1546856167.796 * [misc]progress: [Phase 1 of 3] Setting up. 1546856167.796 * * * [misc]progress: [1/2] Preparing points 1546856167.796 * * * * [misc]points: Sampling 256 additional inputs, on iter 0 have 0 / 256 1546856167.858 * * * * [misc]points: Filtering points with unrepresentable outputs 1546856167.858 * * * * [misc]points: Sampling 192 additional inputs, on iter 1 have 64 / 256 1546856167.905 * * * * [misc]points: Filtering points with unrepresentable outputs 1546856167.905 * * * * [misc]points: Sampling 147 additional inputs, on iter 2 have 109 / 256 1546856167.943 * * * * [misc]points: Filtering points with unrepresentable outputs 1546856167.943 * * * * [misc]points: Sampling 113 additional inputs, on iter 3 have 143 / 256 1546856167.974 * * * * [misc]points: Filtering points with unrepresentable outputs 1546856167.975 * * * * [misc]points: Sampling 84 additional inputs, on iter 4 have 172 / 256 1546856168.015 * * * * [misc]points: Filtering points with unrepresentable outputs 1546856168.015 * * * * [misc]points: Sampling 61 additional inputs, on iter 5 have 195 / 256 1546856168.028 * * * * [misc]points: Filtering points with unrepresentable outputs 1546856168.028 * * * * [misc]points: Sampling 46 additional inputs, on iter 6 have 210 / 256 1546856168.037 * * * * [misc]points: Filtering points with unrepresentable outputs 1546856168.037 * * * * [misc]points: Sampling 32 additional inputs, on iter 7 have 224 / 256 1546856168.046 * * * * [misc]points: Filtering points with unrepresentable outputs 1546856168.046 * * * * [misc]points: Sampling 26 additional inputs, on iter 8 have 230 / 256 1546856168.058 * * * * [misc]points: Filtering points with unrepresentable outputs 1546856168.058 * * * * [misc]points: Sampling 17 additional inputs, on iter 9 have 239 / 256 1546856168.068 * * * * [misc]points: Filtering points with unrepresentable outputs 1546856168.068 * * * * [misc]points: Sampling 10 additional inputs, on iter 10 have 246 / 256 1546856168.076 * * * * [misc]points: Filtering points with unrepresentable outputs 1546856168.077 * * * * [misc]points: Sampling 8 additional inputs, on iter 11 have 248 / 256 1546856168.085 * * * * [misc]points: Filtering points with unrepresentable outputs 1546856168.085 * * * * [misc]points: Sampling 7 additional inputs, on iter 12 have 249 / 256 1546856168.093 * * * * [misc]points: Filtering points with unrepresentable outputs 1546856168.093 * * * * [misc]points: Sampling 5 additional inputs, on iter 13 have 251 / 256 1546856168.100 * * * * [misc]points: Filtering points with unrepresentable outputs 1546856168.100 * * * * [misc]points: Sampling 4 additional inputs, on iter 14 have 252 / 256 1546856168.107 * * * * [misc]points: Filtering points with unrepresentable outputs 1546856168.107 * * * * [misc]points: Sampling 4 additional inputs, on iter 15 have 253 / 256 1546856168.114 * * * * [misc]points: Filtering points with unrepresentable outputs 1546856168.114 * * * * [exit]points: Sampled 256 points with exact outputs 1546856168.114 * * * [misc]progress: [2/2] Setting up program. 1546856168.120 * [misc]progress: [Phase 2 of 3] Improving. 1546856168.120 * * * * [misc]progress: [ 1 / 1 ] simplifiying candidate # 1546856168.121 * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) 1546856168.121 * * [misc]simplify: iters left: 6 (13 enodes) 1546856168.126 * * [misc]simplify: iters left: 5 (28 enodes) 1546856168.134 * * [misc]simplify: iters left: 4 (44 enodes) 1546856168.146 * * [misc]simplify: iters left: 3 (54 enodes) 1546856168.181 * * [misc]simplify: iters left: 2 (57 enodes) 1546856168.196 * * [misc]simplify: iters left: 1 (65 enodes) 1546856168.205 * [exit]simplify: Simplified to (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)) 1546856168.205 * [misc]simplify: Simplified (2) to (λ (k n) (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) 1546856168.212 * * [misc]progress: iteration 1 / 4 1546856168.212 * * * [misc]progress: picking best candidate 1546856168.217 * * * * [misc]pick: Picked # 1546856168.217 * * * [misc]progress: localizing error 1546856168.238 * * * [misc]progress: generating rewritten candidates 1546856168.239 * * * * [misc]progress: [ 1 / 3 ] rewriting at (2 1) 1546856168.240 * * * * [misc]progress: [ 2 / 3 ] rewriting at (2 1 1) 1546856168.241 * * * * [misc]progress: [ 3 / 3 ] rewriting at (2) 1546856168.251 * * * [misc]progress: generating series expansions 1546856168.251 * * * * [misc]progress: [ 1 / 3 ] generating series at (2 1) 1546856168.251 * [misc]backup-simplify: Simplify (pow (* PI (* n 2)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 1546856168.251 * [misc]approximate: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 1546856168.251 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1546856168.251 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1546856168.251 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1546856168.251 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546856168.251 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856168.251 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856168.251 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546856168.251 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856168.251 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856168.251 * [misc]taylor: Taking taylor expansion of k in k 1546856168.251 * [misc]backup-simplify: Simplify 0 into 0 1546856168.251 * [misc]backup-simplify: Simplify 1 into 1 1546856168.251 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1546856168.251 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1546856168.251 * [misc]taylor: Taking taylor expansion of 2 in k 1546856168.251 * [misc]backup-simplify: Simplify 2 into 2 1546856168.251 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1546856168.251 * [misc]taylor: Taking taylor expansion of n in k 1546856168.251 * [misc]backup-simplify: Simplify n into n 1546856168.251 * [misc]taylor: Taking taylor expansion of PI in k 1546856168.251 * [misc]backup-simplify: Simplify PI into PI 1546856168.251 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1546856168.252 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1546856168.252 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1546856168.252 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546856168.252 * [misc]backup-simplify: Simplify (- 0) into 0 1546856168.252 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546856168.252 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1546856168.253 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1546856168.253 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546856168.253 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546856168.253 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546856168.253 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546856168.253 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856168.253 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856168.253 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546856168.253 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856168.253 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856168.253 * [misc]taylor: Taking taylor expansion of k in n 1546856168.253 * [misc]backup-simplify: Simplify k into k 1546856168.253 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546856168.253 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546856168.253 * [misc]taylor: Taking taylor expansion of 2 in n 1546856168.253 * [misc]backup-simplify: Simplify 2 into 2 1546856168.253 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546856168.253 * [misc]taylor: Taking taylor expansion of n in n 1546856168.253 * [misc]backup-simplify: Simplify 0 into 0 1546856168.253 * [misc]backup-simplify: Simplify 1 into 1 1546856168.253 * [misc]taylor: Taking taylor expansion of PI in n 1546856168.253 * [misc]backup-simplify: Simplify PI into PI 1546856168.254 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546856168.254 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546856168.254 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546856168.255 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546856168.256 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856168.256 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546856168.256 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546856168.256 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546856168.256 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546856168.257 * [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)))) 1546856168.258 * [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))))) 1546856168.258 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546856168.258 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546856168.258 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546856168.258 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546856168.258 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856168.258 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856168.258 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546856168.258 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856168.258 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856168.258 * [misc]taylor: Taking taylor expansion of k in n 1546856168.258 * [misc]backup-simplify: Simplify k into k 1546856168.258 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546856168.258 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546856168.258 * [misc]taylor: Taking taylor expansion of 2 in n 1546856168.258 * [misc]backup-simplify: Simplify 2 into 2 1546856168.258 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546856168.258 * [misc]taylor: Taking taylor expansion of n in n 1546856168.258 * [misc]backup-simplify: Simplify 0 into 0 1546856168.258 * [misc]backup-simplify: Simplify 1 into 1 1546856168.258 * [misc]taylor: Taking taylor expansion of PI in n 1546856168.258 * [misc]backup-simplify: Simplify PI into PI 1546856168.259 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546856168.259 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546856168.259 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546856168.260 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546856168.261 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856168.261 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546856168.261 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546856168.261 