938929.290 * [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)))) 1546938929.290 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1546938929.290 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1546938929.290 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546938929.290 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546938929.290 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938929.290 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.290 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546938929.290 * [misc]taylor: Taking taylor expansion of k in k 1546938929.291 * [misc]backup-simplify: Simplify 0 into 0 1546938929.291 * [misc]backup-simplify: Simplify 1 into 1 1546938929.291 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546938929.291 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938929.291 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.291 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1546938929.291 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1546938929.291 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1546938929.291 * [misc]taylor: Taking taylor expansion of -2 in k 1546938929.291 * [misc]backup-simplify: Simplify -2 into -2 1546938929.291 * [misc]taylor: Taking taylor expansion of PI in k 1546938929.291 * [misc]backup-simplify: Simplify PI into PI 1546938929.291 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546938929.292 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546938929.292 * [misc]taylor: Taking taylor expansion of (log n) in k 1546938929.292 * [misc]taylor: Taking taylor expansion of n in k 1546938929.292 * [misc]backup-simplify: Simplify n into n 1546938929.292 * [misc]backup-simplify: Simplify (log n) into (log n) 1546938929.292 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546938929.292 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546938929.292 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1546938929.293 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1546938929.293 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1546938929.294 * [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)))) 1546938929.295 * [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)))) 1546938929.296 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546938929.297 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1546938929.299 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1546938929.299 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546938929.300 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546938929.300 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938929.301 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546938929.301 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1546938929.303 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546938929.303 * [misc]taylor: Taking taylor expansion of 0 in k 1546938929.303 * [misc]backup-simplify: Simplify 0 into 0 1546938929.303 * [misc]backup-simplify: Simplify 0 into 0 1546938929.303 * [misc]backup-simplify: Simplify 0 into 0 1546938929.304 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938929.305 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1546938929.307 * [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 1546938929.308 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546938929.308 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1546938929.308 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938929.308 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546938929.309 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1546938929.310 * [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 1546938929.310 * [misc]taylor: Taking taylor expansion of 0 in k 1546938929.310 * [misc]backup-simplify: Simplify 0 into 0 1546938929.310 * [misc]backup-simplify: Simplify 0 into 0 1546938929.310 * [misc]backup-simplify: Simplify 0 into 0 1546938929.310 * [misc]backup-simplify: Simplify 0 into 0 1546938929.311 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938929.312 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546938929.317 * [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 1546938929.317 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546938929.318 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1546938929.318 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938929.318 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546938929.319 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 1546938929.321 * [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 1546938929.321 * [misc]taylor: Taking taylor expansion of 0 in k 1546938929.321 * [misc]backup-simplify: Simplify 0 into 0 1546938929.321 * [misc]backup-simplify: Simplify 0 into 0 1546938929.321 * [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))))) 1546938929.321 * * * * [misc]progress: [ 2 / 4 ] generating series at (2 1 1 1) 1546938929.323 * [misc]backup-simplify: Simplify (pow (* PI (* n 2)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 1546938929.323 * [misc]approximate: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 1546938929.323 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1546938929.323 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1546938929.323 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1546938929.323 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546938929.323 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938929.323 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.323 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546938929.323 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938929.323 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.323 * [misc]taylor: Taking taylor expansion of k in k 1546938929.323 * [misc]backup-simplify: Simplify 0 into 0 1546938929.323 * [misc]backup-simplify: Simplify 1 into 1 1546938929.323 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1546938929.323 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1546938929.323 * [misc]taylor: Taking taylor expansion of 2 in k 1546938929.323 * [misc]backup-simplify: Simplify 2 into 2 1546938929.323 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1546938929.323 * [misc]taylor: Taking taylor expansion of n in k 1546938929.323 * [misc]backup-simplify: Simplify n into n 1546938929.323 * [misc]taylor: Taking taylor expansion of PI in k 1546938929.323 * [misc]backup-simplify: Simplify PI into PI 1546938929.323 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1546938929.323 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1546938929.323 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1546938929.323 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546938929.324 * [misc]backup-simplify: Simplify (- 0) into 0 1546938929.324 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546938929.324 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1546938929.324 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1546938929.324 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546938929.324 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546938929.324 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546938929.324 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546938929.324 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938929.324 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.324 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546938929.324 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938929.324 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.324 * [misc]taylor: Taking taylor expansion of k in n 1546938929.324 * [misc]backup-simplify: Simplify k into k 1546938929.324 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546938929.324 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546938929.324 * [misc]taylor: Taking taylor expansion of 2 in n 1546938929.324 * [misc]backup-simplify: Simplify 2 into 2 1546938929.324 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546938929.324 * [misc]taylor: Taking taylor expansion of n in n 1546938929.324 * [misc]backup-simplify: Simplify 0 into 0 1546938929.324 * [misc]backup-simplify: Simplify 1 into 1 1546938929.324 * [misc]taylor: Taking taylor expansion of PI in n 1546938929.324 * [misc]backup-simplify: Simplify PI into PI 1546938929.324 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546938929.324 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546938929.325 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546938929.325 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546938929.326 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546938929.326 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546938929.326 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546938929.326 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546938929.326 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546938929.327 * [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)))) 1546938929.327 * [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))))) 1546938929.327 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546938929.327 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546938929.327 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546938929.327 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546938929.327 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938929.327 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.327 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546938929.327 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938929.327 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.327 * [misc]taylor: Taking taylor expansion of k in n 1546938929.327 * [misc]backup-simplify: Simplify k into k 1546938929.327 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546938929.327 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546938929.327 * [misc]taylor: Taking taylor expansion of 2 in n 1546938929.327 * [misc]backup-simplify: Simplify 2 into 2 1546938929.327 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546938929.327 * [misc]taylor: Taking taylor expansion of n in n 1546938929.327 * [misc]backup-simplify: Simplify 0 into 0 1546938929.327 * [misc]backup-simplify: Simplify 1 into 1 1546938929.327 * [misc]taylor: Taking taylor expansion of PI in n 1546938929.327 * [misc]backup-simplify: Simplify PI into PI 1546938929.327 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546938929.328 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546938929.328 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546938929.328 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546938929.329 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546938929.329 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546938929.329 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546938929.329 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546938929.329 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546938929.330 * [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)))) 1546938929.330 * [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))))) 1546938929.330 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1546938929.330 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1546938929.330 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546938929.330 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938929.330 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.330 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546938929.330 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938929.330 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.330 * [misc]taylor: Taking taylor expansion of k in k 1546938929.330 * [misc]backup-simplify: Simplify 0 into 0 1546938929.330 * [misc]backup-simplify: Simplify 1 into 1 1546938929.330 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1546938929.330 * [misc]taylor: Taking taylor expansion of (log n) in k 1546938929.330 * [misc]taylor: Taking taylor expansion of n in k 1546938929.330 * [misc]backup-simplify: Simplify n into n 1546938929.330 * [misc]backup-simplify: Simplify (log n) into (log n) 1546938929.330 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1546938929.330 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1546938929.330 * [misc]taylor: Taking taylor expansion of 2 in k 1546938929.330 * [misc]backup-simplify: Simplify 2 into 2 1546938929.330 * [misc]taylor: Taking taylor expansion of PI in k 1546938929.330 * [misc]backup-simplify: Simplify PI into PI 1546938929.331 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546938929.331 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546938929.331 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546938929.331 * [misc]backup-simplify: Simplify (- 0) into 0 1546938929.331 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546938929.332 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546938929.332 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1546938929.333 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1546938929.333 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1546938929.335 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546938929.336 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1546938929.338 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546938929.339 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1546938929.339 * [misc]backup-simplify: Simplify (- 0) into 0 1546938929.339 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938929.340 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546938929.340 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1546938929.342 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1546938929.342 * [misc]taylor: Taking taylor expansion of 0 in k 1546938929.342 * [misc]backup-simplify: Simplify 0 into 0 1546938929.342 * [misc]backup-simplify: Simplify 0 into 0 1546938929.343 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1546938929.343 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546938929.346 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546938929.346 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938929.347 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1546938929.347 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546938929.347 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546938929.348 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1546938929.349 * [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))))))) 1546938929.350 * [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))))))) 1546938929.352 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1546938929.354 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1546938929.358 * [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 1546938929.359 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1546938929.359 * [misc]backup-simplify: Simplify (- 0) into 0 1546938929.359 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938929.360 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546938929.361 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1546938929.363 * [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 1546938929.363 * [misc]taylor: Taking taylor expansion of 0 in k 1546938929.363 * [misc]backup-simplify: Simplify 0 into 0 1546938929.363 * [misc]backup-simplify: Simplify 0 into 0 1546938929.363 * [misc]backup-simplify: Simplify 0 into 0 1546938929.364 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1546938929.365 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546938929.368 * [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 1546938929.368 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938929.369 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1546938929.369 * [misc]backup-simplify: Simplify (- 0) into 0 1546938929.369 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938929.369 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1546938929.371 * [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))))) 1546938929.372 * [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))))) 1546938929.375 * [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))))) 1546938929.375 * [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)))) 1546938929.375 * [misc]approximate: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 1546938929.375 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1546938929.375 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1546938929.375 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1546938929.375 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546938929.375 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938929.375 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.375 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546938929.375 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938929.375 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.375 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546938929.375 * [misc]taylor: Taking taylor expansion of k in k 1546938929.375 * [misc]backup-simplify: Simplify 0 into 0 1546938929.375 * [misc]backup-simplify: Simplify 1 into 1 1546938929.376 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546938929.376 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1546938929.376 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1546938929.376 * [misc]taylor: Taking taylor expansion of 2 in k 1546938929.376 * [misc]backup-simplify: Simplify 2 into 2 1546938929.376 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546938929.376 * [misc]taylor: Taking taylor expansion of PI in k 1546938929.376 * [misc]backup-simplify: Simplify PI into PI 1546938929.376 * [misc]taylor: Taking taylor expansion of n in k 1546938929.376 * [misc]backup-simplify: Simplify n into n 1546938929.376 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546938929.376 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1546938929.376 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1546938929.376 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546938929.376 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546938929.376 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546938929.376 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1546938929.376 * [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)))) 1546938929.376 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546938929.376 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546938929.376 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546938929.376 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546938929.376 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938929.376 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.376 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546938929.376 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938929.377 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.377 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938929.377 * [misc]taylor: Taking taylor expansion of k in n 1546938929.377 * [misc]backup-simplify: Simplify k into k 1546938929.377 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938929.377 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546938929.377 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546938929.377 * [misc]taylor: Taking taylor expansion of 2 in n 1546938929.377 * [misc]backup-simplify: Simplify 2 into 2 1546938929.377 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546938929.377 * [misc]taylor: Taking taylor expansion of PI in n 1546938929.377 * [misc]backup-simplify: Simplify PI into PI 1546938929.377 * [misc]taylor: Taking taylor expansion of n in n 1546938929.377 * [misc]backup-simplify: Simplify 0 into 0 1546938929.377 * [misc]backup-simplify: Simplify 1 into 1 1546938929.377 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546938929.377 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546938929.378 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546938929.378 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546938929.378 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546938929.378 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546938929.378 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546938929.379 * [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))) 1546938929.379 * [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)))) 1546938929.379 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546938929.379 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546938929.379 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546938929.379 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546938929.379 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938929.379 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.379 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546938929.379 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938929.379 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.379 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938929.379 * [misc]taylor: Taking taylor expansion of k in n 1546938929.379 * [misc]backup-simplify: Simplify k into k 1546938929.379 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938929.379 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546938929.379 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546938929.379 * [misc]taylor: Taking taylor expansion of 2 in n 1546938929.379 * [misc]backup-simplify: Simplify 2 into 2 1546938929.379 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546938929.379 * [misc]taylor: Taking taylor expansion of PI in n 1546938929.379 * [misc]backup-simplify: Simplify PI into PI 1546938929.380 * [misc]taylor: Taking taylor expansion of n in n 1546938929.380 * [misc]backup-simplify: Simplify 0 into 0 1546938929.380 * [misc]backup-simplify: Simplify 1 into 1 1546938929.380 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546938929.380 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546938929.380 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546938929.380 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546938929.380 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546938929.380 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546938929.381 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546938929.381 * [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))) 1546938929.382 * [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)))) 1546938929.382 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1546938929.382 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1546938929.382 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546938929.382 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938929.382 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.382 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546938929.382 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938929.382 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.382 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546938929.382 * [misc]taylor: Taking taylor expansion of k in k 1546938929.382 * [misc]backup-simplify: Simplify 0 into 0 1546938929.382 * [misc]backup-simplify: Simplify 1 into 1 1546938929.382 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546938929.382 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1546938929.382 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1546938929.382 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1546938929.382 * [misc]taylor: Taking taylor expansion of 2 in k 1546938929.382 * [misc]backup-simplify: Simplify 2 into 2 1546938929.382 * [misc]taylor: Taking taylor expansion of PI in k 1546938929.382 * [misc]backup-simplify: Simplify PI into PI 1546938929.382 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546938929.382 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546938929.382 * [misc]taylor: Taking taylor expansion of (log n) in k 1546938929.383 * [misc]taylor: Taking taylor expansion of n in k 1546938929.383 * [misc]backup-simplify: Simplify n into n 1546938929.383 * [misc]backup-simplify: Simplify (log n) into (log n) 1546938929.383 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546938929.383 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546938929.383 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546938929.383 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1546938929.383 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1546938929.384 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1546938929.384 * [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)))) 1546938929.384 * [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)))) 1546938929.385 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546938929.385 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546938929.387 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546938929.387 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546938929.387 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546938929.387 * [misc]backup-simplify: Simplify (- 0) into 0 1546938929.387 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938929.388 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546938929.388 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1546938929.389 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546938929.389 * [misc]taylor: Taking taylor expansion of 0 in k 1546938929.389 * [misc]backup-simplify: Simplify 0 into 0 1546938929.389 * [misc]backup-simplify: Simplify 0 into 0 1546938929.389 * [misc]backup-simplify: Simplify 0 into 0 1546938929.390 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938929.391 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546938929.394 * [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 1546938929.394 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546938929.394 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1546938929.394 * [misc]backup-simplify: Simplify (- 0) into 0 1546938929.394 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938929.395 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546938929.395 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1546938929.397 * [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 1546938929.397 * [misc]taylor: Taking taylor expansion of 0 in k 1546938929.397 * [misc]backup-simplify: Simplify 0 into 0 1546938929.397 * [misc]backup-simplify: Simplify 0 into 0 1546938929.397 * [misc]backup-simplify: Simplify 0 into 0 1546938929.397 * [misc]backup-simplify: Simplify 0 into 0 1546938929.398 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938929.399 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546938929.406 * [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 1546938929.407 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546938929.407 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1546938929.407 * [misc]backup-simplify: Simplify (- 0) into 0 1546938929.408 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938929.408 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546938929.409 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1546938929.413 * [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 1546938929.413 * [misc]taylor: Taking taylor expansion of 0 in k 1546938929.413 * [misc]backup-simplify: Simplify 0 into 0 1546938929.413 * [misc]backup-simplify: Simplify 0 into 0 1546938929.413 * [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))))) 1546938929.414 * [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)) 1546938929.414 * [misc]approximate: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 1546938929.414 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1546938929.414 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1546938929.414 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1546938929.414 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546938929.414 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546938929.414 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938929.414 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.414 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546938929.414 * [misc]taylor: Taking taylor expansion of k in k 1546938929.414 * [misc]backup-simplify: Simplify 0 into 0 1546938929.414 * [misc]backup-simplify: Simplify 1 into 1 1546938929.414 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546938929.414 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938929.414 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.414 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1546938929.414 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1546938929.414 * [misc]taylor: Taking taylor expansion of -2 in k 1546938929.414 * [misc]backup-simplify: Simplify -2 into -2 1546938929.414 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546938929.414 * [misc]taylor: Taking taylor expansion of PI in k 1546938929.414 * [misc]backup-simplify: Simplify PI into PI 1546938929.415 * [misc]taylor: Taking taylor expansion of n in k 1546938929.415 * [misc]backup-simplify: Simplify n into n 1546938929.415 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546938929.415 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1546938929.415 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1546938929.415 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546938929.415 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546938929.415 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1546938929.415 * [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))) 1546938929.415 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546938929.416 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546938929.416 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546938929.416 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546938929.416 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546938929.416 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938929.416 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.416 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938929.416 * [misc]taylor: Taking taylor expansion of k in n 1546938929.416 * [misc]backup-simplify: Simplify k into k 1546938929.416 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938929.416 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938929.416 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.416 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546938929.416 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546938929.416 * [misc]taylor: Taking taylor expansion of -2 in n 1546938929.416 * [misc]backup-simplify: Simplify -2 into -2 1546938929.416 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546938929.416 * [misc]taylor: Taking taylor expansion of PI in n 1546938929.416 * [misc]backup-simplify: Simplify PI into PI 1546938929.416 * [misc]taylor: Taking taylor expansion of n in n 1546938929.416 * [misc]backup-simplify: Simplify 0 into 0 1546938929.416 * [misc]backup-simplify: Simplify 1 into 1 1546938929.417 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546938929.417 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546938929.417 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546938929.417 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546938929.417 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546938929.418 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546938929.419 * [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))) 1546938929.419 * [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)))) 1546938929.419 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546938929.419 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546938929.420 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546938929.420 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546938929.420 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546938929.420 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938929.420 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.420 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938929.420 * [misc]taylor: Taking taylor expansion of k in n 1546938929.420 * [misc]backup-simplify: Simplify k into k 1546938929.420 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938929.420 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938929.420 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.420 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546938929.420 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546938929.420 * [misc]taylor: Taking taylor expansion of -2 in n 1546938929.420 * [misc]backup-simplify: Simplify -2 into -2 1546938929.420 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546938929.420 * [misc]taylor: Taking taylor expansion of PI in n 1546938929.420 * [misc]backup-simplify: Simplify PI into PI 1546938929.420 * [misc]taylor: Taking taylor expansion of n in n 1546938929.420 * [misc]backup-simplify: Simplify 0 into 0 1546938929.420 * [misc]backup-simplify: Simplify 1 into 1 1546938929.420 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546938929.421 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546938929.421 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546938929.421 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546938929.421 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546938929.422 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546938929.423 * [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))) 1546938929.423 * [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)))) 1546938929.423 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1546938929.423 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1546938929.423 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546938929.423 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546938929.423 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938929.423 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.423 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546938929.423 * [misc]taylor: Taking taylor expansion of k in k 1546938929.424 * [misc]backup-simplify: Simplify 0 into 0 1546938929.424 * [misc]backup-simplify: Simplify 1 into 1 1546938929.424 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546938929.424 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938929.424 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.424 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1546938929.424 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1546938929.424 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1546938929.424 * [misc]taylor: Taking taylor expansion of -2 in k 1546938929.424 * [misc]backup-simplify: Simplify -2 into -2 1546938929.424 * [misc]taylor: Taking taylor expansion of PI in k 1546938929.424 * [misc]backup-simplify: Simplify PI into PI 1546938929.424 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546938929.424 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546938929.424 * [misc]taylor: Taking taylor expansion of (log n) in k 1546938929.424 * [misc]taylor: Taking taylor expansion of n in k 1546938929.424 * [misc]backup-simplify: Simplify n into n 1546938929.424 * [misc]backup-simplify: Simplify (log n) into (log n) 1546938929.424 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546938929.425 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546938929.425 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1546938929.425 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1546938929.425 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1546938929.426 * [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)))) 1546938929.426 * [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)))) 1546938929.427 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546938929.427 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1546938929.429 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1546938929.429 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546938929.429 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546938929.429 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938929.430 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546938929.430 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1546938929.431 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546938929.431 * [misc]taylor: Taking taylor expansion of 0 in k 1546938929.431 * [misc]backup-simplify: Simplify 0 into 0 1546938929.431 * [misc]backup-simplify: Simplify 0 into 0 1546938929.431 * [misc]backup-simplify: Simplify 0 into 0 1546938929.432 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938929.432 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1546938929.436 * [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 1546938929.436 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546938929.436 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1546938929.436 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938929.437 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546938929.437 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1546938929.438 * [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 1546938929.438 * [misc]taylor: Taking taylor expansion of 0 in k 1546938929.438 * [misc]backup-simplify: Simplify 0 into 0 1546938929.439 * [misc]backup-simplify: Simplify 0 into 0 1546938929.439 * [misc]backup-simplify: Simplify 0 into 0 1546938929.439 * [misc]backup-simplify: Simplify 0 into 0 1546938929.440 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938929.441 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546938929.445 * [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 1546938929.445 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546938929.446 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1546938929.446 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938929.446 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546938929.448 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 1546938929.450 * [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 1546938929.450 * [misc]taylor: Taking taylor expansion of 0 in k 1546938929.450 * [misc]backup-simplify: Simplify 0 into 0 1546938929.450 * [misc]backup-simplify: Simplify 0 into 0 1546938929.451 * [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))))) 1546938929.451 * * * * [misc]progress: [ 3 / 4 ] generating series at (2) 1546938929.452 * [misc]backup-simplify: Simplify (* (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))) into (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) 1546938929.452 * [misc]approximate: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (n k) around 0 1546938929.452 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 1546938929.452 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1546938929.452 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546938929.452 * [misc]taylor: Taking taylor expansion of k in k 1546938929.452 * [misc]backup-simplify: Simplify 0 into 0 1546938929.452 * [misc]backup-simplify: Simplify 1 into 1 1546938929.452 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546938929.452 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546938929.453 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546938929.453 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1546938929.453 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1546938929.453 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1546938929.453 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546938929.453 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938929.453 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.453 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546938929.453 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938929.453 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.453 * [misc]taylor: Taking taylor expansion of k in k 1546938929.453 * [misc]backup-simplify: Simplify 0 into 0 1546938929.453 * [misc]backup-simplify: Simplify 1 into 1 1546938929.453 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1546938929.453 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1546938929.453 * [misc]taylor: Taking taylor expansion of 2 in k 1546938929.453 * [misc]backup-simplify: Simplify 2 into 2 1546938929.453 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1546938929.453 * [misc]taylor: Taking taylor expansion of n in k 1546938929.453 * [misc]backup-simplify: Simplify n into n 1546938929.453 * [misc]taylor: Taking taylor expansion of PI in k 1546938929.453 * [misc]backup-simplify: Simplify PI into PI 1546938929.454 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1546938929.454 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1546938929.454 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1546938929.454 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546938929.454 * [misc]backup-simplify: Simplify (- 0) into 0 1546938929.454 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546938929.454 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1546938929.454 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1546938929.454 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 1546938929.455 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1546938929.455 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938929.455 * [misc]taylor: Taking taylor expansion of k in n 1546938929.455 * [misc]backup-simplify: Simplify k into k 1546938929.455 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938929.455 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1546938929.455 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546938929.455 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1546938929.455 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546938929.455 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546938929.455 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546938929.455 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546938929.455 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938929.455 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.455 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546938929.455 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938929.455 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.455 * [misc]taylor: Taking taylor expansion of k in n 1546938929.455 * [misc]backup-simplify: Simplify k into k 1546938929.455 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546938929.455 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546938929.455 * [misc]taylor: Taking taylor expansion of 2 in n 1546938929.455 * [misc]backup-simplify: Simplify 2 into 2 1546938929.455 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546938929.455 * [misc]taylor: Taking taylor expansion of n in n 1546938929.455 * [misc]backup-simplify: Simplify 0 into 0 1546938929.456 * [misc]backup-simplify: Simplify 1 into 1 1546938929.456 * [misc]taylor: Taking taylor expansion of PI in n 1546938929.456 * [misc]backup-simplify: Simplify PI into PI 1546938929.456 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546938929.456 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546938929.457 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546938929.457 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546938929.458 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546938929.458 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546938929.458 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546938929.458 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546938929.459 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546938929.459 * [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)))) 1546938929.460 * [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))))) 1546938929.460 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 1546938929.460 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1546938929.460 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938929.460 * [misc]taylor: Taking taylor expansion of k in n 1546938929.460 * [misc]backup-simplify: Simplify k into k 1546938929.460 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938929.460 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1546938929.460 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546938929.460 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1546938929.460 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546938929.461 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546938929.461 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546938929.461 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546938929.461 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938929.461 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.461 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546938929.461 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938929.461 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.461 * [misc]taylor: Taking taylor expansion of k in n 1546938929.461 * [misc]backup-simplify: Simplify k into k 1546938929.461 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546938929.461 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546938929.461 * [misc]taylor: Taking taylor expansion of 2 in n 1546938929.461 * [misc]backup-simplify: Simplify 2 into 2 1546938929.461 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546938929.461 * [misc]taylor: Taking taylor expansion of n in n 1546938929.461 * [misc]backup-simplify: Simplify 0 into 0 1546938929.461 * [misc]backup-simplify: Simplify 1 into 1 1546938929.461 * [misc]taylor: Taking taylor expansion of PI in n 1546938929.461 * [misc]backup-simplify: Simplify PI into PI 1546938929.461 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546938929.461 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546938929.462 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546938929.463 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546938929.463 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546938929.463 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546938929.463 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546938929.463 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546938929.464 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546938929.465 * [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)))) 1546938929.465 * [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))))) 1546938929.466 * [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))) 1546938929.466 * [misc]taylor: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k))) in k 1546938929.466 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1546938929.466 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1546938929.466 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546938929.466 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938929.466 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.466 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546938929.466 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938929.466 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.466 * [misc]taylor: Taking taylor expansion of k in k 1546938929.466 * [misc]backup-simplify: Simplify 0 into 0 1546938929.466 * [misc]backup-simplify: Simplify 1 into 1 1546938929.466 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1546938929.467 * [misc]taylor: Taking taylor expansion of (log n) in k 1546938929.467 * [misc]taylor: Taking taylor expansion of n in k 1546938929.467 * [misc]backup-simplify: Simplify n into n 1546938929.467 * [misc]backup-simplify: Simplify (log n) into (log n) 1546938929.467 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1546938929.467 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1546938929.467 * [misc]taylor: Taking taylor expansion of 2 in k 1546938929.467 * [misc]backup-simplify: Simplify 2 into 2 1546938929.467 * [misc]taylor: Taking taylor expansion of PI in k 1546938929.467 * [misc]backup-simplify: Simplify PI into PI 1546938929.467 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546938929.468 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546938929.468 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546938929.468 * [misc]backup-simplify: Simplify (- 0) into 0 1546938929.468 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546938929.469 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546938929.469 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1546938929.470 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1546938929.470 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1546938929.470 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546938929.470 * [misc]taylor: Taking taylor expansion of k in k 1546938929.470 * [misc]backup-simplify: Simplify 0 into 0 1546938929.470 * [misc]backup-simplify: Simplify 1 into 1 1546938929.470 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546938929.470 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546938929.471 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546938929.471 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) into 0 1546938929.471 * [misc]backup-simplify: Simplify 0 into 0 1546938929.472 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546938929.473 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1546938929.476 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546938929.476 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1546938929.476 * [misc]backup-simplify: Simplify (- 0) into 0 1546938929.477 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938929.477 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546938929.478 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1546938929.479 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1546938929.480 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 k)) 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))) into 0 1546938929.480 * [misc]taylor: Taking taylor expansion of 0 in k 1546938929.480 * [misc]backup-simplify: Simplify 0 into 0 1546938929.481 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1546938929.482 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546938929.484 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546938929.485 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938929.485 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1546938929.485 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546938929.485 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546938929.486 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1546938929.488 * [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))))))) 1546938929.490 * [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))))))) 1546938929.490 * [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))))))) 1546938929.492 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1546938929.493 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1546938929.495 * [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 1546938929.496 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1546938929.496 * [misc]backup-simplify: Simplify (- 0) into 0 1546938929.496 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938929.496 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546938929.497 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1546938929.498 * [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 1546938929.498 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546938929.499 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 1546938929.499 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))))) into 0 1546938929.499 * [misc]taylor: Taking taylor expansion of 0 in k 1546938929.499 * [misc]backup-simplify: Simplify 0 into 0 1546938929.499 * [misc]backup-simplify: Simplify 0 into 0 1546938929.499 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1546938929.500 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1546938929.501 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1546938929.502 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546938929.504 * [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 1546938929.505 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938929.505 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1546938929.505 * [misc]backup-simplify: Simplify (- 0) into 0 1546938929.505 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938929.505 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1546938929.507 * [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))))) 1546938929.509 * [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)))))))) 1546938929.511 * [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)))))))) 1546938929.512 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1546938929.513 