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546856168.261 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546856168.262 * [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)))) 1546856168.263 * [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))))) 1546856168.263 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1546856168.263 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1546856168.263 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546856168.263 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856168.263 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856168.263 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546856168.263 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856168.263 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856168.263 * [misc]taylor: Taking taylor expansion of k in k 1546856168.263 * [misc]backup-simplify: Simplify 0 into 0 1546856168.263 * [misc]backup-simplify: Simplify 1 into 1 1546856168.263 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1546856168.263 * [misc]taylor: Taking taylor expansion of (log n) in k 1546856168.263 * [misc]taylor: Taking taylor expansion of n in k 1546856168.263 * [misc]backup-simplify: Simplify n into n 1546856168.263 * [misc]backup-simplify: Simplify (log n) into (log n) 1546856168.263 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1546856168.263 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1546856168.263 * [misc]taylor: Taking taylor expansion of 2 in k 1546856168.263 * [misc]backup-simplify: Simplify 2 into 2 1546856168.263 * [misc]taylor: Taking taylor expansion of PI in k 1546856168.263 * [misc]backup-simplify: Simplify PI into PI 1546856168.264 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546856168.264 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856168.264 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546856168.264 * [misc]backup-simplify: Simplify (- 0) into 0 1546856168.265 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546856168.265 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546856168.266 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1546856168.266 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1546856168.267 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1546856168.268 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546856168.269 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1546856168.272 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546856168.272 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1546856168.272 * [misc]backup-simplify: Simplify (- 0) into 0 1546856168.277 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856168.277 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546856168.278 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1546856168.279 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1546856168.279 * [misc]taylor: Taking taylor expansion of 0 in k 1546856168.279 * [misc]backup-simplify: Simplify 0 into 0 1546856168.279 * [misc]backup-simplify: Simplify 0 into 0 1546856168.280 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1546856168.280 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546856168.281 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546856168.282 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856168.282 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1546856168.282 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546856168.282 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546856168.282 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1546856168.283 * [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))))))) 1546856168.284 * [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))))))) 1546856168.285 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1546856168.286 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1546856168.289 * [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 1546856168.289 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1546856168.289 * [misc]backup-simplify: Simplify (- 0) into 0 1546856168.289 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856168.290 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546856168.290 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1546856168.292 * [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 1546856168.292 * [misc]taylor: Taking taylor expansion of 0 in k 1546856168.292 * [misc]backup-simplify: Simplify 0 into 0 1546856168.292 * [misc]backup-simplify: Simplify 0 into 0 1546856168.292 * [misc]backup-simplify: Simplify 0 into 0 1546856168.293 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1546856168.293 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546856168.296 * [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 1546856168.296 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856168.297 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1546856168.297 * [misc]backup-simplify: Simplify (- 0) into 0 1546856168.297 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856168.297 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1546856168.299 * [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))))) 1546856168.300 * [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))))) 1546856168.304 * [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))))) 1546856168.304 * [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)))) 1546856168.304 * [misc]approximate: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 1546856168.304 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1546856168.304 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1546856168.304 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1546856168.305 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546856168.305 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856168.305 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856168.305 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546856168.305 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856168.305 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856168.305 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546856168.305 * [misc]taylor: Taking taylor expansion of k in k 1546856168.305 * [misc]backup-simplify: Simplify 0 into 0 1546856168.305 * [misc]backup-simplify: Simplify 1 into 1 1546856168.305 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546856168.305 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1546856168.305 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1546856168.305 * [misc]taylor: Taking taylor expansion of 2 in k 1546856168.305 * [misc]backup-simplify: Simplify 2 into 2 1546856168.305 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546856168.305 * [misc]taylor: Taking taylor expansion of PI in k 1546856168.305 * [misc]backup-simplify: Simplify PI into PI 1546856168.305 * [misc]taylor: Taking taylor expansion of n in k 1546856168.305 * [misc]backup-simplify: Simplify n into n 1546856168.305 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546856168.305 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1546856168.305 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1546856168.306 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546856168.306 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546856168.306 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546856168.306 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1546856168.306 * [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)))) 1546856168.306 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546856168.306 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546856168.306 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546856168.307 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546856168.307 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856168.307 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856168.307 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546856168.307 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856168.307 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856168.307 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546856168.307 * [misc]taylor: Taking taylor expansion of k in n 1546856168.307 * [misc]backup-simplify: Simplify k into k 1546856168.307 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546856168.307 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546856168.307 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546856168.307 * [misc]taylor: Taking taylor expansion of 2 in n 1546856168.307 * [misc]backup-simplify: Simplify 2 into 2 1546856168.307 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856168.307 * [misc]taylor: Taking taylor expansion of PI in n 1546856168.307 * [misc]backup-simplify: Simplify PI into PI 1546856168.307 * [misc]taylor: Taking taylor expansion of n in n 1546856168.307 * [misc]backup-simplify: Simplify 0 into 0 1546856168.307 * [misc]backup-simplify: Simplify 1 into 1 1546856168.308 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856168.308 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546856168.309 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856168.309 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546856168.309 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546856168.309 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546856168.310 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546856168.310 * [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))) 1546856168.311 * [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)))) 1546856168.311 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546856168.311 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546856168.311 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546856168.311 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546856168.311 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856168.311 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856168.311 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546856168.311 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856168.311 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856168.311 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546856168.311 * [misc]taylor: Taking taylor expansion of k in n 1546856168.311 * [misc]backup-simplify: Simplify k into k 1546856168.311 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546856168.311 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546856168.311 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546856168.311 * [misc]taylor: Taking taylor expansion of 2 in n 1546856168.311 * [misc]backup-simplify: Simplify 2 into 2 1546856168.311 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856168.311 * [misc]taylor: Taking taylor expansion of PI in n 1546856168.311 * [misc]backup-simplify: Simplify PI into PI 1546856168.311 * [misc]taylor: Taking taylor expansion of n in n 1546856168.312 * [misc]backup-simplify: Simplify 0 into 0 1546856168.312 * [misc]backup-simplify: Simplify 1 into 1 1546856168.312 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856168.312 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546856168.312 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856168.313 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546856168.313 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546856168.313 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546856168.313 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546856168.314 * [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))) 1546856168.315 * [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)))) 1546856168.315 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1546856168.315 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1546856168.315 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546856168.315 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856168.315 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856168.315 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546856168.315 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856168.315 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856168.315 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546856168.315 * [misc]taylor: Taking taylor expansion of k in k 1546856168.315 * [misc]backup-simplify: Simplify 0 into 0 1546856168.315 * [misc]backup-simplify: Simplify 1 into 1 1546856168.315 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546856168.315 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1546856168.315 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1546856168.315 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1546856168.315 * [misc]taylor: Taking taylor expansion of 2 in k 1546856168.315 * [misc]backup-simplify: Simplify 2 into 2 1546856168.315 * [misc]taylor: Taking taylor expansion of PI in k 1546856168.315 * [misc]backup-simplify: Simplify PI into PI 1546856168.316 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546856168.316 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856168.316 * [misc]taylor: Taking taylor expansion of (log n) in k 1546856168.316 * [misc]taylor: Taking taylor expansion of n in k 1546856168.316 * [misc]backup-simplify: Simplify n into n 1546856168.316 * [misc]backup-simplify: Simplify (log n) into (log n) 1546856168.316 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546856168.316 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546856168.317 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546856168.317 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1546856168.317 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1546856168.318 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1546856168.318 * [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)))) 1546856168.319 * [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)))) 1546856168.320 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546856168.321 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546856168.323 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546856168.324 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546856168.324 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546856168.324 * [misc]backup-simplify: Simplify (- 0) into 0 1546856168.324 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856168.325 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546856168.325 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1546856168.327 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546856168.327 * [misc]taylor: Taking taylor expansion of 0 in k 1546856168.327 * [misc]backup-simplify: Simplify 0 into 0 1546856168.327 * [misc]backup-simplify: Simplify 0 into 0 1546856168.327 * [misc]backup-simplify: Simplify 0 into 0 1546856168.328 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856168.329 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546856168.334 * [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 1546856168.335 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546856168.335 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1546856168.335 * [misc]backup-simplify: Simplify (- 0) into 0 1546856168.335 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856168.336 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546856168.337 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1546856168.339 * [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 1546856168.339 * [misc]taylor: Taking taylor expansion of 0 in k 1546856168.339 * [misc]backup-simplify: Simplify 0 into 0 1546856168.339 * [misc]backup-simplify: Simplify 0 into 0 1546856168.339 * [misc]backup-simplify: Simplify 0 into 0 1546856168.339 * [misc]backup-simplify: Simplify 0 into 0 1546856168.341 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856168.342 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546856168.346 * [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 1546856168.346 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546856168.347 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1546856168.347 * [misc]backup-simplify: Simplify (- 0) into 0 1546856168.347 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856168.347 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546856168.348 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1546856168.350 * [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 1546856168.350 * [misc]taylor: Taking taylor expansion of 0 in k 1546856168.350 * [misc]backup-simplify: Simplify 0 into 0 1546856168.350 * [misc]backup-simplify: Simplify 0 into 0 1546856168.351 * [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))))) 1546856168.351 * [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)) 1546856168.351 * [misc]approximate: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 1546856168.351 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1546856168.351 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1546856168.351 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1546856168.351 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546856168.351 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546856168.351 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856168.351 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856168.351 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546856168.351 * [misc]taylor: Taking taylor expansion of k in k 1546856168.351 * [misc]backup-simplify: Simplify 0 into 0 1546856168.351 * [misc]backup-simplify: Simplify 1 into 1 1546856168.351 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546856168.351 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856168.351 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856168.351 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1546856168.351 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1546856168.351 * [misc]taylor: Taking taylor expansion of -2 in k 1546856168.351 * [misc]backup-simplify: Simplify -2 into -2 1546856168.351 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546856168.351 * [misc]taylor: Taking taylor expansion of PI in k 1546856168.351 * [misc]backup-simplify: Simplify PI into PI 1546856168.351 * [misc]taylor: Taking taylor expansion of n in k 1546856168.351 * [misc]backup-simplify: Simplify n into n 1546856168.352 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546856168.352 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1546856168.352 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1546856168.352 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546856168.352 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546856168.352 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1546856168.352 * [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))) 1546856168.352 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546856168.352 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546856168.352 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546856168.352 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546856168.352 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546856168.352 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856168.352 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856168.352 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546856168.352 * [misc]taylor: Taking taylor expansion of k in n 1546856168.352 * [misc]backup-simplify: Simplify k into k 1546856168.352 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546856168.352 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856168.352 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856168.352 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546856168.352 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546856168.352 * [misc]taylor: Taking taylor expansion of -2 in n 1546856168.352 * [misc]backup-simplify: Simplify -2 into -2 1546856168.352 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856168.352 * [misc]taylor: Taking taylor expansion of PI in n 1546856168.352 * [misc]backup-simplify: Simplify PI into PI 1546856168.352 * [misc]taylor: Taking taylor expansion of n in n 1546856168.352 * [misc]backup-simplify: Simplify 0 into 0 1546856168.352 * [misc]backup-simplify: Simplify 1 into 1 1546856168.353 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856168.353 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546856168.353 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546856168.353 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546856168.353 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546856168.354 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546856168.354 * [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))) 1546856168.354 * [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)))) 1546856168.354 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546856168.354 