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1546938929.518 * [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 1546938929.518 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 1546938929.518 * [misc]backup-simplify: Simplify (- 0) into 0 1546938929.519 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938929.519 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546938929.520 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 1546938929.524 * [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 1546938929.524 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546938929.524 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 1546938929.525 * [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 1546938929.525 * [misc]taylor: Taking taylor expansion of 0 in k 1546938929.525 * [misc]backup-simplify: Simplify 0 into 0 1546938929.525 * [misc]backup-simplify: Simplify 0 into 0 1546938929.526 * [misc]backup-simplify: Simplify 0 into 0 1546938929.526 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938929.527 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1546938929.530 * [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 1546938929.531 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546938929.541 * [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 1546938929.541 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938929.541 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1546938929.541 * [misc]backup-simplify: Simplify (- 0) into 0 1546938929.542 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938929.543 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 1546938929.547 * [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))))))) 1546938929.556 * [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)))))))))))))) 1546938929.563 * [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)))))))))))))) 1546938929.575 * [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)))))))))))))))))))))) 1546938929.575 * [misc]backup-simplify: Simplify (* (sqrt (/ (pow (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k)))) (sqrt (/ (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))))) 1546938929.575 * [misc]approximate: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0 1546938929.575 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 1546938929.575 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1546938929.575 * [misc]taylor: Taking taylor expansion of k in k 1546938929.575 * [misc]backup-simplify: Simplify 0 into 0 1546938929.575 * [misc]backup-simplify: Simplify 1 into 1 1546938929.576 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546938929.576 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546938929.576 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1546938929.576 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1546938929.576 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1546938929.576 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546938929.576 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938929.576 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.576 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546938929.576 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938929.576 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.576 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546938929.576 * [misc]taylor: Taking taylor expansion of k in k 1546938929.576 * [misc]backup-simplify: Simplify 0 into 0 1546938929.576 * [misc]backup-simplify: Simplify 1 into 1 1546938929.576 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546938929.576 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1546938929.576 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1546938929.576 * [misc]taylor: Taking taylor expansion of 2 in k 1546938929.576 * [misc]backup-simplify: Simplify 2 into 2 1546938929.576 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546938929.576 * [misc]taylor: Taking taylor expansion of PI in k 1546938929.576 * [misc]backup-simplify: Simplify PI into PI 1546938929.577 * [misc]taylor: Taking taylor expansion of n in k 1546938929.577 * [misc]backup-simplify: Simplify n into n 1546938929.577 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546938929.577 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1546938929.577 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1546938929.577 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546938929.577 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546938929.577 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546938929.577 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1546938929.577 * [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)))) 1546938929.577 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1546938929.577 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1546938929.577 * [misc]taylor: Taking taylor expansion of k in n 1546938929.577 * [misc]backup-simplify: Simplify k into k 1546938929.577 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1546938929.577 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1546938929.577 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546938929.577 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546938929.577 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546938929.577 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546938929.577 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938929.577 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.577 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546938929.577 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938929.578 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.578 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938929.578 * [misc]taylor: Taking taylor expansion of k in n 1546938929.578 * [misc]backup-simplify: Simplify k into k 1546938929.578 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938929.578 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546938929.578 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546938929.578 * [misc]taylor: Taking taylor expansion of 2 in n 1546938929.578 * [misc]backup-simplify: Simplify 2 into 2 1546938929.578 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546938929.578 * [misc]taylor: Taking taylor expansion of PI in n 1546938929.578 * [misc]backup-simplify: Simplify PI into PI 1546938929.578 * [misc]taylor: Taking taylor expansion of n in n 1546938929.578 * [misc]backup-simplify: Simplify 0 into 0 1546938929.578 * [misc]backup-simplify: Simplify 1 into 1 1546938929.578 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546938929.578 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546938929.578 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546938929.578 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546938929.579 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546938929.579 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546938929.579 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546938929.579 * [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))) 1546938929.580 * [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)))) 1546938929.580 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1546938929.580 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1546938929.580 * [misc]taylor: Taking taylor expansion of k in n 1546938929.580 * [misc]backup-simplify: Simplify k into k 1546938929.580 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1546938929.580 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1546938929.580 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546938929.580 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546938929.580 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546938929.580 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546938929.580 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938929.580 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.580 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546938929.580 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938929.580 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.580 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938929.580 * [misc]taylor: Taking taylor expansion of k in n 1546938929.580 * [misc]backup-simplify: Simplify k into k 1546938929.580 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938929.580 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546938929.580 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546938929.580 * [misc]taylor: Taking taylor expansion of 2 in n 1546938929.580 * [misc]backup-simplify: Simplify 2 into 2 1546938929.580 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546938929.580 * [misc]taylor: Taking taylor expansion of PI in n 1546938929.580 * [misc]backup-simplify: Simplify PI into PI 1546938929.580 * [misc]taylor: Taking taylor expansion of n in n 1546938929.580 * [misc]backup-simplify: Simplify 0 into 0 1546938929.580 * [misc]backup-simplify: Simplify 1 into 1 1546938929.581 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546938929.581 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546938929.581 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546938929.581 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546938929.581 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546938929.581 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546938929.582 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546938929.582 * [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))) 1546938929.582 * [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)))) 1546938929.583 * [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)) 1546938929.583 * [misc]taylor: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) in k 1546938929.583 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1546938929.583 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1546938929.583 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546938929.583 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938929.583 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.583 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546938929.583 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938929.583 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.583 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546938929.583 * [misc]taylor: Taking taylor expansion of k in k 1546938929.583 * [misc]backup-simplify: Simplify 0 into 0 1546938929.583 * [misc]backup-simplify: Simplify 1 into 1 1546938929.583 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546938929.583 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1546938929.583 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1546938929.583 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1546938929.583 * [misc]taylor: Taking taylor expansion of 2 in k 1546938929.583 * [misc]backup-simplify: Simplify 2 into 2 1546938929.583 * [misc]taylor: Taking taylor expansion of PI in k 1546938929.583 * [misc]backup-simplify: Simplify PI into PI 1546938929.584 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546938929.584 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546938929.584 * [misc]taylor: Taking taylor expansion of (log n) in k 1546938929.584 * [misc]taylor: Taking taylor expansion of n in k 1546938929.584 * [misc]backup-simplify: Simplify n into n 1546938929.584 * [misc]backup-simplify: Simplify (log n) into (log n) 1546938929.584 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546938929.584 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546938929.584 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546938929.584 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1546938929.585 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1546938929.585 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1546938929.586 * [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)))) 1546938929.586 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1546938929.586 * [misc]taylor: Taking taylor expansion of k in k 1546938929.586 * [misc]backup-simplify: Simplify 0 into 0 1546938929.586 * [misc]backup-simplify: Simplify 1 into 1 1546938929.586 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546938929.587 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546938929.587 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) into 0 1546938929.587 * [misc]backup-simplify: Simplify 0 into 0 1546938929.588 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546938929.588 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546938929.590 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546938929.590 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546938929.590 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546938929.590 * [misc]backup-simplify: Simplify (- 0) into 0 1546938929.590 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938929.591 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546938929.591 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1546938929.592 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546938929.593 * [misc]backup-simplify: Simplify (+ (* (sqrt k) 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0 1546938929.593 * [misc]taylor: Taking taylor expansion of 0 in k 1546938929.593 * [misc]backup-simplify: Simplify 0 into 0 1546938929.593 * [misc]backup-simplify: Simplify 0 into 0 1546938929.593 * [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)))))) 1546938929.594 * [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)))))) 1546938929.595 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938929.595 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546938929.599 * [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 1546938929.599 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546938929.599 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1546938929.599 * [misc]backup-simplify: Simplify (- 0) into 0 1546938929.599 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938929.600 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546938929.600 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1546938929.601 * [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 1546938929.602 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 1546938929.602 * [misc]backup-simplify: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0 1546938929.602 * [misc]taylor: Taking taylor expansion of 0 in k 1546938929.602 * [misc]backup-simplify: Simplify 0 into 0 1546938929.602 * [misc]backup-simplify: Simplify 0 into 0 1546938929.602 * [misc]backup-simplify: Simplify 0 into 0 1546938929.603 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1546938929.604 * [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)))))) 1546938929.605 * [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)))))) 1546938929.607 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938929.608 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546938929.616 * [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 1546938929.616 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546938929.617 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1546938929.617 * [misc]backup-simplify: Simplify (- 0) into 0 1546938929.617 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938929.618 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546938929.619 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1546938929.622 * [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 1546938929.622 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 1546938929.623 * [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 1546938929.624 * [misc]taylor: Taking taylor expansion of 0 in k 1546938929.624 * [misc]backup-simplify: Simplify 0 into 0 1546938929.624 * [misc]backup-simplify: Simplify 0 into 0 1546938929.624 * [misc]backup-simplify: Simplify 0 into 0 1546938929.624 * [misc]backup-simplify: Simplify 0 into 0 1546938929.625 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1546938929.626 * [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)))))) 1546938929.627 * [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)))))) 1546938929.629 * [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)))))))) 1546938929.630 * [misc]backup-simplify: Simplify (* (sqrt (/ (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k))))) (sqrt (/ (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))) 1546938929.630 * [misc]approximate: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (n k) around 0 1546938929.630 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 1546938929.630 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1546938929.630 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1546938929.630 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1546938929.630 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546938929.630 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546938929.630 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938929.630 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.630 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546938929.630 * [misc]taylor: Taking taylor expansion of k in k 1546938929.630 * [misc]backup-simplify: Simplify 0 into 0 1546938929.630 * [misc]backup-simplify: Simplify 1 into 1 1546938929.631 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546938929.631 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938929.631 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.631 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1546938929.631 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1546938929.631 * [misc]taylor: Taking taylor expansion of -2 in k 1546938929.631 * [misc]backup-simplify: Simplify -2 into -2 1546938929.631 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546938929.631 * [misc]taylor: Taking taylor expansion of PI in k 1546938929.631 * [misc]backup-simplify: Simplify PI into PI 1546938929.631 * [misc]taylor: Taking taylor expansion of n in k 1546938929.631 * [misc]backup-simplify: Simplify n into n 1546938929.631 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546938929.631 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1546938929.631 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1546938929.631 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546938929.631 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546938929.632 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1546938929.632 * [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))) 1546938929.632 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1546938929.632 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1546938929.632 * [misc]taylor: Taking taylor expansion of -1 in k 1546938929.632 * [misc]backup-simplify: Simplify -1 into -1 1546938929.632 * [misc]taylor: Taking taylor expansion of k in k 1546938929.632 * [misc]backup-simplify: Simplify 0 into 0 1546938929.632 * [misc]backup-simplify: Simplify 1 into 1 1546938929.632 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1546938929.632 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546938929.633 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1546938929.633 * [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)))) 1546938929.633 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 1546938929.633 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546938929.633 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546938929.633 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546938929.633 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546938929.633 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546938929.633 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938929.633 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.633 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938929.633 * [misc]taylor: Taking taylor expansion of k in n 1546938929.633 * [misc]backup-simplify: Simplify k into k 1546938929.634 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938929.634 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938929.634 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.634 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546938929.634 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546938929.634 * [misc]taylor: Taking taylor expansion of -2 in n 1546938929.634 * [misc]backup-simplify: Simplify -2 into -2 1546938929.634 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546938929.634 * [misc]taylor: Taking taylor expansion of PI in n 1546938929.634 * [misc]backup-simplify: Simplify PI into PI 1546938929.634 * [misc]taylor: Taking taylor expansion of n in n 1546938929.634 * [misc]backup-simplify: Simplify 0 into 0 1546938929.634 * [misc]backup-simplify: Simplify 1 into 1 1546938929.634 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546938929.634 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546938929.635 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546938929.635 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546938929.635 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546938929.636 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546938929.636 * [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))) 1546938929.637 * [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)))) 1546938929.637 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1546938929.637 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1546938929.637 * [misc]taylor: Taking taylor expansion of -1 in n 1546938929.637 * [misc]backup-simplify: Simplify -1 into -1 1546938929.637 * [misc]taylor: Taking taylor expansion of k in n 1546938929.637 * [misc]backup-simplify: Simplify k into k 1546938929.637 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1546938929.637 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1546938929.637 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1546938929.637 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1546938929.638 * [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))) 1546938929.638 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 1546938929.638 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546938929.638 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546938929.638 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546938929.638 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546938929.639 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546938929.639 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938929.639 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.639 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938929.639 * [misc]taylor: Taking taylor expansion of k in n 1546938929.639 * [misc]backup-simplify: Simplify k into k 1546938929.639 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938929.639 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938929.639 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.639 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546938929.639 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546938929.639 * [misc]taylor: Taking taylor expansion of -2 in n 1546938929.639 * [misc]backup-simplify: Simplify -2 into -2 1546938929.639 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546938929.639 * [misc]taylor: Taking taylor expansion of PI in n 1546938929.639 * [misc]backup-simplify: Simplify PI into PI 1546938929.639 * [misc]taylor: Taking taylor expansion of n in n 1546938929.639 * [misc]backup-simplify: Simplify 0 into 0 1546938929.639 * [misc]backup-simplify: Simplify 1 into 1 1546938929.639 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546938929.640 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546938929.640 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546938929.640 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546938929.640 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546938929.641 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546938929.641 * [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))) 1546938929.642 * [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)))) 1546938929.642 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1546938929.642 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1546938929.642 * [misc]taylor: Taking taylor expansion of -1 in n 1546938929.642 * [misc]backup-simplify: Simplify -1 into -1 1546938929.642 * [misc]taylor: Taking taylor expansion of k in n 1546938929.642 * [misc]backup-simplify: Simplify k into k 1546938929.642 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1546938929.642 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1546938929.642 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1546938929.643 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1546938929.643 * [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))) 1546938929.643 * [misc]taylor: Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) in k 1546938929.643 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1546938929.643 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1546938929.643 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546938929.643 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546938929.643 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938929.643 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.643 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546938929.643 * [misc]taylor: Taking taylor expansion of k in k 1546938929.643 * [misc]backup-simplify: Simplify 0 into 0 1546938929.643 * [misc]backup-simplify: Simplify 1 into 1 1546938929.644 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546938929.644 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938929.644 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938929.644 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1546938929.644 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1546938929.644 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1546938929.644 * [misc]taylor: Taking taylor expansion of -2 in k 1546938929.644 * [misc]backup-simplify: Simplify -2 into -2 1546938929.644 * [misc]taylor: Taking taylor expansion of PI in k 1546938929.644 * [misc]backup-simplify: Simplify PI into PI 1546938929.644 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546938929.644 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546938929.644 * [misc]taylor: Taking taylor expansion of (log n) in k 1546938929.644 * [misc]taylor: Taking taylor expansion of n in k 1546938929.644 * [misc]backup-simplify: Simplify n into n 1546938929.644 * [misc]backup-simplify: Simplify (log n) into (log n) 1546938929.644 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546938929.644 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546938929.645 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1546938929.645 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1546938929.645 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1546938929.646 * [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)))) 1546938929.646 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1546938929.646 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1546938929.646 * [misc]taylor: Taking taylor expansion of -1 in k 1546938929.646 * [misc]backup-simplify: Simplify -1 into -1 1546938929.646 * [misc]taylor: Taking taylor expansion of k in k 1546938929.646 * [misc]backup-simplify: Simplify 0 into 0 1546938929.646 * [misc]backup-simplify: Simplify 1 into 1 1546938929.646 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1546938929.646 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546938929.646 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1546938929.647 * [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))))) 1546938929.647 * [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))))) 1546938929.648 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546938929.648 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1546938929.650 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1546938929.650 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546938929.650 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546938929.650 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938929.651 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546938929.651 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1546938929.652 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546938929.653 * [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 1546938929.653 * [misc]taylor: Taking taylor expansion of 0 in k 1546938929.653 * [misc]backup-simplify: Simplify 0 into 0 1546938929.653 * [misc]backup-simplify: Simplify 0 into 0 1546938929.653 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1546938929.654 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1546938929.654 * [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)))))) 1546938929.655 * [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)))))) 1546938929.656 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938929.656 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1546938929.659 * [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 1546938929.659 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546938929.660 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1546938929.660 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938929.660 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546938929.661 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1546938929.662 * [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 1546938929.662 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546938929.662 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 1546938929.663 * [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 1546938929.663 * [misc]taylor: Taking taylor expansion of 0 in k 1546938929.663 * [misc]backup-simplify: Simplify 0 into 0 1546938929.663 * [misc]backup-simplify: Simplify 0 into 0 1546938929.663 * [misc]backup-simplify: Simplify 0 into 0 1546938929.663 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938929.664 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1546938929.665 * [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)))))) 1546938929.666 * [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)))))) 1546938929.667 * [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))))))))))) 1546938929.667 * * * * [misc]progress: [ 4 / 4 ] generating series at (2 2 1 1 1) 1546938929.667 * [misc]backup-simplify: Simplify (* PI (* n 2)) into (* 2 (* n PI)) 1546938929.667 * [misc]approximate: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1546938929.667 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546938929.667 * [misc]taylor: Taking taylor expansion of 2 in n 1546938929.667 * [misc]backup-simplify: Simplify 2 into 2 1546938929.667 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546938929.667 * [misc]taylor: Taking taylor expansion of n in n 1546938929.667 * [misc]backup-simplify: Simplify 0 into 0 1546938929.667 * [misc]backup-simplify: Simplify 1 into 1 1546938929.667 * [misc]taylor: Taking taylor expansion of PI in n 1546938929.667 * [misc]backup-simplify: Simplify PI into PI 1546938929.667 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546938929.667 * [misc]taylor: Taking taylor expansion of 2 in n 1546938929.667 * [misc]backup-simplify: Simplify 2 into 2 1546938929.667 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546938929.667 * [misc]taylor: Taking taylor expansion of n in n 1546938929.667 * [misc]backup-simplify: Simplify 0 into 0 1546938929.667 * [misc]backup-simplify: Simplify 1 into 1 1546938929.668 * [misc]taylor: Taking taylor expansion of PI in n 1546938929.668 * [misc]backup-simplify: Simplify PI into PI 1546938929.668 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546938929.668 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546938929.668 * [misc]backup-simplify: Simplify 0 into 0 1546938929.668 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546938929.669 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546938929.669 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546938929.670 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546938929.670 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1546938929.670 * [misc]backup-simplify: Simplify 0 into 0 1546938929.671 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1546938929.672 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1546938929.672 * [misc]backup-simplify: Simplify 0 into 0 1546938929.673 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1546938929.675 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1546938929.675 * [misc]backup-simplify: Simplify 0 into 0 1546938929.676 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1546938929.678 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1546938929.678 * [misc]backup-simplify: Simplify 0 into 0 1546938929.680 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1546938929.682 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1546938929.682 * [misc]backup-simplify: Simplify 0 into 0 1546938929.684 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1546938929.687 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1546938929.687 * [misc]backup-simplify: Simplify 0 into 0 1546938929.687 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1546938929.687 * [misc]backup-simplify: Simplify (* PI (* (/ 1 n) 2)) into (* 2 (/ PI n)) 1546938929.687 * [misc]approximate: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1546938929.687 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546938929.687 * [misc]taylor: Taking taylor expansion of 2 in n 1546938929.687 * [misc]backup-simplify: Simplify 2 into 2 1546938929.687 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546938929.687 * [misc]taylor: Taking taylor expansion of PI in n 1546938929.687 * [misc]backup-simplify: Simplify PI into PI 1546938929.687 * [misc]taylor: Taking taylor expansion of n in n 1546938929.687 * [misc]backup-simplify: Simplify 0 into 0 1546938929.687 * [misc]backup-simplify: Simplify 1 into 1 1546938929.687 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546938929.687 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546938929.687 * [misc]taylor: Taking taylor expansion of 2 in n 1546938929.687 * [misc]backup-simplify: Simplify 2 into 2 1546938929.687 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546938929.687 * [misc]taylor: Taking taylor expansion of PI in n 1546938929.687 * [misc]backup-simplify: Simplify PI into PI 1546938929.687 * [misc]taylor: Taking taylor expansion of n in n 1546938929.687 * [misc]backup-simplify: Simplify 0 into 0 1546938929.688 * [misc]backup-simplify: Simplify 1 into 1 1546938929.688 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546938929.688 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546938929.688 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546938929.689 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546938929.689 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546938929.689 * [misc]backup-simplify: Simplify 0 into 0 1546938929.690 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938929.691 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546938929.691 * [misc]backup-simplify: Simplify 0 into 0 1546938929.692 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938929.693 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546938929.694 * [misc]backup-simplify: Simplify 0 into 0 1546938929.695 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938929.698 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1546938929.698 * [misc]backup-simplify: Simplify 0 into 0 1546938929.701 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938929.704 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1546938929.704 * [misc]backup-simplify: Simplify 0 into 0 1546938929.707 * [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 1546938929.711 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1546938929.711 * [misc]backup-simplify: Simplify 0 into 0 1546938929.711 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 1546938929.712 * [misc]backup-simplify: Simplify (* PI (* (/ 1 (- n)) 2)) into (* -2 (/ PI n)) 1546938929.712 * [misc]approximate: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1546938929.712 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546938929.712 * [misc]taylor: Taking taylor expansion of -2 in n 1546938929.712 * [misc]backup-simplify: Simplify -2 into -2 1546938929.712 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546938929.712 * [misc]taylor: Taking taylor expansion of PI in n 1546938929.712 * [misc]backup-simplify: Simplify PI into PI 1546938929.712 * [misc]taylor: Taking taylor expansion of n in n 1546938929.712 * [misc]backup-simplify: Simplify 0 into 0 1546938929.712 * [misc]backup-simplify: Simplify 1 into 1 1546938929.712 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546938929.712 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546938929.712 * [misc]taylor: Taking taylor expansion of -2 in n 1546938929.712 * [misc]backup-simplify: Simplify -2 into -2 1546938929.712 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546938929.712 * [misc]taylor: Taking taylor expansion of PI in n 1546938929.712 * [misc]backup-simplify: Simplify PI into PI 1546938929.713 * [misc]taylor: Taking taylor expansion of n in n 1546938929.713 * [misc]backup-simplify: Simplify 0 into 0 1546938929.713 * [misc]backup-simplify: Simplify 1 into 1 1546938929.713 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546938929.713 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546938929.714 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546938929.715 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546938929.715 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1546938929.715 * [misc]backup-simplify: Simplify 0 into 0 1546938929.717 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938929.718 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1546938929.718 * [misc]backup-simplify: Simplify 0 into 0 1546938929.720 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938929.721 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546938929.721 * [misc]backup-simplify: Simplify 0 into 0 1546938929.723 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938929.725 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1546938929.725 * [misc]backup-simplify: Simplify 0 into 0 1546938929.727 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938929.729 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1546938929.729 * [misc]backup-simplify: Simplify 0 into 0 1546938929.731 * [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 1546938929.733 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1546938929.733 * [misc]backup-simplify: Simplify 0 into 0 1546938929.733 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 1546938929.733 * * * [misc]progress: simplifying candidates 1546938929.733 * * * * [misc]progress: [ 1 / 126 ] simplifiying candidate # 1546938929.733 * [enter]simplify: Simplifying (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) 1546938929.733 * * [misc]simplify: iters left: 6 (11 enodes) 1546938929.735 * * [misc]simplify: iters left: 5 (21 enodes) 1546938929.738 * * [misc]simplify: iters left: 4 (47 enodes) 1546938929.747 * * [misc]simplify: iters left: 3 (109 enodes) 1546938929.782 * * [misc]simplify: iters left: 2 (300 enodes) 1546938929.937 * [exit]simplify: Simplified to (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) 1546938929.937 * [misc]simplify: Simplified (2 2 1 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)))) (sqrt k))))) 1546938929.937 * * * * [misc]progress: [ 2 / 126 ] simplifiying candidate # 1546938929.937 * * * * [misc]progress: [ 3 / 126 ] simplifiying candidate # 1546938929.937 * [enter]simplify: Simplifying (* PI (* n 2)) 1546938929.937 * * [misc]simplify: iters left: 4 (5 enodes) 1546938929.938 * * [misc]simplify: iters left: 3 (9 enodes) 1546938929.939 * * [misc]simplify: iters left: 2 (15 enodes) 1546938929.941 * * [misc]simplify: iters left: 1 (17 enodes) 1546938929.943 * [exit]simplify: Simplified to (* (* 2 n) PI) 1546938929.943 * [misc]simplify: Simplified (2 2 1 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)))) (sqrt k))))) 1546938929.943 * * * * [misc]progress: [ 4 / 126 ] simplifiying candidate # 1546938929.943 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (/ k 2)) 1546938929.943 * * [misc]simplify: iters left: 5 (8 enodes) 1546938929.944 * * [misc]simplify: iters left: 4 (12 enodes) 1546938929.946 * * [misc]simplify: iters left: 3 (18 enodes) 1546938929.949 * * [misc]simplify: iters left: 2 (20 enodes) 1546938929.954 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ k 2)) 1546938929.954 * [misc]simplify: Simplified (2 2 1 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))) (sqrt k))))) 1546938929.954 * * * * [misc]progress: [ 5 / 126 ] simplifiying candidate # 1546938929.954 * [enter]simplify: Simplifying (cbrt (- 1/2 (/ k 2))) 1546938929.954 * * [misc]simplify: iters left: 5 (6 enodes) 1546938929.956 * * [misc]simplify: iters left: 4 (8 enodes) 1546938929.958 * * [misc]simplify: iters left: 3 (11 enodes) 1546938929.961 * [exit]simplify: Simplified to (cbrt (- 1/2 (/ k 2))) 1546938929.961 * [misc]simplify: Simplified (2 2 1 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)))) (sqrt k))))) 1546938929.961 * * * * [misc]progress: [ 6 / 126 ] simplifiying candidate # 1546938929.962 * [enter]simplify: Simplifying (sqrt (- 1/2 (/ k 2))) 1546938929.962 * * [misc]simplify: iters left: 5 (6 enodes) 1546938929.964 * * [misc]simplify: iters left: 4 (8 enodes) 1546938929.966 * * [misc]simplify: iters left: 3 (11 enodes) 1546938929.969 * [exit]simplify: Simplified to (sqrt (- 1/2 (/ k 2))) 1546938929.969 * [misc]simplify: Simplified (2 2 1 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)))) (sqrt k))))) 1546938929.969 * * * * [misc]progress: [ 7 / 126 ] simplifiying candidate # 1546938929.969 * [enter]simplify: Simplifying (- 1/2 (/ k 2)) 1546938929.969 * * [misc]simplify: iters left: 4 (5 enodes) 1546938929.971 * * [misc]simplify: iters left: 3 (7 enodes) 1546938929.973 * * [misc]simplify: iters left: 2 (10 enodes) 1546938929.975 * [exit]simplify: Simplified to (- 1/2 (/ k 2)) 1546938929.975 * [misc]simplify: Simplified (2 2 1 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))) (sqrt k))))) 1546938929.975 * * * * [misc]progress: [ 8 / 126 ] simplifiying candidate # 1546938929.976 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1546938929.976 * * [misc]simplify: iters left: 5 (9 enodes) 1546938929.977 * * [misc]simplify: iters left: 4 (15 enodes) 1546938929.979 * * [misc]simplify: iters left: 3 (21 enodes) 1546938929.982 * * [misc]simplify: iters left: 2 (22 enodes) 1546938929.984 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1546938929.985 * [misc]simplify: Simplified (2 2 1 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)))) (sqrt k))))) 1546938929.985 * * * * [misc]progress: [ 9 / 126 ] simplifiying candidate # 1546938929.985 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1546938929.985 * * [misc]simplify: iters left: 5 (9 enodes) 1546938929.986 * * [misc]simplify: iters left: 4 (15 enodes) 1546938929.988 * * [misc]simplify: iters left: 3 (21 enodes) 1546938929.991 * * [misc]simplify: iters left: 2 (22 enodes) 1546938929.993 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1546938929.993 * [misc]simplify: Simplified (2 2 1 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)))) (sqrt k))))) 1546938929.994 * * * * [misc]progress: [ 10 / 126 ] simplifiying candidate # 1546938929.994 * [enter]simplify: Simplifying (pow PI (- 1/2 (/ k 2))) 1546938929.994 * * [misc]simplify: iters left: 5 (7 enodes) 1546938929.995 * * [misc]simplify: iters left: 4 (9 enodes) 1546938929.996 * * [misc]simplify: iters left: 3 (12 enodes) 1546938929.998 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1546938929.998 * [misc]simplify: Simplified (2 2 1 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)))) (sqrt k))))) 1546938929.998 * * * * [misc]progress: [ 11 / 126 ] simplifiying candidate # 1546938929.998 * * * * [misc]progress: [ 12 / 126 ] simplifiying candidate # 1546938929.998 * * * * [misc]progress: [ 13 / 126 ] simplifiying candidate # 1546938929.998 * * * * [misc]progress: [ 14 / 126 ] simplifiying candidate # 1546938929.998 * * * * [misc]progress: [ 15 / 126 ] simplifiying candidate # 1546938929.998 * * * * [misc]progress: [ 16 / 126 ] simplifiying candidate # 1546938929.998 * * * * [misc]progress: [ 17 / 126 ] simplifiying candidate # 1546938929.998 * * * * [misc]progress: [ 18 / 126 ] simplifiying candidate # 1546938929.998 * [enter]simplify: Simplifying (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) 1546938929.998 * * [misc]simplify: iters left: 6 (11 enodes) 1546938930.000 * * [misc]simplify: iters left: 5 (21 enodes) 1546938930.004 * * [misc]simplify: iters left: 4 (47 enodes) 1546938930.021 * * [misc]simplify: iters left: 3 (109 enodes) 1546938930.065 * * [misc]simplify: iters left: 2 (300 enodes) 1546938930.239 * [exit]simplify: Simplified to (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) 1546938930.239 * [misc]simplify: Simplified (2 1 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))) (sqrt k))))) 1546938930.239 * * * * [misc]progress: [ 19 / 126 ] simplifiying candidate # 1546938930.239 * * * * [misc]progress: [ 20 / 126 ] simplifiying candidate # 1546938930.240 * [enter]simplify: Simplifying (* PI (* n 2)) 1546938930.240 * * [misc]simplify: iters left: 4 (5 enodes) 1546938930.241 * * [misc]simplify: iters left: 3 (9 enodes) 1546938930.244 * * [misc]simplify: iters left: 2 (15 enodes) 1546938930.248 * * [misc]simplify: iters left: 1 (17 enodes) 1546938930.252 * [exit]simplify: Simplified to (* (* 2 n) PI) 1546938930.252 * [misc]simplify: Simplified (2 1 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))) (sqrt k))))) 1546938930.252 * * * * [misc]progress: [ 21 / 126 ] simplifiying candidate # 1546938930.252 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (/ k 2)) 1546938930.252 * * [misc]simplify: iters left: 5 (8 enodes) 1546938930.254 * * [misc]simplify: iters left: 4 (12 enodes) 1546938930.258 * * [misc]simplify: iters left: 3 (18 enodes) 1546938930.262 * * [misc]simplify: iters left: 2 (20 enodes) 1546938930.267 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ k 2)) 1546938930.267 * [misc]simplify: Simplified (2 1 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))) (sqrt k))))) 1546938930.268 * * * * [misc]progress: [ 22 / 126 ] simplifiying candidate # 1546938930.268 * [enter]simplify: Simplifying (cbrt (- 1/2 (/ k 2))) 1546938930.268 * * [misc]simplify: iters left: 5 (6 enodes) 1546938930.270 * * [misc]simplify: iters left: 4 (8 enodes) 1546938930.272 * * [misc]simplify: iters left: 3 (11 enodes) 1546938930.275 * [exit]simplify: Simplified to (cbrt (- 1/2 (/ k 2))) 1546938930.275 * [misc]simplify: Simplified (2 1 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))) (sqrt k))))) 1546938930.276 * * * * [misc]progress: [ 23 / 126 ] simplifiying candidate # 1546938930.276 * [enter]simplify: Simplifying (sqrt (- 1/2 (/ k 2))) 1546938930.276 * * [misc]simplify: iters left: 5 (6 enodes) 1546938930.278 * * [misc]simplify: iters left: 4 (8 enodes) 1546938930.280 * * [misc]simplify: iters left: 3 (11 enodes) 1546938930.283 * [exit]simplify: Simplified to (sqrt (- 1/2 (/ k 2))) 1546938930.283 * [misc]simplify: Simplified (2 1 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))) (sqrt k))))) 1546938930.283 * * * * [misc]progress: [ 24 / 126 ] simplifiying candidate # 1546938930.283 * [enter]simplify: Simplifying (- 1/2 (/ k 2)) 1546938930.283 * * [misc]simplify: iters left: 4 (5 enodes) 1546938930.285 * * [misc]simplify: iters left: 3 (7 enodes) 1546938930.287 * * [misc]simplify: iters left: 2 (10 enodes) 1546938930.293 * [exit]simplify: Simplified to (- 1/2 (/ k 2)) 1546938930.293 * [misc]simplify: Simplified (2 1 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))) (sqrt k))))) 1546938930.293 * * * * [misc]progress: [ 25 / 126 ] simplifiying candidate # 1546938930.293 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1546938930.293 * * [misc]simplify: iters left: 5 (9 enodes) 1546938930.296 * * [misc]simplify: iters left: 4 (15 enodes) 1546938930.301 * * [misc]simplify: iters left: 3 (21 enodes) 1546938930.306 * * [misc]simplify: iters left: 2 (22 enodes) 1546938930.311 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1546938930.312 * [misc]simplify: Simplified (2 1 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))) (sqrt k))))) 1546938930.312 * * * * [misc]progress: [ 26 / 126 ] simplifiying candidate # 1546938930.312 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1546938930.312 * * [misc]simplify: iters left: 5 (9 enodes) 1546938930.315 * * [misc]simplify: iters left: 4 (15 enodes) 1546938930.319 * * [misc]simplify: iters left: 3 (21 enodes) 1546938930.326 * * [misc]simplify: iters left: 2 (22 enodes) 1546938930.331 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1546938930.332 * [misc]simplify: Simplified (2 1 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))) (sqrt k))))) 1546938930.332 * * * * [misc]progress: [ 27 / 126 ] simplifiying candidate # 1546938930.332 * [enter]simplify: Simplifying (pow PI (- 1/2 (/ k 2))) 1546938930.332 * * [misc]simplify: iters left: 5 (7 enodes) 1546938930.334 * * [misc]simplify: iters left: 4 (9 enodes) 1546938930.337 * * [misc]simplify: iters left: 3 (12 enodes) 1546938930.340 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1546938930.341 * [misc]simplify: Simplified (2 1 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))) (sqrt k))))) 1546938930.341 * * * * [misc]progress: [ 28 / 126 ] simplifiying candidate # 1546938930.341 * * * * [misc]progress: [ 29 / 126 ] simplifiying candidate # 1546938930.341 * * * * [misc]progress: [ 30 / 126 ] simplifiying candidate # 1546938930.341 * * * * [misc]progress: [ 31 / 126 ] simplifiying candidate # 1546938930.341 * * * * [misc]progress: [ 32 / 126 ] simplifiying candidate # 1546938930.341 * * * * [misc]progress: [ 33 / 126 ] simplifiying candidate # 1546938930.341 * * * * [misc]progress: [ 34 / 126 ] simplifiying candidate # 1546938930.341 * * * * [misc]progress: [ 35 / 126 ] simplifiying candidate # 1546938930.341 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)) 1546938930.342 * * [misc]simplify: iters left: 6 (12 enodes) 1546938930.346 * * [misc]simplify: iters left: 5 (18 enodes) 1546938930.351 * * [misc]simplify: iters left: 4 (27 enodes) 1546938930.358 * * [misc]simplify: iters left: 3 (29 enodes) 1546938930.365 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k)) 1546938930.366 * [misc]simplify: Simplified (2 1) to (λ (k n) (pow (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k)) (+ 1/2 1/2))) 1546938930.366 * [enter]simplify: Simplifying (+ 1/2 1/2) 1546938930.366 * * [misc]simplify: iters left: 2 (2 enodes) 1546938930.367 * * [misc]simplify: iters left: 1 (3 enodes) 1546938930.368 * [exit]simplify: Simplified to 1 1546938930.368 * [misc]simplify: Simplified (2 2) to (λ (k n) (pow (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)) 1)) 1546938930.368 * * * * [misc]progress: [ 36 / 126 ] simplifiying candidate # 1546938930.368 * [enter]simplify: Simplifying (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) 1546938930.368 * * [misc]simplify: iters left: 6 (13 enodes) 1546938930.372 * * [misc]simplify: iters left: 5 (19 enodes) 1546938930.377 * * [misc]simplify: iters left: 4 (28 enodes) 1546938930.380 * * [misc]simplify: iters left: 3 (30 enodes) 1546938930.383 * [exit]simplify: Simplified to (sqrt (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k))) 1546938930.384 * [misc]simplify: Simplified (2 1) to (λ (k n) (pow (sqrt (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k))) (+ 1 1))) 1546938930.384 * [enter]simplify: Simplifying (+ 1 1) 1546938930.384 * * [misc]simplify: iters left: 2 (2 enodes) 1546938930.384 * * [misc]simplify: iters left: 1 (5 enodes) 1546938930.385 * [exit]simplify: Simplified to 2 1546938930.385 * [misc]simplify: Simplified (2 2) to (λ (k n) (pow (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) 2)) 1546938930.385 * * * * [misc]progress: [ 37 / 126 ] simplifiying candidate # 1546938930.385 * [enter]simplify: Simplifying (* (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) 1546938930.385 * * [misc]simplify: iters left: 6 (13 enodes) 1546938930.387 * * [misc]simplify: iters left: 5 (23 enodes) 1546938930.390 * * [misc]simplify: iters left: 4 (38 enodes) 1546938930.395 * * [misc]simplify: iters left: 3 (46 enodes) 1546938930.401 * * [misc]simplify: iters left: 2 (49 enodes) 1546938930.406 * [exit]simplify: Simplified to (/ (* (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) k) 1546938930.406 * [misc]simplify: Simplified (2 1) to (λ (k n) (pow (/ (* (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) k) 1/2)) 1546938930.406 * * * * [misc]progress: [ 38 / 126 ] simplifiying candidate # 1546938930.406 * [enter]simplify: Simplifying (* (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))) 1546938930.406 * * [misc]simplify: iters left: 6 (14 enodes) 1546938930.409 * * [misc]simplify: iters left: 5 (20 enodes) 1546938930.416 * * [misc]simplify: iters left: 4 (30 enodes) 1546938930.424 * * [misc]simplify: iters left: 3 (31 enodes) 1546938930.429 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k)) 1546938930.429 * [misc]simplify: Simplified (2 1) to (λ (k n) (pow (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k)) 1)) 1546938930.429 * * * * [misc]progress: [ 39 / 126 ] simplifiying candidate # 1546938930.429 * * * * [misc]progress: [ 40 / 126 ] simplifiying candidate # 1546938930.430 * [enter]simplify: Simplifying (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) 1546938930.430 * * [misc]simplify: iters left: 6 (13 enodes) 1546938930.432 * * [misc]simplify: iters left: 5 (19 enodes) 1546938930.434 * * [misc]simplify: iters left: 4 (28 enodes) 1546938930.438 * * [misc]simplify: iters left: 3 (30 enodes) 1546938930.441 * [exit]simplify: Simplified to (sqrt (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k))) 1546938930.442 * [misc]simplify: Simplified (2 1) to (λ (k n) (pow (sqrt (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k))) (+ 1 1))) 1546938930.442 * * * * [misc]progress: [ 41 / 126 ] simplifiying candidate # 1546938930.442 * * * * [misc]progress: [ 42 / 126 ] simplifiying candidate # 1546938930.442 * [enter]simplify: Simplifying (+ (log (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))) (log (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))))) 1546938930.442 * * [misc]simplify: iters left: 6 (15 enodes) 1546938930.444 * * [misc]simplify: iters left: 5 (21 enodes) 1546938930.447 * * [misc]simplify: iters left: 4 (30 enodes) 1546938930.451 * * [misc]simplify: iters left: 3 (31 enodes) 1546938930.455 * [exit]simplify: Simplified to (+ (log (sqrt (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k)))) (log (sqrt (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k))))) 1546938930.455 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (+ (log (sqrt (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k)))) (log (sqrt (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k))))))) 1546938930.455 * * * * [misc]progress: [ 43 / 126 ] simplifiying candidate # 1546938930.455 * * * * [misc]progress: [ 44 / 126 ] simplifiying candidate # 1546938930.455 * * * * [misc]progress: [ 45 / 126 ] simplifiying candidate # 1546938930.455 * [enter]simplify: Simplifying (* (* (* (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))) (* (* (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))))) 1546938930.455 * * [misc]simplify: iters left: 6 (16 enodes) 1546938930.458 * * [misc]simplify: iters left: 5 (27 enodes) 1546938930.464 * * [misc]simplify: iters left: 4 (53 enodes) 1546938930.473 * * [misc]simplify: iters left: 3 (103 enodes) 1546938930.491 * * [misc]simplify: iters left: 2 (162 enodes) 1546938930.542 * * [misc]simplify: iters left: 1 (265 enodes) 1546938930.648 * [exit]simplify: Simplified to (/ (* (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (/ (* (sqrt k) k) (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) 1546938930.648 * [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)))) (/ (* (sqrt k) k) (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))))) 1546938930.648 * * * * [misc]progress: [ 46 / 126 ] simplifiying candidate # 1546938930.648 * * * * [misc]progress: [ 47 / 126 ] simplifiying candidate # 1546938930.648 * * * * [misc]progress: [ 48 / 126 ] simplifiying candidate # 1546938930.649 * [enter]simplify: Simplifying (* (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) 1546938930.649 * * [misc]simplify: iters left: 6 (13 enodes) 1546938930.651 * * [misc]simplify: iters left: 5 (23 enodes) 1546938930.654 * * [misc]simplify: iters left: 4 (38 enodes) 1546938930.659 * * [misc]simplify: iters left: 3 (46 enodes) 1546938930.664 * * [misc]simplify: iters left: 2 (49 enodes) 1546938930.670 * [exit]simplify: Simplified to (/ (* (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) k) 1546938930.670 * [misc]simplify: Simplified (2 1) to (λ (k n) (sqrt (/ (* (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) k))) 1546938930.670 * * * * [misc]progress: [ 49 / 126 ] simplifiying candidate # 1546938930.670 * * * * [misc]progress: [ 50 / 126 ] simplifiying candidate # 1546938930.670 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- 1/2 (/ k 2))) 1546938930.670 * * [misc]simplify: iters left: 5 (10 enodes) 1546938930.672 * * [misc]simplify: iters left: 4 (16 enodes) 1546938930.676 * * [misc]simplify: iters left: 3 (25 enodes) 1546938930.679 * * [misc]simplify: iters left: 2 (26 enodes) 1546938930.682 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) 1546938930.682 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k))) 1546938930.682 * [enter]simplify: Simplifying (sqrt k) 1546938930.682 * * [misc]simplify: iters left: 1 (2 enodes) 1546938930.683 * [exit]simplify: Simplified to (sqrt k) 1546938930.683 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) 1546938930.683 * * * * [misc]progress: [ 51 / 126 ] simplifiying candidate # 1546938930.683 * [enter]simplify: Simplifying (* (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546938930.683 * * [misc]simplify: iters left: 6 (12 enodes) 1546938930.685 * * [misc]simplify: iters left: 5 (18 enodes) 1546938930.688 * * [misc]simplify: iters left: 4 (28 enodes) 1546938930.691 * * [misc]simplify: iters left: 3 (30 enodes) 1546938930.698 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) 1546938930.699 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (* (sqrt (sqrt k)) (sqrt (sqrt k))))) 1546938930.699 * [enter]simplify: Simplifying (* (sqrt (sqrt k)) (sqrt (sqrt k))) 1546938930.699 * * [misc]simplify: iters left: 4 (4 enodes) 1546938930.701 * [exit]simplify: Simplified to (sqrt k) 1546938930.701 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k))) 1546938930.701 * * * * [misc]progress: [ 52 / 126 ] simplifiying candidate # 1546938930.701 * * * * [misc]progress: [ 53 / 126 ] simplifiying candidate # 1546938930.701 * [enter]simplify: Simplifying (cbrt (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))) 1546938930.701 * * [misc]simplify: iters left: 6 (14 enodes) 1546938930.706 * * [misc]simplify: iters left: 5 (20 enodes) 1546938930.712 * * [misc]simplify: iters left: 4 (29 enodes) 1546938930.719 * * [misc]simplify: iters left: 3 (30 enodes) 1546938930.723 * [exit]simplify: Simplified to (cbrt (sqrt (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k)))) 1546938930.723 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) (* (cbrt (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))) (cbrt (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))))) (cbrt (sqrt (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k)))))) 1546938930.723 * * * * [misc]progress: [ 54 / 126 ] simplifiying candidate # 1546938930.723 * [enter]simplify: Simplifying (sqrt (cbrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))) 1546938930.724 * * [misc]simplify: iters left: 6 (14 enodes) 1546938930.726 * * [misc]simplify: iters left: 5 (20 enodes) 1546938930.728 * * [misc]simplify: iters left: 4 (29 enodes) 1546938930.732 * * [misc]simplify: iters left: 3 (30 enodes) 1546938930.736 * [exit]simplify: Simplified to (sqrt (cbrt (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k)))) 1546938930.736 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (cbrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))))) (sqrt (cbrt (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k)))))) 1546938930.736 * * * * [misc]progress: [ 55 / 126 ] simplifiying candidate # 1546938930.736 * [enter]simplify: Simplifying (sqrt (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))) 1546938930.736 * * [misc]simplify: iters left: 6 (14 enodes) 1546938930.738 * * [misc]simplify: iters left: 5 (20 enodes) 1546938930.741 * * [misc]simplify: iters left: 4 (29 enodes) 1546938930.745 * * [misc]simplify: iters left: 3 (30 enodes) 1546938930.748 * [exit]simplify: Simplified to (sqrt (sqrt (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k)))) 1546938930.748 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))))) (sqrt (sqrt (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k)))))) 1546938930.748 * * * * [misc]progress: [ 56 / 126 ] simplifiying candidate # 1546938930.749 * [enter]simplify: Simplifying (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (sqrt k)))) 1546938930.749 * * [misc]simplify: iters left: 6 (13 enodes) 1546938930.750 * * [misc]simplify: iters left: 5 (19 enodes) 1546938930.753 * * [misc]simplify: iters left: 4 (25 enodes) 1546938930.757 * * [misc]simplify: iters left: 3 (26 enodes) 1546938930.764 * [exit]simplify: Simplified to (sqrt (/ (pow (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt k)))) 1546938930.764 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (* n 2)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (sqrt (/ (pow (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt k)))))) 1546938930.764 * * * * [misc]progress: [ 57 / 126 ] simplifiying candidate # 1546938930.764 * [enter]simplify: Simplifying (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k)))) 1546938930.764 * * [misc]simplify: iters left: 6 (13 enodes) 1546938930.768 * * [misc]simplify: iters left: 5 (19 enodes) 1546938930.774 * * [misc]simplify: iters left: 4 (25 enodes) 1546938930.780 * * [misc]simplify: iters left: 3 (26 enodes) 1546938930.787 * [exit]simplify: Simplified to (sqrt (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k)))) 1546938930.787 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (* n 2)) 1/2) (sqrt (sqrt k))))) (sqrt (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k)))))) 1546938930.787 * * * * [misc]progress: [ 58 / 126 ] simplifiying candidate # 1546938930.787 * [enter]simplify: Simplifying (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) 1546938930.787 * * [misc]simplify: iters left: 6 (12 enodes) 1546938930.791 * * [misc]simplify: iters left: 5 (18 enodes) 1546938930.796 * * [misc]simplify: iters left: 4 (24 enodes) 1546938930.802 * * [misc]simplify: iters left: 3 (25 enodes) 1546938930.809 * [exit]simplify: Simplified to (sqrt (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k))) 1546938930.809 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (* n 2)) 1/2) 1))) (sqrt (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k))))) 1546938930.809 * * * * [misc]progress: [ 59 / 126 ] simplifiying candidate # 1546938930.809 * [enter]simplify: Simplifying (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (sqrt k)))) 1546938930.810 * * [misc]simplify: iters left: 6 (13 enodes) 1546938930.814 * * [misc]simplify: iters left: 5 (19 enodes) 1546938930.820 * * [misc]simplify: iters left: 4 (25 enodes) 1546938930.827 * * [misc]simplify: iters left: 3 (26 enodes) 1546938930.833 * [exit]simplify: Simplified to (sqrt (/ (pow (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt k)))) 1546938930.833 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (* n 2)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (sqrt (/ (pow (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt k)))))) 1546938930.833 * * * * [misc]progress: [ 60 / 126 ] simplifiying candidate # 1546938930.834 * [enter]simplify: Simplifying (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k)))) 1546938930.834 * * [misc]simplify: iters left: 6 (13 enodes) 1546938930.838 * * [misc]simplify: iters left: 5 (19 enodes) 1546938930.843 * * [misc]simplify: iters left: 4 (25 enodes) 1546938930.850 * * [misc]simplify: iters left: 3 (26 enodes) 1546938930.856 * [exit]simplify: Simplified to (sqrt (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k)))) 1546938930.856 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (* n 2)) 1/2) (sqrt (sqrt k))))) (sqrt (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k)))))) 1546938930.857 * * * * [misc]progress: [ 61 / 126 ] simplifiying candidate # 1546938930.857 * [enter]simplify: Simplifying (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) 1546938930.857 * * [misc]simplify: iters left: 6 (12 enodes) 1546938930.861 * * [misc]simplify: iters left: 5 (18 enodes) 1546938930.866 * * [misc]simplify: iters left: 4 (24 enodes) 1546938930.873 * * [misc]simplify: iters left: 3 (25 enodes) 1546938930.879 * [exit]simplify: Simplified to (sqrt (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k))) 1546938930.879 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (* n 2)) 1/2) 1))) (sqrt (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k))))) 1546938930.879 * * * * [misc]progress: [ 62 / 126 ] simplifiying candidate # 1546938930.880 * [enter]simplify: Simplifying (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k)))) 1546938930.880 * * [misc]simplify: iters left: 6 (12 enodes) 1546938930.883 * * [misc]simplify: iters left: 5 (15 enodes) 1546938930.887 * * [misc]simplify: iters left: 4 (18 enodes) 1546938930.892 * [exit]simplify: Simplified to (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k)))) 1546938930.893 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow PI (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k)))))) 1546938930.893 * * * * [misc]progress: [ 63 / 126 ] simplifiying candidate # 1546938930.893 * [enter]simplify: Simplifying (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k)))) 1546938930.893 * * [misc]simplify: iters left: 6 (12 enodes) 1546938930.897 * * [misc]simplify: iters left: 5 (15 enodes) 1546938930.901 * * [misc]simplify: iters left: 4 (18 enodes) 1546938930.906 * [exit]simplify: Simplified to (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k)))) 1546938930.906 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))))) (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))) 1546938930.906 * * * * [misc]progress: [ 64 / 126 ] simplifiying candidate # 1546938930.906 * [enter]simplify: Simplifying (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))) 1546938930.906 * * [misc]simplify: iters left: 6 (11 enodes) 1546938930.909 * * [misc]simplify: iters left: 5 (14 enodes) 1546938930.913 * * [misc]simplify: iters left: 4 (17 enodes) 1546938930.918 * [exit]simplify: Simplified to (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))) 1546938930.918 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow PI (- 1/2 (/ k 2))) 1))) (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))))) 1546938930.918 * * * * [misc]progress: [ 65 / 126 ] simplifiying candidate # 1546938930.918 * [enter]simplify: Simplifying (sqrt (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))) 1546938930.918 * * [misc]simplify: iters left: 6 (15 enodes) 1546938930.923 * * [misc]simplify: iters left: 5 (21 enodes) 1546938930.930 * * [misc]simplify: iters left: 4 (30 enodes) 1546938930.938 * * [misc]simplify: iters left: 3 (31 enodes) 1546938930.946 * [exit]simplify: Simplified to (sqrt (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))) 1546938930.947 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (sqrt (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))) 1546938930.947 * * * * [misc]progress: [ 66 / 126 ] simplifiying candidate # 1546938930.947 * [enter]simplify: Simplifying (sqrt (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) 1546938930.947 * * [misc]simplify: iters left: 6 (15 enodes) 1546938930.952 * * [misc]simplify: iters left: 5 (21 enodes) 1546938930.958 * * [misc]simplify: iters left: 4 (30 enodes) 1546938930.966 * * [misc]simplify: iters left: 3 (31 enodes) 1546938930.974 * [exit]simplify: Simplified to (sqrt (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) 1546938930.975 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt (sqrt k))))) (sqrt (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))) 1546938930.975 * * * * [misc]progress: [ 67 / 126 ] simplifiying candidate # 1546938930.975 * [enter]simplify: Simplifying (sqrt (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt k))) 1546938930.975 * * [misc]simplify: iters left: 6 (14 enodes) 1546938930.980 * * [misc]simplify: iters left: 5 (20 enodes) 1546938930.984 * * [misc]simplify: iters left: 4 (29 enodes) 1546938930.988 * * [misc]simplify: iters left: 3 (30 enodes) 1546938930.991 * [exit]simplify: Simplified to (sqrt (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt k))) 1546938930.991 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1))) (sqrt (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt k))))) 1546938930.991 * * * * [misc]progress: [ 68 / 126 ] simplifiying candidate # 1546938930.992 * [enter]simplify: Simplifying (sqrt (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))) 1546938930.992 * * [misc]simplify: iters left: 6 (15 enodes) 1546938930.994 * * [misc]simplify: iters left: 5 (21 enodes) 1546938930.997 * * [misc]simplify: iters left: 4 (30 enodes) 1546938931.000 * * [misc]simplify: iters left: 3 (31 enodes) 1546938931.004 * [exit]simplify: Simplified to (sqrt (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))) 1546938931.004 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (sqrt (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))) 1546938931.004 * * * * [misc]progress: [ 69 / 126 ] simplifiying candidate # 1546938931.004 * [enter]simplify: Simplifying (sqrt (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) 1546938931.004 * * [misc]simplify: iters left: 6 (15 enodes) 1546938931.006 * * [misc]simplify: iters left: 5 (21 enodes) 1546938931.009 * * [misc]simplify: iters left: 4 (30 enodes) 1546938931.013 * * [misc]simplify: iters left: 3 (31 enodes) 1546938931.018 * [exit]simplify: Simplified to (sqrt (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) 1546938931.018 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) (sqrt (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))) 1546938931.018 * * * * [misc]progress: [ 70 / 126 ] simplifiying candidate # 1546938931.019 * [enter]simplify: Simplifying (sqrt (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt k))) 1546938931.019 * * [misc]simplify: iters left: 6 (14 enodes) 1546938931.021 * * [misc]simplify: iters left: 5 (20 enodes) 1546938931.024 * * [misc]simplify: iters left: 4 (29 enodes) 1546938931.028 * * [misc]simplify: iters left: 3 (30 enodes) 1546938931.032 * [exit]simplify: Simplified to (sqrt (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt k))) 1546938931.032 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1))) (sqrt (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt k))))) 1546938931.032 * * * * [misc]progress: [ 71 / 126 ] simplifiying candidate # 1546938931.032 * [enter]simplify: Simplifying (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (cbrt (sqrt k)))) 1546938931.032 * * [misc]simplify: iters left: 6 (14 enodes) 1546938931.034 * * [misc]simplify: iters left: 5 (20 enodes) 1546938931.037 * * [misc]simplify: iters left: 4 (29 enodes) 1546938931.041 * * [misc]simplify: iters left: 3 (30 enodes) 1546938931.044 * [exit]simplify: Simplified to (sqrt (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (cbrt (sqrt k)))) 1546938931.044 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (sqrt (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (cbrt (sqrt k)))))) 1546938931.044 * * * * [misc]progress: [ 72 / 126 ] simplifiying candidate # 1546938931.044 * [enter]simplify: Simplifying (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))) 1546938931.045 * * [misc]simplify: iters left: 6 (14 enodes) 1546938931.046 * * [misc]simplify: iters left: 5 (20 enodes) 1546938931.049 * * [misc]simplify: iters left: 4 (29 enodes) 1546938931.054 * * [misc]simplify: iters left: 3 (30 enodes) 1546938931.061 * [exit]simplify: Simplified to (sqrt (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))) 1546938931.062 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))) 1546938931.062 * * * * [misc]progress: [ 73 / 126 ] simplifiying candidate # 1546938931.062 * [enter]simplify: Simplifying (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) 1546938931.062 * * [misc]simplify: iters left: 6 (13 enodes) 1546938931.066 * * [misc]simplify: iters left: 5 (19 enodes) 1546938931.071 * * [misc]simplify: iters left: 4 (28 enodes) 1546938931.079 * * [misc]simplify: iters left: 3 (30 enodes) 1546938931.083 * [exit]simplify: Simplified to (sqrt (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k))) 1546938931.083 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 1))) (sqrt (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k))))) 1546938931.083 * * * * [misc]progress: [ 74 / 126 ] simplifiying candidate # 1546938931.083 * [enter]simplify: Simplifying (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) 1546938931.083 * * [misc]simplify: iters left: 6 (13 enodes) 1546938931.085 * * [misc]simplify: iters left: 5 (19 enodes) 1546938931.088 * * [misc]simplify: iters left: 4 (28 enodes) 1546938931.091 * * [misc]simplify: iters left: 3 (30 enodes) 1546938931.095 * [exit]simplify: Simplified to (sqrt (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k))) 1546938931.095 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt 1)) (sqrt (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k))))) 1546938931.095 * * * * [misc]progress: [ 75 / 126 ] simplifiying candidate # 1546938931.095 * [enter]simplify: Simplifying (sqrt (/ 1 (sqrt k))) 1546938931.095 * * [misc]simplify: iters left: 4 (5 enodes) 1546938931.096 * * [misc]simplify: iters left: 3 (7 enodes) 1546938931.097 * [exit]simplify: Simplified to (sqrt (/ 1 (sqrt k))) 1546938931.097 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt (/ 1 (sqrt k))))) 1546938931.097 * * * * [misc]progress: [ 76 / 126 ] simplifiying candidate # 1546938931.097 * [enter]simplify: Simplifying (sqrt (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))) 1546938931.097 * * [misc]simplify: iters left: 6 (14 enodes) 1546938931.099 * * [misc]simplify: iters left: 5 (20 enodes) 1546938931.101 * * [misc]simplify: iters left: 4 (29 enodes) 1546938931.105 * * [misc]simplify: iters left: 3 (30 enodes) 1546938931.108 * [exit]simplify: Simplified to (sqrt (sqrt (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k)))) 1546938931.108 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))))) (sqrt (sqrt (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k)))))) 1546938931.108 * * * * [misc]progress: [ 77 / 126 ] simplifiying candidate # 1546938931.109 * [enter]simplify: Simplifying (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) 1546938931.109 * * [misc]simplify: iters left: 6 (13 enodes) 1546938931.110 * * [misc]simplify: iters left: 5 (19 enodes) 1546938931.115 * * [misc]simplify: iters left: 4 (28 enodes) 1546938931.123 * * [misc]simplify: iters left: 3 (30 enodes) 1546938931.130 * [exit]simplify: Simplified to (sqrt (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k))) 1546938931.130 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) 1) (sqrt (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k))))) 1546938931.130 * * * * [misc]progress: [ 78 / 126 ] simplifiying candidate # 1546938931.130 * [enter]simplify: Simplifying (* (cbrt (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))) (cbrt (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))))) 1546938931.130 * * [misc]simplify: iters left: 6 (15 enodes) 1546938931.135 * * [misc]simplify: iters left: 5 (21 enodes) 1546938931.141 * * [misc]simplify: iters left: 4 (30 enodes) 1546938931.149 * * [misc]simplify: iters left: 3 (31 enodes) 1546938931.157 * [exit]simplify: Simplified to (* (cbrt (sqrt (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k)))) (cbrt (sqrt (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k))))) 1546938931.157 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (* (cbrt (sqrt (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k)))) (cbrt (sqrt (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k))))) (* (cbrt (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))))) 1546938931.157 * * * * [misc]progress: [ 79 / 126 ] simplifiying candidate # 1546938931.157 * [enter]simplify: Simplifying (sqrt (* (cbrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))))) 1546938931.158 * * [misc]simplify: iters left: 6 (15 enodes) 1546938931.162 * * [misc]simplify: iters left: 5 (22 enodes) 1546938931.169 * * [misc]simplify: iters left: 4 (31 enodes) 1546938931.177 * * [misc]simplify: iters left: 3 (33 enodes) 1546938931.186 * [exit]simplify: Simplified to (fabs (cbrt (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k)))) 1546938931.186 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (fabs (cbrt (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k)))) (* (sqrt (cbrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))))) 1546938931.186 * * * * [misc]progress: [ 80 / 126 ] simplifiying candidate # 1546938931.186 * [enter]simplify: Simplifying (sqrt (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))) 1546938931.186 * * [misc]simplify: iters left: 6 (14 enodes) 1546938931.191 * * [misc]simplify: iters left: 5 (20 enodes) 1546938931.197 * * [misc]simplify: iters left: 4 (29 enodes) 1546938931.205 * * [misc]simplify: iters left: 3 (30 enodes) 1546938931.212 * [exit]simplify: Simplified to (sqrt (sqrt (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k)))) 1546938931.213 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (sqrt (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k)))) (* (sqrt (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))))) 1546938931.213 * * * * [misc]progress: [ 81 / 126 ] simplifiying candidate # 1546938931.213 * [enter]simplify: Simplifying (sqrt (/ (pow (* PI (* n 2)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) 1546938931.213 * * [misc]simplify: iters left: 6 (13 enodes) 1546938931.217 * * [misc]simplify: iters left: 5 (20 enodes) 1546938931.223 * * [misc]simplify: iters left: 4 (26 enodes) 1546938931.230 * * [misc]simplify: iters left: 3 (28 enodes) 1546938931.237 * [exit]simplify: Simplified to (sqrt (/ (sqrt (* (* 2 n) PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) 1546938931.237 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (/ (sqrt (* (* 2 n) PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (* (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))))) 1546938931.237 * * * * [misc]progress: [ 82 / 126 ] simplifiying candidate # 1546938931.237 * [enter]simplify: Simplifying (sqrt (/ (pow (* PI (* n 2)) 1/2) (sqrt (sqrt k)))) 1546938931.237 * * [misc]simplify: iters left: 6 (12 enodes) 1546938931.241 * * [misc]simplify: iters left: 5 (17 enodes) 1546938931.246 * * [misc]simplify: iters left: 4 (23 enodes) 1546938931.250 * * [misc]simplify: iters left: 3 (24 enodes) 1546938931.253 * [exit]simplify: Simplified to (sqrt (/ (sqrt (* (* 2 n) PI)) (sqrt (sqrt k)))) 1546938931.253 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (/ (sqrt (* (* 2 n) PI)) (sqrt (sqrt k)))) (* (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))))) 1546938931.253 * * * * [misc]progress: [ 83 / 126 ] simplifiying candidate # 1546938931.253 * [enter]simplify: Simplifying (sqrt (/ (pow (* PI (* n 2)) 1/2) 1)) 1546938931.253 * * [misc]simplify: iters left: 6 (10 enodes) 1546938931.254 * * [misc]simplify: iters left: 5 (17 enodes) 1546938931.257 * * [misc]simplify: iters left: 4 (25 enodes) 1546938931.261 * * [misc]simplify: iters left: 3 (26 enodes) 1546938931.264 * [exit]simplify: Simplified to (sqrt (sqrt (* (* 2 n) PI))) 1546938931.264 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (sqrt (* (* 2 n) PI))) (* (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))))) 1546938931.264 * * * * [misc]progress: [ 84 / 126 ] simplifiying candidate # 1546938931.264 * [enter]simplify: Simplifying (sqrt (/ (pow (* PI (* n 2)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) 1546938931.264 * * [misc]simplify: iters left: 6 (13 enodes) 1546938931.266 * * [misc]simplify: iters left: 5 (20 enodes) 1546938931.268 * * [misc]simplify: iters left: 4 (26 enodes) 1546938931.272 * * [misc]simplify: iters left: 3 (28 enodes) 1546938931.275 * [exit]simplify: Simplified to (sqrt (/ (sqrt (* (* 2 n) PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) 1546938931.275 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (/ (sqrt (* (* 2 n) PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (* (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))))) 1546938931.275 * * * * [misc]progress: [ 85 / 126 ] simplifiying candidate # 1546938931.276 * [enter]simplify: Simplifying (sqrt (/ (pow (* PI (* n 2)) 1/2) (sqrt (sqrt k)))) 1546938931.276 * * [misc]simplify: iters left: 6 (12 enodes) 1546938931.279 * * [misc]simplify: iters left: 5 (17 enodes) 1546938931.283 * * [misc]simplify: iters left: 4 (23 enodes) 1546938931.286 * * [misc]simplify: iters left: 3 (24 enodes) 1546938931.289 * [exit]simplify: Simplified to (sqrt (/ (sqrt (* (* 2 n) PI)) (sqrt (sqrt k)))) 1546938931.289 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (/ (sqrt (* (* 2 n) PI)) (sqrt (sqrt k)))) (* (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))))) 1546938931.289 * * * * [misc]progress: [ 86 / 126 ] simplifiying candidate # 1546938931.290 * [enter]simplify: Simplifying (sqrt (/ (pow (* PI (* n 2)) 1/2) 1)) 1546938931.290 * * [misc]simplify: iters left: 6 (10 enodes) 1546938931.291 * * [misc]simplify: iters left: 5 (17 enodes) 1546938931.294 * * [misc]simplify: iters left: 4 (25 enodes) 1546938931.297 * * [misc]simplify: iters left: 3 (26 enodes) 1546938931.300 * [exit]simplify: Simplified to (sqrt (sqrt (* (* 2 n) PI))) 1546938931.300 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (sqrt (* (* 2 n) PI))) (* (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))))) 1546938931.300 * * * * [misc]progress: [ 87 / 126 ] simplifiying candidate # 1546938931.300 * [enter]simplify: Simplifying (sqrt (/ (pow PI (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) 1546938931.300 * * [misc]simplify: iters left: 6 (12 enodes) 1546938931.302 * * [misc]simplify: iters left: 5 (16 enodes) 1546938931.304 * * [misc]simplify: iters left: 4 (19 enodes) 1546938931.307 * [exit]simplify: Simplified to (sqrt (/ (pow PI (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) 1546938931.307 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (/ (pow PI (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (* (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))))) 1546938931.307 * * * * [misc]progress: [ 88 / 126 ] simplifiying candidate # 1546938931.307 * [enter]simplify: Simplifying (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))) 1546938931.307 * * [misc]simplify: iters left: 6 (11 enodes) 1546938931.309 * * [misc]simplify: iters left: 5 (13 enodes) 1546938931.310 * * [misc]simplify: iters left: 4 (16 enodes) 1546938931.312 * [exit]simplify: Simplified to (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))) 1546938931.312 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (* (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))))) 1546938931.312 * * * * [misc]progress: [ 89 / 126 ] simplifiying candidate # 1546938931.312 * [enter]simplify: Simplifying (sqrt (/ (pow PI (- 1/2 (/ k 2))) 1)) 1546938931.313 * * [misc]simplify: iters left: 6 (10 enodes) 1546938931.314 * * [misc]simplify: iters left: 5 (14 enodes) 1546938931.316 * * [misc]simplify: iters left: 4 (19 enodes) 1546938931.320 * [exit]simplify: Simplified to (sqrt (pow PI (- 1/2 (/ k 2)))) 1546938931.320 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (pow PI (- 1/2 (/ k 2)))) (* (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))))) 1546938931.320 * * * * [misc]progress: [ 90 / 126 ] simplifiying candidate # 1546938931.321 * [enter]simplify: Simplifying (sqrt (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) 1546938931.321 * * [misc]simplify: iters left: 6 (17 enodes) 1546938931.325 * * [misc]simplify: iters left: 5 (29 enodes) 1546938931.333 * * [misc]simplify: iters left: 4 (48 enodes) 1546938931.344 * * [misc]simplify: iters left: 3 (52 enodes) 1546938931.355 * * [misc]simplify: iters left: 2 (55 enodes) 1546938931.368 * [exit]simplify: Simplified to (fabs (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))) 1546938931.368 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (fabs (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))) (* (sqrt (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))) (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))))) 1546938931.368 * * * * [misc]progress: [ 91 / 126 ] simplifiying candidate # 1546938931.368 * [enter]simplify: Simplifying (sqrt (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt (sqrt k)))) 1546938931.368 * * [misc]simplify: iters left: 6 (16 enodes) 1546938931.373 * * [misc]simplify: iters left: 5 (24 enodes) 1546938931.379 * * [misc]simplify: iters left: 4 (35 enodes) 1546938931.388 * * [misc]simplify: iters left: 3 (37 enodes) 1546938931.396 * [exit]simplify: Simplified to (sqrt (/ (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (/ (sqrt (sqrt k)) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))))) 1546938931.396 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (/ (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (/ (sqrt (sqrt k)) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))))) (* (sqrt (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))))) 1546938931.396 * * * * [misc]progress: [ 92 / 126 ] simplifiying candidate # 1546938931.397 * [enter]simplify: Simplifying (sqrt (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1)) 1546938931.397 * * [misc]simplify: iters left: 6 (15 enodes) 1546938931.401 * * [misc]simplify: iters left: 5 (25 enodes) 1546938931.407 * * [misc]simplify: iters left: 4 (41 enodes) 1546938931.416 * * [misc]simplify: iters left: 3 (45 enodes) 1546938931.420 * * [misc]simplify: iters left: 2 (50 enodes) 1546938931.426 * [exit]simplify: Simplified to (fabs (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) 1546938931.426 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (fabs (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) (* (sqrt (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))))) 1546938931.426 * * * * [misc]progress: [ 93 / 126 ] simplifiying candidate # 1546938931.426 * [enter]simplify: Simplifying (sqrt (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) 1546938931.426 * * [misc]simplify: iters left: 6 (16 enodes) 1546938931.429 * * [misc]simplify: iters left: 5 (24 enodes) 1546938931.432 * * [misc]simplify: iters left: 4 (33 enodes) 1546938931.436 * * [misc]simplify: iters left: 3 (34 enodes) 1546938931.440 * [exit]simplify: Simplified to (sqrt (/ (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) 1546938931.440 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (/ (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (* (sqrt (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))) (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))))) 1546938931.440 * * * * [misc]progress: [ 94 / 126 ] simplifiying candidate # 1546938931.441 * [enter]simplify: Simplifying (sqrt (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) 1546938931.441 * * [misc]simplify: iters left: 6 (15 enodes) 1546938931.443 * * [misc]simplify: iters left: 5 (21 enodes) 1546938931.446 * * [misc]simplify: iters left: 4 (30 enodes) 1546938931.450 * * [misc]simplify: iters left: 3 (31 enodes) 1546938931.456 * [exit]simplify: Simplified to (sqrt (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) 1546938931.456 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (* (sqrt (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))))) 1546938931.456 * * * * [misc]progress: [ 95 / 126 ] simplifiying candidate # 1546938931.456 * [enter]simplify: Simplifying (sqrt (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1)) 1546938931.456 * * [misc]simplify: iters left: 6 (14 enodes) 1546938931.461 * * [misc]simplify: iters left: 5 (22 enodes) 1546938931.469 * * [misc]simplify: iters left: 4 (33 enodes) 1546938931.474 * * [misc]simplify: iters left: 3 (35 enodes) 1546938931.477 * [exit]simplify: Simplified to (sqrt (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) 1546938931.478 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) (* (sqrt (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))))) 1546938931.478 * * * * [misc]progress: [ 96 / 126 ] simplifiying candidate # 1546938931.478 * [enter]simplify: Simplifying (sqrt (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))) 1546938931.478 * * [misc]simplify: iters left: 6 (7 enodes) 1546938931.479 * * [misc]simplify: iters left: 5 (11 enodes) 1546938931.480 * [exit]simplify: Simplified to (sqrt (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k)))) 1546938931.480 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k)))) (* (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))))) 1546938931.480 * * * * [misc]progress: [ 97 / 126 ] simplifiying candidate # 1546938931.481 * [enter]simplify: Simplifying (sqrt (/ 1 (sqrt (sqrt k)))) 1546938931.481 * * [misc]simplify: iters left: 5 (6 enodes) 1546938931.481 * * [misc]simplify: iters left: 4 (8 enodes) 1546938931.482 * [exit]simplify: Simplified to (sqrt (/ 1 (sqrt (sqrt k)))) 1546938931.482 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (/ 1 (sqrt (sqrt k)))) (* (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))))) 1546938931.482 * * * * [misc]progress: [ 98 / 126 ] simplifiying candidate # 1546938931.482 * [enter]simplify: Simplifying (sqrt (/ 1 1)) 1546938931.482 * * [misc]simplify: iters left: 3 (3 enodes) 1546938931.483 * * [misc]simplify: iters left: 2 (5 enodes) 1546938931.484 * [exit]simplify: Simplified to 1 1546938931.484 * [misc]simplify: Simplified (2 1) to (λ (k n) (* 1 (* (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))))) 1546938931.484 * * * * [misc]progress: [ 99 / 126 ] simplifiying candidate # 1546938931.484 * [enter]simplify: Simplifying (sqrt 1) 1546938931.484 * * [misc]simplify: iters left: 1 (2 enodes) 1546938931.485 * [exit]simplify: Simplified to 1 1546938931.485 * [misc]simplify: Simplified (2 1) to (λ (k n) (* 1 (* (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))))) 1546938931.485 * * * * [misc]progress: [ 100 / 126 ] simplifiying candidate # 1546938931.485 * [enter]simplify: Simplifying (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1546938931.485 * * [misc]simplify: iters left: 6 (11 enodes) 1546938931.487 * * [misc]simplify: iters left: 5 (17 enodes) 1546938931.489 * * [misc]simplify: iters left: 4 (26 enodes) 1546938931.492 * * [misc]simplify: iters left: 3 (27 enodes) 1546938931.496 * [exit]simplify: Simplified to (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) 1546938931.496 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (* (sqrt (/ 1 (sqrt k))) (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))))) 1546938931.496 * * * * [misc]progress: [ 101 / 126 ] simplifiying candidate # 1546938931.496 * [enter]simplify: Simplifying (sqrt (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))) 1546938931.496 * * [misc]simplify: iters left: 6 (14 enodes) 1546938931.498 * * [misc]simplify: iters left: 5 (20 enodes) 1546938931.501 * * [misc]simplify: iters left: 4 (29 enodes) 1546938931.505 * * [misc]simplify: iters left: 3 (30 enodes) 1546938931.509 * [exit]simplify: Simplified to (sqrt (sqrt (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k)))) 1546938931.509 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (sqrt (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k)))) (* (sqrt (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))))) 1546938931.509 * * * * [misc]progress: [ 102 / 126 ] simplifiying candidate # 1546938931.509 * * * * [misc]progress: [ 103 / 126 ] simplifiying candidate # 1546938931.509 * [enter]simplify: Simplifying (sqrt (sqrt k)) 1546938931.509 * * [misc]simplify: iters left: 2 (3 enodes) 1546938931.509 * [exit]simplify: Simplified to (sqrt (sqrt k)) 1546938931.509 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (* (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt (sqrt k)))) 1546938931.509 * * * * [misc]progress: [ 104 / 126 ] simplifiying candidate # 1546938931.510 * [enter]simplify: Simplifying (* (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))) 1546938931.510 * * [misc]simplify: iters left: 6 (15 enodes) 1546938931.512 * * [misc]simplify: iters left: 5 (22 enodes) 1546938931.518 * * [misc]simplify: iters left: 4 (31 enodes) 1546938931.526 * * [misc]simplify: iters left: 3 (33 enodes) 1546938931.533 * [exit]simplify: Simplified to (* (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k)))) 1546938931.533 * [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)))) 1546938931.533 * * * * [misc]progress: [ 105 / 126 ] simplifiying candidate # 1546938931.533 * * * * [misc]progress: [ 106 / 126 ] simplifiying candidate # 1546938931.533 * * * * [misc]progress: [ 107 / 126 ] simplifiying candidate # 1546938931.533 * * * * [misc]progress: [ 108 / 126 ] simplifiying candidate # 1546938931.533 * * * * [misc]progress: [ 109 / 126 ] simplifiying candidate # 1546938931.533 * * * * [misc]progress: [ 110 / 126 ] simplifiying candidate # 1546938931.533 * * * * [misc]progress: [ 111 / 126 ] simplifiying candidate # 1546938931.533 * * * * [misc]progress: [ 112 / 126 ] simplifiying candidate # 1546938931.534 * * * * [misc]progress: [ 113 / 126 ] simplifiying candidate # 1546938931.534 * * * * [misc]progress: [ 114 / 126 ] simplifiying candidate # 1546938931.534 * * * * [misc]progress: [ 115 / 126 ] simplifiying candidate # 1546938931.534 * [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))))) 1546938931.534 * * [misc]simplify: iters left: 6 (37 enodes) 1546938931.547 * * [misc]simplify: iters left: 5 (105 enodes) 1546938931.584 * * [misc]simplify: iters left: 4 (339 enodes) 1546938931.776 * [exit]simplify: Simplified to (+ (+ (* (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) -1/2) (+ (* (* (* k (log n)) (* k (log n))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (pow (* PI 2) 1/2) (pow n 1/2)))) (* (* k k) (+ (* (* (log (* PI 2)) (log (* PI 2))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (* (* (log n) (pow n 1/2)) (pow (* PI 2) 1/2)) (* (log (* PI 2)) 1/4))))) 1546938931.776 * [misc]simplify: Simplified (2 2 1 1) to (λ (k n) (* (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (+ (+ (* (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) -1/2) (+ (* (* (* k (log n)) (* k (log n))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (pow (* PI 2) 1/2) (pow n 1/2)))) (* (* k k) (+ (* (* (log (* PI 2)) (log (* PI 2))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (* (* (log n) (pow n 1/2)) (pow (* PI 2) 1/2)) (* (log (* PI 2)) 1/4))))) (sqrt k))))) 1546938931.776 * * * * [misc]progress: [ 116 / 126 ] simplifiying candidate # 1546938931.776 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 1546938931.777 * * [misc]simplify: iters left: 6 (15 enodes) 1546938931.783 * * [misc]simplify: iters left: 5 (33 enodes) 1546938931.794 * * [misc]simplify: iters left: 4 (64 enodes) 1546938931.818 * * [misc]simplify: iters left: 3 (171 enodes) 1546938931.925 * [exit]simplify: Simplified to (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow n (- 1/2 (* 1/2 k)))) 1546938931.925 * [misc]simplify: Simplified (2 2 1 1) to (λ (k n) (* (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow n (- 1/2 (* 1/2 k)))) (sqrt k))))) 1546938931.925 * * * * [misc]progress: [ 117 / 126 ] simplifiying candidate # 1546938931.926 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 1546938931.926 * * [misc]simplify: iters left: 6 (15 enodes) 1546938931.929 * * [misc]simplify: iters left: 5 (30 enodes) 1546938931.934 * * [misc]simplify: iters left: 4 (65 enodes) 1546938931.948 * * [misc]simplify: iters left: 3 (200 enodes) 1546938932.040 * [exit]simplify: Simplified to (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))) 1546938932.040 * [misc]simplify: Simplified (2 2 1 1) to (λ (k n) (* (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))) (sqrt k))))) 1546938932.040 * * * * [misc]progress: [ 118 / 126 ] simplifiying candidate # 1546938932.040 * [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))))) 1546938932.040 * * [misc]simplify: iters left: 6 (37 enodes) 1546938932.048 * * [misc]simplify: iters left: 5 (105 enodes) 1546938932.073 * * [misc]simplify: iters left: 4 (339 enodes) 1546938932.227 * [exit]simplify: Simplified to (+ (+ (* (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) -1/2) (+ (* (* (* k (log n)) (* k (log n))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (pow (* PI 2) 1/2) (pow n 1/2)))) (* (* k k) (+ (* (* (log (* PI 2)) (log (* PI 2))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (* (* (log n) (pow n 1/2)) (pow (* PI 2) 1/2)) (* (log (* PI 2)) 1/4))))) 1546938932.227 * [misc]simplify: Simplified (2 1 1 1) to (λ (k n) (* (sqrt (/ (+ (+ (* (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) -1/2) (+ (* (* (* k (log n)) (* k (log n))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (pow (* PI 2) 1/2) (pow n 1/2)))) (* (* k k) (+ (* (* (log (* PI 2)) (log (* PI 2))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (* (* (log n) (pow n 1/2)) (pow (* PI 2) 1/2)) (* (log (* PI 2)) 1/4))))) (sqrt k))) (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))))) 1546938932.227 * * * * [misc]progress: [ 119 / 126 ] simplifiying candidate # 1546938932.227 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 1546938932.227 * * [misc]simplify: iters left: 6 (15 enodes) 1546938932.231 * * [misc]simplify: iters left: 5 (33 enodes) 1546938932.241 * * [misc]simplify: iters left: 4 (64 enodes) 1546938932.260 * * [misc]simplify: iters left: 3 (171 enodes) 1546938932.345 * [exit]simplify: Simplified to (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow n (- 1/2 (* 1/2 k)))) 1546938932.345 * [misc]simplify: Simplified (2 1 1 1) to (λ (k n) (* (sqrt (/ (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow n (- 1/2 (* 1/2 k)))) (sqrt k))) (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))))) 1546938932.345 * * * * [misc]progress: [ 120 / 126 ] simplifiying candidate # 1546938932.345 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 1546938932.346 * * [misc]simplify: iters left: 6 (15 enodes) 1546938932.349 * * [misc]simplify: iters left: 5 (30 enodes) 1546938932.355 * * [misc]simplify: iters left: 4 (65 enodes) 1546938932.369 * * [misc]simplify: iters left: 3 (200 enodes) 1546938932.459 * [exit]simplify: Simplified to (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))) 1546938932.459 * [misc]simplify: Simplified (2 1 1 1) to (λ (k n) (* (sqrt (/ (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))) (sqrt k))) (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))))) 1546938932.459 * * * * [misc]progress: [ 121 / 126 ] simplifiying candidate # 1546938932.460 * [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)))))))))))))))))))))) 1546938932.460 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1546938932.460 * * * * [misc]progress: [ 122 / 126 ] simplifiying candidate # 1546938932.460 * [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)))))))) 1546938932.460 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1546938932.460 * * * * [misc]progress: [ 123 / 126 ] simplifiying candidate # 1546938932.460 * [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))))))))))) 1546938932.460 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1546938932.460 * * * * [misc]progress: [ 124 / 126 ] simplifiying candidate # 1546938932.460 * [enter]simplify: Simplifying (* 2 (* n PI)) 1546938932.460 * * [misc]simplify: iters left: 4 (5 enodes) 1546938932.461 * * [misc]simplify: iters left: 3 (9 enodes) 1546938932.463 * * [misc]simplify: iters left: 2 (15 enodes) 1546938932.465 * * [misc]simplify: iters left: 1 (17 enodes) 1546938932.466 * [exit]simplify: Simplified to (* (* PI n) 2) 1546938932.467 * [misc]simplify: Simplified (2 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))) (sqrt k))))) 1546938932.467 * * * * [misc]progress: [ 125 / 126 ] simplifiying candidate # 1546938932.467 * [enter]simplify: Simplifying (* 2 (* n PI)) 1546938932.467 * * [misc]simplify: iters left: 4 (5 enodes) 1546938932.471 * * [misc]simplify: iters left: 3 (9 enodes) 1546938932.472 * * [misc]simplify: iters left: 2 (15 enodes) 1546938932.474 * * [misc]simplify: iters left: 1 (17 enodes) 1546938932.476 * [exit]simplify: Simplified to (* (* PI n) 2) 1546938932.476 * [misc]simplify: Simplified (2 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))) (sqrt k))))) 1546938932.476 * * * * [misc]progress: [ 126 / 126 ] simplifiying candidate # 1546938932.476 * [enter]simplify: Simplifying (* 2 (* n PI)) 1546938932.476 * * [misc]simplify: iters left: 4 (5 enodes) 1546938932.477 * * [misc]simplify: iters left: 3 (9 enodes) 1546938932.478 * * [misc]simplify: iters left: 2 (15 enodes) 1546938932.480 * * [misc]simplify: iters left: 1 (17 enodes) 1546938932.482 * [exit]simplify: Simplified to (* (* PI n) 2) 1546938932.482 * [misc]simplify: Simplified (2 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))) (sqrt k))))) 1546938932.482 * * * [misc]progress: adding candidates to table 1546938934.336 * * [misc]progress: iteration 4 / 4 1546938934.337 * * * [misc]progress: picking best candidate 1546938934.355 * * * * [misc]pick: Picked # 1546938934.355 * * * [misc]progress: localizing error 1546938934.382 * * * [misc]progress: generating rewritten candidates 1546938934.382 * * * * [misc]progress: [ 1 / 4 ] rewriting at (2 1) 1546938934.383 * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 2 1) 1546938934.386 * * * * [misc]progress: [ 3 / 4 ] rewriting at (2 2) 1546938934.395 * * * * [misc]progress: [ 4 / 4 ] rewriting at (2) 1546938934.411 * * * [misc]progress: generating series expansions 1546938934.411 * * * * [misc]progress: [ 1 / 4 ] generating series at (2 1) 1546938934.412 * [misc]backup-simplify: Simplify (pow PI (- 1/2 (/ k 2))) into (pow PI (- 1/2 (* 1/2 k))) 1546938934.412 * [misc]approximate: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in (k) around 0 1546938934.412 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 1546938934.412 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 1546938934.412 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 1546938934.412 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546938934.412 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938934.412 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.412 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546938934.412 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938934.412 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.412 * [misc]taylor: Taking taylor expansion of k in k 1546938934.412 * [misc]backup-simplify: Simplify 0 into 0 1546938934.412 * [misc]backup-simplify: Simplify 1 into 1 1546938934.412 * [misc]taylor: Taking taylor expansion of (log PI) in k 1546938934.412 * [misc]taylor: Taking taylor expansion of PI in k 1546938934.412 * [misc]backup-simplify: Simplify PI into PI 1546938934.413 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1546938934.413 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546938934.413 * [misc]backup-simplify: Simplify (- 0) into 0 1546938934.413 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546938934.414 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1546938934.415 * [misc]backup-simplify: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 1546938934.415 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 1546938934.415 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 1546938934.415 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 1546938934.415 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546938934.415 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938934.415 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.415 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546938934.415 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938934.415 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.415 * [misc]taylor: Taking taylor expansion of k in k 1546938934.415 * [misc]backup-simplify: Simplify 0 into 0 1546938934.415 * [misc]backup-simplify: Simplify 1 into 1 1546938934.415 * [misc]taylor: Taking taylor expansion of (log PI) in k 1546938934.415 * [misc]taylor: Taking taylor expansion of PI in k 1546938934.415 * [misc]backup-simplify: Simplify PI into PI 1546938934.415 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1546938934.415 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546938934.416 * [misc]backup-simplify: Simplify (- 0) into 0 1546938934.416 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546938934.416 