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546856168.354 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546856168.355 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546856168.355 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546856168.355 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856168.355 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856168.355 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546856168.355 * [misc]taylor: Taking taylor expansion of k in n 1546856168.355 * [misc]backup-simplify: Simplify k into k 1546856168.355 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546856168.355 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856168.355 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856168.355 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546856168.355 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546856168.355 * [misc]taylor: Taking taylor expansion of -2 in n 1546856168.355 * [misc]backup-simplify: Simplify -2 into -2 1546856168.355 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856168.355 * [misc]taylor: Taking taylor expansion of PI in n 1546856168.355 * [misc]backup-simplify: Simplify PI into PI 1546856168.355 * [misc]taylor: Taking taylor expansion of n in n 1546856168.355 * [misc]backup-simplify: Simplify 0 into 0 1546856168.355 * [misc]backup-simplify: Simplify 1 into 1 1546856168.355 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856168.355 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546856168.355 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546856168.355 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546856168.356 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546856168.356 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546856168.356 * [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))) 1546856168.357 * [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)))) 1546856168.357 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1546856168.357 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1546856168.357 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546856168.357 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546856168.357 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856168.357 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856168.357 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546856168.357 * [misc]taylor: Taking taylor expansion of k in k 1546856168.357 * [misc]backup-simplify: Simplify 0 into 0 1546856168.357 * [misc]backup-simplify: Simplify 1 into 1 1546856168.357 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546856168.357 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856168.357 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856168.357 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1546856168.357 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1546856168.357 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1546856168.357 * [misc]taylor: Taking taylor expansion of -2 in k 1546856168.357 * [misc]backup-simplify: Simplify -2 into -2 1546856168.357 * [misc]taylor: Taking taylor expansion of PI in k 1546856168.357 * [misc]backup-simplify: Simplify PI into PI 1546856168.357 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546856168.358 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546856168.358 * [misc]taylor: Taking taylor expansion of (log n) in k 1546856168.358 * [misc]taylor: Taking taylor expansion of n in k 1546856168.358 * [misc]backup-simplify: Simplify n into n 1546856168.358 * [misc]backup-simplify: Simplify (log n) into (log n) 1546856168.358 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546856168.358 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546856168.358 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1546856168.358 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1546856168.359 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1546856168.359 * [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)))) 1546856168.359 * [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)))) 1546856168.360 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546856168.361 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1546856168.362 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1546856168.362 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546856168.362 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546856168.362 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856168.363 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546856168.363 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1546856168.364 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546856168.364 * [misc]taylor: Taking taylor expansion of 0 in k 1546856168.364 * [misc]backup-simplify: Simplify 0 into 0 1546856168.364 * [misc]backup-simplify: Simplify 0 into 0 1546856168.364 * [misc]backup-simplify: Simplify 0 into 0 1546856168.365 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856168.366 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1546856168.370 * [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 1546856168.370 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546856168.371 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1546856168.371 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856168.372 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546856168.372 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1546856168.375 * [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 1546856168.375 * [misc]taylor: Taking taylor expansion of 0 in k 1546856168.375 * [misc]backup-simplify: Simplify 0 into 0 1546856168.375 * [misc]backup-simplify: Simplify 0 into 0 1546856168.375 * [misc]backup-simplify: Simplify 0 into 0 1546856168.375 * [misc]backup-simplify: Simplify 0 into 0 1546856168.377 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856168.379 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546856168.387 * [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 1546856168.387 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546856168.388 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1546856168.388 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856168.389 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546856168.390 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 1546856168.393 * [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 1546856168.393 * [misc]taylor: Taking taylor expansion of 0 in k 1546856168.393 * [misc]backup-simplify: Simplify 0 into 0 1546856168.393 * [misc]backup-simplify: Simplify 0 into 0 1546856168.394 * [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))))) 1546856168.394 * * * * [misc]progress: [ 2 / 3 ] generating series at (2 1 1) 1546856168.394 * [misc]backup-simplify: Simplify (* PI (* n 2)) into (* 2 (* n PI)) 1546856168.394 * [misc]approximate: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1546856168.394 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546856168.394 * [misc]taylor: Taking taylor expansion of 2 in n 1546856168.395 * [misc]backup-simplify: Simplify 2 into 2 1546856168.395 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546856168.395 * [misc]taylor: Taking taylor expansion of n in n 1546856168.395 * [misc]backup-simplify: Simplify 0 into 0 1546856168.395 * [misc]backup-simplify: Simplify 1 into 1 1546856168.395 * [misc]taylor: Taking taylor expansion of PI in n 1546856168.395 * [misc]backup-simplify: Simplify PI into PI 1546856168.395 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546856168.395 * [misc]taylor: Taking taylor expansion of 2 in n 1546856168.395 * [misc]backup-simplify: Simplify 2 into 2 1546856168.395 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546856168.395 * [misc]taylor: Taking taylor expansion of n in n 1546856168.395 * [misc]backup-simplify: Simplify 0 into 0 1546856168.395 * [misc]backup-simplify: Simplify 1 into 1 1546856168.395 * [misc]taylor: Taking taylor expansion of PI in n 1546856168.395 * [misc]backup-simplify: Simplify PI into PI 1546856168.395 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546856168.396 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546856168.396 * [misc]backup-simplify: Simplify 0 into 0 1546856168.396 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546856168.397 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546856168.397 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546856168.398 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546856168.399 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1546856168.400 * [misc]backup-simplify: Simplify 0 into 0 1546856168.401 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1546856168.403 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1546856168.403 * [misc]backup-simplify: Simplify 0 into 0 1546856168.405 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1546856168.407 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1546856168.407 * [misc]backup-simplify: Simplify 0 into 0 1546856168.412 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1546856168.414 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1546856168.414 * [misc]backup-simplify: Simplify 0 into 0 1546856168.418 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1546856168.422 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1546856168.422 * [misc]backup-simplify: Simplify 0 into 0 1546856168.425 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1546856168.427 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1546856168.427 * [misc]backup-simplify: Simplify 0 into 0 1546856168.428 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1546856168.428 * [misc]backup-simplify: Simplify (* PI (* (/ 1 n) 2)) into (* 2 (/ PI n)) 1546856168.428 * [misc]approximate: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1546856168.428 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546856168.428 * [misc]taylor: Taking taylor expansion of 2 in n 1546856168.428 * [misc]backup-simplify: Simplify 2 into 2 1546856168.428 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856168.428 * [misc]taylor: Taking taylor expansion of PI in n 1546856168.428 * [misc]backup-simplify: Simplify PI into PI 1546856168.428 * [misc]taylor: Taking taylor expansion of n in n 1546856168.428 * [misc]backup-simplify: Simplify 0 into 0 1546856168.428 * [misc]backup-simplify: Simplify 1 into 1 1546856168.428 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856168.428 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546856168.428 * [misc]taylor: Taking taylor expansion of 2 in n 1546856168.428 * [misc]backup-simplify: Simplify 2 into 2 1546856168.428 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856168.428 * [misc]taylor: Taking taylor expansion of PI in n 1546856168.428 * [misc]backup-simplify: Simplify PI into PI 1546856168.428 * [misc]taylor: Taking taylor expansion of n in n 1546856168.428 * [misc]backup-simplify: Simplify 0 into 0 1546856168.428 * [misc]backup-simplify: Simplify 1 into 1 1546856168.428 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856168.428 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546856168.429 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546856168.429 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546856168.430 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546856168.430 * [misc]backup-simplify: Simplify 0 into 0 1546856168.430 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856168.431 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546856168.431 * [misc]backup-simplify: Simplify 0 into 0 1546856168.432 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856168.433 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546856168.433 * [misc]backup-simplify: Simplify 0 into 0 1546856168.434 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856168.435 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1546856168.435 * [misc]backup-simplify: Simplify 0 into 0 1546856168.437 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856168.438 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1546856168.438 * [misc]backup-simplify: Simplify 0 into 0 1546856168.440 * [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 1546856168.442 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1546856168.442 * [misc]backup-simplify: Simplify 0 into 0 1546856168.442 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 1546856168.442 * [misc]backup-simplify: Simplify (* PI (* (/ 1 (- n)) 2)) into (* -2 (/ PI n)) 1546856168.442 * [misc]approximate: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1546856168.442 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546856168.442 * [misc]taylor: Taking taylor expansion of -2 in n 1546856168.442 * [misc]backup-simplify: Simplify -2 into -2 1546856168.442 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856168.442 * [misc]taylor: Taking taylor expansion of PI in n 1546856168.442 * [misc]backup-simplify: Simplify PI into PI 1546856168.442 * [misc]taylor: Taking taylor expansion of n in n 1546856168.442 * [misc]backup-simplify: Simplify 0 into 0 1546856168.442 * [misc]backup-simplify: Simplify 1 into 1 1546856168.442 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856168.442 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546856168.442 * [misc]taylor: Taking taylor expansion of -2 in n 1546856168.442 * [misc]backup-simplify: Simplify -2 into -2 1546856168.442 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856168.442 * [misc]taylor: Taking taylor expansion of PI in n 1546856168.442 * [misc]backup-simplify: Simplify PI into PI 1546856168.442 * [misc]taylor: Taking taylor expansion of n in n 1546856168.442 * [misc]backup-simplify: Simplify 0 into 0 1546856168.442 * [misc]backup-simplify: Simplify 1 into 1 1546856168.443 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856168.443 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546856168.443 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546856168.444 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546856168.444 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1546856168.444 * [misc]backup-simplify: Simplify 0 into 0 1546856168.445 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856168.445 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1546856168.445 * [misc]backup-simplify: Simplify 0 into 0 1546856168.446 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856168.447 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546856168.447 * [misc]backup-simplify: Simplify 0 into 0 1546856168.449 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856168.450 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1546856168.450 * [misc]backup-simplify: Simplify 0 into 0 1546856168.451 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856168.453 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1546856168.453 * [misc]backup-simplify: Simplify 0 into 0 1546856168.454 * [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 1546856168.456 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1546856168.456 * [misc]backup-simplify: Simplify 0 into 0 1546856168.456 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 1546856168.456 * * * * [misc]progress: [ 3 / 3 ] generating series at (2) 1546856168.457 * [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)))) 1546856168.457 * [misc]approximate: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (n k) around 0 1546856168.457 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 1546856168.457 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1546856168.457 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546856168.457 * [misc]taylor: Taking taylor expansion of k in k 1546856168.457 * [misc]backup-simplify: Simplify 0 into 0 1546856168.457 * [misc]backup-simplify: Simplify 1 into 1 1546856168.457 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546856168.457 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546856168.458 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546856168.458 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1546856168.458 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1546856168.458 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1546856168.458 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546856168.458 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856168.458 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856168.458 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546856168.458 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856168.458 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856168.458 * [misc]taylor: Taking taylor expansion of k in k 1546856168.458 * [misc]backup-simplify: Simplify 0 into 0 1546856168.458 * [misc]backup-simplify: Simplify 1 into 1 1546856168.458 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1546856168.458 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1546856168.458 * [misc]taylor: Taking taylor expansion of 2 in k 1546856168.458 * [misc]backup-simplify: Simplify 2 into 2 1546856168.458 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1546856168.458 * [misc]taylor: Taking taylor expansion of n in k 1546856168.458 * [misc]backup-simplify: Simplify n into n 1546856168.458 * [misc]taylor: Taking taylor expansion of PI in k 1546856168.458 * [misc]backup-simplify: Simplify PI into PI 1546856168.458 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1546856168.458 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1546856168.458 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1546856168.458 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546856168.458 * [misc]backup-simplify: Simplify (- 0) into 0 1546856168.458 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546856168.458 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1546856168.458 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1546856168.458 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 1546856168.459 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1546856168.459 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546856168.459 * [misc]taylor: Taking taylor expansion of k in n 1546856168.459 * [misc]backup-simplify: Simplify k into k 1546856168.459 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546856168.459 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1546856168.459 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546856168.459 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1546856168.459 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546856168.459 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546856168.459 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546856168.459 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546856168.459 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856168.459 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856168.459 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546856168.459 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856168.459 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856168.459 * [misc]taylor: Taking taylor expansion of k in n 1546856168.459 * [misc]backup-simplify: Simplify k into k 1546856168.459 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546856168.459 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546856168.459 * [misc]taylor: Taking taylor expansion of 2 in n 1546856168.459 * [misc]backup-simplify: Simplify 2 into 2 1546856168.459 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546856168.459 * [misc]taylor: Taking taylor expansion of n in n 1546856168.459 * [misc]backup-simplify: Simplify 0 into 0 1546856168.459 * [misc]backup-simplify: Simplify 1 into 1 1546856168.459 * [misc]taylor: Taking taylor expansion of PI in n 1546856168.459 * [misc]backup-simplify: Simplify PI into PI 1546856168.459 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546856168.459 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546856168.460 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546856168.460 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546856168.460 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856168.461 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546856168.461 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546856168.461 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546856168.461 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546856168.461 * [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)))) 1546856168.462 * [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))))) 1546856168.462 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 1546856168.462 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1546856168.462 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546856168.462 * [misc]taylor: Taking taylor expansion of k in n 1546856168.462 * [misc]backup-simplify: Simplify k into k 1546856168.462 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546856168.462 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1546856168.462 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546856168.462 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1546856168.462 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546856168.462 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546856168.462 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546856168.462 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546856168.462 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856168.462 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856168.462 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546856168.462 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856168.462 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856168.462 * [misc]taylor: Taking taylor expansion of k in n 1546856168.462 * [misc]backup-simplify: Simplify k into k 1546856168.462 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546856168.462 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546856168.462 * [misc]taylor: Taking taylor expansion of 2 in n 1546856168.462 * [misc]backup-simplify: Simplify 2 into 2 1546856168.462 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546856168.462 * [misc]taylor: Taking taylor expansion of n in n 1546856168.462 * [misc]backup-simplify: Simplify 0 into 0 1546856168.462 * [misc]backup-simplify: Simplify 1 into 1 1546856168.462 * [misc]taylor: Taking taylor expansion of PI in n 1546856168.462 * [misc]backup-simplify: Simplify PI into PI 1546856168.463 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546856168.463 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546856168.463 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546856168.464 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546856168.464 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856168.464 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546856168.464 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546856168.464 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546856168.465 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546856168.466 * [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)))) 1546856168.466 * [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))))) 1546856168.467 * [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))) 1546856168.467 * [misc]taylor: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k))) in k 1546856168.467 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1546856168.467 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1546856168.467 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546856168.467 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856168.467 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856168.467 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546856168.467 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856168.467 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856168.467 * [misc]taylor: Taking taylor expansion of k in k 1546856168.467 * [misc]backup-simplify: Simplify 0 into 0 1546856168.467 * [misc]backup-simplify: Simplify 1 into 1 1546856168.467 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1546856168.467 * [misc]taylor: Taking taylor expansion of (log n) in k 1546856168.467 * [misc]taylor: Taking taylor expansion of n in k 1546856168.468 * [misc]backup-simplify: Simplify n into n 1546856168.468 * [misc]backup-simplify: Simplify (log n) into (log n) 1546856168.468 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1546856168.468 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1546856168.468 * [misc]taylor: Taking taylor expansion of 2 in k 1546856168.468 * [misc]backup-simplify: Simplify 2 into 2 1546856168.468 * [misc]taylor: Taking taylor expansion of PI in k 1546856168.468 * [misc]backup-simplify: Simplify PI into PI 1546856168.468 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546856168.468 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856168.469 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546856168.469 * [misc]backup-simplify: Simplify (- 0) into 0 1546856168.469 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546856168.470 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546856168.470 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1546856168.471 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1546856168.471 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1546856168.471 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546856168.471 * [misc]taylor: Taking taylor expansion of k in k 1546856168.471 * [misc]backup-simplify: Simplify 0 into 0 1546856168.471 * [misc]backup-simplify: Simplify 1 into 1 1546856168.471 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546856168.471 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546856168.472 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546856168.473 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) into 0 1546856168.473 * [misc]backup-simplify: Simplify 0 into 0 1546856168.474 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546856168.475 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1546856168.477 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546856168.478 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1546856168.478 * [misc]backup-simplify: Simplify (- 0) into 0 1546856168.478 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856168.479 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546856168.479 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1546856168.481 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1546856168.481 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 k)) 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))) into 0 1546856168.481 * [misc]taylor: Taking taylor expansion of 0 in k 1546856168.481 * [misc]backup-simplify: Simplify 0 into 0 1546856168.482 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1546856168.483 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546856168.486 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546856168.486 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856168.486 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1546856168.486 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546856168.486 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546856168.487 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1546856168.489 * [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))))))) 1546856168.491 * [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))))))) 1546856168.491 * [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))))))) 1546856168.493 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1546856168.495 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1546856168.500 * [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 1546856168.500 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1546856168.500 * [misc]backup-simplify: Simplify (- 0) into 0 1546856168.500 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856168.501 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546856168.502 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1546856168.504 * [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 1546856168.504 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546856168.505 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 1546856168.506 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))))) into 0 1546856168.506 * [misc]taylor: Taking taylor expansion of 0 in k 1546856168.506 * [misc]backup-simplify: Simplify 0 into 0 1546856168.506 * [misc]backup-simplify: Simplify 0 into 0 1546856168.506 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1546856168.507 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1546856168.509 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1546856168.510 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546856168.515 * [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 1546856168.515 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856168.515 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1546856168.516 * [misc]backup-simplify: Simplify (- 0) into 0 1546856168.516 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856168.517 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1546856168.519 * [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))))) 1546856168.524 * [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)))))))) 1546856168.527 * [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)))))))) 1546856168.529 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1546856168.532 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1546856168.540 * [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 1546856168.540 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 1546856168.540 * [misc]backup-simplify: Simplify (- 0) into 0 1546856168.540 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856168.541 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546856168.542 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 1546856168.547 * [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 1546856168.547 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546856168.548 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 1546856168.549 * [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 1546856168.549 * [misc]taylor: Taking taylor expansion of 0 in k 1546856168.549 * [misc]backup-simplify: Simplify 0 into 0 1546856168.549 * [misc]backup-simplify: Simplify 0 into 0 1546856168.549 * [misc]backup-simplify: Simplify 0 into 0 1546856168.549 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856168.551 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1546856168.553 * [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 1546856168.555 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546856168.563 * [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 1546856168.563 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856168.564 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1546856168.564 * [misc]backup-simplify: Simplify (- 0) into 0 1546856168.564 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856168.565 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 1546856168.569 * [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))))))) 