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1546938934.417 * [misc]backup-simplify: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 1546938934.417 * [misc]backup-simplify: Simplify (pow PI 1/2) into (pow PI 1/2) 1546938934.424 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 1546938934.425 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1546938934.425 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546938934.425 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546938934.426 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (log PI))) into (- (* 1/2 (log PI))) 1546938934.429 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 1) 1)))) into (* -1/2 (* (log PI) (sqrt PI))) 1546938934.431 * [misc]backup-simplify: Simplify (* -1/2 (* (log PI) (sqrt PI))) into (* -1/2 (* (log PI) (sqrt PI))) 1546938934.435 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 1546938934.435 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1546938934.435 * [misc]backup-simplify: Simplify (- 0) into 0 1546938934.436 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938934.437 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log PI)))) into 0 1546938934.441 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI))) 1546938934.443 * [misc]backup-simplify: Simplify (* 1/8 (* (pow (log PI) 2) (sqrt PI))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI))) 1546938934.446 * [misc]backup-simplify: Simplify (+ (* (* 1/8 (* (pow (log PI) 2) (sqrt PI))) (pow k 2)) (+ (* (* -1/2 (* (log PI) (sqrt PI))) k) (pow PI 1/2))) into (- (+ (pow PI 1/2) (* 1/8 (* (* (pow (log PI) 2) (pow k 2)) (sqrt PI)))) (* 1/2 (* (* (log PI) k) (sqrt PI)))) 1546938934.446 * [misc]backup-simplify: Simplify (pow PI (- 1/2 (/ (/ 1 k) 2))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1546938934.446 * [misc]approximate: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in (k) around 0 1546938934.446 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 1546938934.446 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 1546938934.446 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 1546938934.446 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546938934.446 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938934.446 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.446 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546938934.446 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938934.446 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.446 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546938934.446 * [misc]taylor: Taking taylor expansion of k in k 1546938934.446 * [misc]backup-simplify: Simplify 0 into 0 1546938934.446 * [misc]backup-simplify: Simplify 1 into 1 1546938934.447 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546938934.447 * [misc]taylor: Taking taylor expansion of (log PI) in k 1546938934.447 * [misc]taylor: Taking taylor expansion of PI in k 1546938934.447 * [misc]backup-simplify: Simplify PI into PI 1546938934.447 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1546938934.447 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546938934.447 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546938934.448 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546938934.448 * [misc]backup-simplify: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 1546938934.448 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1546938934.448 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 1546938934.448 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 1546938934.448 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 1546938934.448 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546938934.449 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938934.449 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.449 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546938934.449 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938934.449 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.449 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546938934.449 * [misc]taylor: Taking taylor expansion of k in k 1546938934.449 * [misc]backup-simplify: Simplify 0 into 0 1546938934.449 * [misc]backup-simplify: Simplify 1 into 1 1546938934.449 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546938934.449 * [misc]taylor: Taking taylor expansion of (log PI) in k 1546938934.449 * [misc]taylor: Taking taylor expansion of PI in k 1546938934.449 * [misc]backup-simplify: Simplify PI into PI 1546938934.449 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1546938934.449 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546938934.450 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546938934.450 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546938934.450 * [misc]backup-simplify: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 1546938934.451 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1546938934.451 * [misc]backup-simplify: Simplify (pow PI (- 1/2 (* 1/2 (/ 1 k)))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1546938934.451 * [misc]backup-simplify: Simplify 0 into 0 1546938934.451 * [misc]backup-simplify: Simplify 0 into 0 1546938934.451 * [misc]backup-simplify: Simplify 0 into 0 1546938934.451 * [misc]backup-simplify: Simplify 0 into 0 1546938934.451 * [misc]backup-simplify: Simplify 0 into 0 1546938934.451 * [misc]backup-simplify: Simplify 0 into 0 1546938934.451 * [misc]backup-simplify: Simplify (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k))))) into (pow PI (- 1/2 (* 1/2 k))) 1546938934.451 * [misc]backup-simplify: Simplify (pow PI (- 1/2 (/ (/ 1 (- k)) 2))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1546938934.451 * [misc]approximate: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in (k) around 0 1546938934.451 * [misc]taylor: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 1546938934.451 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 1546938934.451 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 1546938934.452 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546938934.452 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546938934.452 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938934.452 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.452 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546938934.452 * [misc]taylor: Taking taylor expansion of k in k 1546938934.452 * [misc]backup-simplify: Simplify 0 into 0 1546938934.452 * [misc]backup-simplify: Simplify 1 into 1 1546938934.452 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546938934.452 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938934.452 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.452 * [misc]taylor: Taking taylor expansion of (log PI) in k 1546938934.452 * [misc]taylor: Taking taylor expansion of PI in k 1546938934.452 * [misc]backup-simplify: Simplify PI into PI 1546938934.452 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1546938934.452 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546938934.453 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546938934.453 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1546938934.453 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1546938934.453 * [misc]taylor: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 1546938934.453 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 1546938934.454 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 1546938934.454 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546938934.454 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546938934.454 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938934.454 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.454 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546938934.454 * [misc]taylor: Taking taylor expansion of k in k 1546938934.454 * [misc]backup-simplify: Simplify 0 into 0 1546938934.454 * [misc]backup-simplify: Simplify 1 into 1 1546938934.454 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546938934.454 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938934.454 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.454 * [misc]taylor: Taking taylor expansion of (log PI) in k 1546938934.454 * [misc]taylor: Taking taylor expansion of PI in k 1546938934.454 * [misc]backup-simplify: Simplify PI into PI 1546938934.454 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1546938934.454 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546938934.455 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546938934.455 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1546938934.455 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1546938934.456 * [misc]backup-simplify: Simplify (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1546938934.456 * [misc]backup-simplify: Simplify 0 into 0 1546938934.456 * [misc]backup-simplify: Simplify 0 into 0 1546938934.456 * [misc]backup-simplify: Simplify 0 into 0 1546938934.456 * [misc]backup-simplify: Simplify 0 into 0 1546938934.456 * [misc]backup-simplify: Simplify 0 into 0 1546938934.456 * [misc]backup-simplify: Simplify 0 into 0 1546938934.456 * [misc]backup-simplify: Simplify (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)) into (pow PI (- 1/2 (* 1/2 k))) 1546938934.456 * * * * [misc]progress: [ 2 / 4 ] generating series at (2 2 1) 1546938934.456 * [misc]backup-simplify: Simplify (pow (* n 2) (- 1/2 (/ k 2))) into (pow (* 2 n) (- 1/2 (* 1/2 k))) 1546938934.456 * [misc]approximate: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in (n k) around 0 1546938934.456 * [misc]taylor: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in k 1546938934.456 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in k 1546938934.456 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in k 1546938934.457 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546938934.457 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938934.457 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.457 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546938934.457 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938934.457 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.457 * [misc]taylor: Taking taylor expansion of k in k 1546938934.457 * [misc]backup-simplify: Simplify 0 into 0 1546938934.457 * [misc]backup-simplify: Simplify 1 into 1 1546938934.457 * [misc]taylor: Taking taylor expansion of (log (* 2 n)) in k 1546938934.457 * [misc]taylor: Taking taylor expansion of (* 2 n) in k 1546938934.457 * [misc]taylor: Taking taylor expansion of 2 in k 1546938934.457 * [misc]backup-simplify: Simplify 2 into 2 1546938934.457 * [misc]taylor: Taking taylor expansion of n in k 1546938934.457 * [misc]backup-simplify: Simplify n into n 1546938934.457 * [misc]backup-simplify: Simplify (* 2 n) into (* 2 n) 1546938934.457 * [misc]backup-simplify: Simplify (log (* 2 n)) into (log (* 2 n)) 1546938934.457 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546938934.457 * [misc]backup-simplify: Simplify (- 0) into 0 1546938934.457 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546938934.458 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 n))) into (* 1/2 (log (* 2 n))) 1546938934.458 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 n)))) into (pow (* 2 n) 1/2) 1546938934.458 * [misc]taylor: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in n 1546938934.458 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in n 1546938934.458 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in n 1546938934.458 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546938934.458 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938934.458 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.458 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546938934.458 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938934.458 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.458 * [misc]taylor: Taking taylor expansion of k in n 1546938934.458 * [misc]backup-simplify: Simplify k into k 1546938934.458 * [misc]taylor: Taking taylor expansion of (log (* 2 n)) in n 1546938934.458 * [misc]taylor: Taking taylor expansion of (* 2 n) in n 1546938934.458 * [misc]taylor: Taking taylor expansion of 2 in n 1546938934.458 * [misc]backup-simplify: Simplify 2 into 2 1546938934.458 * [misc]taylor: Taking taylor expansion of n in n 1546938934.458 * [misc]backup-simplify: Simplify 0 into 0 1546938934.458 * [misc]backup-simplify: Simplify 1 into 1 1546938934.458 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546938934.459 * [misc]backup-simplify: Simplify (+ (* 2 1) (* 0 0)) into 2 1546938934.459 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1546938934.459 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546938934.459 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546938934.459 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546938934.459 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 1546938934.460 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (+ (log 2) (log n))) into (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) 1546938934.460 * [misc]backup-simplify: Simplify (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) into (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) 1546938934.460 * [misc]taylor: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in n 1546938934.460 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in n 1546938934.460 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in n 1546938934.460 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546938934.460 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938934.460 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.460 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546938934.460 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938934.460 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.460 * [misc]taylor: Taking taylor expansion of k in n 1546938934.460 * [misc]backup-simplify: Simplify k into k 1546938934.460 * [misc]taylor: Taking taylor expansion of (log (* 2 n)) in n 1546938934.460 * [misc]taylor: Taking taylor expansion of (* 2 n) in n 1546938934.461 * [misc]taylor: Taking taylor expansion of 2 in n 1546938934.461 * [misc]backup-simplify: Simplify 2 into 2 1546938934.461 * [misc]taylor: Taking taylor expansion of n in n 1546938934.461 * [misc]backup-simplify: Simplify 0 into 0 1546938934.461 * [misc]backup-simplify: Simplify 1 into 1 1546938934.461 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546938934.461 * [misc]backup-simplify: Simplify (+ (* 2 1) (* 0 0)) into 2 1546938934.461 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1546938934.461 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546938934.461 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546938934.462 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546938934.462 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 1546938934.462 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (+ (log 2) (log n))) into (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) 1546938934.462 * [misc]backup-simplify: Simplify (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) into (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) 1546938934.463 * [misc]taylor: Taking taylor expansion of (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) in k 1546938934.463 * [misc]taylor: Taking taylor expansion of (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) in k 1546938934.463 * [misc]taylor: Taking taylor expansion of (+ (log 2) (log n)) in k 1546938934.463 * [misc]taylor: Taking taylor expansion of (log 2) in k 1546938934.463 * [misc]taylor: Taking taylor expansion of 2 in k 1546938934.463 * [misc]backup-simplify: Simplify 2 into 2 1546938934.463 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1546938934.463 * [misc]taylor: Taking taylor expansion of (log n) in k 1546938934.463 * [misc]taylor: Taking taylor expansion of n in k 1546938934.463 * [misc]backup-simplify: Simplify n into n 1546938934.463 * [misc]backup-simplify: Simplify (log n) into (log n) 1546938934.463 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546938934.463 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938934.463 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.463 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546938934.463 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938934.463 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.463 * [misc]taylor: Taking taylor expansion of k in k 1546938934.463 * [misc]backup-simplify: Simplify 0 into 0 1546938934.463 * [misc]backup-simplify: Simplify 1 into 1 1546938934.464 * [misc]backup-simplify: Simplify (+ (log 2) (log n)) into (+ (log 2) (log n)) 1546938934.464 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546938934.464 * [misc]backup-simplify: Simplify (- 0) into 0 1546938934.464 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546938934.464 * [misc]backup-simplify: Simplify (* (+ (log 2) (log n)) 1/2) into (* 1/2 (+ (log 2) (log n))) 1546938934.465 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log 2) (log n)))) into (exp (* 1/2 (+ (log 2) (log n)))) 1546938934.465 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log 2) (log n)))) into (exp (* 1/2 (+ (log 2) (log n)))) 1546938934.465 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 1) (* 0 0))) into 0 1546938934.468 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 1546938934.468 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1546938934.468 * [misc]backup-simplify: Simplify (- 0) into 0 1546938934.468 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938934.469 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 1546938934.469 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log 2) (log n)))) into 0 1546938934.470 * [misc]backup-simplify: Simplify (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546938934.470 * [misc]taylor: Taking taylor expansion of 0 in k 1546938934.470 * [misc]backup-simplify: Simplify 0 into 0 1546938934.470 * [misc]backup-simplify: Simplify 0 into 0 1546938934.471 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1546938934.471 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546938934.471 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546938934.474 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 1546938934.474 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1546938934.475 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938934.475 * [misc]backup-simplify: Simplify (+ (* (+ (log 2) (log n)) -1/2) (* 0 1/2)) into (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 1546938934.476 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) 1546938934.476 * [misc]backup-simplify: Simplify (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) into (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) 1546938934.477 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1546938934.481 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 1546938934.482 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1546938934.482 * [misc]backup-simplify: Simplify (- 0) into 0 1546938934.482 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938934.483 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 1546938934.483 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log 2) (log n))))) into 0 1546938934.485 * [misc]backup-simplify: Simplify (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1546938934.485 * [misc]taylor: Taking taylor expansion of 0 in k 1546938934.485 * [misc]backup-simplify: Simplify 0 into 0 1546938934.485 * [misc]backup-simplify: Simplify 0 into 0 1546938934.485 * [misc]backup-simplify: Simplify 0 into 0 1546938934.486 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1546938934.486 * [misc]backup-simplify: Simplify (- 0) into 0 1546938934.486 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938934.491 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 1546938934.492 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1546938934.492 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938934.493 * [misc]backup-simplify: Simplify (+ (* (+ (log 2) (log n)) 0) (+ (* 0 -1/2) (* 0 1/2))) into 0 1546938934.495 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))) 1546938934.496 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))) into (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))) 1546938934.499 * [misc]backup-simplify: Simplify (+ (* (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) (* k 1)) (exp (* 1/2 (+ (log 2) (log n)))))) into (- (+ (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (* (pow (log 2) 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (pow k 2)))) (+ (* 1/4 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) (pow k 2))))) (* 1/8 (* (exp (* 1/2 (+ (log 2) (log n)))) (* (pow (log n) 2) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) k))) (* 1/2 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) k))))) 1546938934.499 * [misc]backup-simplify: Simplify (pow (* (/ 1 n) 2) (- 1/2 (/ (/ 1 k) 2))) into (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) 1546938934.499 * [misc]approximate: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 1546938934.499 * [misc]taylor: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in k 1546938934.500 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in k 1546938934.500 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in k 1546938934.500 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546938934.500 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938934.500 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.500 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546938934.500 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938934.500 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.500 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546938934.500 * [misc]taylor: Taking taylor expansion of k in k 1546938934.500 * [misc]backup-simplify: Simplify 0 into 0 1546938934.500 * [misc]backup-simplify: Simplify 1 into 1 1546938934.500 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546938934.500 * [misc]taylor: Taking taylor expansion of (log (/ 2 n)) in k 1546938934.500 * [misc]taylor: Taking taylor expansion of (/ 2 n) in k 1546938934.500 * [misc]taylor: Taking taylor expansion of 2 in k 1546938934.500 * [misc]backup-simplify: Simplify 2 into 2 1546938934.500 * [misc]taylor: Taking taylor expansion of n in k 1546938934.500 * [misc]backup-simplify: Simplify n into n 1546938934.500 * [misc]backup-simplify: Simplify (/ 2 n) into (/ 2 n) 1546938934.500 * [misc]backup-simplify: Simplify (log (/ 2 n)) into (log (/ 2 n)) 1546938934.501 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546938934.501 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546938934.501 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546938934.501 * [misc]backup-simplify: Simplify (* -1/2 (log (/ 2 n))) into (* -1/2 (log (/ 2 n))) 1546938934.501 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) into (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) 1546938934.501 * [misc]taylor: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546938934.501 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 1546938934.501 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 1546938934.501 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546938934.501 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938934.501 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.501 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546938934.501 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938934.501 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.501 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938934.501 * [misc]taylor: Taking taylor expansion of k in n 1546938934.501 * [misc]backup-simplify: Simplify k into k 1546938934.502 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938934.502 * [misc]taylor: Taking taylor expansion of (log (/ 2 n)) in n 1546938934.502 * [misc]taylor: Taking taylor expansion of (/ 2 n) in n 1546938934.502 * [misc]taylor: Taking taylor expansion of 2 in n 1546938934.502 * [misc]backup-simplify: Simplify 2 into 2 1546938934.502 * [misc]taylor: Taking taylor expansion of n in n 1546938934.502 * [misc]backup-simplify: Simplify 0 into 0 1546938934.502 * [misc]backup-simplify: Simplify 1 into 1 1546938934.502 * [misc]backup-simplify: Simplify (/ 2 1) into 2 1546938934.502 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1546938934.502 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546938934.502 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546938934.502 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546938934.503 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 1546938934.503 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 1546938934.503 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 1546938934.503 * [misc]taylor: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546938934.503 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 1546938934.503 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 1546938934.503 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546938934.503 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938934.504 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.504 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546938934.504 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938934.504 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.504 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938934.504 * [misc]taylor: Taking taylor expansion of k in n 1546938934.504 * [misc]backup-simplify: Simplify k into k 1546938934.504 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938934.504 * [misc]taylor: Taking taylor expansion of (log (/ 2 n)) in n 1546938934.504 * [misc]taylor: Taking taylor expansion of (/ 2 n) in n 1546938934.504 * [misc]taylor: Taking taylor expansion of 2 in n 1546938934.504 * [misc]backup-simplify: Simplify 2 into 2 1546938934.504 * [misc]taylor: Taking taylor expansion of n in n 1546938934.504 * [misc]backup-simplify: Simplify 0 into 0 1546938934.504 * [misc]backup-simplify: Simplify 1 into 1 1546938934.504 * [misc]backup-simplify: Simplify (/ 2 1) into 2 1546938934.504 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1546938934.504 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546938934.504 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546938934.505 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546938934.505 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 1546938934.505 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 1546938934.506 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 1546938934.506 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) in k 1546938934.506 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) in k 1546938934.506 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546938934.506 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938934.506 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.506 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546938934.506 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938934.506 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.506 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546938934.506 * [misc]taylor: Taking taylor expansion of k in k 1546938934.506 * [misc]backup-simplify: Simplify 0 into 0 1546938934.506 * [misc]backup-simplify: Simplify 1 into 1 1546938934.506 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546938934.506 * [misc]taylor: Taking taylor expansion of (- (log 2) (log n)) in k 1546938934.506 * [misc]taylor: Taking taylor expansion of (log 2) in k 1546938934.506 * [misc]taylor: Taking taylor expansion of 2 in k 1546938934.506 * [misc]backup-simplify: Simplify 2 into 2 1546938934.506 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1546938934.507 * [misc]taylor: Taking taylor expansion of (log n) in k 1546938934.507 * [misc]taylor: Taking taylor expansion of n in k 1546938934.507 * [misc]backup-simplify: Simplify n into n 1546938934.507 * [misc]backup-simplify: Simplify (log n) into (log n) 1546938934.507 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546938934.507 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546938934.507 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546938934.507 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1546938934.507 * [misc]backup-simplify: Simplify (+ (log 2) (- (log n))) into (- (log 2) (log n)) 1546938934.508 * [misc]backup-simplify: Simplify (* -1/2 (- (log 2) (log n))) into (* -1/2 (- (log 2) (log n))) 1546938934.508 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 1546938934.508 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 1546938934.509 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)))) into 0 1546938934.511 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 1546938934.511 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546938934.512 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546938934.512 * [misc]backup-simplify: Simplify (- 0) into 0 1546938934.512 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938934.512 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 1546938934.513 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log 2) (log n)))) into 0 1546938934.514 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546938934.514 * [misc]taylor: Taking taylor expansion of 0 in k 1546938934.514 * [misc]backup-simplify: Simplify 0 into 0 1546938934.514 * [misc]backup-simplify: Simplify 0 into 0 1546938934.514 * [misc]backup-simplify: Simplify 0 into 0 1546938934.514 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938934.519 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 1546938934.519 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546938934.519 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1546938934.519 * [misc]backup-simplify: Simplify (- 0) into 0 1546938934.520 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938934.520 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 1546938934.520 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log 2) (log n))))) into 0 1546938934.523 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1546938934.523 * [misc]taylor: Taking taylor expansion of 0 in k 1546938934.523 * [misc]backup-simplify: Simplify 0 into 0 1546938934.523 * [misc]backup-simplify: Simplify 0 into 0 1546938934.523 * [misc]backup-simplify: Simplify 0 into 0 1546938934.523 * [misc]backup-simplify: Simplify 0 into 0 1546938934.523 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938934.530 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 1546938934.530 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546938934.531 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1546938934.531 * [misc]backup-simplify: Simplify (- 0) into 0 1546938934.531 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938934.531 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 1546938934.532 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log 2) (log n)))))) into 0 1546938934.535 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1546938934.535 * [misc]taylor: Taking taylor expansion of 0 in k 1546938934.535 * [misc]backup-simplify: Simplify 0 into 0 1546938934.535 * [misc]backup-simplify: Simplify 0 into 0 1546938934.536 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log 2) (log (/ 1 n))))) into (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) 1546938934.536 * [misc]backup-simplify: Simplify (pow (* (/ 1 (- n)) 2) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) 1546938934.536 * [misc]approximate: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 1546938934.536 * [misc]taylor: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1546938934.536 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in k 1546938934.536 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in k 1546938934.536 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546938934.536 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546938934.536 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938934.536 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.536 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546938934.536 * [misc]taylor: Taking taylor expansion of k in k 1546938934.536 * [misc]backup-simplify: Simplify 0 into 0 1546938934.536 * [misc]backup-simplify: Simplify 1 into 1 1546938934.536 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546938934.536 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938934.536 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.536 * [misc]taylor: Taking taylor expansion of (log (/ -2 n)) in k 1546938934.536 * [misc]taylor: Taking taylor expansion of (/ -2 n) in k 1546938934.536 * [misc]taylor: Taking taylor expansion of -2 in k 1546938934.536 * [misc]backup-simplify: Simplify -2 into -2 1546938934.536 * [misc]taylor: Taking taylor expansion of n in k 1546938934.537 * [misc]backup-simplify: Simplify n into n 1546938934.537 * [misc]backup-simplify: Simplify (/ -2 n) into (/ -2 n) 1546938934.537 * [misc]backup-simplify: Simplify (log (/ -2 n)) into (log (/ -2 n)) 1546938934.537 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546938934.537 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546938934.537 * [misc]backup-simplify: Simplify (* 1/2 (log (/ -2 n))) into (* 1/2 (log (/ -2 n))) 1546938934.537 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) into (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) 1546938934.537 * [misc]taylor: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546938934.537 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 1546938934.537 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 1546938934.537 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546938934.537 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546938934.537 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938934.537 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.537 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938934.537 * [misc]taylor: Taking taylor expansion of k in n 1546938934.538 * [misc]backup-simplify: Simplify k into k 1546938934.538 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938934.538 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938934.538 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.538 * [misc]taylor: Taking taylor expansion of (log (/ -2 n)) in n 1546938934.538 * [misc]taylor: Taking taylor expansion of (/ -2 n) in n 1546938934.538 * [misc]taylor: Taking taylor expansion of -2 in n 1546938934.538 * [misc]backup-simplify: Simplify -2 into -2 1546938934.538 * [misc]taylor: Taking taylor expansion of n in n 1546938934.538 * [misc]backup-simplify: Simplify 0 into 0 1546938934.538 * [misc]backup-simplify: Simplify 1 into 1 1546938934.538 * [misc]backup-simplify: Simplify (/ -2 1) into -2 1546938934.538 * [misc]backup-simplify: Simplify (log -2) into (log -2) 1546938934.538 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546938934.538 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546938934.539 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 1546938934.539 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 1546938934.539 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 1546938934.539 * [misc]taylor: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546938934.539 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 1546938934.539 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 1546938934.539 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546938934.539 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546938934.539 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938934.540 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.540 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938934.540 * [misc]taylor: Taking taylor expansion of k in n 1546938934.540 * [misc]backup-simplify: Simplify k into k 1546938934.540 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938934.540 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938934.540 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.540 * [misc]taylor: Taking taylor expansion of (log (/ -2 n)) in n 1546938934.540 * [misc]taylor: Taking taylor expansion of (/ -2 n) in n 1546938934.540 * [misc]taylor: Taking taylor expansion of -2 in n 1546938934.540 * [misc]backup-simplify: Simplify -2 into -2 1546938934.540 * [misc]taylor: Taking taylor expansion of n in n 1546938934.540 * [misc]backup-simplify: Simplify 0 into 0 1546938934.540 * [misc]backup-simplify: Simplify 1 into 1 1546938934.540 * [misc]backup-simplify: Simplify (/ -2 1) into -2 1546938934.540 * [misc]backup-simplify: Simplify (log -2) into (log -2) 1546938934.540 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546938934.540 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546938934.541 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 1546938934.541 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 1546938934.541 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 1546938934.541 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) in k 1546938934.542 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) in k 1546938934.542 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546938934.542 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546938934.542 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938934.542 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.542 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546938934.542 * [misc]taylor: Taking taylor expansion of k in k 1546938934.542 * [misc]backup-simplify: Simplify 0 into 0 1546938934.542 * [misc]backup-simplify: Simplify 1 into 1 1546938934.542 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546938934.542 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938934.542 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.542 * [misc]taylor: Taking taylor expansion of (- (log -2) (log n)) in k 1546938934.542 * [misc]taylor: Taking taylor expansion of (log -2) in k 1546938934.542 * [misc]taylor: Taking taylor expansion of -2 in k 1546938934.542 * [misc]backup-simplify: Simplify -2 into -2 1546938934.542 * [misc]backup-simplify: Simplify (log -2) into (log -2) 1546938934.542 * [misc]taylor: Taking taylor expansion of (log n) in k 1546938934.542 * [misc]taylor: Taking taylor expansion of n in k 1546938934.542 * [misc]backup-simplify: Simplify n into n 1546938934.542 * [misc]backup-simplify: Simplify (log n) into (log n) 1546938934.543 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546938934.543 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546938934.543 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1546938934.543 * [misc]backup-simplify: Simplify (+ (log -2) (- (log n))) into (- (log -2) (log n)) 1546938934.543 * [misc]backup-simplify: Simplify (* 1/2 (- (log -2) (log n))) into (* 1/2 (- (log -2) (log n))) 1546938934.543 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 1546938934.544 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 1546938934.544 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -2 (/ 0 1)))) into 0 1546938934.547 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -2 1)))) 1) into 0 1546938934.547 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546938934.548 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546938934.548 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938934.548 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 1546938934.549 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log -2) (log n)))) into 0 1546938934.550 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546938934.550 * [misc]taylor: Taking taylor expansion of 0 in k 1546938934.550 * [misc]backup-simplify: Simplify 0 into 0 1546938934.550 * [misc]backup-simplify: Simplify 0 into 0 1546938934.550 * [misc]backup-simplify: Simplify 0 into 0 1546938934.550 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -2 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938934.555 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -2 1)))) 2) into 0 1546938934.555 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546938934.556 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1546938934.556 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938934.556 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 1546938934.557 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log -2) (log n))))) into 0 1546938934.559 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1546938934.559 * [misc]taylor: Taking taylor expansion of 0 in k 1546938934.559 * [misc]backup-simplify: Simplify 0 into 0 1546938934.559 * [misc]backup-simplify: Simplify 0 into 0 1546938934.559 * [misc]backup-simplify: Simplify 0 into 0 1546938934.559 * [misc]backup-simplify: Simplify 0 into 0 1546938934.560 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -2 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938934.568 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow -2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow -2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow -2 1)))) 6) into 0 1546938934.568 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546938934.569 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1546938934.569 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938934.569 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 1546938934.570 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log -2) (log n)))))) into 0 1546938934.574 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1546938934.574 * [misc]taylor: Taking taylor expansion of 0 in k 1546938934.574 * [misc]backup-simplify: Simplify 0 into 0 1546938934.574 * [misc]backup-simplify: Simplify 0 into 0 1546938934.574 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -2) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) 1546938934.575 * * * * [misc]progress: [ 3 / 4 ] generating series at (2 2) 1546938934.575 * [misc]backup-simplify: Simplify (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)) into (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) 1546938934.575 * [misc]approximate: Taking taylor expansion of (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in (n k) around 0 1546938934.575 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in k 1546938934.575 * [misc]taylor: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in k 1546938934.575 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in k 1546938934.575 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in k 1546938934.575 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546938934.575 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938934.575 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.575 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546938934.575 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938934.575 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.575 * [misc]taylor: Taking taylor expansion of k in k 1546938934.575 * [misc]backup-simplify: Simplify 0 into 0 1546938934.575 * [misc]backup-simplify: Simplify 1 into 1 1546938934.575 * [misc]taylor: Taking taylor expansion of (log (* 2 n)) in k 1546938934.575 * [misc]taylor: Taking taylor expansion of (* 2 n) in k 1546938934.575 * [misc]taylor: Taking taylor expansion of 2 in k 1546938934.575 * [misc]backup-simplify: Simplify 2 into 2 1546938934.575 * [misc]taylor: Taking taylor expansion of n in k 1546938934.575 * [misc]backup-simplify: Simplify n into n 1546938934.575 * [misc]backup-simplify: Simplify (* 2 n) into (* 2 n) 1546938934.575 * [misc]backup-simplify: Simplify (log (* 2 n)) into (log (* 2 n)) 1546938934.575 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546938934.576 * [misc]backup-simplify: Simplify (- 0) into 0 1546938934.576 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546938934.576 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 n))) into (* 1/2 (log (* 2 n))) 1546938934.576 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 n)))) into (pow (* 2 n) 1/2) 1546938934.576 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1546938934.576 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546938934.576 * [misc]taylor: Taking taylor expansion of k in k 1546938934.576 * [misc]backup-simplify: Simplify 0 into 0 1546938934.576 * [misc]backup-simplify: Simplify 1 into 1 1546938934.576 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546938934.576 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546938934.577 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546938934.577 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in n 1546938934.577 * [misc]taylor: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in n 1546938934.577 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in n 1546938934.577 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in n 1546938934.577 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546938934.577 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938934.577 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.577 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546938934.577 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938934.577 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.577 * [misc]taylor: Taking taylor expansion of k in n 1546938934.577 * [misc]backup-simplify: Simplify k into k 1546938934.577 * [misc]taylor: Taking taylor expansion of (log (* 2 n)) in n 1546938934.577 * [misc]taylor: Taking taylor expansion of (* 2 n) in n 1546938934.577 * [misc]taylor: Taking taylor expansion of 2 in n 1546938934.577 * [misc]backup-simplify: Simplify 2 into 2 1546938934.577 * [misc]taylor: Taking taylor expansion of n in n 1546938934.577 * [misc]backup-simplify: Simplify 0 into 0 1546938934.577 * [misc]backup-simplify: Simplify 1 into 1 1546938934.577 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546938934.577 * [misc]backup-simplify: Simplify (+ (* 2 1) (* 0 0)) into 2 1546938934.577 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1546938934.577 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546938934.577 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546938934.577 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546938934.578 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 1546938934.578 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (+ (log 2) (log n))) into (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) 1546938934.578 * [misc]backup-simplify: Simplify (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) into (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) 1546938934.578 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1546938934.578 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938934.578 * [misc]taylor: Taking taylor expansion of k in n 1546938934.578 * [misc]backup-simplify: Simplify k into k 1546938934.578 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938934.578 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1546938934.578 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546938934.578 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1546938934.578 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in n 1546938934.578 * [misc]taylor: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in n 1546938934.578 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in n 1546938934.578 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in n 1546938934.578 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546938934.578 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938934.578 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.578 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546938934.578 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938934.578 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.578 * [misc]taylor: Taking taylor expansion of k in n 1546938934.578 * [misc]backup-simplify: Simplify k into k 1546938934.578 * [misc]taylor: Taking taylor expansion of (log (* 2 n)) in n 1546938934.578 * [misc]taylor: Taking taylor expansion of (* 2 n) in n 1546938934.578 * [misc]taylor: Taking taylor expansion of 2 in n 1546938934.578 * [misc]backup-simplify: Simplify 2 into 2 1546938934.578 * [misc]taylor: Taking taylor expansion of n in n 1546938934.579 * [misc]backup-simplify: Simplify 0 into 0 1546938934.579 * [misc]backup-simplify: Simplify 1 into 1 1546938934.579 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546938934.579 * [misc]backup-simplify: Simplify (+ (* 2 1) (* 0 0)) into 2 1546938934.579 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1546938934.579 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546938934.579 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546938934.579 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546938934.579 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 1546938934.579 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (+ (log 2) (log n))) into (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) 1546938934.580 * [misc]backup-simplify: Simplify (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) into (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) 1546938934.580 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1546938934.580 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938934.580 * [misc]taylor: Taking taylor expansion of k in n 1546938934.580 * [misc]backup-simplify: Simplify k into k 1546938934.580 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938934.580 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1546938934.580 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546938934.580 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1546938934.580 * [misc]backup-simplify: Simplify (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) into (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) 1546938934.580 * [misc]taylor: Taking taylor expansion of (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in k 1546938934.580 * [misc]taylor: Taking taylor expansion of (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) in k 1546938934.580 * [misc]taylor: Taking taylor expansion of (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) in k 1546938934.580 * [misc]taylor: Taking taylor expansion of (+ (log 2) (log n)) in k 1546938934.580 * [misc]taylor: Taking taylor expansion of (log 2) in k 1546938934.580 * [misc]taylor: Taking taylor expansion of 2 in k 1546938934.580 * [misc]backup-simplify: Simplify 2 into 2 1546938934.580 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1546938934.580 * [misc]taylor: Taking taylor expansion of (log n) in k 1546938934.580 * [misc]taylor: Taking taylor expansion of n in k 1546938934.580 * [misc]backup-simplify: Simplify n into n 1546938934.581 * [misc]backup-simplify: Simplify (log n) into (log n) 1546938934.581 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546938934.581 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938934.581 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.581 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546938934.581 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938934.581 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.581 * [misc]taylor: Taking taylor expansion of k in k 1546938934.581 * [misc]backup-simplify: Simplify 0 into 0 1546938934.581 * [misc]backup-simplify: Simplify 1 into 1 1546938934.581 * [misc]backup-simplify: Simplify (+ (log 2) (log n)) into (+ (log 2) (log n)) 1546938934.581 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546938934.581 * [misc]backup-simplify: Simplify (- 0) into 0 1546938934.581 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546938934.581 * [misc]backup-simplify: Simplify (* (+ (log 2) (log n)) 1/2) into (* 1/2 (+ (log 2) (log n))) 1546938934.581 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log 2) (log n)))) into (exp (* 1/2 (+ (log 2) (log n)))) 1546938934.581 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1546938934.581 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546938934.581 * [misc]taylor: Taking taylor expansion of k in k 1546938934.581 * [misc]backup-simplify: Simplify 0 into 0 1546938934.581 * [misc]backup-simplify: Simplify 1 into 1 1546938934.582 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546938934.582 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546938934.582 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546938934.582 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) 0) into 0 1546938934.582 * [misc]backup-simplify: Simplify 0 into 0 1546938934.582 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 1) (* 0 0))) into 0 1546938934.584 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 1546938934.584 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1546938934.584 * [misc]backup-simplify: Simplify (- 0) into 0 1546938934.584 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938934.584 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 1546938934.584 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log 2) (log n)))) into 0 1546938934.585 * [misc]backup-simplify: Simplify (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546938934.586 * [misc]backup-simplify: Simplify (+ (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) 0) (* 0 (sqrt (/ 1 k)))) into 0 1546938934.586 * [misc]taylor: Taking taylor expansion of 0 in k 1546938934.586 * [misc]backup-simplify: Simplify 0 into 0 1546938934.586 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1546938934.586 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546938934.586 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546938934.587 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 1546938934.588 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1546938934.588 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938934.589 * [misc]backup-simplify: Simplify (+ (* (+ (log 2) (log n)) -1/2) (* 0 1/2)) into (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 1546938934.590 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) 1546938934.590 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log 2) (log n)))) +nan.0) (* (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) 0)) into (- (* +nan.0 (exp (* 1/2 (+ (log 2) (log n)))))) 1546938934.590 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (+ (log 2) (log n)))))) into (- (* +nan.0 (exp (* 1/2 (+ (log 2) (log n)))))) 1546938934.591 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546938934.591 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 1546938934.591 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1546938934.594 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 1546938934.594 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1546938934.594 * [misc]backup-simplify: Simplify (- 0) into 0 1546938934.594 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938934.594 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 1546938934.595 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log 2) (log n))))) into 0 1546938934.596 * [misc]backup-simplify: Simplify (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1546938934.597 * [misc]backup-simplify: Simplify (+ (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k))))) into 0 1546938934.597 * [misc]taylor: Taking taylor expansion of 0 in k 1546938934.597 * [misc]backup-simplify: Simplify 0 into 0 1546938934.597 * [misc]backup-simplify: Simplify 0 into 0 1546938934.597 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1546938934.598 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1546938934.599 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1546938934.599 * [misc]backup-simplify: Simplify (- 0) into 0 1546938934.599 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938934.603 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 1546938934.605 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1546938934.605 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938934.606 * [misc]backup-simplify: Simplify (+ (* (+ (log 2) (log n)) 0) (+ (* 0 -1/2) (* 0 1/2))) into 0 1546938934.607 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))) 1546938934.610 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log 2) (log n)))) +nan.0) (+ (* (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) +nan.0) (* (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))) 0))) into (- (+ (* +nan.0 (* (log 2) (exp (* 1/2 (+ (log 2) (log n)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (- (* +nan.0 (exp (* 1/2 (+ (log 2) (log n)))))))))) 1546938934.611 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (log 2) (exp (* 1/2 (+ (log 2) (log n)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (- (* +nan.0 (exp (* 1/2 (+ (log 2) (log n)))))))))) into (- (+ (* +nan.0 (* (log 2) (exp (* 1/2 (+ (log 2) (log n)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (- (* +nan.0 (exp (* 1/2 (+ (log 2) (log n)))))))))) 1546938934.611 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546938934.612 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 1546938934.612 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))) into 0 1546938934.619 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 1546938934.619 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 1546938934.620 * [misc]backup-simplify: Simplify (- 0) into 0 1546938934.620 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938934.620 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 1546938934.621 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log 2) (log n)))))) into 0 1546938934.624 * [misc]backup-simplify: Simplify (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1546938934.625 * [misc]backup-simplify: Simplify (+ (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k)))))) into 0 1546938934.625 * [misc]taylor: Taking taylor expansion of 0 in k 1546938934.625 * [misc]backup-simplify: Simplify 0 into 0 1546938934.625 * [misc]backup-simplify: Simplify 0 into 0 1546938934.625 * [misc]backup-simplify: Simplify 0 into 0 1546938934.625 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938934.626 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1546938934.627 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1546938934.627 * [misc]backup-simplify: Simplify (- 0) into 0 1546938934.627 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938934.633 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 1546938934.636 * [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 1546938934.636 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938934.637 * [misc]backup-simplify: Simplify (+ (* (+ (log 2) (log n)) 0) (+ (* 0 0) (+ (* 0 -1/2) (* 0 1/2)))) into 0 1546938934.639 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 3) 6)) (* (/ (pow (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (log 2) (pow (log n) 2))) (+ (* 1/16 (* (pow (log 2) 2) (log n))) (* 1/48 (pow (log 2) 3))))) (exp (* 1/2 (+ (log 2) (log n)))))) 1546938934.644 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log 2) (log n)))) +nan.0) (+ (* (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) +nan.0) (+ (* (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))) +nan.0) (* (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (log 2) (pow (log n) 2))) (+ (* 1/16 (* (pow (log 2) 2) (log n))) (* 1/48 (pow (log 2) 3))))) (exp (* 1/2 (+ (log 2) (log n)))))) 0)))) into (- (+ (* +nan.0 (* (log 2) (exp (* 1/2 (+ (log 2) (log n)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log 2) (log n))))) (- (+ (* +nan.0 (* (pow (log 2) 2) (exp (* 1/2 (+ (log 2) (log n)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2))) (- (* +nan.0 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))))))))))))))) 1546938934.648 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (log 2) (exp (* 1/2 (+ (log 2) (log n)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log 2) (log n))))) (- (+ (* +nan.0 (* (pow (log 2) 2) (exp (* 1/2 (+ (log 2) (log n)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2))) (- (* +nan.0 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))))))))))))))) into (- (+ (* +nan.0 (* (log 2) (exp (* 1/2 (+ (log 2) (log n)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log 2) (log n))))) (- (+ (* +nan.0 (* (pow (log 2) 2) (exp (* 1/2 (+ (log 2) (log n)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2))) (- (* +nan.0 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))))))))))))))) 1546938934.655 * [misc]backup-simplify: Simplify (+ (* (- (+ (* +nan.0 (* (log 2) (exp (* 1/2 (+ (log 2) (log n)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log 2) (log n))))) (- (+ (* +nan.0 (* (pow (log 2) 2) (exp (* 1/2 (+ (log 2) (log n)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2))) (- (* +nan.0 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (log 2) (exp (* 1/2 (+ (log 2) (log n)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (- (* +nan.0 (exp (* 1/2 (+ (log 2) (log n)))))))))) (* k 1)) (- (* +nan.0 (exp (* 1/2 (+ (log 2) (log n)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) k))) (- (+ (* +nan.0 (* (pow (log 2) 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (pow k 2)))) (- (+ (* +nan.0 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) k)) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (pow k 2)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log 2) (log n))))) (- (+ (* +nan.0 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (pow k 2)))))))))))))))))))))) 1546938934.655 * [misc]backup-simplify: Simplify (/ (pow (* (/ 1 n) 2) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) into (* (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) 1546938934.655 * [misc]approximate: Taking taylor expansion of (* (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in (n k) around 0 1546938934.655 * [misc]taylor: Taking taylor expansion of (* (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in k 1546938934.655 * [misc]taylor: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in k 1546938934.655 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in k 1546938934.656 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in k 1546938934.656 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546938934.656 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938934.656 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.656 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546938934.656 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938934.656 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.656 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546938934.656 * [misc]taylor: Taking taylor expansion of k in k 1546938934.656 * [misc]backup-simplify: Simplify 0 into 0 1546938934.656 * [misc]backup-simplify: Simplify 1 into 1 1546938934.656 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546938934.656 * [misc]taylor: Taking taylor expansion of (log (/ 2 n)) in k 1546938934.656 * [misc]taylor: Taking taylor expansion of (/ 2 n) in k 1546938934.656 * [misc]taylor: Taking taylor expansion of 2 in k 1546938934.656 * [misc]backup-simplify: Simplify 2 into 2 1546938934.656 * [misc]taylor: Taking taylor expansion of n in k 1546938934.656 * [misc]backup-simplify: Simplify n into n 1546938934.656 * [misc]backup-simplify: Simplify (/ 2 n) into (/ 2 n) 1546938934.656 * [misc]backup-simplify: Simplify (log (/ 2 n)) into (log (/ 2 n)) 1546938934.657 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546938934.657 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546938934.657 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546938934.657 * [misc]backup-simplify: Simplify (* -1/2 (log (/ 2 n))) into (* -1/2 (log (/ 2 n))) 1546938934.657 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) into (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) 1546938934.657 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1546938934.657 * [misc]taylor: Taking taylor expansion of k in k 1546938934.657 * [misc]backup-simplify: Simplify 0 into 0 1546938934.657 * [misc]backup-simplify: Simplify 1 into 1 1546938934.657 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546938934.658 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546938934.658 * [misc]taylor: Taking taylor expansion of (* (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in n 1546938934.658 * [misc]taylor: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546938934.658 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 1546938934.658 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 1546938934.658 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546938934.658 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938934.658 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.658 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546938934.658 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938934.658 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.658 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938934.659 * [misc]taylor: Taking taylor expansion of k in n 1546938934.659 * [misc]backup-simplify: Simplify k into k 1546938934.659 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938934.659 * [misc]taylor: Taking taylor expansion of (log (/ 2 n)) in n 1546938934.659 * [misc]taylor: Taking taylor expansion of (/ 2 n) in n 1546938934.659 * [misc]taylor: Taking taylor expansion of 2 in n 1546938934.659 * [misc]backup-simplify: Simplify 2 into 2 1546938934.659 * [misc]taylor: Taking taylor expansion of n in n 1546938934.659 * [misc]backup-simplify: Simplify 0 into 0 1546938934.659 * [misc]backup-simplify: Simplify 1 into 1 1546938934.659 * [misc]backup-simplify: Simplify (/ 2 1) into 2 1546938934.659 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1546938934.659 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546938934.659 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546938934.660 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546938934.660 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 1546938934.660 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 1546938934.661 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 1546938934.661 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1546938934.661 * [misc]taylor: Taking taylor expansion of k in n 1546938934.661 * [misc]backup-simplify: Simplify k into k 1546938934.661 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1546938934.661 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1546938934.661 * [misc]taylor: Taking taylor expansion of (* (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in n 1546938934.661 * [misc]taylor: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546938934.661 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 1546938934.661 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 1546938934.661 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546938934.661 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938934.661 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.661 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546938934.661 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938934.661 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.661 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938934.661 * [misc]taylor: Taking taylor expansion of k in n 1546938934.661 * [misc]backup-simplify: Simplify k into k 1546938934.661 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938934.661 * [misc]taylor: Taking taylor expansion of (log (/ 2 n)) in n 1546938934.661 * [misc]taylor: Taking taylor expansion of (/ 2 n) in n 1546938934.661 * [misc]taylor: Taking taylor expansion of 2 in n 1546938934.662 * [misc]backup-simplify: Simplify 2 into 2 1546938934.662 * [misc]taylor: Taking taylor expansion of n in n 1546938934.662 * [misc]backup-simplify: Simplify 0 into 0 1546938934.662 * [misc]backup-simplify: Simplify 1 into 1 1546938934.662 * [misc]backup-simplify: Simplify (/ 2 1) into 2 1546938934.662 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1546938934.662 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546938934.662 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546938934.662 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546938934.663 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 1546938934.663 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 1546938934.663 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 1546938934.663 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1546938934.663 * [misc]taylor: Taking taylor expansion of k in n 1546938934.663 * [misc]backup-simplify: Simplify k into k 1546938934.663 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1546938934.664 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1546938934.664 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (sqrt k)) into (* (sqrt k) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) 1546938934.664 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) in k 1546938934.664 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1546938934.664 * [misc]taylor: Taking taylor expansion of k in k 1546938934.664 * [misc]backup-simplify: Simplify 0 into 0 1546938934.664 * [misc]backup-simplify: Simplify 1 into 1 1546938934.664 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546938934.665 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546938934.665 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) in k 1546938934.665 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) in k 1546938934.665 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546938934.665 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938934.665 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.665 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546938934.665 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938934.665 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.665 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546938934.665 * [misc]taylor: Taking taylor expansion of k in k 1546938934.665 * [misc]backup-simplify: Simplify 0 into 0 1546938934.665 * [misc]backup-simplify: Simplify 1 into 1 1546938934.665 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546938934.666 * [misc]taylor: Taking taylor expansion of (- (log 2) (log n)) in k 1546938934.666 * [misc]taylor: Taking taylor expansion of (log 2) in k 1546938934.666 * [misc]taylor: Taking taylor expansion of 2 in k 1546938934.666 * [misc]backup-simplify: Simplify 2 into 2 1546938934.666 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1546938934.666 * [misc]taylor: Taking taylor expansion of (log n) in k 1546938934.666 * [misc]taylor: Taking taylor expansion of n in k 1546938934.666 * [misc]backup-simplify: Simplify n into n 1546938934.666 * [misc]backup-simplify: Simplify (log n) into (log n) 1546938934.666 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546938934.667 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546938934.667 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546938934.667 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1546938934.667 * [misc]backup-simplify: Simplify (+ (log 2) (- (log n))) into (- (log 2) (log n)) 1546938934.667 * [misc]backup-simplify: Simplify (* -1/2 (- (log 2) (log n))) into (* -1/2 (- (log 2) (log n))) 1546938934.668 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 1546938934.668 * [misc]backup-simplify: Simplify (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) into 0 1546938934.668 * [misc]backup-simplify: Simplify 0 into 0 1546938934.668 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)))) into 0 1546938934.671 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 1546938934.671 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546938934.671 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546938934.672 * [misc]backup-simplify: Simplify (- 0) into 0 1546938934.672 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938934.672 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 1546938934.672 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log 2) (log n)))) into 0 1546938934.674 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546938934.674 * [misc]backup-simplify: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 0) (* 0 (sqrt k))) into 0 1546938934.674 * [misc]taylor: Taking taylor expansion of 0 in k 1546938934.674 * [misc]backup-simplify: Simplify 0 into 0 1546938934.674 * [misc]backup-simplify: Simplify 0 into 0 1546938934.675 * [misc]backup-simplify: Simplify (+ (* 0 0) (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) 1546938934.675 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) 1546938934.676 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 1546938934.676 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938934.680 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 1546938934.681 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546938934.681 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1546938934.681 * [misc]backup-simplify: Simplify (- 0) into 0 1546938934.681 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938934.682 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 1546938934.682 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log 2) (log n))))) into 0 1546938934.684 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1546938934.685 * [misc]backup-simplify: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 0) (+ (* 0 0) (* 0 (sqrt k)))) into 0 1546938934.685 * [misc]taylor: Taking taylor expansion of 0 in k 1546938934.685 * [misc]backup-simplify: Simplify 0 into 0 1546938934.685 * [misc]backup-simplify: Simplify 0 into 0 1546938934.685 * [misc]backup-simplify: Simplify 0 into 0 1546938934.686 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1546938934.687 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) 1546938934.687 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) 1546938934.688 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 1546938934.688 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938934.695 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 1546938934.695 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546938934.696 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1546938934.696 * [misc]backup-simplify: Simplify (- 0) into 0 1546938934.696 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938934.697 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 1546938934.697 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log 2) (log n)))))) into 0 1546938934.700 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1546938934.701 * [misc]backup-simplify: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt k))))) into 0 1546938934.701 * [misc]taylor: Taking taylor expansion of 0 in k 1546938934.701 * [misc]backup-simplify: Simplify 0 into 0 1546938934.701 * [misc]backup-simplify: Simplify 0 into 0 1546938934.701 * [misc]backup-simplify: Simplify 0 into 0 1546938934.701 * [misc]backup-simplify: Simplify 0 into 0 1546938934.702 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1546938934.702 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* +nan.0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) 1546938934.702 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) 1546938934.703 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log 2) (log (/ 1 n))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log 2) (log (/ 1 n))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log 2) (log (/ 1 n))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) k)) (- (* +nan.0 (/ (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) (pow k 2)))))))) 1546938934.703 * [misc]backup-simplify: Simplify (/ (pow (* (/ 1 (- n)) 2) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) into (/ (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) 1546938934.703 * [misc]approximate: Taking taylor expansion of (/ (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (n k) around 0 1546938934.703 * [misc]taylor: Taking taylor expansion of (/ (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 1546938934.703 * [misc]taylor: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1546938934.704 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in k 1546938934.704 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in k 1546938934.704 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546938934.704 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546938934.704 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938934.704 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.704 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546938934.704 * [misc]taylor: Taking taylor expansion of k in k 1546938934.704 * [misc]backup-simplify: Simplify 0 into 0 1546938934.704 * [misc]backup-simplify: Simplify 1 into 1 1546938934.704 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546938934.704 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938934.704 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.704 * [misc]taylor: Taking taylor expansion of (log (/ -2 n)) in k 1546938934.704 * [misc]taylor: Taking taylor expansion of (/ -2 n) in k 1546938934.704 * [misc]taylor: Taking taylor expansion of -2 in k 1546938934.704 * [misc]backup-simplify: Simplify -2 into -2 1546938934.704 * [misc]taylor: Taking taylor expansion of n in k 1546938934.704 * [misc]backup-simplify: Simplify n into n 1546938934.704 * [misc]backup-simplify: Simplify (/ -2 n) into (/ -2 n) 1546938934.704 * [misc]backup-simplify: Simplify (log (/ -2 n)) into (log (/ -2 n)) 1546938934.704 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546938934.704 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546938934.704 * [misc]backup-simplify: Simplify (* 1/2 (log (/ -2 n))) into (* 1/2 (log (/ -2 n))) 1546938934.704 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) into (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) 1546938934.704 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1546938934.704 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1546938934.704 * [misc]taylor: Taking taylor expansion of -1 in k 1546938934.704 * [misc]backup-simplify: Simplify -1 into -1 1546938934.704 * [misc]taylor: Taking taylor expansion of k in k 1546938934.704 * [misc]backup-simplify: Simplify 0 into 0 1546938934.704 * [misc]backup-simplify: Simplify 1 into 1 1546938934.705 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1546938934.705 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546938934.705 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1546938934.705 * [misc]backup-simplify: Simplify (/ (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) +nan.0) into (* +nan.0 (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2))) 1546938934.705 * [misc]taylor: Taking taylor expansion of (/ (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 1546938934.705 * [misc]taylor: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546938934.705 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 1546938934.705 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 1546938934.705 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546938934.705 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546938934.705 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938934.705 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.705 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938934.705 * [misc]taylor: Taking taylor expansion of k in n 1546938934.705 * [misc]backup-simplify: Simplify k into k 1546938934.705 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938934.705 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938934.705 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.705 * [misc]taylor: Taking taylor expansion of (log (/ -2 n)) in n 1546938934.705 * [misc]taylor: Taking taylor expansion of (/ -2 n) in n 1546938934.706 * [misc]taylor: Taking taylor expansion of -2 in n 1546938934.706 * [misc]backup-simplify: Simplify -2 into -2 1546938934.706 * [misc]taylor: Taking taylor expansion of n in n 1546938934.706 * [misc]backup-simplify: Simplify 0 into 0 1546938934.706 * [misc]backup-simplify: Simplify 1 into 1 1546938934.706 * [misc]backup-simplify: Simplify (/ -2 1) into -2 1546938934.706 * [misc]backup-simplify: Simplify (log -2) into (log -2) 1546938934.706 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546938934.706 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546938934.706 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 1546938934.706 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 1546938934.707 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 1546938934.707 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1546938934.707 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1546938934.707 * [misc]taylor: Taking taylor expansion of -1 in n 1546938934.707 * [misc]backup-simplify: Simplify -1 into -1 1546938934.707 * [misc]taylor: Taking taylor expansion of k in n 1546938934.707 * [misc]backup-simplify: Simplify k into k 1546938934.707 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1546938934.707 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1546938934.707 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1546938934.707 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1546938934.707 * [misc]backup-simplify: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt (/ -1 k))) 1546938934.707 * [misc]taylor: Taking taylor expansion of (/ (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 1546938934.707 * [misc]taylor: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546938934.707 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 1546938934.707 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 1546938934.707 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546938934.707 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546938934.707 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938934.707 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.707 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938934.707 * [misc]taylor: Taking taylor expansion of k in n 1546938934.707 * [misc]backup-simplify: Simplify k into k 1546938934.707 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938934.707 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938934.707 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.707 * [misc]taylor: Taking taylor expansion of (log (/ -2 n)) in n 1546938934.707 * [misc]taylor: Taking taylor expansion of (/ -2 n) in n 1546938934.707 * [misc]taylor: Taking taylor expansion of -2 in n 1546938934.707 * [misc]backup-simplify: Simplify -2 into -2 1546938934.707 * [misc]taylor: Taking taylor expansion of n in n 1546938934.708 * [misc]backup-simplify: Simplify 0 into 0 1546938934.708 * [misc]backup-simplify: Simplify 1 into 1 1546938934.708 * [misc]backup-simplify: Simplify (/ -2 1) into -2 1546938934.708 * [misc]backup-simplify: Simplify (log -2) into (log -2) 1546938934.708 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546938934.708 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546938934.708 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 1546938934.708 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 1546938934.709 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 1546938934.709 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1546938934.709 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1546938934.709 * [misc]taylor: Taking taylor expansion of -1 in n 1546938934.709 * [misc]backup-simplify: Simplify -1 into -1 1546938934.709 * [misc]taylor: Taking taylor expansion of k in n 1546938934.709 * [misc]backup-simplify: Simplify k into k 1546938934.709 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1546938934.709 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1546938934.709 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1546938934.709 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1546938934.709 * [misc]backup-simplify: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt (/ -1 k))) 1546938934.709 * [misc]taylor: Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt (/ -1 k))) in k 1546938934.709 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) in k 1546938934.709 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) in k 1546938934.710 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546938934.710 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546938934.710 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938934.710 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.710 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546938934.710 * [misc]taylor: Taking taylor expansion of k in k 1546938934.710 * [misc]backup-simplify: Simplify 0 into 0 1546938934.710 * [misc]backup-simplify: Simplify 1 into 1 1546938934.710 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546938934.710 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938934.710 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.710 * [misc]taylor: Taking taylor expansion of (- (log -2) (log n)) in k 1546938934.710 * [misc]taylor: Taking taylor expansion of (log -2) in k 1546938934.710 * [misc]taylor: Taking taylor expansion of -2 in k 1546938934.710 * [misc]backup-simplify: Simplify -2 into -2 1546938934.710 * [misc]backup-simplify: Simplify (log -2) into (log -2) 1546938934.710 * [misc]taylor: Taking taylor expansion of (log n) in k 1546938934.710 * [misc]taylor: Taking taylor expansion of n in k 1546938934.710 * [misc]backup-simplify: Simplify n into n 1546938934.710 * [misc]backup-simplify: Simplify (log n) into (log n) 1546938934.710 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546938934.710 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546938934.710 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1546938934.710 * [misc]backup-simplify: Simplify (+ (log -2) (- (log n))) into (- (log -2) (log n)) 1546938934.711 * [misc]backup-simplify: Simplify (* 1/2 (- (log -2) (log n))) into (* 1/2 (- (log -2) (log n))) 1546938934.711 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 1546938934.711 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1546938934.711 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1546938934.711 * [misc]taylor: Taking taylor expansion of -1 in k 1546938934.711 * [misc]backup-simplify: Simplify -1 into -1 1546938934.711 * [misc]taylor: Taking taylor expansion of k in k 1546938934.711 * [misc]backup-simplify: Simplify 0 into 0 1546938934.711 * [misc]backup-simplify: Simplify 1 into 1 1546938934.711 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1546938934.711 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546938934.712 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1546938934.712 * [misc]backup-simplify: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) +nan.0) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))) 1546938934.712 * [misc]backup-simplify: Simplify (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))) 1546938934.712 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -2 (/ 0 1)))) into 0 1546938934.714 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -2 1)))) 1) into 0 1546938934.714 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546938934.714 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546938934.714 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938934.714 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 1546938934.714 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log -2) (log n)))) into 0 1546938934.715 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546938934.716 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0 1546938934.716 * [misc]taylor: Taking taylor expansion of 0 in k 1546938934.716 * [misc]backup-simplify: Simplify 0 into 0 1546938934.716 * [misc]backup-simplify: Simplify 0 into 0 1546938934.716 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1546938934.716 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1546938934.717 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))))) 1546938934.717 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))))) 1546938934.718 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -2 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938934.720 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -2 1)))) 2) into 0 1546938934.720 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546938934.721 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1546938934.721 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938934.721 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 1546938934.721 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log -2) (log n))))) into 0 1546938934.723 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1546938934.723 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546938934.723 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 1546938934.723 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0 1546938934.724 * [misc]taylor: Taking taylor expansion of 0 in k 1546938934.724 * [misc]backup-simplify: Simplify 0 into 0 1546938934.724 * [misc]backup-simplify: Simplify 0 into 0 1546938934.724 * [misc]backup-simplify: Simplify 0 into 0 1546938934.724 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938934.725 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1546938934.726 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))))) 1546938934.726 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))))) 1546938934.727 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -2) (log (/ 1 (- n)))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -2) (log (/ 1 (- n)))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -2) (log (/ 1 (- n))))))))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (pow k 2))) (- (+ (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n)))))) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) k))))))) 1546938934.727 * * * * [misc]progress: [ 4 / 4 ] generating series at (2) 1546938934.728 * [misc]backup-simplify: Simplify (* (pow PI (- 1/2 (/ k 2))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))) into (* (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) 1546938934.728 * [misc]approximate: Taking taylor expansion of (* (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in (k n) around 0 1546938934.728 * [misc]taylor: Taking taylor expansion of (* (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in n 1546938934.728 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) in n 1546938934.728 * [misc]taylor: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in n 1546938934.728 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in n 1546938934.728 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in n 1546938934.728 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546938934.728 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938934.728 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.728 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546938934.728 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938934.728 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.728 * [misc]taylor: Taking taylor expansion of k in n 1546938934.728 * [misc]backup-simplify: Simplify k into k 1546938934.728 * [misc]taylor: Taking taylor expansion of (log (* 2 n)) in n 1546938934.728 * [misc]taylor: Taking taylor expansion of (* 2 n) in n 1546938934.728 * [misc]taylor: Taking taylor expansion of 2 in n 1546938934.728 * [misc]backup-simplify: Simplify 2 into 2 1546938934.728 * [misc]taylor: Taking taylor expansion of n in n 1546938934.728 * [misc]backup-simplify: Simplify 0 into 0 1546938934.728 * [misc]backup-simplify: Simplify 1 into 1 1546938934.728 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546938934.728 * [misc]backup-simplify: Simplify (+ (* 2 1) (* 0 0)) into 2 1546938934.728 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1546938934.728 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546938934.729 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546938934.729 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546938934.729 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 1546938934.729 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (+ (log 2) (log n))) into (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) 1546938934.729 * [misc]backup-simplify: Simplify (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) into (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) 1546938934.729 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in n 1546938934.729 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in n 1546938934.729 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in n 1546938934.729 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546938934.729 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938934.729 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.729 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546938934.729 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938934.729 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.729 * [misc]taylor: Taking taylor expansion of k in n 1546938934.729 * [misc]backup-simplify: Simplify k into k 1546938934.729 * [misc]taylor: Taking taylor expansion of (log PI) in n 1546938934.729 * [misc]taylor: Taking taylor expansion of PI in n 1546938934.729 * [misc]backup-simplify: Simplify PI into PI 1546938934.730 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1546938934.730 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546938934.730 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546938934.730 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546938934.730 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (log PI)) into (* (- 1/2 (* 1/2 k)) (log PI)) 1546938934.730 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 k)) (log PI))) into (pow PI (- 1/2 (* 1/2 k))) 1546938934.730 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1546938934.730 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938934.730 * [misc]taylor: Taking taylor expansion of k in n 1546938934.730 * [misc]backup-simplify: Simplify k into k 1546938934.730 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938934.730 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1546938934.730 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546938934.730 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1546938934.730 * [misc]taylor: Taking taylor expansion of (* (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in k 1546938934.731 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) in k 1546938934.731 * [misc]taylor: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in k 1546938934.731 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in k 1546938934.731 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in k 1546938934.731 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546938934.731 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938934.731 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.731 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546938934.731 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938934.731 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.731 * [misc]taylor: Taking taylor expansion of k in k 1546938934.731 * [misc]backup-simplify: Simplify 0 into 0 1546938934.731 * [misc]backup-simplify: Simplify 1 into 1 1546938934.731 * [misc]taylor: Taking taylor expansion of (log (* 2 n)) in k 1546938934.731 * [misc]taylor: Taking taylor expansion of (* 2 n) in k 1546938934.731 * [misc]taylor: Taking taylor expansion of 2 in k 1546938934.731 * [misc]backup-simplify: Simplify 2 into 2 1546938934.731 * [misc]taylor: Taking taylor expansion of n in k 1546938934.731 * [misc]backup-simplify: Simplify n into n 1546938934.731 * [misc]backup-simplify: Simplify (* 2 n) into (* 2 n) 1546938934.731 * [misc]backup-simplify: Simplify (log (* 2 n)) into (log (* 2 n)) 1546938934.731 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546938934.731 * [misc]backup-simplify: Simplify (- 0) into 0 1546938934.731 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546938934.731 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 n))) into (* 1/2 (log (* 2 n))) 1546938934.731 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 n)))) into (pow (* 2 n) 1/2) 1546938934.731 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 1546938934.731 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 1546938934.731 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 1546938934.731 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546938934.731 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938934.731 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.731 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546938934.731 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938934.731 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.731 * [misc]taylor: Taking taylor expansion of k in k 1546938934.731 * [misc]backup-simplify: Simplify 0 into 0 1546938934.731 * [misc]backup-simplify: Simplify 1 into 1 1546938934.732 * [misc]taylor: Taking taylor expansion of (log PI) in k 1546938934.732 * [misc]taylor: Taking taylor expansion of PI in k 1546938934.732 * [misc]backup-simplify: Simplify PI into PI 1546938934.732 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1546938934.732 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546938934.732 * [misc]backup-simplify: Simplify (- 0) into 0 1546938934.732 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546938934.732 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1546938934.733 * [misc]backup-simplify: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 1546938934.733 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1546938934.733 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546938934.733 * [misc]taylor: Taking taylor expansion of k in k 1546938934.733 * [misc]backup-simplify: Simplify 0 into 0 1546938934.733 * [misc]backup-simplify: Simplify 1 into 1 1546938934.733 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546938934.733 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546938934.733 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546938934.733 * [misc]taylor: Taking taylor expansion of (* (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in k 1546938934.733 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) in k 1546938934.733 * [misc]taylor: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in k 1546938934.733 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in k 1546938934.733 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in k 1546938934.733 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546938934.733 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938934.733 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.733 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546938934.733 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938934.733 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.734 * [misc]taylor: Taking taylor expansion of k in k 1546938934.734 * [misc]backup-simplify: Simplify 0 into 0 1546938934.734 * [misc]backup-simplify: Simplify 1 into 1 1546938934.734 * [misc]taylor: Taking taylor expansion of (log (* 2 n)) in k 1546938934.734 * [misc]taylor: Taking taylor expansion of (* 2 n) in k 1546938934.734 * [misc]taylor: Taking taylor expansion of 2 in k 1546938934.734 * [misc]backup-simplify: Simplify 2 into 2 1546938934.734 * [misc]taylor: Taking taylor expansion of n in k 1546938934.734 * [misc]backup-simplify: Simplify n into n 1546938934.734 * [misc]backup-simplify: Simplify (* 2 n) into (* 2 n) 1546938934.734 * [misc]backup-simplify: Simplify (log (* 2 n)) into (log (* 2 n)) 1546938934.734 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546938934.734 * [misc]backup-simplify: Simplify (- 0) into 0 1546938934.734 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546938934.734 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 n))) into (* 1/2 (log (* 2 n))) 1546938934.734 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 n)))) into (pow (* 2 n) 1/2) 1546938934.734 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 1546938934.734 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 1546938934.734 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 1546938934.734 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546938934.734 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938934.734 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.734 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546938934.734 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938934.734 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.734 * [misc]taylor: Taking taylor expansion of k in k 1546938934.734 * [misc]backup-simplify: Simplify 0 into 0 1546938934.734 * [misc]backup-simplify: Simplify 1 into 1 1546938934.734 * [misc]taylor: Taking taylor expansion of (log PI) in k 1546938934.734 * [misc]taylor: Taking taylor expansion of PI in k 1546938934.734 * [misc]backup-simplify: Simplify PI into PI 1546938934.735 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1546938934.735 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546938934.735 * [misc]backup-simplify: Simplify (- 0) into 0 1546938934.735 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546938934.735 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1546938934.736 * [misc]backup-simplify: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 1546938934.736 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1546938934.736 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546938934.736 * [misc]taylor: Taking taylor expansion of k in k 1546938934.736 * [misc]backup-simplify: Simplify 0 into 0 1546938934.736 * [misc]backup-simplify: Simplify 1 into 1 1546938934.736 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546938934.736 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546938934.736 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546938934.736 * [misc]backup-simplify: Simplify (* (pow (* 2 n) 1/2) (pow PI 1/2)) into (sqrt (* PI (* n 2))) 1546938934.736 * [misc]backup-simplify: Simplify (* (sqrt (* PI (* n 2))) 0) into 0 1546938934.737 * [misc]taylor: Taking taylor expansion of 0 in n 1546938934.737 * [misc]backup-simplify: Simplify 0 into 0 1546938934.737 * [misc]backup-simplify: Simplify 0 into 0 1546938934.738 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 1546938934.738 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1546938934.738 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546938934.738 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546938934.739 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (log PI))) into (- (* 1/2 (log PI))) 1546938934.741 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 1) 1)))) into (* -1/2 (* (log PI) (sqrt PI))) 1546938934.741 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 n)) into 0 1546938934.741 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 n) 1)))) 1) into 0 1546938934.742 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1546938934.742 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546938934.742 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546938934.742 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 n)))) into (- (* 1/2 (log (* 2 n)))) 1546938934.742 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 n)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 n)))) 1) 1)))) into (* -1/2 (* (sqrt (* n 2)) (log (* 2 n)))) 1546938934.743 * [misc]backup-simplify: Simplify (+ (* (pow (* 2 n) 1/2) (* -1/2 (* (log PI) (sqrt PI)))) (* (* -1/2 (* (sqrt (* n 2)) (log (* 2 n)))) (pow PI 1/2))) into (- (+ (* 1/2 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (* 1/2 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n)))))) 1546938934.744 * [misc]backup-simplify: Simplify (+ (* (sqrt (* PI (* n 2))) +nan.0) (* (- (+ (* 1/2 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (* 1/2 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n)))))) 0)) into (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) 1546938934.744 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 1546938934.744 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 1546938934.744 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546938934.744 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546938934.744 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1546938934.744 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1546938934.744 * [misc]taylor: Taking taylor expansion of 2 in n 1546938934.744 * [misc]backup-simplify: Simplify 2 into 2 1546938934.744 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1546938934.744 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1546938934.744 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1546938934.744 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546938934.744 * [misc]taylor: Taking taylor expansion of n in n 1546938934.744 * [misc]backup-simplify: Simplify 0 into 0 1546938934.744 * [misc]backup-simplify: Simplify 1 into 1 1546938934.744 * [misc]taylor: Taking taylor expansion of PI in n 1546938934.744 * [misc]backup-simplify: Simplify PI into PI 1546938934.745 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546938934.745 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546938934.745 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546938934.745 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1546938934.746 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1546938934.746 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1546938934.746 * [misc]backup-simplify: Simplify (- 0) into 0 1546938934.746 * [misc]backup-simplify: Simplify 0 into 0 1546938934.746 * [misc]backup-simplify: Simplify 0 into 0 1546938934.746 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1546938934.747 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1546938934.751 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 1546938934.751 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1546938934.751 * [misc]backup-simplify: Simplify (- 0) into 0 1546938934.751 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938934.753 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log PI)))) into 0 1546938934.757 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI))) 1546938934.758 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 n))) into 0 1546938934.759 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 n) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 n) 1)))) 2) into 0 1546938934.759 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1546938934.760 * [misc]backup-simplify: Simplify (- 0) into 0 1546938934.760 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938934.760 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 n))))) into 0 1546938934.761 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 n)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* n 2)) (pow (log (* 2 n)) 2))) 1546938934.765 * [misc]backup-simplify: Simplify (+ (* (pow (* 2 n) 1/2) (* 1/8 (* (pow (log PI) 2) (sqrt PI)))) (+ (* (* -1/2 (* (sqrt (* n 2)) (log (* 2 n)))) (* -1/2 (* (log PI) (sqrt PI)))) (* (* 1/8 (* (sqrt (* n 2)) (pow (log (* 2 n)) 2))) (pow PI 1/2)))) into (+ (* 1/8 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (+ (* 1/8 (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (sqrt (* PI n)))) (* 1/4 (* (sqrt (* PI n)) (* (sqrt 2) (* (log (* 2 n)) (log PI))))))) 1546938934.769 * [misc]backup-simplify: Simplify (+ (* (sqrt (* PI (* n 2))) +nan.0) (+ (* (- (+ (* 1/2 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (* 1/2 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n)))))) +nan.0) (* (+ (* 1/8 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (+ (* 1/8 (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (sqrt (* PI n)))) (* 1/4 (* (sqrt (* PI n)) (* (sqrt 2) (* (log (* 2 n)) (log PI))))))) 0))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n))))))))) 1546938934.769 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n))))))))) in n 1546938934.769 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n)))))))) in n 1546938934.769 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) in n 1546938934.769 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546938934.769 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546938934.769 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (log PI)) (sqrt (* PI n))) in n 1546938934.769 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log PI)) in n 1546938934.769 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1546938934.769 * [misc]taylor: Taking taylor expansion of 2 in n 1546938934.769 * [misc]backup-simplify: Simplify 2 into 2 1546938934.769 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1546938934.770 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1546938934.770 * [misc]taylor: Taking taylor expansion of (log PI) in n 1546938934.770 * [misc]taylor: Taking taylor expansion of PI in n 1546938934.770 * [misc]backup-simplify: Simplify PI into PI 1546938934.770 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1546938934.770 * [misc]taylor: Taking taylor expansion of (sqrt (* PI n)) in n 1546938934.770 * [misc]taylor: Taking taylor expansion of (* PI n) in n 1546938934.770 * [misc]taylor: Taking taylor expansion of PI in n 1546938934.770 * [misc]backup-simplify: Simplify PI into PI 1546938934.770 * [misc]taylor: Taking taylor expansion of n in n 1546938934.770 * [misc]backup-simplify: Simplify 0 into 0 1546938934.770 * [misc]backup-simplify: Simplify 1 into 1 1546938934.771 * [misc]backup-simplify: Simplify (* PI 0) into 0 1546938934.771 * [misc]backup-simplify: Simplify (+ (* PI 1) (* 0 0)) into PI 1546938934.771 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546938934.772 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1546938934.772 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n))))))) in n 1546938934.772 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n)))))) in n 1546938934.772 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 1546938934.772 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546938934.772 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546938934.772 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1546938934.772 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1546938934.772 * [misc]taylor: Taking taylor expansion of 2 in n 1546938934.772 * [misc]backup-simplify: Simplify 2 into 2 1546938934.772 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1546938934.773 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1546938934.773 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1546938934.773 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546938934.773 * [misc]taylor: Taking taylor expansion of n in n 1546938934.773 * [misc]backup-simplify: Simplify 0 into 0 1546938934.773 * [misc]backup-simplify: Simplify 1 into 1 1546938934.773 * [misc]taylor: Taking taylor expansion of PI in n 1546938934.773 * [misc]backup-simplify: Simplify PI into PI 1546938934.773 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546938934.774 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546938934.774 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546938934.774 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1546938934.774 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n))))) in n 1546938934.774 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n)))) in n 1546938934.774 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546938934.774 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546938934.774 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n))) in n 1546938934.774 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log (* 2 n))) in n 1546938934.774 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1546938934.775 * [misc]taylor: Taking taylor expansion of 2 in n 1546938934.775 * [misc]backup-simplify: Simplify 2 into 2 1546938934.775 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1546938934.775 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1546938934.775 * [misc]taylor: Taking taylor expansion of (log (* 2 n)) in n 1546938934.775 * [misc]taylor: Taking taylor expansion of (* 2 n) in n 1546938934.775 * [misc]taylor: Taking taylor expansion of 2 in n 1546938934.775 * [misc]backup-simplify: Simplify 2 into 2 1546938934.775 * [misc]taylor: Taking taylor expansion of n in n 1546938934.775 * [misc]backup-simplify: Simplify 0 into 0 1546938934.775 * [misc]backup-simplify: Simplify 1 into 1 1546938934.775 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546938934.775 * [misc]backup-simplify: Simplify (+ (* 2 1) (* 0 0)) into 2 1546938934.776 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1546938934.776 * [misc]taylor: Taking taylor expansion of (sqrt (* PI n)) in n 1546938934.776 * [misc]taylor: Taking taylor expansion of (* PI n) in n 1546938934.776 * [misc]taylor: Taking taylor expansion of PI in n 1546938934.776 * [misc]backup-simplify: Simplify PI into PI 1546938934.776 * [misc]taylor: Taking taylor expansion of n in n 1546938934.776 * [misc]backup-simplify: Simplify 0 into 0 1546938934.776 * [misc]backup-simplify: Simplify 1 into 1 1546938934.776 * [misc]backup-simplify: Simplify (* PI 0) into 0 1546938934.776 * [misc]backup-simplify: Simplify (+ (* PI 1) (* 0 0)) into PI 1546938934.776 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546938934.777 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1546938934.777 * [misc]backup-simplify: Simplify (* (sqrt 2) (log PI)) into (* (sqrt 2) (log PI)) 1546938934.778 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (log PI)) 0) into 0 1546938934.778 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1546938934.778 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1546938934.778 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1546938934.778 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 1546938934.778 * [misc]backup-simplify: Simplify (* (sqrt 2) (+ (log 2) (log n))) into (* (+ (log 2) (log n)) (sqrt 2)) 1546938934.779 * [misc]backup-simplify: Simplify (* (* (+ (log 2) (log n)) (sqrt 2)) 0) into 0 1546938934.779 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1546938934.779 * [misc]backup-simplify: Simplify (- 0) into 0 1546938934.779 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938934.779 * [misc]backup-simplify: Simplify (- 0) into 0 1546938934.779 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938934.779 * [misc]backup-simplify: Simplify (- 0) into 0 1546938934.779 * [misc]backup-simplify: Simplify 0 into 0 1546938934.780 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1546938934.781 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1546938934.782 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 1546938934.783 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI))) 1546938934.783 * [misc]backup-simplify: Simplify 0 into 0 1546938934.783 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938934.783 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1546938934.788 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0 1546938934.788 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1546938934.788 * [misc]backup-simplify: Simplify (- 0) into 0 1546938934.788 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938934.789 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log PI))))) into 0 1546938934.794 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 3) 6)) (* (/ (pow (- (* 1/2 (log PI))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (pow (log PI) 3) (sqrt PI))) 1546938934.794 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 n)))) into 0 1546938934.796 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 n) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 n) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 n) 1)))) 6) into 0 1546938934.796 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1546938934.796 * [misc]backup-simplify: Simplify (- 0) into 0 1546938934.796 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938934.796 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log (* 2 n)))))) into 0 1546938934.797 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 n)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 n)))) 3) 6)) (* (/ (pow (- (* 1/2 (log (* 2 n)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (sqrt (* n 2)) (pow (log (* 2 n)) 3))) 1546938934.801 * [misc]backup-simplify: Simplify (+ (* (pow (* 2 n) 1/2) (* -1/48 (* (pow (log PI) 3) (sqrt PI)))) (+ (* (* -1/2 (* (sqrt (* n 2)) (log (* 2 n)))) (* 1/8 (* (pow (log PI) 2) (sqrt PI)))) (+ (* (* 1/8 (* (sqrt (* n 2)) (pow (log (* 2 n)) 2))) (* -1/2 (* (log PI) (sqrt PI)))) (* (* -1/48 (* (sqrt (* n 2)) (pow (log (* 2 n)) 3))) (pow PI 1/2))))) into (- (+ (* 1/48 (* (* (sqrt 2) (pow (log (* 2 n)) 3)) (sqrt (* PI n)))) (+ (* 1/16 (* (sqrt (* PI n)) (* (sqrt 2) (* (log (* 2 n)) (pow (log PI) 2))))) (+ (* 1/48 (* (* (sqrt 2) (pow (log PI) 3)) (sqrt (* PI n)))) (* 1/16 (* (sqrt (* PI n)) (* (sqrt 2) (* (pow (log (* 2 n)) 2) (log PI))))))))) 1546938934.806 * [misc]backup-simplify: Simplify (+ (* (sqrt (* PI (* n 2))) +nan.0) (+ (* (- (+ (* 1/2 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (* 1/2 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n)))))) +nan.0) (+ (* (+ (* 1/8 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (+ (* 1/8 (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (sqrt (* PI n)))) (* 1/4 (* (sqrt (* PI n)) (* (sqrt 2) (* (log (* 2 n)) (log PI))))))) +nan.0) (* (- (+ (* 1/48 (* (* (sqrt 2) (pow (log (* 2 n)) 3)) (sqrt (* PI n)))) (+ (* 1/16 (* (sqrt (* PI n)) (* (sqrt 2) (* (log (* 2 n)) (pow (log PI) 2))))) (+ (* 1/48 (* (* (sqrt 2) (pow (log PI) 3)) (sqrt (* PI n)))) (* 1/16 (* (sqrt (* PI n)) (* (sqrt 2) (* (pow (log (* 2 n)) 2) (log PI))))))))) 0)))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 n)) (log PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n))))))))))))))) 1546938934.806 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 n)) (log PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n))))))))))))))) in n 1546938934.806 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 n)) (log PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n)))))))))))))) in n 1546938934.806 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) in n 1546938934.806 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546938934.806 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546938934.806 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (log PI)) (sqrt (* PI n))) in n 1546938934.806 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log PI)) in n 1546938934.806 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1546938934.806 * [misc]taylor: Taking taylor expansion of 2 in n 1546938934.806 * [misc]backup-simplify: Simplify 2 into 2 1546938934.806 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1546938934.807 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1546938934.807 * [misc]taylor: Taking taylor expansion of (log PI) in n 1546938934.807 * [misc]taylor: Taking taylor expansion of PI in n 1546938934.807 * [misc]backup-simplify: Simplify PI into PI 1546938934.807 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1546938934.807 * [misc]taylor: Taking taylor expansion of (sqrt (* PI n)) in n 1546938934.807 * [misc]taylor: Taking taylor expansion of (* PI n) in n 1546938934.807 * [misc]taylor: Taking taylor expansion of PI in n 1546938934.807 * [misc]backup-simplify: Simplify PI into PI 1546938934.807 * [misc]taylor: Taking taylor expansion of n in n 1546938934.807 * [misc]backup-simplify: Simplify 0 into 0 1546938934.807 * [misc]backup-simplify: Simplify 1 into 1 1546938934.807 * [misc]backup-simplify: Simplify (* PI 0) into 0 1546938934.807 * [misc]backup-simplify: Simplify (+ (* PI 1) (* 0 0)) into PI 1546938934.808 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546938934.808 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1546938934.808 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 n)) (log PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n))))))))))))) in n 1546938934.808 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 n)) (log PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n)))))))))))) in n 1546938934.808 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) in n 1546938934.808 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546938934.808 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546938934.808 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n))) in n 1546938934.808 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (log PI) 2)) in n 1546938934.808 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1546938934.808 * [misc]taylor: Taking taylor expansion of 2 in n 1546938934.808 * [misc]backup-simplify: Simplify 2 into 2 1546938934.808 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1546938934.808 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1546938934.808 * [misc]taylor: Taking taylor expansion of (pow (log PI) 2) in n 1546938934.808 * [misc]taylor: Taking taylor expansion of (log PI) in n 1546938934.808 * [misc]taylor: Taking taylor expansion of PI in n 1546938934.808 * [misc]backup-simplify: Simplify PI into PI 1546938934.808 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1546938934.809 * [misc]taylor: Taking taylor expansion of (sqrt (* PI n)) in n 1546938934.809 * [misc]taylor: Taking taylor expansion of (* PI n) in n 1546938934.809 * [misc]taylor: Taking taylor expansion of PI in n 1546938934.809 * [misc]backup-simplify: Simplify PI into PI 1546938934.809 * [misc]taylor: Taking taylor expansion of n in n 1546938934.809 * [misc]backup-simplify: Simplify 0 into 0 1546938934.809 * [misc]backup-simplify: Simplify 1 into 1 1546938934.809 * [misc]backup-simplify: Simplify (* PI 0) into 0 1546938934.809 * [misc]backup-simplify: Simplify (+ (* PI 1) (* 0 0)) into PI 1546938934.809 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546938934.810 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1546938934.810 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 n)) (log PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n))))))))))) in n 1546938934.810 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 n)) (log PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n)))))))))) in n 1546938934.810 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (sqrt (* PI n)))) in n 1546938934.810 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546938934.810 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546938934.810 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (sqrt (* PI n))) in n 1546938934.810 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (log (* 2 n)) 2)) in n 1546938934.810 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1546938934.810 * [misc]taylor: Taking taylor expansion of 2 in n 1546938934.810 * [misc]backup-simplify: Simplify 2 into 2 1546938934.810 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1546938934.810 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1546938934.810 * [misc]taylor: Taking taylor expansion of (pow (log (* 2 n)) 2) in n 1546938934.810 * [misc]taylor: Taking taylor expansion of (log (* 2 n)) in n 1546938934.810 * [misc]taylor: Taking taylor expansion of (* 2 n) in n 1546938934.810 * [misc]taylor: Taking taylor expansion of 2 in n 1546938934.810 * [misc]backup-simplify: Simplify 2 into 2 1546938934.810 * [misc]taylor: Taking taylor expansion of n in n 1546938934.810 * [misc]backup-simplify: Simplify 0 into 0 1546938934.810 * [misc]backup-simplify: Simplify 1 into 1 1546938934.810 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546938934.810 * [misc]backup-simplify: Simplify (+ (* 2 1) (* 0 0)) into 2 1546938934.810 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1546938934.811 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 1546938934.811 * [misc]taylor: Taking taylor expansion of (sqrt (* PI n)) in n 1546938934.811 * [misc]taylor: Taking taylor expansion of (* PI n) in n 1546938934.811 * [misc]taylor: Taking taylor expansion of PI in n 1546938934.811 * [misc]backup-simplify: Simplify PI into PI 1546938934.811 * [misc]taylor: Taking taylor expansion of n in n 1546938934.811 * [misc]backup-simplify: Simplify 0 into 0 1546938934.811 * [misc]backup-simplify: Simplify 1 into 1 1546938934.811 * [misc]backup-simplify: Simplify (* PI 0) into 0 1546938934.811 * [misc]backup-simplify: Simplify (+ (* PI 1) (* 0 0)) into PI 1546938934.811 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546938934.812 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1546938934.812 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 n)) (log PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n))))))))) in n 1546938934.812 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 n)) (log PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n)))))))) in n 1546938934.812 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (* (log (* 2 n)) (log PI))) (sqrt (* n PI)))) in n 1546938934.812 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546938934.812 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546938934.812 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (* (log (* 2 n)) (log PI))) (sqrt (* n PI))) in n 1546938934.812 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* (log (* 2 n)) (log PI))) in n 1546938934.812 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1546938934.812 * [misc]taylor: Taking taylor expansion of 2 in n 1546938934.812 * [misc]backup-simplify: Simplify 2 into 2 1546938934.812 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1546938934.812 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1546938934.812 * [misc]taylor: Taking taylor expansion of (* (log (* 2 n)) (log PI)) in n 1546938934.812 * [misc]taylor: Taking taylor expansion of (log (* 2 n)) in n 1546938934.812 * [misc]taylor: Taking taylor expansion of (* 2 n) in n 1546938934.812 * [misc]taylor: Taking taylor expansion of 2 in n 1546938934.812 * [misc]backup-simplify: Simplify 2 into 2 1546938934.812 * [misc]taylor: Taking taylor expansion of n in n 1546938934.812 * [misc]backup-simplify: Simplify 0 into 0 1546938934.812 * [misc]backup-simplify: Simplify 1 into 1 1546938934.812 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546938934.813 * [misc]backup-simplify: Simplify (+ (* 2 1) (* 0 0)) into 2 1546938934.813 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1546938934.813 * [misc]taylor: Taking taylor expansion of (log PI) in n 1546938934.813 * [misc]taylor: Taking taylor expansion of PI in n 1546938934.813 * [misc]backup-simplify: Simplify PI into PI 1546938934.813 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1546938934.813 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1546938934.813 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546938934.813 * [misc]taylor: Taking taylor expansion of n in n 1546938934.813 * [misc]backup-simplify: Simplify 0 into 0 1546938934.813 * [misc]backup-simplify: Simplify 1 into 1 1546938934.813 * [misc]taylor: Taking taylor expansion of PI in n 1546938934.813 * [misc]backup-simplify: Simplify PI into PI 1546938934.813 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546938934.814 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546938934.814 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546938934.814 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1546938934.814 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n))))))) in n 1546938934.814 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n)))))) in n 1546938934.814 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 1546938934.814 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546938934.814 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546938934.814 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1546938934.814 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1546938934.814 * [misc]taylor: Taking taylor expansion of 2 in n 1546938934.814 * [misc]backup-simplify: Simplify 2 into 2 1546938934.815 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1546938934.815 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1546938934.815 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1546938934.815 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546938934.815 * [misc]taylor: Taking taylor expansion of n in n 1546938934.815 * [misc]backup-simplify: Simplify 0 into 0 1546938934.815 * [misc]backup-simplify: Simplify 1 into 1 1546938934.815 * [misc]taylor: Taking taylor expansion of PI in n 1546938934.815 * [misc]backup-simplify: Simplify PI into PI 1546938934.815 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546938934.815 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546938934.815 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546938934.816 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1546938934.816 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n))))) in n 1546938934.816 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n)))) in n 1546938934.816 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546938934.816 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546938934.816 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n))) in n 1546938934.816 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log (* 2 n))) in n 1546938934.816 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1546938934.816 * [misc]taylor: Taking taylor expansion of 2 in n 1546938934.816 * [misc]backup-simplify: Simplify 2 into 2 1546938934.816 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1546938934.816 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1546938934.816 * [misc]taylor: Taking taylor expansion of (log (* 2 n)) in n 1546938934.816 * [misc]taylor: Taking taylor expansion of (* 2 n) in n 1546938934.816 * [misc]taylor: Taking taylor expansion of 2 in n 1546938934.816 * [misc]backup-simplify: Simplify 2 into 2 1546938934.816 * [misc]taylor: Taking taylor expansion of n in n 1546938934.816 * [misc]backup-simplify: Simplify 0 into 0 1546938934.816 * [misc]backup-simplify: Simplify 1 into 1 1546938934.816 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546938934.817 * [misc]backup-simplify: Simplify (+ (* 2 1) (* 0 0)) into 2 1546938934.817 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1546938934.817 * [misc]taylor: Taking taylor expansion of (sqrt (* PI n)) in n 1546938934.817 * [misc]taylor: Taking taylor expansion of (* PI n) in n 1546938934.817 * [misc]taylor: Taking taylor expansion of PI in n 1546938934.817 * [misc]backup-simplify: Simplify PI into PI 1546938934.817 * [misc]taylor: Taking taylor expansion of n in n 1546938934.817 * [misc]backup-simplify: Simplify 0 into 0 1546938934.817 * [misc]backup-simplify: Simplify 1 into 1 1546938934.817 * [misc]backup-simplify: Simplify (* PI 0) into 0 1546938934.817 * [misc]backup-simplify: Simplify (+ (* PI 1) (* 0 0)) into PI 1546938934.817 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546938934.818 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1546938934.818 * [misc]backup-simplify: Simplify (* (sqrt 2) (log PI)) into (* (sqrt 2) (log PI)) 1546938934.819 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (log PI)) 0) into 0 1546938934.819 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1546938934.819 * [misc]backup-simplify: Simplify (* (log PI) (log PI)) into (pow (log PI) 2) 1546938934.820 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow (log PI) 2)) into (* (sqrt 2) (pow (log PI) 2)) 1546938934.820 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (pow (log PI) 2)) 0) into 0 1546938934.821 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1546938934.821 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 1546938934.821 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 1546938934.821 * [misc]backup-simplify: Simplify (* (+ (log 2) (log n)) (+ (log 2) (log n))) into (pow (+ (log 2) (log n)) 2) 1546938934.822 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow (+ (log 2) (log n)) 2)) into (* (pow (+ (log 2) (log n)) 2) (sqrt 2)) 1546938934.822 * [misc]backup-simplify: Simplify (* (* (pow (+ (log 2) (log n)) 2) (sqrt 2)) 0) into 0 1546938934.822 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1546938934.822 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 1546938934.822 * [misc]backup-simplify: Simplify (* (+ (log 2) (log n)) (log PI)) into (* (+ (log 2) (log n)) (log PI)) 1546938934.823 * [misc]backup-simplify: Simplify (* (sqrt 2) (* (+ (log 2) (log n)) (log PI))) into (* (+ (log 2) (log n)) (* (sqrt 2) (log PI))) 1546938934.823 * [misc]backup-simplify: Simplify (* (* (+ (log 2) (log n)) (* (sqrt 2) (log PI))) 0) into 0 1546938934.823 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1546938934.823 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1546938934.824 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1546938934.824 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 1546938934.824 * [misc]backup-simplify: Simplify (* (sqrt 2) (+ (log 2) (log n))) into (* (+ (log 2) (log n)) (sqrt 2)) 1546938934.824 * [misc]backup-simplify: Simplify (* (* (+ (log 2) (log n)) (sqrt 2)) 0) into 0 1546938934.824 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1546938934.824 * [misc]backup-simplify: Simplify (- 0) into 0 1546938934.825 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938934.825 * [misc]backup-simplify: Simplify (- 0) into 0 1546938934.825 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938934.825 * [misc]backup-simplify: Simplify (- 0) into 0 1546938934.825 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938934.825 * [misc]backup-simplify: Simplify (- 0) into 0 1546938934.825 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938934.825 * [misc]backup-simplify: Simplify (- 0) into 0 1546938934.825 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938934.825 * [misc]backup-simplify: Simplify (- 0) into 0 1546938934.825 * [misc]backup-simplify: Simplify 0 into 0 1546938934.827 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 1546938934.827 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (log PI))) into 0 1546938934.828 * [misc]backup-simplify: Simplify (+ (* (* (sqrt 2) (log PI)) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) (* (log PI) PI)))) 1546938934.830 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) (* (log PI) PI))))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) (* (log PI) PI)))) 1546938934.831 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1546938934.832 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1546938934.832 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 1) (* 0 0))) into 0 1546938934.835 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 1546938934.835 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 1546938934.836 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log 2) (log n)))) into 0 1546938934.837 * [misc]backup-simplify: Simplify (+ (* (* (+ (log 2) (log n)) (sqrt 2)) (* +nan.0 PI)) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (log 2) (* (sqrt 2) PI)))))) 1546938934.840 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (log 2) (* (sqrt 2) PI))))))) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (log 2) (* (sqrt 2) PI)))))) 1546938934.841 * [misc]backup-simplify: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (log 2) (* (sqrt 2) PI))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (log 2) (* (sqrt 2) PI)))))) 1546938934.843 * [misc]backup-simplify: Simplify (+ (- (* +nan.0 (* (sqrt 2) PI))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (log 2) (* (sqrt 2) PI))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))) 1546938934.845 * [misc]backup-simplify: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI)))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))) 1546938934.848 * [misc]backup-simplify: Simplify (+ (- (* +nan.0 (* (sqrt 2) (* (log PI) PI)))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI)))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))))) 1546938934.853 * [misc]backup-simplify: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI)))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))))) 1546938934.859 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))))) 1546938934.861 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546938934.862 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 1546938934.864 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1546938934.866 * [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)))) 1546938934.870 * [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)))) 1546938934.871 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 1546938934.873 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 1546938934.882 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) (pow (* n 1) 2)) (+ (* (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +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) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log PI) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))))))))) 1546938934.883 * [misc]backup-simplify: Simplify (* (pow PI (- 1/2 (/ (/ 1 k) 2))) (/ (pow (* (/ 1 n) 2) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k)))) into (* (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) 1546938934.883 * [misc]approximate: Taking taylor expansion of (* (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in (k n) around 0 1546938934.883 * [misc]taylor: Taking taylor expansion of (* (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in n 1546938934.883 * [misc]taylor: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) in n 1546938934.883 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in n 1546938934.883 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in n 1546938934.883 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in n 1546938934.883 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546938934.883 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938934.883 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.883 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546938934.883 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938934.883 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.883 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938934.883 * [misc]taylor: Taking taylor expansion of k in n 1546938934.883 * [misc]backup-simplify: Simplify k into k 1546938934.883 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938934.883 * [misc]taylor: Taking taylor expansion of (log PI) in n 1546938934.883 * [misc]taylor: Taking taylor expansion of PI in n 1546938934.883 * [misc]backup-simplify: Simplify PI into PI 1546938934.884 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1546938934.884 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546938934.884 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546938934.884 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546938934.884 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) into (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) 1546938934.885 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1546938934.885 * [misc]taylor: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546938934.885 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 1546938934.885 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 1546938934.885 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546938934.885 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938934.885 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.885 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546938934.885 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938934.885 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.885 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938934.885 * [misc]taylor: Taking taylor expansion of k in n 1546938934.885 * [misc]backup-simplify: Simplify k into k 1546938934.885 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938934.885 * [misc]taylor: Taking taylor expansion of (log (/ 2 n)) in n 1546938934.885 * [misc]taylor: Taking taylor expansion of (/ 2 n) in n 1546938934.885 * [misc]taylor: Taking taylor expansion of 2 in n 1546938934.885 * [misc]backup-simplify: Simplify 2 into 2 1546938934.885 * [misc]taylor: Taking taylor expansion of n in n 1546938934.885 * [misc]backup-simplify: Simplify 0 into 0 1546938934.885 * [misc]backup-simplify: Simplify 1 into 1 1546938934.886 * [misc]backup-simplify: Simplify (/ 2 1) into 2 1546938934.886 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1546938934.886 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546938934.886 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546938934.886 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546938934.886 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 1546938934.887 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 1546938934.887 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 1546938934.887 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1546938934.887 * [misc]taylor: Taking taylor expansion of k in n 1546938934.887 * [misc]backup-simplify: Simplify k into k 1546938934.888 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1546938934.888 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1546938934.888 * [misc]taylor: Taking taylor expansion of (* (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in k 1546938934.888 * [misc]taylor: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) in k 1546938934.888 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 1546938934.888 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 1546938934.888 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 1546938934.888 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546938934.888 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938934.888 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.888 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546938934.888 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938934.888 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.888 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546938934.888 * [misc]taylor: Taking taylor expansion of k in k 1546938934.888 * [misc]backup-simplify: Simplify 0 into 0 1546938934.888 * [misc]backup-simplify: Simplify 1 into 1 1546938934.888 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546938934.888 * [misc]taylor: Taking taylor expansion of (log PI) in k 1546938934.888 * [misc]taylor: Taking taylor expansion of PI in k 1546938934.888 * [misc]backup-simplify: Simplify PI into PI 1546938934.889 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1546938934.889 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546938934.889 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546938934.889 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546938934.890 * [misc]backup-simplify: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 1546938934.890 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1546938934.890 * [misc]taylor: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in k 1546938934.890 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in k 1546938934.890 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in k 1546938934.890 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546938934.890 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938934.890 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.890 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546938934.890 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938934.890 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.890 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546938934.890 * [misc]taylor: Taking taylor expansion of k in k 1546938934.890 * [misc]backup-simplify: Simplify 0 into 0 1546938934.890 * [misc]backup-simplify: Simplify 1 into 1 1546938934.891 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546938934.891 * [misc]taylor: Taking taylor expansion of (log (/ 2 n)) in k 1546938934.891 * [misc]taylor: Taking taylor expansion of (/ 2 n) in k 1546938934.891 * [misc]taylor: Taking taylor expansion of 2 in k 1546938934.891 * [misc]backup-simplify: Simplify 2 into 2 1546938934.891 * [misc]taylor: Taking taylor expansion of n in k 1546938934.891 * [misc]backup-simplify: Simplify n into n 1546938934.891 * [misc]backup-simplify: Simplify (/ 2 n) into (/ 2 n) 1546938934.891 * [misc]backup-simplify: Simplify (log (/ 2 n)) into (log (/ 2 n)) 1546938934.891 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546938934.891 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546938934.891 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546938934.891 * [misc]backup-simplify: Simplify (* -1/2 (log (/ 2 n))) into (* -1/2 (log (/ 2 n))) 1546938934.892 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) into (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) 1546938934.892 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1546938934.892 * [misc]taylor: Taking taylor expansion of k in k 1546938934.892 * [misc]backup-simplify: Simplify 0 into 0 1546938934.892 * [misc]backup-simplify: Simplify 1 into 1 1546938934.892 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546938934.892 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546938934.892 * [misc]taylor: Taking taylor expansion of (* (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in k 1546938934.892 * [misc]taylor: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) in k 1546938934.892 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 1546938934.892 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 1546938934.892 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 1546938934.893 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546938934.893 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938934.893 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.893 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546938934.893 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938934.893 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.893 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546938934.893 * [misc]taylor: Taking taylor expansion of k in k 1546938934.893 * [misc]backup-simplify: Simplify 0 into 0 1546938934.893 * [misc]backup-simplify: Simplify 1 into 1 1546938934.893 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546938934.893 * [misc]taylor: Taking taylor expansion of (log PI) in k 1546938934.893 * [misc]taylor: Taking taylor expansion of PI in k 1546938934.893 * [misc]backup-simplify: Simplify PI into PI 1546938934.893 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1546938934.893 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546938934.894 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546938934.894 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546938934.894 * [misc]backup-simplify: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 1546938934.894 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1546938934.894 * [misc]taylor: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in k 1546938934.894 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in k 1546938934.894 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in k 1546938934.894 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546938934.894 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938934.894 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.894 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546938934.894 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938934.894 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.894 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546938934.894 * [misc]taylor: Taking taylor expansion of k in k 1546938934.894 * [misc]backup-simplify: Simplify 0 into 0 1546938934.894 * [misc]backup-simplify: Simplify 1 into 1 1546938934.895 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546938934.895 * [misc]taylor: Taking taylor expansion of (log (/ 2 n)) in k 1546938934.895 * [misc]taylor: Taking taylor expansion of (/ 2 n) in k 1546938934.895 * [misc]taylor: Taking taylor expansion of 2 in k 1546938934.895 * [misc]backup-simplify: Simplify 2 into 2 1546938934.895 * [misc]taylor: Taking taylor expansion of n in k 1546938934.895 * [misc]backup-simplify: Simplify n into n 1546938934.895 * [misc]backup-simplify: Simplify (/ 2 n) into (/ 2 n) 1546938934.895 * [misc]backup-simplify: Simplify (log (/ 2 n)) into (log (/ 2 n)) 1546938934.895 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546938934.895 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546938934.895 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546938934.895 * [misc]backup-simplify: Simplify (* -1/2 (log (/ 2 n))) into (* -1/2 (log (/ 2 n))) 1546938934.895 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) into (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) 1546938934.895 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1546938934.895 * [misc]taylor: Taking taylor expansion of k in k 1546938934.895 * [misc]backup-simplify: Simplify 0 into 0 1546938934.895 * [misc]backup-simplify: Simplify 1 into 1 1546938934.896 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546938934.896 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546938934.896 * [misc]backup-simplify: Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) into (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) 1546938934.896 * [misc]backup-simplify: Simplify (* (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) 0) into 0 1546938934.896 * [misc]taylor: Taking taylor expansion of 0 in n 1546938934.896 * [misc]backup-simplify: Simplify 0 into 0 1546938934.896 * [misc]backup-simplify: Simplify 0 into 0 1546938934.896 * [misc]backup-simplify: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (* 0 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))) into 0 1546938934.897 * [misc]backup-simplify: Simplify (+ (* (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (* 0 0)) into (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))))) 1546938934.897 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))))) in n 1546938934.897 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))) in n 1546938934.897 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546938934.897 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546938934.897 * [misc]taylor: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) in n 1546938934.897 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in n 1546938934.897 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in n 1546938934.897 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in n 1546938934.897 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546938934.897 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938934.897 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.897 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546938934.897 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938934.897 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.897 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938934.897 * [misc]taylor: Taking taylor expansion of k in n 1546938934.897 * [misc]backup-simplify: Simplify k into k 1546938934.897 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938934.897 * [misc]taylor: Taking taylor expansion of (log PI) in n 1546938934.897 * [misc]taylor: Taking taylor expansion of PI in n 1546938934.897 * [misc]backup-simplify: Simplify PI into PI 1546938934.897 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1546938934.897 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546938934.897 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546938934.897 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546938934.898 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) into (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) 1546938934.898 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1546938934.898 * [misc]taylor: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546938934.898 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 1546938934.898 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 1546938934.898 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546938934.898 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938934.898 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.898 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546938934.898 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938934.898 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.898 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938934.898 * [misc]taylor: Taking taylor expansion of k in n 1546938934.898 * [misc]backup-simplify: Simplify k into k 1546938934.898 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938934.898 * [misc]taylor: Taking taylor expansion of (log (/ 2 n)) in n 1546938934.898 * [misc]taylor: Taking taylor expansion of (/ 2 n) in n 1546938934.898 * [misc]taylor: Taking taylor expansion of 2 in n 1546938934.898 * [misc]backup-simplify: Simplify 2 into 2 1546938934.898 * [misc]taylor: Taking taylor expansion of n in n 1546938934.898 * [misc]backup-simplify: Simplify 0 into 0 1546938934.898 * [misc]backup-simplify: Simplify 1 into 1 1546938934.898 * [misc]backup-simplify: Simplify (/ 2 1) into 2 1546938934.898 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1546938934.899 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546938934.899 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546938934.899 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546938934.899 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 1546938934.899 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 1546938934.899 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 1546938934.900 * [misc]backup-simplify: Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) into (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) 1546938934.900 * [misc]backup-simplify: Simplify (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) into (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) 1546938934.900 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) into (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) 1546938934.900 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) into (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) 1546938934.900 * [misc]backup-simplify: Simplify 0 into 0 1546938934.901 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1546938934.901 * [misc]backup-simplify: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (* 0 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))))) into 0 1546938934.902 * [misc]backup-simplify: Simplify (+ (* (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))))) 1546938934.902 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))))) in n 1546938934.902 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))) in n 1546938934.902 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546938934.902 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546938934.902 * [misc]taylor: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) in n 1546938934.902 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in n 1546938934.902 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in n 1546938934.902 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in n 1546938934.902 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546938934.902 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938934.902 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.902 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546938934.902 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938934.902 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.902 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938934.902 * [misc]taylor: Taking taylor expansion of k in n 1546938934.902 * [misc]backup-simplify: Simplify k into k 1546938934.902 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938934.902 * [misc]taylor: Taking taylor expansion of (log PI) in n 1546938934.902 * [misc]taylor: Taking taylor expansion of PI in n 1546938934.902 * [misc]backup-simplify: Simplify PI into PI 1546938934.902 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1546938934.902 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546938934.902 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546938934.902 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546938934.903 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) into (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) 1546938934.903 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1546938934.903 * [misc]taylor: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546938934.903 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 1546938934.903 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 1546938934.903 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546938934.903 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938934.903 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.903 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546938934.903 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938934.903 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.903 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938934.903 * [misc]taylor: Taking taylor expansion of k in n 1546938934.903 * [misc]backup-simplify: Simplify k into k 1546938934.903 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938934.903 * [misc]taylor: Taking taylor expansion of (log (/ 2 n)) in n 1546938934.903 * [misc]taylor: Taking taylor expansion of (/ 2 n) in n 1546938934.903 * [misc]taylor: Taking taylor expansion of 2 in n 1546938934.903 * [misc]backup-simplify: Simplify 2 into 2 1546938934.903 * [misc]taylor: Taking taylor expansion of n in n 1546938934.903 * [misc]backup-simplify: Simplify 0 into 0 1546938934.903 * [misc]backup-simplify: Simplify 1 into 1 1546938934.903 * [misc]backup-simplify: Simplify (/ 2 1) into 2 1546938934.904 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1546938934.904 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546938934.904 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546938934.904 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546938934.904 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 1546938934.904 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 