1546856168.578 * [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)))))))))))))) 1546856168.584 * [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)))))))))))))) 1546856168.595 * [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)))))))))))))))))))))) 1546856168.596 * [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))))) 1546856168.596 * [misc]approximate: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0 1546856168.596 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 1546856168.596 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1546856168.596 * [misc]taylor: Taking taylor expansion of k in k 1546856168.596 * [misc]backup-simplify: Simplify 0 into 0 1546856168.596 * [misc]backup-simplify: Simplify 1 into 1 1546856168.596 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546856168.597 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546856168.597 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1546856168.597 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1546856168.597 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1546856168.597 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546856168.597 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856168.597 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856168.597 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546856168.597 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856168.597 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856168.597 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546856168.597 * [misc]taylor: Taking taylor expansion of k in k 1546856168.597 * [misc]backup-simplify: Simplify 0 into 0 1546856168.597 * [misc]backup-simplify: Simplify 1 into 1 1546856168.597 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546856168.597 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1546856168.598 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1546856168.598 * [misc]taylor: Taking taylor expansion of 2 in k 1546856168.598 * [misc]backup-simplify: Simplify 2 into 2 1546856168.598 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546856168.598 * [misc]taylor: Taking taylor expansion of PI in k 1546856168.598 * [misc]backup-simplify: Simplify PI into PI 1546856168.598 * [misc]taylor: Taking taylor expansion of n in k 1546856168.598 * [misc]backup-simplify: Simplify n into n 1546856168.598 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546856168.598 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1546856168.598 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1546856168.598 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546856168.598 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546856168.598 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546856168.599 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1546856168.599 * [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)))) 1546856168.599 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1546856168.599 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1546856168.599 * [misc]taylor: Taking taylor expansion of k in n 1546856168.599 * [misc]backup-simplify: Simplify k into k 1546856168.599 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1546856168.599 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1546856168.599 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546856168.599 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546856168.599 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546856168.599 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546856168.599 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856168.599 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856168.599 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546856168.599 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856168.599 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856168.599 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546856168.599 * [misc]taylor: Taking taylor expansion of k in n 1546856168.599 * [misc]backup-simplify: Simplify k into k 1546856168.599 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546856168.599 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546856168.599 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546856168.599 * [misc]taylor: Taking taylor expansion of 2 in n 1546856168.600 * [misc]backup-simplify: Simplify 2 into 2 1546856168.600 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856168.600 * [misc]taylor: Taking taylor expansion of PI in n 1546856168.600 * [misc]backup-simplify: Simplify PI into PI 1546856168.600 * [misc]taylor: Taking taylor expansion of n in n 1546856168.600 * [misc]backup-simplify: Simplify 0 into 0 1546856168.600 * [misc]backup-simplify: Simplify 1 into 1 1546856168.600 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856168.600 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546856168.601 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856168.601 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546856168.601 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546856168.601 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546856168.602 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546856168.603 * [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))) 1546856168.603 * [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)))) 1546856168.603 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1546856168.603 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1546856168.604 * [misc]taylor: Taking taylor expansion of k in n 1546856168.604 * [misc]backup-simplify: Simplify k into k 1546856168.604 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1546856168.604 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1546856168.604 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546856168.604 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546856168.604 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546856168.604 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546856168.604 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856168.604 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856168.604 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546856168.604 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856168.604 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856168.604 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546856168.604 * [misc]taylor: Taking taylor expansion of k in n 1546856168.604 * [misc]backup-simplify: Simplify k into k 1546856168.604 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546856168.604 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546856168.604 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546856168.604 * [misc]taylor: Taking taylor expansion of 2 in n 1546856168.604 * [misc]backup-simplify: Simplify 2 into 2 1546856168.604 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856168.604 * [misc]taylor: Taking taylor expansion of PI in n 1546856168.604 * [misc]backup-simplify: Simplify PI into PI 1546856168.604 * [misc]taylor: Taking taylor expansion of n in n 1546856168.604 * [misc]backup-simplify: Simplify 0 into 0 1546856168.604 * [misc]backup-simplify: Simplify 1 into 1 1546856168.605 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856168.605 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546856168.605 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856168.605 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546856168.605 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546856168.606 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546856168.606 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546856168.607 * [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))) 1546856168.608 * [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)))) 1546856168.608 * [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)) 1546856168.608 * [misc]taylor: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) in k 1546856168.608 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1546856168.608 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1546856168.608 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546856168.609 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856168.609 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856168.609 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546856168.609 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856168.609 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856168.609 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546856168.609 * [misc]taylor: Taking taylor expansion of k in k 1546856168.609 * [misc]backup-simplify: Simplify 0 into 0 1546856168.609 * [misc]backup-simplify: Simplify 1 into 1 1546856168.609 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546856168.609 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1546856168.609 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1546856168.609 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1546856168.609 * [misc]taylor: Taking taylor expansion of 2 in k 1546856168.609 * [misc]backup-simplify: Simplify 2 into 2 1546856168.609 * [misc]taylor: Taking taylor expansion of PI in k 1546856168.609 * [misc]backup-simplify: Simplify PI into PI 1546856168.609 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546856168.610 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856168.610 * [misc]taylor: Taking taylor expansion of (log n) in k 1546856168.610 * [misc]taylor: Taking taylor expansion of n in k 1546856168.610 * [misc]backup-simplify: Simplify n into n 1546856168.610 * [misc]backup-simplify: Simplify (log n) into (log n) 1546856168.610 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546856168.610 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546856168.611 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546856168.611 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1546856168.611 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1546856168.612 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1546856168.612 * [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)))) 1546856168.613 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1546856168.613 * [misc]taylor: Taking taylor expansion of k in k 1546856168.613 * [misc]backup-simplify: Simplify 0 into 0 1546856168.613 * [misc]backup-simplify: Simplify 1 into 1 1546856168.613 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546856168.613 