1546938934.904 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 1546938934.905 * [misc]backup-simplify: Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) into (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) 1546938934.905 * [misc]backup-simplify: Simplify (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) into (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) 1546938934.905 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) into (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) 1546938934.906 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) into (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) 1546938934.906 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)))) into 0 1546938934.907 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 1546938934.907 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546938934.907 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546938934.908 * [misc]backup-simplify: Simplify (- 0) into 0 1546938934.908 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938934.908 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 1546938934.908 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log 2) (log n)))) into 0 1546938934.909 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546938934.910 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 1546938934.910 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546938934.910 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546938934.911 * [misc]backup-simplify: Simplify (- 0) into 0 1546938934.911 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938934.911 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (log PI))) into 0 1546938934.912 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 1546938934.912 * [misc]backup-simplify: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) into 0 1546938934.912 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) into 0 1546938934.913 * [misc]backup-simplify: Simplify (- 0) into 0 1546938934.913 * [misc]backup-simplify: Simplify 0 into 0 1546938934.913 * [misc]backup-simplify: Simplify 0 into 0 1546938934.913 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1546938934.914 * [misc]backup-simplify: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 1546938934.914 * [misc]backup-simplify: Simplify (+ (* (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))))) 1546938934.914 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))))) in n 1546938934.914 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))) in n 1546938934.914 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546938934.914 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546938934.914 * [misc]taylor: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) in n 1546938934.914 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in n 1546938934.914 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in n 1546938934.914 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in n 1546938934.914 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546938934.914 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938934.914 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.914 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546938934.914 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938934.914 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.914 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938934.914 * [misc]taylor: Taking taylor expansion of k in n 1546938934.914 * [misc]backup-simplify: Simplify k into k 1546938934.914 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938934.914 * [misc]taylor: Taking taylor expansion of (log PI) in n 1546938934.914 * [misc]taylor: Taking taylor expansion of PI in n 1546938934.914 * [misc]backup-simplify: Simplify PI into PI 1546938934.915 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1546938934.915 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546938934.915 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546938934.915 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546938934.915 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) into (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) 1546938934.915 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1546938934.915 * [misc]taylor: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546938934.915 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 1546938934.915 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 1546938934.915 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546938934.915 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938934.915 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.915 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546938934.915 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938934.915 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.915 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938934.915 * [misc]taylor: Taking taylor expansion of k in n 1546938934.915 * [misc]backup-simplify: Simplify k into k 1546938934.915 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938934.915 * [misc]taylor: Taking taylor expansion of (log (/ 2 n)) in n 1546938934.916 * [misc]taylor: Taking taylor expansion of (/ 2 n) in n 1546938934.916 * [misc]taylor: Taking taylor expansion of 2 in n 1546938934.916 * [misc]backup-simplify: Simplify 2 into 2 1546938934.916 * [misc]taylor: Taking taylor expansion of n in n 1546938934.916 * [misc]backup-simplify: Simplify 0 into 0 1546938934.916 * [misc]backup-simplify: Simplify 1 into 1 1546938934.916 * [misc]backup-simplify: Simplify (/ 2 1) into 2 1546938934.916 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1546938934.916 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546938934.916 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546938934.916 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546938934.916 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 1546938934.916 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 1546938934.917 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 1546938934.917 * [misc]backup-simplify: Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) into (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) 1546938934.917 * [misc]backup-simplify: Simplify (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) into (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) 1546938934.917 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) into (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) 1546938934.918 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) into (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) 1546938934.919 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k))))) (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log 2) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k))))) (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log 2) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k))))) (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log 2) (log (/ 1 n)))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (* (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))) (pow k 2))) (- (+ (* +nan.0 (/ (* (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))) k)) (- (* +nan.0 (/ (* (pow PI (- 1/2 (* 1/2 k))) (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k))))) (pow k 3)))))))) 1546938934.919 * [misc]backup-simplify: Simplify (* (pow PI (- 1/2 (/ (/ 1 (- k)) 2))) (/ (pow (* (/ 1 (- n)) 2) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k))))) into (/ (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) 1546938934.919 * [misc]approximate: Taking taylor expansion of (/ (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) in (k n) around 0 1546938934.919 * [misc]taylor: Taking taylor expansion of (/ (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) in n 1546938934.919 * [misc]taylor: Taking taylor expansion of (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in n 1546938934.919 * [misc]taylor: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546938934.919 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 1546938934.919 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 1546938934.919 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546938934.919 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546938934.919 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938934.919 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.920 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938934.920 * [misc]taylor: Taking taylor expansion of k in n 1546938934.920 * [misc]backup-simplify: Simplify k into k 1546938934.920 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938934.920 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938934.920 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.920 * [misc]taylor: Taking taylor expansion of (log (/ -2 n)) in n 1546938934.920 * [misc]taylor: Taking taylor expansion of (/ -2 n) in n 1546938934.920 * [misc]taylor: Taking taylor expansion of -2 in n 1546938934.920 * [misc]backup-simplify: Simplify -2 into -2 1546938934.920 * [misc]taylor: Taking taylor expansion of n in n 1546938934.920 * [misc]backup-simplify: Simplify 0 into 0 1546938934.920 * [misc]backup-simplify: Simplify 1 into 1 1546938934.920 * [misc]backup-simplify: Simplify (/ -2 1) into -2 1546938934.920 * [misc]backup-simplify: Simplify (log -2) into (log -2) 1546938934.920 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546938934.920 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546938934.920 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 1546938934.920 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 1546938934.921 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 1546938934.921 * [misc]taylor: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546938934.921 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in n 1546938934.921 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in n 1546938934.921 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546938934.921 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546938934.921 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938934.921 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.921 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938934.921 * [misc]taylor: Taking taylor expansion of k in n 1546938934.921 * [misc]backup-simplify: Simplify k into k 1546938934.921 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938934.921 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938934.921 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.921 * [misc]taylor: Taking taylor expansion of (log PI) in n 1546938934.921 * [misc]taylor: Taking taylor expansion of PI in n 1546938934.921 * [misc]backup-simplify: Simplify PI into PI 1546938934.921 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1546938934.921 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546938934.921 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546938934.922 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) 1546938934.922 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1546938934.922 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1546938934.922 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1546938934.922 * [misc]taylor: Taking taylor expansion of -1 in n 1546938934.922 * [misc]backup-simplify: Simplify -1 into -1 1546938934.922 * [misc]taylor: Taking taylor expansion of k in n 1546938934.922 * [misc]backup-simplify: Simplify k into k 1546938934.922 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1546938934.922 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1546938934.922 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1546938934.922 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1546938934.922 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 1546938934.923 * [misc]backup-simplify: Simplify (/ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) into (/ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) 1546938934.923 * [misc]taylor: Taking taylor expansion of (/ (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) in k 1546938934.923 * [misc]taylor: Taking taylor expansion of (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in k 1546938934.923 * [misc]taylor: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1546938934.923 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in k 1546938934.923 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in k 1546938934.923 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546938934.923 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546938934.923 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938934.923 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.923 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546938934.923 * [misc]taylor: Taking taylor expansion of k in k 1546938934.923 * [misc]backup-simplify: Simplify 0 into 0 1546938934.923 * [misc]backup-simplify: Simplify 1 into 1 1546938934.923 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546938934.923 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938934.923 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.923 * [misc]taylor: Taking taylor expansion of (log (/ -2 n)) in k 1546938934.923 * [misc]taylor: Taking taylor expansion of (/ -2 n) in k 1546938934.923 * [misc]taylor: Taking taylor expansion of -2 in k 1546938934.923 * [misc]backup-simplify: Simplify -2 into -2 1546938934.923 * [misc]taylor: Taking taylor expansion of n in k 1546938934.923 * [misc]backup-simplify: Simplify n into n 1546938934.923 * [misc]backup-simplify: Simplify (/ -2 n) into (/ -2 n) 1546938934.923 * [misc]backup-simplify: Simplify (log (/ -2 n)) into (log (/ -2 n)) 1546938934.923 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546938934.924 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546938934.924 * [misc]backup-simplify: Simplify (* 1/2 (log (/ -2 n))) into (* 1/2 (log (/ -2 n))) 1546938934.924 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) into (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) 1546938934.924 * [misc]taylor: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 1546938934.924 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 1546938934.924 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 1546938934.924 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546938934.924 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546938934.924 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938934.924 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.924 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546938934.924 * [misc]taylor: Taking taylor expansion of k in k 1546938934.924 * [misc]backup-simplify: Simplify 0 into 0 1546938934.924 * [misc]backup-simplify: Simplify 1 into 1 1546938934.924 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546938934.924 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938934.924 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.924 * [misc]taylor: Taking taylor expansion of (log PI) in k 1546938934.924 * [misc]taylor: Taking taylor expansion of PI in k 1546938934.924 * [misc]backup-simplify: Simplify PI into PI 1546938934.924 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1546938934.924 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546938934.924 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546938934.925 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1546938934.925 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1546938934.925 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1546938934.925 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1546938934.925 * [misc]taylor: Taking taylor expansion of -1 in k 1546938934.925 * [misc]backup-simplify: Simplify -1 into -1 1546938934.925 * [misc]taylor: Taking taylor expansion of k in k 1546938934.925 * [misc]backup-simplify: Simplify 0 into 0 1546938934.925 * [misc]backup-simplify: Simplify 1 into 1 1546938934.925 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1546938934.925 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546938934.926 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1546938934.926 * [misc]backup-simplify: Simplify (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 1546938934.926 * [misc]backup-simplify: Simplify (/ (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) +nan.0) into (* +nan.0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 1546938934.926 * [misc]taylor: Taking taylor expansion of (/ (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) in k 1546938934.926 * [misc]taylor: Taking taylor expansion of (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in k 1546938934.926 * [misc]taylor: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1546938934.926 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in k 1546938934.926 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in k 1546938934.926 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546938934.926 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546938934.926 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938934.926 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.926 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546938934.926 * [misc]taylor: Taking taylor expansion of k in k 1546938934.926 * [misc]backup-simplify: Simplify 0 into 0 1546938934.926 * [misc]backup-simplify: Simplify 1 into 1 1546938934.926 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546938934.926 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938934.926 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.926 * [misc]taylor: Taking taylor expansion of (log (/ -2 n)) in k 1546938934.926 * [misc]taylor: Taking taylor expansion of (/ -2 n) in k 1546938934.926 * [misc]taylor: Taking taylor expansion of -2 in k 1546938934.926 * [misc]backup-simplify: Simplify -2 into -2 1546938934.926 * [misc]taylor: Taking taylor expansion of n in k 1546938934.926 * [misc]backup-simplify: Simplify n into n 1546938934.926 * [misc]backup-simplify: Simplify (/ -2 n) into (/ -2 n) 1546938934.926 * [misc]backup-simplify: Simplify (log (/ -2 n)) into (log (/ -2 n)) 1546938934.927 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546938934.927 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546938934.927 * [misc]backup-simplify: Simplify (* 1/2 (log (/ -2 n))) into (* 1/2 (log (/ -2 n))) 1546938934.927 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) into (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) 1546938934.927 * [misc]taylor: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 1546938934.927 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 1546938934.927 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 1546938934.927 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546938934.927 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546938934.927 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938934.927 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.927 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546938934.927 * [misc]taylor: Taking taylor expansion of k in k 1546938934.927 * [misc]backup-simplify: Simplify 0 into 0 1546938934.927 * [misc]backup-simplify: Simplify 1 into 1 1546938934.927 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546938934.927 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546938934.927 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.927 * [misc]taylor: Taking taylor expansion of (log PI) in k 1546938934.927 * [misc]taylor: Taking taylor expansion of PI in k 1546938934.927 * [misc]backup-simplify: Simplify PI into PI 1546938934.927 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1546938934.928 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546938934.928 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546938934.928 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1546938934.928 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1546938934.928 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1546938934.928 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1546938934.928 * [misc]taylor: Taking taylor expansion of -1 in k 1546938934.928 * [misc]backup-simplify: Simplify -1 into -1 1546938934.928 * [misc]taylor: Taking taylor expansion of k in k 1546938934.928 * [misc]backup-simplify: Simplify 0 into 0 1546938934.928 * [misc]backup-simplify: Simplify 1 into 1 1546938934.928 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1546938934.929 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546938934.929 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1546938934.929 * [misc]backup-simplify: Simplify (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 1546938934.929 * [misc]backup-simplify: Simplify (/ (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) +nan.0) into (* +nan.0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 1546938934.929 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1546938934.929 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546938934.929 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546938934.929 * [misc]taylor: Taking taylor expansion of (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in n 1546938934.929 * [misc]taylor: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546938934.929 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 1546938934.929 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 1546938934.929 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546938934.929 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546938934.929 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938934.929 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.929 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938934.929 * [misc]taylor: Taking taylor expansion of k in n 1546938934.929 * [misc]backup-simplify: Simplify k into k 1546938934.929 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938934.929 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938934.929 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.930 * [misc]taylor: Taking taylor expansion of (log (/ -2 n)) in n 1546938934.930 * [misc]taylor: Taking taylor expansion of (/ -2 n) in n 1546938934.930 * [misc]taylor: Taking taylor expansion of -2 in n 1546938934.930 * [misc]backup-simplify: Simplify -2 into -2 1546938934.930 * [misc]taylor: Taking taylor expansion of n in n 1546938934.930 * [misc]backup-simplify: Simplify 0 into 0 1546938934.930 * [misc]backup-simplify: Simplify 1 into 1 1546938934.930 * [misc]backup-simplify: Simplify (/ -2 1) into -2 1546938934.930 * [misc]backup-simplify: Simplify (log -2) into (log -2) 1546938934.930 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546938934.930 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546938934.930 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 1546938934.930 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 1546938934.931 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 1546938934.931 * [misc]taylor: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546938934.931 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in n 1546938934.931 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in n 1546938934.931 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546938934.931 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546938934.931 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938934.931 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.931 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938934.931 * [misc]taylor: Taking taylor expansion of k in n 1546938934.931 * [misc]backup-simplify: Simplify k into k 1546938934.931 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938934.931 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938934.931 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.931 * [misc]taylor: Taking taylor expansion of (log PI) in n 1546938934.931 * [misc]taylor: Taking taylor expansion of PI in n 1546938934.931 * [misc]backup-simplify: Simplify PI into PI 1546938934.931 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1546938934.931 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546938934.931 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546938934.931 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) 1546938934.932 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1546938934.932 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 1546938934.932 * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 1546938934.932 * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 1546938934.933 * [misc]backup-simplify: Simplify (+ (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) 0) (* 0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into 0 1546938934.933 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1546938934.934 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1546938934.934 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 1546938934.934 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) in n 1546938934.934 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1546938934.934 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546938934.934 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546938934.934 * [misc]taylor: Taking taylor expansion of (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in n 1546938934.934 * [misc]taylor: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546938934.934 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 1546938934.934 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 1546938934.934 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546938934.934 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546938934.934 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938934.934 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.934 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938934.934 * [misc]taylor: Taking taylor expansion of k in n 1546938934.934 * [misc]backup-simplify: Simplify k into k 1546938934.934 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938934.934 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938934.934 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.934 * [misc]taylor: Taking taylor expansion of (log (/ -2 n)) in n 1546938934.934 * [misc]taylor: Taking taylor expansion of (/ -2 n) in n 1546938934.934 * [misc]taylor: Taking taylor expansion of -2 in n 1546938934.934 * [misc]backup-simplify: Simplify -2 into -2 1546938934.934 * [misc]taylor: Taking taylor expansion of n in n 1546938934.934 * [misc]backup-simplify: Simplify 0 into 0 1546938934.934 * [misc]backup-simplify: Simplify 1 into 1 1546938934.935 * [misc]backup-simplify: Simplify (/ -2 1) into -2 1546938934.935 * [misc]backup-simplify: Simplify (log -2) into (log -2) 1546938934.935 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546938934.935 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546938934.935 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 1546938934.935 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 1546938934.935 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 1546938934.935 * [misc]taylor: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546938934.935 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in n 1546938934.935 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in n 1546938934.935 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546938934.935 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546938934.936 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938934.936 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.936 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938934.936 * [misc]taylor: Taking taylor expansion of k in n 1546938934.936 * [misc]backup-simplify: Simplify k into k 1546938934.936 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938934.936 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938934.936 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.936 * [misc]taylor: Taking taylor expansion of (log PI) in n 1546938934.936 * [misc]taylor: Taking taylor expansion of PI in n 1546938934.936 * [misc]backup-simplify: Simplify PI into PI 1546938934.936 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1546938934.936 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546938934.936 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546938934.936 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) 1546938934.936 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1546938934.937 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 1546938934.937 * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 1546938934.937 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 1546938934.938 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 1546938934.939 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 1546938934.939 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546938934.939 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546938934.939 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938934.940 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (log PI))) into 0 1546938934.941 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 1546938934.941 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -2 (/ 0 1)))) into 0 1546938934.942 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -2 1)))) 1) into 0 1546938934.942 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546938934.943 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546938934.943 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546938934.943 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 1546938934.943 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log -2) (log n)))) into 0 1546938934.944 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546938934.944 * [misc]backup-simplify: Simplify (+ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 0) (* 0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into 0 1546938934.945 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into 0 1546938934.945 * [misc]backup-simplify: Simplify 0 into 0 1546938934.945 * [misc]backup-simplify: Simplify (+ (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (* 0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into 0 1546938934.945 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546938934.946 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1546938934.947 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 1546938934.947 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) in n 1546938934.947 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1546938934.947 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546938934.947 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546938934.947 * [misc]taylor: Taking taylor expansion of (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in n 1546938934.947 * [misc]taylor: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546938934.947 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 1546938934.947 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 1546938934.947 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546938934.947 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546938934.947 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938934.947 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.947 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938934.947 * [misc]taylor: Taking taylor expansion of k in n 1546938934.947 * [misc]backup-simplify: Simplify k into k 1546938934.947 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938934.947 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938934.947 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.947 * [misc]taylor: Taking taylor expansion of (log (/ -2 n)) in n 1546938934.947 * [misc]taylor: Taking taylor expansion of (/ -2 n) in n 1546938934.947 * [misc]taylor: Taking taylor expansion of -2 in n 1546938934.947 * [misc]backup-simplify: Simplify -2 into -2 1546938934.947 * [misc]taylor: Taking taylor expansion of n in n 1546938934.947 * [misc]backup-simplify: Simplify 0 into 0 1546938934.947 * [misc]backup-simplify: Simplify 1 into 1 1546938934.947 * [misc]backup-simplify: Simplify (/ -2 1) into -2 1546938934.947 * [misc]backup-simplify: Simplify (log -2) into (log -2) 1546938934.947 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546938934.948 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546938934.948 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 1546938934.948 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 1546938934.948 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 1546938934.948 * [misc]taylor: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546938934.948 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in n 1546938934.948 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in n 1546938934.948 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546938934.948 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546938934.948 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938934.948 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.948 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546938934.948 * [misc]taylor: Taking taylor expansion of k in n 1546938934.948 * [misc]backup-simplify: Simplify k into k 1546938934.948 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546938934.948 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546938934.948 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546938934.948 * [misc]taylor: Taking taylor expansion of (log PI) in n 1546938934.948 * [misc]taylor: Taking taylor expansion of PI in n 1546938934.948 * [misc]backup-simplify: Simplify PI into PI 1546938934.949 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1546938934.949 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546938934.949 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546938934.949 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) 1546938934.949 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1546938934.949 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 1546938934.950 * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 1546938934.950 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 1546938934.950 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 1546938934.952 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -2) (log (/ 1 (- n)))))) (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -2) (log (/ 1 (- n)))))) (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))))) (* 1 (/ 1 (- k)))) (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -2) (log (/ 1 (- n)))))) (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)))))) into (- (+ (* +nan.0 (* (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (pow PI (- 1/2 (* 1/2 k))))) (- (+ (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (pow PI (- 1/2 (* 1/2 k)))) k)) (- (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (pow PI (- 1/2 (* 1/2 k)))) (pow k 2)))))))) 1546938934.952 * * * [misc]progress: simplifying candidates 1546938934.952 * * * * [misc]progress: [ 1 / 133 ] simplifiying candidate # 1546938934.952 * * * * [misc]progress: [ 2 / 133 ] simplifiying candidate # 1546938934.952 * [enter]simplify: Simplifying (pow PI (/ k 2)) 1546938934.952 * * [misc]simplify: iters left: 3 (5 enodes) 1546938934.955 * [exit]simplify: Simplified to (pow PI (/ k 2)) 1546938934.955 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (/ (pow PI 1/2) (pow PI (/ k 2))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1546938934.955 * * * * [misc]progress: [ 3 / 133 ] simplifiying candidate # 1546938934.955 * [enter]simplify: Simplifying (cbrt (- 1/2 (/ k 2))) 1546938934.955 * * [misc]simplify: iters left: 5 (6 enodes) 1546938934.956 * * [misc]simplify: iters left: 4 (8 enodes) 1546938934.959 * * [misc]simplify: iters left: 3 (11 enodes) 1546938934.962 * [exit]simplify: Simplified to (cbrt (- 1/2 (/ k 2))) 1546938934.962 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (pow (pow PI (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1546938934.962 * * * * [misc]progress: [ 4 / 133 ] simplifiying candidate # 1546938934.962 * [enter]simplify: Simplifying (sqrt (- 1/2 (/ k 2))) 1546938934.962 * * [misc]simplify: iters left: 5 (6 enodes) 1546938934.964 * * [misc]simplify: iters left: 4 (8 enodes) 1546938934.966 * * [misc]simplify: iters left: 3 (11 enodes) 1546938934.969 * [exit]simplify: Simplified to (sqrt (- 1/2 (/ k 2))) 1546938934.969 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (pow (pow PI (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1546938934.969 * * * * [misc]progress: [ 5 / 133 ] simplifiying candidate # 1546938934.970 * [enter]simplify: Simplifying (- 1/2 (/ k 2)) 1546938934.970 * * [misc]simplify: iters left: 4 (5 enodes) 1546938934.971 * * [misc]simplify: iters left: 3 (7 enodes) 1546938934.973 * * [misc]simplify: iters left: 2 (10 enodes) 1546938934.976 * [exit]simplify: Simplified to (- 1/2 (/ k 2)) 1546938934.976 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (pow (pow PI 1) (- 1/2 (/ k 2))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1546938934.976 * * * * [misc]progress: [ 6 / 133 ] simplifiying candidate # 1546938934.976 * [enter]simplify: Simplifying (pow PI (- (/ k 2))) 1546938934.976 * * [misc]simplify: iters left: 5 (6 enodes) 1546938934.978 * * [misc]simplify: iters left: 4 (8 enodes) 1546938934.980 * [exit]simplify: Simplified to (pow PI (/ (- k) 2)) 1546938934.980 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (* (pow PI 1/2) (pow PI (/ (- k) 2))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1546938934.980 * * * * [misc]progress: [ 7 / 133 ] simplifiying candidate # 1546938934.981 * [enter]simplify: Simplifying (pow PI (- (/ k 2))) 1546938934.981 * * [misc]simplify: iters left: 5 (6 enodes) 1546938934.982 * * [misc]simplify: iters left: 4 (8 enodes) 1546938934.985 * [exit]simplify: Simplified to (pow PI (/ (- k) 2)) 1546938934.985 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (* (pow PI 1/2) (pow PI (/ (- k) 2))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1546938934.985 * * * * [misc]progress: [ 8 / 133 ] simplifiying candidate # 1546938934.985 * * * * [misc]progress: [ 9 / 133 ] simplifiying candidate # 1546938934.985 * * * * [misc]progress: [ 10 / 133 ] simplifiying candidate # 1546938934.985 * * * * [misc]progress: [ 11 / 133 ] simplifiying candidate # 1546938934.985 * * * * [misc]progress: [ 12 / 133 ] simplifiying candidate # 1546938934.985 * * * * [misc]progress: [ 13 / 133 ] simplifiying candidate # 1546938934.985 * * * * [misc]progress: [ 14 / 133 ] simplifiying candidate # 1546938934.985 * * * * [misc]progress: [ 15 / 133 ] simplifiying candidate # 1546938934.986 * [enter]simplify: Simplifying (* (log (* n 2)) (- 1/2 (/ k 2))) 1546938934.986 * * [misc]simplify: iters left: 6 (9 enodes) 1546938934.988 * * [misc]simplify: iters left: 5 (16 enodes) 1546938934.991 * * [misc]simplify: iters left: 4 (32 enodes) 1546938934.997 * * [misc]simplify: iters left: 3 (68 enodes) 1546938935.011 * * [misc]simplify: iters left: 2 (171 enodes) 1546938935.046 * * [misc]simplify: iters left: 1 (342 enodes) 1546938935.183 * [exit]simplify: Simplified to (* (log (* n 2)) (- 1/2 (/ k 2))) 1546938935.183 * [misc]simplify: Simplified (2 2 1 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (exp (* (log (* n 2)) (- 1/2 (/ k 2)))) (sqrt k)))) 1546938935.183 * * * * [misc]progress: [ 16 / 133 ] simplifiying candidate # 1546938935.183 * * * * [misc]progress: [ 17 / 133 ] simplifiying candidate # 1546938935.183 * [enter]simplify: Simplifying (* n 2) 1546938935.183 * * [misc]simplify: iters left: 2 (3 enodes) 1546938935.184 * * [misc]simplify: iters left: 1 (4 enodes) 1546938935.184 * [exit]simplify: Simplified to (* n 2) 1546938935.184 * [misc]simplify: Simplified (2 2 1 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (pow (* n 2) (* 1 (- 1/2 (/ k 2)))) (sqrt k)))) 1546938935.184 * * * * [misc]progress: [ 18 / 133 ] simplifiying candidate # 1546938935.184 * [enter]simplify: Simplifying (pow (* n 2) (/ k 2)) 1546938935.184 * * [misc]simplify: iters left: 3 (6 enodes) 1546938935.185 * * [misc]simplify: iters left: 2 (7 enodes) 1546938935.186 * [exit]simplify: Simplified to (pow (* n 2) (/ k 2)) 1546938935.186 * [misc]simplify: Simplified (2 2 1 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (/ (pow (* n 2) 1/2) (pow (* n 2) (/ k 2))) (sqrt k)))) 1546938935.186 * * * * [misc]progress: [ 19 / 133 ] simplifiying candidate # 1546938935.186 * [enter]simplify: Simplifying (cbrt (- 1/2 (/ k 2))) 1546938935.186 * * [misc]simplify: iters left: 5 (6 enodes) 1546938935.187 * * [misc]simplify: iters left: 4 (8 enodes) 1546938935.188 * * [misc]simplify: iters left: 3 (11 enodes) 1546938935.190 * [exit]simplify: Simplified to (cbrt (- 1/2 (/ k 2))) 1546938935.190 * [misc]simplify: Simplified (2 2 1 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (pow (pow (* n 2) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))) (sqrt k)))) 1546938935.190 * * * * [misc]progress: [ 20 / 133 ] simplifiying candidate # 1546938935.190 * [enter]simplify: Simplifying (sqrt (- 1/2 (/ k 2))) 1546938935.190 * * [misc]simplify: iters left: 5 (6 enodes) 1546938935.191 * * [misc]simplify: iters left: 4 (8 enodes) 1546938935.192 * * [misc]simplify: iters left: 3 (11 enodes) 1546938935.193 * [exit]simplify: Simplified to (sqrt (- 1/2 (/ k 2))) 1546938935.193 * [misc]simplify: Simplified (2 2 1 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (pow (pow (* n 2) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))) (sqrt k)))) 1546938935.193 * * * * [misc]progress: [ 21 / 133 ] simplifiying candidate # 1546938935.193 * [enter]simplify: Simplifying (- 1/2 (/ k 2)) 1546938935.193 * * [misc]simplify: iters left: 4 (5 enodes) 1546938935.194 * * [misc]simplify: iters left: 3 (7 enodes) 1546938935.195 * * [misc]simplify: iters left: 2 (10 enodes) 1546938935.196 * [exit]simplify: Simplified to (- 1/2 (/ k 2)) 1546938935.196 * [misc]simplify: Simplified (2 2 1 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (pow (pow (* n 2) 1) (- 1/2 (/ k 2))) (sqrt k)))) 1546938935.196 * * * * [misc]progress: [ 22 / 133 ] simplifiying candidate # 1546938935.196 * [enter]simplify: Simplifying (pow (* n 2) (- (/ k 2))) 1546938935.197 * * [misc]simplify: iters left: 5 (7 enodes) 1546938935.198 * * [misc]simplify: iters left: 4 (10 enodes) 1546938935.199 * [exit]simplify: Simplified to (pow (* n 2) (- (/ k 2))) 1546938935.199 * [misc]simplify: Simplified (2 2 1 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (* (pow (* n 2) 1/2) (pow (* n 2) (- (/ k 2)))) (sqrt k)))) 1546938935.199 * * * * [misc]progress: [ 23 / 133 ] simplifiying candidate # 1546938935.199 * [enter]simplify: Simplifying (pow (* n 2) (- (/ k 2))) 1546938935.199 * * [misc]simplify: iters left: 5 (7 enodes) 1546938935.201 * * [misc]simplify: iters left: 4 (10 enodes) 1546938935.204 * [exit]simplify: Simplified to (pow (* n 2) (- (/ k 2))) 1546938935.204 * [misc]simplify: Simplified (2 2 1 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (* (pow (* n 2) 1/2) (pow (* n 2) (- (/ k 2)))) (sqrt k)))) 1546938935.204 * * * * [misc]progress: [ 24 / 133 ] simplifiying candidate # 1546938935.204 * [enter]simplify: Simplifying (pow n (- 1/2 (/ k 2))) 1546938935.204 * * [misc]simplify: iters left: 5 (7 enodes) 1546938935.207 * * [misc]simplify: iters left: 4 (9 enodes) 1546938935.209 * * [misc]simplify: iters left: 3 (12 enodes) 1546938935.213 * [exit]simplify: Simplified to (pow n (- 1/2 (/ k 2))) 1546938935.213 * [misc]simplify: Simplified (2 2 1 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (* (pow n (- 1/2 (/ k 2))) (pow 2 (- 1/2 (/ k 2)))) (sqrt k)))) 1546938935.213 * * * * [misc]progress: [ 25 / 133 ] simplifiying candidate # 1546938935.213 * * * * [misc]progress: [ 26 / 133 ] simplifiying candidate # 1546938935.213 * * * * [misc]progress: [ 27 / 133 ] simplifiying candidate # 1546938935.213 * * * * [misc]progress: [ 28 / 133 ] simplifiying candidate # 1546938935.213 * * * * [misc]progress: [ 29 / 133 ] simplifiying candidate # 1546938935.213 * * * * [misc]progress: [ 30 / 133 ] simplifiying candidate # 1546938935.213 * * * * [misc]progress: [ 31 / 133 ] simplifiying candidate # 1546938935.213 * * * * [misc]progress: [ 32 / 133 ] simplifiying candidate # 1546938935.213 * * * * [misc]progress: [ 33 / 133 ] simplifiying candidate # 1546938935.214 * [enter]simplify: Simplifying (- (* (log (* n 2)) (- 1/2 (/ k 2))) (log (sqrt k))) 1546938935.214 * * [misc]simplify: iters left: 6 (12 enodes) 1546938935.217 * * [misc]simplify: iters left: 5 (21 enodes) 1546938935.220 * * [misc]simplify: iters left: 4 (38 enodes) 1546938935.229 * * [misc]simplify: iters left: 3 (98 enodes) 1546938935.260 * * [misc]simplify: iters left: 2 (325 enodes) 1546938935.423 * [exit]simplify: Simplified to (- (* (log (* n 2)) (- 1/2 (/ k 2))) (log (sqrt k))) 1546938935.424 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (exp (- (* (log (* n 2)) (- 1/2 (/ k 2))) (log (sqrt k)))))) 1546938935.424 * * * * [misc]progress: [ 34 / 133 ] simplifiying candidate # 1546938935.424 * [enter]simplify: Simplifying (- (* (log (* n 2)) (- 1/2 (/ k 2))) (log (sqrt k))) 1546938935.424 * * [misc]simplify: iters left: 6 (12 enodes) 1546938935.426 * * [misc]simplify: iters left: 5 (21 enodes) 1546938935.430 * * [misc]simplify: iters left: 4 (38 enodes) 1546938935.438 * * [misc]simplify: iters left: 3 (98 enodes) 1546938935.479 * * [misc]simplify: iters left: 2 (325 enodes) 1546938935.656 * [exit]simplify: Simplified to (- (* (log (* n 2)) (- 1/2 (/ k 2))) (log (sqrt k))) 1546938935.657 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (exp (- (* (log (* n 2)) (- 1/2 (/ k 2))) (log (sqrt k)))))) 1546938935.657 * * * * [misc]progress: [ 35 / 133 ] simplifiying candidate # 1546938935.657 * [enter]simplify: Simplifying (- (log (pow (* n 2) (- 1/2 (/ k 2)))) (log (sqrt k))) 1546938935.657 * * [misc]simplify: iters left: 6 (12 enodes) 1546938935.661 * * [misc]simplify: iters left: 5 (19 enodes) 1546938935.667 * * [misc]simplify: iters left: 4 (28 enodes) 1546938935.675 * * [misc]simplify: iters left: 3 (44 enodes) 1546938935.692 * * [misc]simplify: iters left: 2 (124 enodes) 1546938935.759 * * [misc]simplify: iters left: 1 (453 enodes) 1546938936.038 * [exit]simplify: Simplified to (- (* (log (* n 2)) (- 1/2 (/ k 2))) (log (sqrt k))) 1546938936.038 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (exp (- (* (log (* n 2)) (- 1/2 (/ k 2))) (log (sqrt k)))))) 1546938936.038 * * * * [misc]progress: [ 36 / 133 ] simplifiying candidate # 1546938936.039 * * * * [misc]progress: [ 37 / 133 ] simplifiying candidate # 1546938936.039 * * * * [misc]progress: [ 38 / 133 ] simplifiying candidate # 1546938936.039 * [enter]simplify: Simplifying (/ (* (* (pow (* n 2) (- 1/2 (/ k 2))) (pow (* n 2) (- 1/2 (/ k 2)))) (pow (* n 2) (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k))) 1546938936.039 * * [misc]simplify: iters left: 6 (14 enodes) 1546938936.041 * * [misc]simplify: iters left: 5 (26 enodes) 1546938936.045 * * [misc]simplify: iters left: 4 (57 enodes) 1546938936.055 * * [misc]simplify: iters left: 3 (112 enodes) 1546938936.080 * * [misc]simplify: iters left: 2 (189 enodes) 1546938936.137 * * [misc]simplify: iters left: 1 (316 enodes) 1546938936.293 * [exit]simplify: Simplified to (* (/ (pow (* n 2) (- 1/2 (/ k 2))) (* k (sqrt k))) (* (pow (* n 2) (- 1/2 (/ k 2))) (pow (* n 2) (- 1/2 (/ k 2))))) 1546938936.293 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (cbrt (* (/ (pow (* n 2) (- 1/2 (/ k 2))) (* k (sqrt k))) (* (pow (* n 2) (- 1/2 (/ k 2))) (pow (* n 2) (- 1/2 (/ k 2)))))))) 1546938936.293 * * * * [misc]progress: [ 39 / 133 ] simplifiying candidate # 1546938936.293 * * * * [misc]progress: [ 40 / 133 ] simplifiying candidate # 1546938936.293 * * * * [misc]progress: [ 41 / 133 ] simplifiying candidate # 1546938936.293 * * * * [misc]progress: [ 42 / 133 ] simplifiying candidate # 1546938936.293 * * * * [misc]progress: [ 43 / 133 ] simplifiying candidate # 1546938936.293 * [enter]simplify: Simplifying (/ (pow (* n 2) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1546938936.294 * * [misc]simplify: iters left: 6 (10 enodes) 1546938936.297 * * [misc]simplify: iters left: 5 (14 enodes) 1546938936.301 * [exit]simplify: Simplified to (/ (sqrt (* n 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1546938936.301 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (/ (sqrt (* n 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n 2) (- (/ k 2))) (cbrt (sqrt k)))))) 1546938936.301 * [enter]simplify: Simplifying (/ (pow (* n 2) (- (/ k 2))) (cbrt (sqrt k))) 1546938936.301 * * [misc]simplify: iters left: 6 (10 enodes) 1546938936.304 * * [misc]simplify: iters left: 5 (13 enodes) 1546938936.308 * [exit]simplify: Simplified to (/ (pow (* n 2) (/ (- k) 2)) (cbrt (sqrt k))) 1546938936.308 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (/ (sqrt (* n 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n 2) (/ (- k) 2)) (cbrt (sqrt k)))))) 1546938936.308 * * * * [misc]progress: [ 44 / 133 ] simplifiying candidate # 1546938936.308 * [enter]simplify: Simplifying (/ (pow (* n 2) 1/2) (sqrt (sqrt k))) 1546938936.308 * * [misc]simplify: iters left: 5 (9 enodes) 1546938936.311 * * [misc]simplify: iters left: 4 (11 enodes) 1546938936.314 * [exit]simplify: Simplified to (/ (sqrt (* n 2)) (sqrt (sqrt k))) 1546938936.315 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (/ (sqrt (* n 2)) (sqrt (sqrt k))) (/ (pow (* n 2) (- (/ k 2))) (sqrt (sqrt k)))))) 1546938936.315 * [enter]simplify: Simplifying (/ (pow (* n 2) (- (/ k 2))) (sqrt (sqrt k))) 1546938936.315 * * [misc]simplify: iters left: 6 (10 enodes) 1546938936.318 * * [misc]simplify: iters left: 5 (13 enodes) 1546938936.322 * [exit]simplify: Simplified to (/ (pow (* n 2) (/ (- k) 2)) (sqrt (sqrt k))) 1546938936.322 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (/ (sqrt (* n 2)) (sqrt (sqrt k))) (/ (pow (* n 2) (/ (- k) 2)) (sqrt (sqrt k)))))) 1546938936.322 * * * * [misc]progress: [ 45 / 133 ] simplifiying candidate # 1546938936.322 * [enter]simplify: Simplifying (/ (pow (* n 2) 1/2) 1) 1546938936.322 * * [misc]simplify: iters left: 5 (7 enodes) 1546938936.324 * * [misc]simplify: iters left: 4 (11 enodes) 1546938936.328 * * [misc]simplify: iters left: 3 (13 enodes) 1546938936.331 * [exit]simplify: Simplified to (sqrt (* n 2)) 1546938936.331 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (sqrt (* n 2)) (/ (pow (* n 2) (- (/ k 2))) (sqrt k))))) 1546938936.331 * [enter]simplify: Simplifying (/ (pow (* n 2) (- (/ k 2))) (sqrt k)) 1546938936.331 * * [misc]simplify: iters left: 6 (9 enodes) 1546938936.334 * * [misc]simplify: iters left: 5 (12 enodes) 1546938936.337 * [exit]simplify: Simplified to (/ (pow (* n 2) (- (/ k 2))) (sqrt k)) 1546938936.337 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (sqrt (* n 2)) (/ (pow (* n 2) (- (/ k 2))) (sqrt k))))) 1546938936.337 * * * * [misc]progress: [ 46 / 133 ] simplifiying candidate # 1546938936.337 * [enter]simplify: Simplifying (/ (pow (* n 2) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1546938936.338 * * [misc]simplify: iters left: 6 (10 enodes) 1546938936.340 * * [misc]simplify: iters left: 5 (14 enodes) 1546938936.344 * [exit]simplify: Simplified to (/ (sqrt (* n 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1546938936.344 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (/ (sqrt (* n 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n 2) (- (/ k 2))) (cbrt (sqrt k)))))) 1546938936.344 * [enter]simplify: Simplifying (/ (pow (* n 2) (- (/ k 2))) (cbrt (sqrt k))) 1546938936.344 * * [misc]simplify: iters left: 6 (10 enodes) 1546938936.347 * * [misc]simplify: iters left: 5 (13 enodes) 1546938936.350 * [exit]simplify: Simplified to (/ (pow (* n 2) (/ (- k) 2)) (cbrt (sqrt k))) 1546938936.350 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (/ (sqrt (* n 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n 2) (/ (- k) 2)) (cbrt (sqrt k)))))) 1546938936.350 * * * * [misc]progress: [ 47 / 133 ] simplifiying candidate # 1546938936.351 * [enter]simplify: Simplifying (/ (pow (* n 2) 1/2) (sqrt (sqrt k))) 1546938936.351 * * [misc]simplify: iters left: 5 (9 enodes) 1546938936.353 * * [misc]simplify: iters left: 4 (11 enodes) 1546938936.356 * [exit]simplify: Simplified to (/ (sqrt (* n 2)) (sqrt (sqrt k))) 1546938936.357 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (/ (sqrt (* n 2)) (sqrt (sqrt k))) (/ (pow (* n 2) (- (/ k 2))) (sqrt (sqrt k)))))) 1546938936.357 * [enter]simplify: Simplifying (/ (pow (* n 2) (- (/ k 2))) (sqrt (sqrt k))) 1546938936.357 * * [misc]simplify: iters left: 6 (10 enodes) 1546938936.360 * * [misc]simplify: iters left: 5 (13 enodes) 1546938936.364 * [exit]simplify: Simplified to (/ (pow (* n 2) (/ (- k) 2)) (sqrt (sqrt k))) 1546938936.364 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (/ (sqrt (* n 2)) (sqrt (sqrt k))) (/ (pow (* n 2) (/ (- k) 2)) (sqrt (sqrt k)))))) 1546938936.364 * * * * [misc]progress: [ 48 / 133 ] simplifiying candidate # 1546938936.365 * [enter]simplify: Simplifying (/ (pow (* n 2) 1/2) 1) 1546938936.365 * * [misc]simplify: iters left: 5 (7 enodes) 1546938936.367 * * [misc]simplify: iters left: 4 (11 enodes) 1546938936.370 * * [misc]simplify: iters left: 3 (13 enodes) 1546938936.373 * [exit]simplify: Simplified to (sqrt (* n 2)) 1546938936.373 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (sqrt (* n 2)) (/ (pow (* n 2) (- (/ k 2))) (sqrt k))))) 1546938936.373 * [enter]simplify: Simplifying (/ (pow (* n 2) (- (/ k 2))) (sqrt k)) 1546938936.373 * * [misc]simplify: iters left: 6 (9 enodes) 1546938936.376 * * [misc]simplify: iters left: 5 (12 enodes) 1546938936.382 * [exit]simplify: Simplified to (/ (pow (* n 2) (- (/ k 2))) (sqrt k)) 1546938936.382 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (sqrt (* n 2)) (/ (pow (* n 2) (- (/ k 2))) (sqrt k))))) 1546938936.382 * * * * [misc]progress: [ 49 / 133 ] simplifiying candidate # 1546938936.382 * [enter]simplify: Simplifying (/ (pow n (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1546938936.383 * * [misc]simplify: iters left: 6 (11 enodes) 1546938936.386 * * [misc]simplify: iters left: 5 (15 enodes) 1546938936.389 * * [misc]simplify: iters left: 4 (18 enodes) 1546938936.391 * [exit]simplify: Simplified to (/ (pow n (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1546938936.391 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (/ (pow n (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow 2 (- 1/2 (/ k 2))) (cbrt (sqrt k)))))) 1546938936.391 * [enter]simplify: Simplifying (/ (pow 2 (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1546938936.391 * * [misc]simplify: iters left: 6 (9 enodes) 1546938936.393 * * [misc]simplify: iters left: 5 (11 enodes) 1546938936.394 * * [misc]simplify: iters left: 4 (14 enodes) 1546938936.396 * [exit]simplify: Simplified to (/ (pow 2 (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1546938936.396 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (/ (pow n (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow 2 (- 1/2 (/ k 2))) (cbrt (sqrt k)))))) 1546938936.396 * * * * [misc]progress: [ 50 / 133 ] simplifiying candidate # 1546938936.396 * [enter]simplify: Simplifying (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1546938936.396 * * [misc]simplify: iters left: 6 (10 enodes) 1546938936.398 * * [misc]simplify: iters left: 5 (12 enodes) 1546938936.399 * * [misc]simplify: iters left: 4 (15 enodes) 1546938936.401 * [exit]simplify: Simplified to (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1546938936.402 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow 2 (- 1/2 (/ k 2))) (sqrt (sqrt k)))))) 1546938936.402 * [enter]simplify: Simplifying (/ (pow 2 (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1546938936.402 * * [misc]simplify: iters left: 6 (9 enodes) 1546938936.403 * * [misc]simplify: iters left: 5 (11 enodes) 1546938936.406 * * [misc]simplify: iters left: 4 (14 enodes) 1546938936.410 * [exit]simplify: Simplified to (/ (pow 2 (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1546938936.410 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow 2 (- 1/2 (/ k 2))) (sqrt (sqrt k)))))) 1546938936.410 * * * * [misc]progress: [ 51 / 133 ] simplifiying candidate # 1546938936.410 * [enter]simplify: Simplifying (/ (pow n (- 1/2 (/ k 2))) 1) 1546938936.411 * * [misc]simplify: iters left: 6 (9 enodes) 1546938936.413 * * [misc]simplify: iters left: 5 (13 enodes) 1546938936.417 * * [misc]simplify: iters left: 4 (18 enodes) 1546938936.421 * [exit]simplify: Simplified to (pow n (- 1/2 (/ k 2))) 1546938936.422 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow 2 (- 1/2 (/ k 2))) (sqrt k))))) 1546938936.422 * [enter]simplify: Simplifying (/ (pow 2 (- 1/2 (/ k 2))) (sqrt k)) 1546938936.422 * * [misc]simplify: iters left: 6 (8 enodes) 1546938936.424 * * [misc]simplify: iters left: 5 (10 enodes) 1546938936.427 * * [misc]simplify: iters left: 4 (13 enodes) 1546938936.430 * [exit]simplify: Simplified to (/ (pow 2 (- 1/2 (/ k 2))) (sqrt k)) 1546938936.430 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow 2 (- 1/2 (/ k 2))) (sqrt k))))) 1546938936.430 * * * * [misc]progress: [ 52 / 133 ] simplifiying candidate # 1546938936.431 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (pow (* n 2) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1546938936.431 * * [misc]simplify: iters left: 6 (14 enodes) 1546938936.435 * * [misc]simplify: iters left: 5 (23 enodes) 1546938936.442 * * [misc]simplify: iters left: 4 (35 enodes) 1546938936.449 * * [misc]simplify: iters left: 3 (38 enodes) 1546938936.453 * * [misc]simplify: iters left: 2 (41 enodes) 1546938936.459 * [exit]simplify: Simplified to (* (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))) 1546938936.459 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (* (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))) (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))) 1546938936.459 * [enter]simplify: Simplifying (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1546938936.459 * * [misc]simplify: iters left: 6 (12 enodes) 1546938936.461 * * [misc]simplify: iters left: 5 (15 enodes) 1546938936.463 * * [misc]simplify: iters left: 4 (18 enodes) 1546938936.467 * [exit]simplify: Simplified to (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1546938936.467 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (/ (* (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (pow (* n 2) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))) 1546938936.467 * * * * [misc]progress: [ 53 / 133 ] simplifiying candidate # 1546938936.467 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (pow (* n 2) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) 1546938936.467 * * [misc]simplify: iters left: 6 (13 enodes) 1546938936.471 * * [misc]simplify: iters left: 5 (18 enodes) 1546938936.476 * * [misc]simplify: iters left: 4 (23 enodes) 1546938936.483 * * [misc]simplify: iters left: 3 (24 enodes) 1546938936.490 * [exit]simplify: Simplified to (* (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (cbrt (pow (* n 2) (- 1/2 (/ k 2))))) 1546938936.490 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (* (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (cbrt (pow (* n 2) (- 1/2 (/ k 2))))) (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))) 1546938936.490 * [enter]simplify: Simplifying (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1546938936.490 * * [misc]simplify: iters left: 6 (12 enodes) 1546938936.494 * * [misc]simplify: iters left: 5 (15 enodes) 1546938936.500 * * [misc]simplify: iters left: 4 (18 enodes) 1546938936.505 * [exit]simplify: Simplified to (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1546938936.505 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (/ (* (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (pow (* n 2) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))) 1546938936.505 * * * * [misc]progress: [ 54 / 133 ] simplifiying candidate # 1546938936.506 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (pow (* n 2) (- 1/2 (/ k 2))))) 1) 1546938936.506 * * [misc]simplify: iters left: 6 (12 enodes) 1546938936.510 * * [misc]simplify: iters left: 5 (19 enodes) 1546938936.516 * * [misc]simplify: iters left: 4 (28 enodes) 1546938936.524 * * [misc]simplify: iters left: 3 (42 enodes) 1546938936.535 * * [misc]simplify: iters left: 2 (68 enodes) 1546938936.553 * [exit]simplify: Simplified to (* (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (pow (* n 2) (- 1/2 (/ k 2))))) 1546938936.553 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (* (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (pow (* n 2) (- 1/2 (/ k 2))))) (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt k))))) 1546938936.554 * [enter]simplify: Simplifying (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt k)) 1546938936.554 * * [misc]simplify: iters left: 6 (11 enodes) 1546938936.557 * * [misc]simplify: iters left: 5 (14 enodes) 1546938936.561 * * [misc]simplify: iters left: 4 (17 enodes) 1546938936.566 * [exit]simplify: Simplified to (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt k)) 1546938936.566 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (* (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (pow (* n 2) (- 1/2 (/ k 2))))) (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt k))))) 1546938936.566 * * * * [misc]progress: [ 55 / 133 ] simplifiying candidate # 1546938936.566 * [enter]simplify: Simplifying (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1546938936.567 * * [misc]simplify: iters left: 6 (13 enodes) 1546938936.570 * * [misc]simplify: iters left: 5 (18 enodes) 1546938936.576 * * [misc]simplify: iters left: 4 (21 enodes) 1546938936.581 * [exit]simplify: Simplified to (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1546938936.582 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))) 1546938936.582 * [enter]simplify: Simplifying (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1546938936.582 * * [misc]simplify: iters left: 6 (12 enodes) 1546938936.586 * * [misc]simplify: iters left: 5 (15 enodes) 1546938936.590 * * [misc]simplify: iters left: 4 (18 enodes) 1546938936.595 * [exit]simplify: Simplified to (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1546938936.595 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))) 1546938936.595 * * * * [misc]progress: [ 56 / 133 ] simplifiying candidate # 1546938936.595 * [enter]simplify: Simplifying (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1546938936.596 * * [misc]simplify: iters left: 6 (12 enodes) 1546938936.599 * * [misc]simplify: iters left: 5 (15 enodes) 1546938936.602 * * [misc]simplify: iters left: 4 (18 enodes) 1546938936.606 * [exit]simplify: Simplified to (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1546938936.606 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))) 1546938936.607 * [enter]simplify: Simplifying (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1546938936.607 * * [misc]simplify: iters left: 6 (12 enodes) 1546938936.610 * * [misc]simplify: iters left: 5 (15 enodes) 1546938936.613 * * [misc]simplify: iters left: 4 (18 enodes) 1546938936.617 * [exit]simplify: Simplified to (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1546938936.617 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))) 1546938936.617 * * * * [misc]progress: [ 57 / 133 ] simplifiying candidate # 1546938936.618 * [enter]simplify: Simplifying (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) 1) 1546938936.618 * * [misc]simplify: iters left: 6 (11 enodes) 1546938936.621 * * [misc]simplify: iters left: 5 (16 enodes) 1546938936.624 * * [misc]simplify: iters left: 4 (21 enodes) 1546938936.627 * [exit]simplify: Simplified to (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) 1546938936.627 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt k))))) 1546938936.627 * [enter]simplify: Simplifying (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt k)) 1546938936.627 * * [misc]simplify: iters left: 6 (11 enodes) 1546938936.628 * * [misc]simplify: iters left: 5 (14 enodes) 1546938936.631 * * [misc]simplify: iters left: 4 (17 enodes) 1546938936.633 * [exit]simplify: Simplified to (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt k)) 1546938936.633 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt k))))) 1546938936.633 * * * * [misc]progress: [ 58 / 133 ] simplifiying candidate # 1546938936.633 * [enter]simplify: Simplifying (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1546938936.633 * * [misc]simplify: iters left: 6 (6 enodes) 1546938936.635 * * [misc]simplify: iters left: 5 (10 enodes) 1546938936.636 * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) 1546938936.636 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k)))))) 1546938936.638 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1546938936.638 * * [misc]simplify: iters left: 6 (11 enodes) 1546938936.639 * * [misc]simplify: iters left: 5 (14 enodes) 1546938936.641 * * [misc]simplify: iters left: 4 (17 enodes) 1546938936.643 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1546938936.644 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k)))))) 1546938936.644 * * * * [misc]progress: [ 59 / 133 ] simplifiying candidate # 1546938936.644 * [enter]simplify: Simplifying (/ 1 (sqrt (sqrt k))) 1546938936.644 * * [misc]simplify: iters left: 4 (5 enodes) 1546938936.644 * * [misc]simplify: iters left: 3 (7 enodes) 1546938936.645 * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt k))) 1546938936.645 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))) 1546938936.645 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1546938936.645 * * [misc]simplify: iters left: 6 (11 enodes) 1546938936.647 * * [misc]simplify: iters left: 5 (14 enodes) 1546938936.649 * * [misc]simplify: iters left: 4 (17 enodes) 1546938936.651 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1546938936.651 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))) 1546938936.651 * * * * [misc]progress: [ 60 / 133 ] simplifiying candidate # 1546938936.651 * [enter]simplify: Simplifying (/ 1 1) 1546938936.652 * * [misc]simplify: iters left: 2 (2 enodes) 1546938936.652 * * [misc]simplify: iters left: 1 (4 enodes) 1546938936.653 * [exit]simplify: Simplified to 1 1546938936.653 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* 1 (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))))) 1546938936.653 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)) 1546938936.653 * * [misc]simplify: iters left: 6 (10 enodes) 1546938936.656 * * [misc]simplify: iters left: 5 (13 enodes) 1546938936.660 * * [misc]simplify: iters left: 4 (16 enodes) 1546938936.664 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)) 1546938936.664 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* 1 (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))))) 1546938936.664 * * * * [misc]progress: [ 61 / 133 ] simplifiying candidate # 1546938936.664 * * * * [misc]progress: [ 62 / 133 ] simplifiying candidate # 1546938936.664 * * * * [misc]progress: [ 63 / 133 ] simplifiying candidate # 1546938936.664 * * * * [misc]progress: [ 64 / 133 ] simplifiying candidate # 1546938936.665 * [enter]simplify: Simplifying (cbrt (sqrt k)) 1546938936.665 * * [misc]simplify: iters left: 2 (3 enodes) 1546938936.666 * [exit]simplify: Simplified to (cbrt (sqrt k)) 1546938936.666 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (/ (pow (* n 2) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k))))) 1546938936.666 * * * * [misc]progress: [ 65 / 133 ] simplifiying candidate # 1546938936.666 * [enter]simplify: Simplifying (sqrt (sqrt k)) 1546938936.666 * * [misc]simplify: iters left: 2 (3 enodes) 1546938936.667 * [exit]simplify: Simplified to (sqrt (sqrt k)) 1546938936.667 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k))))) 1546938936.667 * * * * [misc]progress: [ 66 / 133 ] simplifiying candidate # 1546938936.667 * [enter]simplify: Simplifying (sqrt k) 1546938936.667 * * [misc]simplify: iters left: 1 (2 enodes) 1546938936.668 * [exit]simplify: Simplified to (sqrt k) 1546938936.668 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (/ (pow (* n 2) (- 1/2 (/ k 2))) 1) (sqrt k)))) 1546938936.668 * * * * [misc]progress: [ 67 / 133 ] simplifiying candidate # 1546938936.668 * [enter]simplify: Simplifying (pow (* n 2) 1/2) 1546938936.668 * * [misc]simplify: iters left: 3 (5 enodes) 1546938936.670 * * [misc]simplify: iters left: 2 (7 enodes) 1546938936.672 * [exit]simplify: Simplified to (sqrt (* n 2)) 1546938936.672 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (sqrt (* n 2)) (/ (sqrt k) (pow (* n 2) (- (/ k 2))))))) 1546938936.672 * * * * [misc]progress: [ 68 / 133 ] simplifiying candidate # 1546938936.672 * [enter]simplify: Simplifying (pow (* n 2) 1/2) 1546938936.672 * * [misc]simplify: iters left: 3 (5 enodes) 1546938936.674 * * [misc]simplify: iters left: 2 (7 enodes) 1546938936.676 * [exit]simplify: Simplified to (sqrt (* n 2)) 1546938936.676 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (sqrt (* n 2)) (/ (sqrt k) (pow (* n 2) (- (/ k 2))))))) 1546938936.676 * * * * [misc]progress: [ 69 / 133 ] simplifiying candidate # 1546938936.676 * [enter]simplify: Simplifying (pow n (- 1/2 (/ k 2))) 1546938936.676 * * [misc]simplify: iters left: 5 (7 enodes) 1546938936.678 * * [misc]simplify: iters left: 4 (9 enodes) 1546938936.681 * * [misc]simplify: iters left: 3 (12 enodes) 1546938936.684 * [exit]simplify: Simplified to (pow n (- 1/2 (/ k 2))) 1546938936.684 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (pow n (- 1/2 (/ k 2))) (/ (sqrt k) (pow 2 (- 1/2 (/ k 2))))))) 1546938936.684 * * * * [misc]progress: [ 70 / 133 ] simplifiying candidate # 1546938936.684 * [enter]simplify: Simplifying (* (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (pow (* n 2) (- 1/2 (/ k 2))))) 1546938936.685 * * [misc]simplify: iters left: 6 (10 enodes) 1546938936.688 * * [misc]simplify: iters left: 5 (13 enodes) 1546938936.692 * * [misc]simplify: iters left: 4 (16 enodes) 1546938936.696 * [exit]simplify: Simplified to (* (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (pow (* n 2) (- 1/2 (/ k 2))))) 1546938936.696 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (* (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (pow (* n 2) (- 1/2 (/ k 2))))) (/ (sqrt k) (cbrt (pow (* n 2) (- 1/2 (/ k 2)))))))) 1546938936.696 * * * * [misc]progress: [ 71 / 133 ] simplifiying candidate # 1546938936.697 * [enter]simplify: Simplifying (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) 1546938936.697 * * [misc]simplify: iters left: 6 (9 enodes) 1546938936.700 * * [misc]simplify: iters left: 5 (12 enodes) 1546938936.703 * * [misc]simplify: iters left: 4 (15 enodes) 1546938936.707 * [exit]simplify: Simplified to (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) 1546938936.707 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* n 2) (- 1/2 (/ k 2)))))))) 1546938936.707 * * * * [misc]progress: [ 72 / 133 ] simplifiying candidate # 1546938936.707 * * * * [misc]progress: [ 73 / 133 ] simplifiying candidate # 1546938936.707 * [enter]simplify: Simplifying (pow (* n 2) 1/2) 1546938936.708 * * [misc]simplify: iters left: 3 (5 enodes) 1546938936.709 * * [misc]simplify: iters left: 2 (7 enodes) 1546938936.711 * [exit]simplify: Simplified to (sqrt (* n 2)) 1546938936.711 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (sqrt (* n 2)) (* (sqrt k) (pow (* n 2) (/ k 2)))))) 1546938936.711 * * * * [misc]progress: [ 74 / 133 ] simplifiying candidate # 1546938936.711 * * * * [misc]progress: [ 75 / 133 ] simplifiying candidate # 1546938936.711 * [enter]simplify: Simplifying (+ (* (log PI) (- 1/2 (/ k 2))) (- (* (log (* n 2)) (- 1/2 (/ k 2))) (log (sqrt k)))) 1546938936.712 * * [misc]simplify: iters left: 6 (16 enodes) 1546938936.717 * * [misc]simplify: iters left: 5 (29 enodes) 1546938936.727 * * [misc]simplify: iters left: 4 (60 enodes) 1546938936.755 * * [misc]simplify: iters left: 3 (191 enodes) 1546938936.868 * [exit]simplify: Simplified to (- (* (+ (log PI) (log (* 2 n))) (- 1/2 (/ k 2))) (log (sqrt k))) 1546938936.868 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (+ (log PI) (log (* 2 n))) (- 1/2 (/ k 2))) (log (sqrt k))))) 1546938936.868 * * * * [misc]progress: [ 76 / 133 ] simplifiying candidate # 1546938936.868 * [enter]simplify: Simplifying (+ (* (log PI) (- 1/2 (/ k 2))) (- (* (log (* n 2)) (- 1/2 (/ k 2))) (log (sqrt k)))) 1546938936.868 * * [misc]simplify: iters left: 6 (16 enodes) 1546938936.873 * * [misc]simplify: iters left: 5 (29 enodes) 1546938936.878 * * [misc]simplify: iters left: 4 (60 enodes) 1546938936.892 * * [misc]simplify: iters left: 3 (191 enodes) 1546938937.009 * [exit]simplify: Simplified to (- (* (+ (log PI) (log (* 2 n))) (- 1/2 (/ k 2))) (log (sqrt k))) 1546938937.009 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (+ (log PI) (log (* 2 n))) (- 1/2 (/ k 2))) (log (sqrt k))))) 1546938937.009 * * * * [misc]progress: [ 77 / 133 ] simplifiying candidate # 1546938937.009 * [enter]simplify: Simplifying (+ (* (log PI) (- 1/2 (/ k 2))) (- (log (pow (* n 2) (- 1/2 (/ k 2)))) (log (sqrt k)))) 1546938937.009 * * [misc]simplify: iters left: 6 (16 enodes) 1546938937.012 * * [misc]simplify: iters left: 5 (27 enodes) 1546938937.016 * * [misc]simplify: iters left: 4 (50 enodes) 1546938937.026 * * [misc]simplify: iters left: 3 (114 enodes) 1546938937.071 * * [misc]simplify: iters left: 2 (426 enodes) 1546938937.433 * [exit]simplify: Simplified to (- (* (+ (log PI) (log (* 2 n))) (- 1/2 (/ k 2))) (log (sqrt k))) 1546938937.433 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (+ (log PI) (log (* 2 n))) (- 1/2 (/ k 2))) (log (sqrt k))))) 1546938937.433 * * * * [misc]progress: [ 78 / 133 ] simplifiying candidate # 1546938937.433 * [enter]simplify: Simplifying (+ (* (log PI) (- 1/2 (/ k 2))) (log (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1546938937.434 * * [misc]simplify: iters left: 6 (15 enodes) 1546938937.436 * * [misc]simplify: iters left: 5 (23 enodes) 1546938937.439 * * [misc]simplify: iters left: 4 (40 enodes) 1546938937.454 * * [misc]simplify: iters left: 3 (82 enodes) 1546938937.475 * * [misc]simplify: iters left: 2 (187 enodes) 1546938937.566 * [exit]simplify: Simplified to (- (* (+ (log PI) (log (* 2 n))) (- 1/2 (/ k 2))) (log (sqrt k))) 1546938937.566 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (+ (log PI) (log (* 2 n))) (- 1/2 (/ k 2))) (log (sqrt k))))) 1546938937.566 * * * * [misc]progress: [ 79 / 133 ] simplifiying candidate # 1546938937.567 * [enter]simplify: Simplifying (+ (log (pow PI (- 1/2 (/ k 2)))) (- (* (log (* n 2)) (- 1/2 (/ k 2))) (log (sqrt k)))) 1546938937.567 * * [misc]simplify: iters left: 6 (16 enodes) 1546938937.570 * * [misc]simplify: iters left: 5 (30 enodes) 1546938937.575 * * [misc]simplify: iters left: 4 (56 enodes) 1546938937.590 * * [misc]simplify: iters left: 3 (161 enodes) 1546938937.667 * [exit]simplify: Simplified to (- (* (+ (log PI) (log (* n 2))) (- 1/2 (/ k 2))) (log (sqrt k))) 1546938937.667 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (+ (log PI) (log (* n 2))) (- 1/2 (/ k 2))) (log (sqrt k))))) 1546938937.667 * * * * [misc]progress: [ 80 / 133 ] simplifiying candidate # 1546938937.667 * [enter]simplify: Simplifying (+ (log (pow PI (- 1/2 (/ k 2)))) (- (* (log (* n 2)) (- 1/2 (/ k 2))) (log (sqrt k)))) 1546938937.667 * * [misc]simplify: iters left: 6 (16 enodes) 1546938937.673 * * [misc]simplify: iters left: 5 (30 enodes) 1546938937.682 * * [misc]simplify: iters left: 4 (56 enodes) 1546938937.704 * * [misc]simplify: iters left: 3 (161 enodes) 1546938937.776 * [exit]simplify: Simplified to (- (* (+ (log PI) (log (* n 2))) (- 1/2 (/ k 2))) (log (sqrt k))) 1546938937.776 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (+ (log PI) (log (* n 2))) (- 1/2 (/ k 2))) (log (sqrt k))))) 1546938937.776 * * * * [misc]progress: [ 81 / 133 ] simplifiying candidate # 1546938937.776 * [enter]simplify: Simplifying (+ (log (pow PI (- 1/2 (/ k 2)))) (- (log (pow (* n 2) (- 1/2 (/ k 2)))) (log (sqrt k)))) 1546938937.776 * * [misc]simplify: iters left: 6 (16 enodes) 1546938937.781 * * [misc]simplify: iters left: 5 (28 enodes) 1546938937.790 * * [misc]simplify: iters left: 4 (46 enodes) 1546938937.803 * * [misc]simplify: iters left: 3 (83 enodes) 1546938937.827 * * [misc]simplify: iters left: 2 (323 enodes) 1546938938.129 * [exit]simplify: Simplified to (- (* (+ (log (* n 2)) (log PI)) (- 1/2 (/ k 2))) (log (sqrt k))) 1546938938.129 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (+ (log (* n 2)) (log PI)) (- 1/2 (/ k 2))) (log (sqrt k))))) 1546938938.129 * * * * [misc]progress: [ 82 / 133 ] simplifiying candidate # 1546938938.130 * [enter]simplify: Simplifying (+ (log (pow PI (- 1/2 (/ k 2)))) (log (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1546938938.130 * * [misc]simplify: iters left: 6 (15 enodes) 1546938938.133 * * [misc]simplify: iters left: 5 (24 enodes) 1546938938.136 * * [misc]simplify: iters left: 4 (36 enodes) 1546938938.141 * * [misc]simplify: iters left: 3 (60 enodes) 1546938938.154 * * [misc]simplify: iters left: 2 (163 enodes) 1546938938.219 * [exit]simplify: Simplified to (- (* (+ (log PI) (log (* n 2))) (- 1/2 (/ k 2))) (log (sqrt k))) 1546938938.219 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (+ (log PI) (log (* n 2))) (- 1/2 (/ k 2))) (log (sqrt k))))) 1546938938.220 * * * * [misc]progress: [ 83 / 133 ] simplifiying candidate # 1546938938.220 * * * * [misc]progress: [ 84 / 133 ] simplifiying candidate # 1546938938.220 * * * * [misc]progress: [ 85 / 133 ] simplifiying candidate # 1546938938.220 * [enter]simplify: Simplifying (* (* (* (pow PI (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))) (pow PI (- 1/2 (/ k 2)))) (/ (* (* (pow (* n 2) (- 1/2 (/ k 2))) (pow (* n 2) (- 1/2 (/ k 2)))) (pow (* n 2) (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))) 1546938938.220 * * [misc]simplify: iters left: 6 (19 enodes) 1546938938.227 * * [misc]simplify: iters left: 5 (37 enodes) 1546938938.242 * * [misc]simplify: iters left: 4 (114 enodes) 1546938938.310 * * [misc]simplify: iters left: 3 (443 enodes) 1546938938.675 * [exit]simplify: Simplified to (* (* (/ (pow (* 2 n) (- 1/2 (/ k 2))) (sqrt k)) (* (pow (* 2 n) (- 1/2 (/ k 2))) (pow (* 2 n) (- 1/2 (/ k 2))))) (* (/ (pow PI (- 1/2 (/ k 2))) k) (* (pow PI (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))))) 1546938938.675 * [misc]simplify: Simplified (2 1) to (λ (k n) (cbrt (* (* (/ (pow (* 2 n) (- 1/2 (/ k 2))) (sqrt k)) (* (pow (* 2 n) (- 1/2 (/ k 2))) (pow (* 2 n) (- 1/2 (/ k 2))))) (* (/ (pow PI (- 1/2 (/ k 2))) k) (* (pow PI (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))))))) 1546938938.675 * * * * [misc]progress: [ 86 / 133 ] simplifiying candidate # 1546938938.676 * [enter]simplify: Simplifying (* (* (* (pow PI (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))) (pow PI (- 1/2 (/ k 2)))) (* (* (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1546938938.676 * * [misc]simplify: iters left: 6 (17 enodes) 1546938938.681 * * [misc]simplify: iters left: 5 (33 enodes) 1546938938.692 * * [misc]simplify: iters left: 4 (87 enodes) 1546938938.720 * * [misc]simplify: iters left: 3 (222 enodes) 1546938938.799 * [exit]simplify: Simplified to (* (* (* (pow PI (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))) (/ (pow (* 2 n) (- 1/2 (/ k 2))) (sqrt k))) (* (/ (pow (* 2 n) (- 1/2 (/ k 2))) k) (* (pow (* 2 n) (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))))) 1546938938.799 * [misc]simplify: Simplified (2 1) to (λ (k n) (cbrt (* (* (* (pow PI (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))) (/ (pow (* 2 n) (- 1/2 (/ k 2))) (sqrt k))) (* (/ (pow (* 2 n) (- 1/2 (/ k 2))) k) (* (pow (* 2 n) (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))))))) 1546938938.799 * * * * [misc]progress: [ 87 / 133 ] simplifiying candidate # 1546938938.799 * * * * [misc]progress: [ 88 / 133 ] simplifiying candidate # 1546938938.799 * * * * [misc]progress: [ 89 / 133 ] simplifiying candidate # 1546938938.799 * * * * [misc]progress: [ 90 / 133 ] simplifiying candidate # 1546938938.799 * [enter]simplify: Simplifying (* (pow PI 1/2) (pow (* n 2) (- 1/2 (/ k 2)))) 1546938938.799 * * [misc]simplify: iters left: 6 (11 enodes) 1546938938.803 * * [misc]simplify: iters left: 5 (16 enodes) 1546938938.807 * * [misc]simplify: iters left: 4 (19 enodes) 1546938938.812 * [exit]simplify: Simplified to (* (sqrt PI) (pow (* n 2) (- 1/2 (/ k 2)))) 1546938938.812 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (* (sqrt PI) (pow (* n 2) (- 1/2 (/ k 2)))) (* (pow PI (/ k 2)) (sqrt k)))) 1546938938.812 * [enter]simplify: Simplifying (* (pow PI (/ k 2)) (sqrt k)) 1546938938.812 * * [misc]simplify: iters left: 5 (7 enodes) 1546938938.814 * * [misc]simplify: iters left: 4 (8 enodes) 1546938938.816 * [exit]simplify: Simplified to (* (pow PI (/ k 2)) (sqrt k)) 1546938938.816 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (* (sqrt PI) (pow (* n 2) (- 1/2 (/ k 2)))) (* (pow PI (/ k 2)) (sqrt k)))) 1546938938.816 * * * * [misc]progress: [ 91 / 133 ] simplifiying candidate # 1546938938.816 * * * * [misc]progress: [ 92 / 133 ] simplifiying candidate # 1546938938.817 * [enter]simplify: Simplifying (cbrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))) 1546938938.817 * * [misc]simplify: iters left: 6 (11 enodes) 1546938938.820 * * [misc]simplify: iters left: 5 (14 enodes) 1546938938.824 * * [misc]simplify: iters left: 4 (17 enodes) 1546938938.828 * [exit]simplify: Simplified to (cbrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))) 1546938938.828 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow PI (- 1/2 (/ k 2))) (* (cbrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))))) (cbrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))))) 1546938938.828 * * * * [misc]progress: [ 93 / 133 ] simplifiying candidate # 1546938938.828 * [enter]simplify: Simplifying (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))) 1546938938.828 * * [misc]simplify: iters left: 6 (11 enodes) 1546938938.830 * * [misc]simplify: iters left: 5 (14 enodes) 1546938938.832 * * [misc]simplify: iters left: 4 (17 enodes) 1546938938.835 * [exit]simplify: Simplified to (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))) 1546938938.835 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow PI (- 1/2 (/ k 2))) (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))))) 1546938938.835 * * * * [misc]progress: [ 94 / 133 ] simplifiying candidate # 1546938938.835 * [enter]simplify: Simplifying (/ (pow (* n 2) (- (/ k 2))) (cbrt (sqrt k))) 1546938938.835 * * [misc]simplify: iters left: 6 (10 enodes) 1546938938.837 * * [misc]simplify: iters left: 5 (13 enodes) 1546938938.838 * [exit]simplify: Simplified to (/ (pow (* n 2) (/ (- k) 2)) (cbrt (sqrt k))) 1546938938.838 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow PI (- 1/2 (/ k 2))) (/ (pow (* n 2) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow (* n 2) (/ (- k) 2)) (cbrt (sqrt k))))) 1546938938.838 * * * * [misc]progress: [ 95 / 133 ] simplifiying candidate # 1546938938.839 * [enter]simplify: Simplifying (/ (pow (* n 2) (- (/ k 2))) (sqrt (sqrt k))) 1546938938.839 * * [misc]simplify: iters left: 6 (10 enodes) 1546938938.840 * * [misc]simplify: iters left: 5 (13 enodes) 1546938938.842 * [exit]simplify: Simplified to (/ (pow (* n 2) (/ (- k) 2)) (sqrt (sqrt k))) 1546938938.842 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow PI (- 1/2 (/ k 2))) (/ (pow (* n 2) 1/2) (sqrt (sqrt k)))) (/ (pow (* n 2) (/ (- k) 2)) (sqrt (sqrt k))))) 1546938938.842 * * * * [misc]progress: [ 96 / 133 ] simplifiying candidate # 1546938938.842 * [enter]simplify: Simplifying (/ (pow (* n 2) (- (/ k 2))) (sqrt k)) 1546938938.842 * * [misc]simplify: iters left: 6 (9 enodes) 1546938938.843 * * [misc]simplify: iters left: 5 (12 enodes) 1546938938.845 * [exit]simplify: Simplified to (/ (pow (* n 2) (- (/ k 2))) (sqrt k)) 1546938938.845 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow PI (- 1/2 (/ k 2))) (/ (pow (* n 2) 1/2) 1)) (/ (pow (* n 2) (- (/ k 2))) (sqrt k)))) 1546938938.845 * * * * [misc]progress: [ 97 / 133 ] simplifiying candidate # 1546938938.845 * [enter]simplify: Simplifying (/ (pow (* n 2) (- (/ k 2))) (cbrt (sqrt k))) 1546938938.845 * * [misc]simplify: iters left: 6 (10 enodes) 1546938938.847 * * [misc]simplify: iters left: 5 (13 enodes) 1546938938.849 * [exit]simplify: Simplified to (/ (pow (* n 2) (/ (- k) 2)) (cbrt (sqrt k))) 1546938938.849 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow PI (- 1/2 (/ k 2))) (/ (pow (* n 2) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow (* n 2) (/ (- k) 2)) (cbrt (sqrt k))))) 1546938938.849 * * * * [misc]progress: [ 98 / 133 ] simplifiying candidate # 1546938938.849 * [enter]simplify: Simplifying (/ (pow (* n 2) (- (/ k 2))) (sqrt (sqrt k))) 1546938938.849 * * [misc]simplify: iters left: 6 (10 enodes) 1546938938.850 * * [misc]simplify: iters left: 5 (13 enodes) 1546938938.852 * [exit]simplify: Simplified to (/ (pow (* n 2) (/ (- k) 2)) (sqrt (sqrt k))) 1546938938.852 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow PI (- 1/2 (/ k 2))) (/ (pow (* n 2) 1/2) (sqrt (sqrt k)))) (/ (pow (* n 2) (/ (- k) 2)) (sqrt (sqrt k))))) 1546938938.852 * * * * [misc]progress: [ 99 / 133 ] simplifiying candidate # 1546938938.852 * [enter]simplify: Simplifying (/ (pow (* n 2) (- (/ k 2))) (sqrt k)) 1546938938.852 * * [misc]simplify: iters left: 6 (9 enodes) 1546938938.854 * * [misc]simplify: iters left: 5 (12 enodes) 1546938938.855 * [exit]simplify: Simplified to (/ (pow (* n 2) (- (/ k 2))) (sqrt k)) 1546938938.855 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow PI (- 1/2 (/ k 2))) (/ (pow (* n 2) 1/2) 1)) (/ (pow (* n 2) (- (/ k 2))) (sqrt k)))) 1546938938.855 * * * * [misc]progress: [ 100 / 133 ] simplifiying candidate # 1546938938.856 * [enter]simplify: Simplifying (/ (pow 2 (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1546938938.856 * * [misc]simplify: iters left: 6 (9 enodes) 1546938938.858 * * [misc]simplify: iters left: 5 (11 enodes) 1546938938.861 * * [misc]simplify: iters left: 4 (14 enodes) 1546938938.865 * [exit]simplify: Simplified to (/ (pow 2 (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1546938938.865 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow PI (- 1/2 (/ k 2))) (/ (pow n (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow 2 (- 1/2 (/ k 2))) (cbrt (sqrt k))))) 1546938938.865 * * * * [misc]progress: [ 101 / 133 ] simplifiying candidate # 1546938938.865 * [enter]simplify: Simplifying (/ (pow 2 (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1546938938.866 * * [misc]simplify: iters left: 6 (9 enodes) 1546938938.868 * * [misc]simplify: iters left: 5 (11 enodes) 1546938938.871 * * [misc]simplify: iters left: 4 (14 enodes) 1546938938.875 * [exit]simplify: Simplified to (/ (pow 2 (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1546938938.875 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow PI (- 1/2 (/ k 2))) (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (/ (pow 2 (- 1/2 (/ k 2))) (sqrt (sqrt k))))) 1546938938.875 * * * * [misc]progress: [ 102 / 133 ] simplifiying candidate # 1546938938.875 * [enter]simplify: Simplifying (/ (pow 2 (- 1/2 (/ k 2))) (sqrt k)) 1546938938.875 * * [misc]simplify: iters left: 6 (8 enodes) 1546938938.876 * * [misc]simplify: iters left: 5 (10 enodes) 1546938938.879 * * [misc]simplify: iters left: 4 (13 enodes) 1546938938.881 * [exit]simplify: Simplified to (/ (pow 2 (- 1/2 (/ k 2))) (sqrt k)) 1546938938.881 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow PI (- 1/2 (/ k 2))) (/ (pow n (- 1/2 (/ k 2))) 1)) (/ (pow 2 (- 1/2 (/ k 2))) (sqrt k)))) 1546938938.881 * * * * [misc]progress: [ 103 / 133 ] simplifiying candidate # 1546938938.881 * [enter]simplify: Simplifying (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1546938938.881 * * [misc]simplify: iters left: 6 (12 enodes) 1546938938.883 * * [misc]simplify: iters left: 5 (15 enodes) 1546938938.885 * * [misc]simplify: iters left: 4 (18 enodes) 1546938938.888 * [exit]simplify: Simplified to (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1546938938.888 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow PI (- 1/2 (/ k 2))) (/ (* (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (pow (* n 2) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))) 1546938938.888 * * * * [misc]progress: [ 104 / 133 ] simplifiying candidate # 1546938938.888 * [enter]simplify: Simplifying (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1546938938.888 * * [misc]simplify: iters left: 6 (12 enodes) 1546938938.890 * * [misc]simplify: iters left: 5 (15 enodes) 1546938938.892 * * [misc]simplify: iters left: 4 (18 enodes) 1546938938.894 * [exit]simplify: Simplified to (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1546938938.894 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow PI (- 1/2 (/ k 2))) (/ (* (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (pow (* n 2) (- 1/2 (/ k 2))))) (sqrt (sqrt k)))) (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) 1546938938.894 * * * * [misc]progress: [ 105 / 133 ] simplifiying candidate # 1546938938.894 * [enter]simplify: Simplifying (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt k)) 1546938938.894 * * [misc]simplify: iters left: 6 (11 enodes) 1546938938.896 * * [misc]simplify: iters left: 5 (14 enodes) 1546938938.898 * * [misc]simplify: iters left: 4 (17 enodes) 1546938938.900 * [exit]simplify: Simplified to (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt k)) 1546938938.900 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow PI (- 1/2 (/ k 2))) (/ (* (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (pow (* n 2) (- 1/2 (/ k 2))))) 1)) (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt k)))) 1546938938.900 * * * * [misc]progress: [ 106 / 133 ] simplifiying candidate # 1546938938.901 * [enter]simplify: Simplifying (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1546938938.901 * * [misc]simplify: iters left: 6 (12 enodes) 1546938938.902 * * [misc]simplify: iters left: 5 (15 enodes) 1546938938.904 * * [misc]simplify: iters left: 4 (18 enodes) 1546938938.906 * [exit]simplify: Simplified to (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1546938938.907 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow PI (- 1/2 (/ k 2))) (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))) 1546938938.907 * * * * [misc]progress: [ 107 / 133 ] simplifiying candidate # 1546938938.907 * [enter]simplify: Simplifying (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1546938938.907 * * [misc]simplify: iters left: 6 (12 enodes) 1546938938.910 * * [misc]simplify: iters left: 5 (15 enodes) 1546938938.914 * * [misc]simplify: iters left: 4 (18 enodes) 1546938938.917 * [exit]simplify: Simplified to (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1546938938.917 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow PI (- 1/2 (/ k 2))) (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) 1546938938.917 * * * * [misc]progress: [ 108 / 133 ] simplifiying candidate # 1546938938.917 * [enter]simplify: Simplifying (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt k)) 1546938938.917 * * [misc]simplify: iters left: 6 (11 enodes) 1546938938.919 * * [misc]simplify: iters left: 5 (14 enodes) 1546938938.920 * * [misc]simplify: iters left: 4 (17 enodes) 1546938938.923 * [exit]simplify: Simplified to (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt k)) 1546938938.923 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow PI (- 1/2 (/ k 2))) (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) 1)) (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt k)))) 1546938938.923 * * * * [misc]progress: [ 109 / 133 ] simplifiying candidate # 1546938938.923 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1546938938.923 * * [misc]simplify: iters left: 6 (11 enodes) 1546938938.924 * * [misc]simplify: iters left: 5 (14 enodes) 1546938938.926 * * [misc]simplify: iters left: 4 (17 enodes) 1546938938.928 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1546938938.928 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow PI (- 1/2 (/ k 2))) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))))) 1546938938.928 * * * * [misc]progress: [ 110 / 133 ] simplifiying candidate # 1546938938.928 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1546938938.929 * * [misc]simplify: iters left: 6 (11 enodes) 1546938938.930 * * [misc]simplify: iters left: 5 (14 enodes) 1546938938.932 * * [misc]simplify: iters left: 4 (17 enodes) 1546938938.934 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1546938938.934 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow PI (- 1/2 (/ k 2))) (/ 1 (sqrt (sqrt k)))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) 1546938938.934 * * * * [misc]progress: [ 111 / 133 ] simplifiying candidate # 1546938938.934 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)) 1546938938.934 * * [misc]simplify: iters left: 6 (10 enodes) 1546938938.936 * * [misc]simplify: iters left: 5 (13 enodes) 1546938938.937 * * [misc]simplify: iters left: 4 (16 enodes) 1546938938.939 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)) 1546938938.939 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow PI (- 1/2 (/ k 2))) (/ 1 1)) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1546938938.939 * * * * [misc]progress: [ 112 / 133 ] simplifiying candidate # 1546938938.940 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)) 1546938938.940 * * [misc]simplify: iters left: 6 (10 enodes) 1546938938.941 * * [misc]simplify: iters left: 5 (13 enodes) 1546938938.943 * * [misc]simplify: iters left: 4 (16 enodes) 1546938938.947 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)) 1546938938.947 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow PI (- 1/2 (/ k 2))) 1) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1546938938.947 * * * * [misc]progress: [ 113 / 133 ] simplifiying candidate # 1546938938.947 * [enter]simplify: Simplifying (/ 1 (sqrt k)) 1546938938.947 * * [misc]simplify: iters left: 3 (4 enodes) 1546938938.948 * * [misc]simplify: iters left: 2 (6 enodes) 1546938938.950 * [exit]simplify: Simplified to (/ 1 (sqrt k)) 1546938938.950 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow PI (- 1/2 (/ k 2))) (pow (* n 2) (- 1/2 (/ k 2)))) (/ 1 (sqrt k)))) 1546938938.950 * * * * [misc]progress: [ 114 / 133 ] simplifiying candidate # 1546938938.950 * [enter]simplify: Simplifying (pow PI 1/2) 1546938938.950 * * [misc]simplify: iters left: 1 (3 enodes) 1546938938.951 * [exit]simplify: Simplified to (sqrt PI) 1546938938.951 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt PI) (* (pow PI (- (/ k 2))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))))) 1546938938.951 * * * * [misc]progress: [ 115 / 133 ] simplifiying candidate # 1546938938.951 * [enter]simplify: Simplifying (pow PI 1/2) 1546938938.951 * * [misc]simplify: iters left: 1 (3 enodes) 1546938938.952 * [exit]simplify: Simplified to (sqrt PI) 1546938938.952 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt PI) (* (pow PI (- (/ k 2))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))))) 1546938938.952 * * * * [misc]progress: [ 116 / 133 ] simplifiying candidate # 1546938938.952 * [enter]simplify: Simplifying (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) 1546938938.952 * * [misc]simplify: iters left: 6 (9 enodes) 1546938938.953 * * [misc]simplify: iters left: 5 (11 enodes) 1546938938.955 * * [misc]simplify: iters left: 4 (14 enodes) 1546938938.957 * [exit]simplify: Simplified to (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) 1546938938.957 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) (* (cbrt (pow PI (- 1/2 (/ k 2)))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))))) 1546938938.957 * * * * [misc]progress: [ 117 / 133 ] simplifiying candidate # 1546938938.957 * [enter]simplify: Simplifying (sqrt (pow PI (- 1/2 (/ k 2)))) 1546938938.957 * * [misc]simplify: iters left: 6 (8 enodes) 1546938938.958 * * [misc]simplify: iters left: 5 (10 enodes) 1546938938.960 * * [misc]simplify: iters left: 4 (13 enodes) 1546938938.961 * [exit]simplify: Simplified to (sqrt (pow PI (- 1/2 (/ k 2)))) 1546938938.961 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (pow PI (- 1/2 (/ k 2)))) (* (sqrt (pow PI (- 1/2 (/ k 2)))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))))) 1546938938.961 * * * * [misc]progress: [ 118 / 133 ] simplifiying candidate # 1546938938.962 * * * * [misc]progress: [ 119 / 133 ] simplifiying candidate # 1546938938.962 * [enter]simplify: Simplifying (sqrt k) 1546938938.962 * * [misc]simplify: iters left: 1 (2 enodes) 1546938938.962 * [exit]simplify: Simplified to (sqrt k) 1546938938.962 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (* (pow PI (- 1/2 (/ k 2))) (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt k))) 1546938938.962 * * * * [misc]progress: [ 120 / 133 ] simplifiying candidate # 1546938938.962 * [enter]simplify: Simplifying (* (pow PI 1/2) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))) 1546938938.962 * * [misc]simplify: iters left: 6 (13 enodes) 1546938938.964 * * [misc]simplify: iters left: 5 (20 enodes) 1546938938.967 * * [misc]simplify: iters left: 4 (27 enodes) 1546938938.970 * * [misc]simplify: iters left: 3 (29 enodes) 1546938938.973 * * [misc]simplify: iters left: 2 (31 enodes) 1546938938.976 * * [misc]simplify: iters left: 1 (32 enodes) 1546938938.982 * [exit]simplify: Simplified to (* (/ (sqrt PI) (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))) 1546938938.982 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (* (/ (sqrt PI) (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))) (pow PI (/ k 2)))) 1546938938.982 * * * * [misc]progress: [ 121 / 133 ] simplifiying candidate # 1546938938.982 * * * * [misc]progress: [ 122 / 133 ] simplifiying candidate # 1546938938.982 * [enter]simplify: Simplifying (- (+ (pow PI 1/2) (* 1/8 (* (* (pow (log PI) 2) (pow k 2)) (sqrt PI)))) (* 1/2 (* (* (log PI) k) (sqrt PI)))) 1546938938.982 * * [misc]simplify: iters left: 6 (18 enodes) 1546938938.989 * * [misc]simplify: iters left: 5 (39 enodes) 1546938939.004 * * [misc]simplify: iters left: 4 (104 enodes) 1546938939.029 * * [misc]simplify: iters left: 3 (275 enodes) 1546938939.146 * [exit]simplify: Simplified to (+ (* (* (* k (log PI)) (* k (log PI))) (* (sqrt PI) 1/8)) (+ (* (* k (log PI)) (* (sqrt PI) -1/2)) (sqrt PI))) 1546938939.146 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (+ (* (* (* k (log PI)) (* k (log PI))) (* (sqrt PI) 1/8)) (+ (* (* k (log PI)) (* (sqrt PI) -1/2)) (sqrt PI))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1546938939.146 * * * * [misc]progress: [ 123 / 133 ] simplifiying candidate # 1546938939.146 * [enter]simplify: Simplifying (pow PI (- 1/2 (* 1/2 k))) 1546938939.146 * * [misc]simplify: iters left: 5 (6 enodes) 1546938939.147 * * [misc]simplify: iters left: 4 (9 enodes) 1546938939.149 * * [misc]simplify: iters left: 3 (17 enodes) 1546938939.152 * * [misc]simplify: iters left: 2 (20 enodes) 1546938939.154 * * [misc]simplify: iters left: 1 (24 enodes) 1546938939.159 * [exit]simplify: Simplified to (pow PI (- 1/2 (* k 1/2))) 1546938939.159 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (pow PI (- 1/2 (* k 1/2))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1546938939.159 * * * * [misc]progress: [ 124 / 133 ] simplifiying candidate # 1546938939.159 * [enter]simplify: Simplifying (pow PI (- 1/2 (* 1/2 k))) 1546938939.159 * * [misc]simplify: iters left: 5 (6 enodes) 1546938939.160 * * [misc]simplify: iters left: 4 (9 enodes) 1546938939.162 * * [misc]simplify: iters left: 3 (17 enodes) 1546938939.164 * * [misc]simplify: iters left: 2 (20 enodes) 1546938939.169 * * [misc]simplify: iters left: 1 (24 enodes) 1546938939.179 * [exit]simplify: Simplified to (pow PI (- 1/2 (* k 1/2))) 1546938939.179 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (pow PI (- 1/2 (* k 1/2))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1546938939.179 * * * * [misc]progress: [ 125 / 133 ] simplifiying candidate # 1546938939.179 * [enter]simplify: Simplifying (- (+ (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (* (pow (log 2) 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (pow k 2)))) (+ (* 1/4 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) (pow k 2))))) (* 1/8 (* (exp (* 1/2 (+ (log 2) (log n)))) (* (pow (log n) 2) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) k))) (* 1/2 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) k))))) 1546938939.180 * * [misc]simplify: iters left: 6 (35 enodes) 1546938939.194 * * [misc]simplify: iters left: 5 (99 enodes) 1546938939.223 * * [misc]simplify: iters left: 4 (298 enodes) 1546938939.371 * [exit]simplify: Simplified to (+ (- (* (pow n 1/2) (pow 2 1/2)) (* (* 1/2 k) (* (* (pow n 1/2) (pow 2 1/2)) (+ (log 2) (log n))))) (+ (* (* (log 2) 1/8) (* (* (pow n 1/2) (pow 2 1/2)) (* (* k k) (log 2)))) (* (* (pow n 1/2) (pow 2 1/2)) (+ (* (* 1/4 (log 2)) (* (* k k) (log n))) (* (* 1/8 (log n)) (* (* k k) (log n))))))) 1546938939.371 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (+ (- (* (pow n 1/2) (pow 2 1/2)) (* (* 1/2 k) (* (* (pow n 1/2) (pow 2 1/2)) (+ (log 2) (log n))))) (+ (* (* (log 2) 1/8) (* (* (pow n 1/2) (pow 2 1/2)) (* (* k k) (log 2)))) (* (* (pow n 1/2) (pow 2 1/2)) (+ (* (* 1/4 (log 2)) (* (* k k) (log n))) (* (* 1/8 (log n)) (* (* k k) (log n))))))) (sqrt k)))) 1546938939.371 * * * * [misc]progress: [ 126 / 133 ] simplifiying candidate # 1546938939.371 * [enter]simplify: Simplifying (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) 1546938939.371 * * [misc]simplify: iters left: 6 (13 enodes) 1546938939.377 * * [misc]simplify: iters left: 5 (27 enodes) 1546938939.385 * * [misc]simplify: iters left: 4 (53 enodes) 1546938939.404 * * [misc]simplify: iters left: 3 (116 enodes) 1546938939.440 * * [misc]simplify: iters left: 2 (362 enodes) 1546938939.715 * [exit]simplify: Simplified to (pow (sqrt (* n 2)) (- 1 k)) 1546938939.716 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (pow (sqrt (* n 2)) (- 1 k)) (sqrt k)))) 1546938939.716 * * * * [misc]progress: [ 127 / 133 ] simplifiying candidate # 1546938939.716 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) 1546938939.716 * * [misc]simplify: iters left: 6 (13 enodes) 1546938939.721 * * [misc]simplify: iters left: 5 (24 enodes) 1546938939.730 * * [misc]simplify: iters left: 4 (54 enodes) 1546938939.752 * * [misc]simplify: iters left: 3 (143 enodes) 1546938939.799 * [exit]simplify: Simplified to (pow (exp (- 1/2 (* 1/2 k))) (- (log -2) (log (/ -1 n)))) 1546938939.799 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (pow (exp (- 1/2 (* 1/2 k))) (- (log -2) (log (/ -1 n)))) (sqrt k)))) 1546938939.799 * * * * [misc]progress: [ 128 / 133 ] simplifiying candidate # 1546938939.799 * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) k))) (- (+ (* +nan.0 (* (pow (log 2) 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (pow k 2)))) (- (+ (* +nan.0 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) k)) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (pow k 2)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log 2) (log n))))) (- (+ (* +nan.0 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (pow k 2)))))))))))))))))))))) 1546938939.799 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) +nan.0)) 1546938939.799 * * * * [misc]progress: [ 129 / 133 ] simplifiying candidate # 1546938939.800 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) k)) (- (* +nan.0 (/ (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) (pow k 2)))))))) 1546938939.800 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) +nan.0)) 1546938939.800 * * * * [misc]progress: [ 130 / 133 ] simplifiying candidate # 1546938939.800 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (pow k 2))) (- (+ (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n)))))) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) k))))))) 1546938939.800 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) +nan.0)) 1546938939.800 * * * * [misc]progress: [ 131 / 133 ] simplifiying candidate # 1546938939.800 * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log PI) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))))))))) 1546938939.800 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1546938939.800 * * * * [misc]progress: [ 132 / 133 ] simplifiying candidate # 1546938939.800 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (* (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))) (pow k 2))) (- (+ (* +nan.0 (/ (* (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))) k)) (- (* +nan.0 (/ (* (pow PI (- 1/2 (* 1/2 k))) (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k))))) (pow k 3)))))))) 1546938939.800 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1546938939.800 * * * * [misc]progress: [ 133 / 133 ] simplifiying candidate # 1546938939.800 * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (pow PI (- 1/2 (* 1/2 k))))) (- (+ (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (pow PI (- 1/2 (* 1/2 k)))) k)) (- (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (pow PI (- 1/2 (* 1/2 k)))) (pow k 2)))))))) 1546938939.800 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1546938939.801 * * * [misc]progress: adding candidates to table 1546938941.511 * [misc]progress: [Phase 3 of 3] Extracting. 1546938941.511 * * [misc]regime: Finding splitpoints for: (# # # # # #) 1546938941.513 * * * [misc]regime-changes: Trying 2 branch expressions: (n k) 1546938941.513 * * * * [misc]regimes: Trying to branch on n from (# # # # # #) 1546938941.593 * * * * [misc]regimes: Trying to branch on k from (# # # # # #) 1546938941.662 * * * [misc]regime: Found split indices: #