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546856168.614 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) into 0 1546856168.614 * [misc]backup-simplify: Simplify 0 into 0 1546856168.615 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546856168.616 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546856168.618 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546856168.619 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546856168.619 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546856168.619 * [misc]backup-simplify: Simplify (- 0) into 0 1546856168.619 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856168.620 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546856168.620 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1546856168.622 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546856168.623 * [misc]backup-simplify: Simplify (+ (* (sqrt k) 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0 1546856168.623 * [misc]taylor: Taking taylor expansion of 0 in k 1546856168.623 * [misc]backup-simplify: Simplify 0 into 0 1546856168.623 * [misc]backup-simplify: Simplify 0 into 0 1546856168.624 * [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)))))) 1546856168.624 * [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)))))) 1546856168.626 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856168.627 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546856168.632 * [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 1546856168.632 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546856168.632 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1546856168.632 * [misc]backup-simplify: Simplify (- 0) into 0 1546856168.632 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856168.633 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546856168.633 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1546856168.635 * [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 1546856168.635 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 1546856168.636 * [misc]backup-simplify: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0 1546856168.636 * [misc]taylor: Taking taylor expansion of 0 in k 1546856168.636 * [misc]backup-simplify: Simplify 0 into 0 1546856168.636 * [misc]backup-simplify: Simplify 0 into 0 1546856168.636 * [misc]backup-simplify: Simplify 0 into 0 1546856168.636 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1546856168.637 * [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)))))) 1546856168.637 * [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)))))) 1546856168.638 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856168.639 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546856168.644 * [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 1546856168.644 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546856168.644 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1546856168.644 * [misc]backup-simplify: Simplify (- 0) into 0 1546856168.644 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856168.645 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546856168.645 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1546856168.648 * [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 1546856168.648 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 1546856168.648 * [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 1546856168.648 * [misc]taylor: Taking taylor expansion of 0 in k 1546856168.648 * [misc]backup-simplify: Simplify 0 into 0 1546856168.649 * [misc]backup-simplify: Simplify 0 into 0 1546856168.649 * [misc]backup-simplify: Simplify 0 into 0 1546856168.649 * [misc]backup-simplify: Simplify 0 into 0 1546856168.649 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1546856168.650 * [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)))))) 1546856168.650 * [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)))))) 1546856168.652 * [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)))))))) 1546856168.652 * [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))) 1546856168.652 * [misc]approximate: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (n k) around 0 1546856168.652 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 1546856168.652 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1546856168.652 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1546856168.652 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1546856168.652 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546856168.652 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546856168.652 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856168.652 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856168.652 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546856168.652 * [misc]taylor: Taking taylor expansion of k in k 1546856168.652 * [misc]backup-simplify: Simplify 0 into 0 1546856168.652 * [misc]backup-simplify: Simplify 1 into 1 1546856168.652 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546856168.652 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856168.652 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856168.652 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1546856168.652 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1546856168.652 * [misc]taylor: Taking taylor expansion of -2 in k 1546856168.652 * [misc]backup-simplify: Simplify -2 into -2 1546856168.652 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546856168.652 * [misc]taylor: Taking taylor expansion of PI in k 1546856168.652 * [misc]backup-simplify: Simplify PI into PI 1546856168.652 * [misc]taylor: Taking taylor expansion of n in k 1546856168.652 * [misc]backup-simplify: Simplify n into n 1546856168.652 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546856168.653 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1546856168.653 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1546856168.653 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546856168.653 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546856168.653 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1546856168.653 * [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))) 1546856168.653 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1546856168.653 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1546856168.653 * [misc]taylor: Taking taylor expansion of -1 in k 1546856168.653 * [misc]backup-simplify: Simplify -1 into -1 1546856168.653 * [misc]taylor: Taking taylor expansion of k in k 1546856168.653 * [misc]backup-simplify: Simplify 0 into 0 1546856168.653 * [misc]backup-simplify: Simplify 1 into 1 1546856168.653 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1546856168.653 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546856168.654 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1546856168.654 * [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)))) 1546856168.654 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 1546856168.654 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546856168.654 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546856168.654 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546856168.654 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546856168.654 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546856168.654 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856168.654 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856168.654 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546856168.654 * [misc]taylor: Taking taylor expansion of k in n 1546856168.654 * [misc]backup-simplify: Simplify k into k 1546856168.654 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546856168.654 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856168.654 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856168.654 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546856168.654 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546856168.654 * [misc]taylor: Taking taylor expansion of -2 in n 1546856168.654 * [misc]backup-simplify: Simplify -2 into -2 1546856168.654 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856168.654 * [misc]taylor: Taking taylor expansion of PI in n 1546856168.654 * [misc]backup-simplify: Simplify PI into PI 1546856168.654 * [misc]taylor: Taking taylor expansion of n in n 1546856168.654 * [misc]backup-simplify: Simplify 0 into 0 1546856168.654 * [misc]backup-simplify: Simplify 1 into 1 1546856168.654 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856168.655 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546856168.655 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546856168.655 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546856168.655 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546856168.655 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546856168.656 * [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))) 1546856168.656 * [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)))) 1546856168.656 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1546856168.656 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1546856168.656 * [misc]taylor: Taking taylor expansion of -1 in n 1546856168.656 * [misc]backup-simplify: Simplify -1 into -1 1546856168.656 * [misc]taylor: Taking taylor expansion of k in n 1546856168.656 * [misc]backup-simplify: Simplify k into k 1546856168.656 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1546856168.656 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1546856168.656 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1546856168.656 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1546856168.657 * [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))) 1546856168.657 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 1546856168.657 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546856168.657 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546856168.657 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546856168.657 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546856168.657 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546856168.657 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856168.657 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856168.657 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546856168.657 * [misc]taylor: Taking taylor expansion of k in n 1546856168.657 * [misc]backup-simplify: Simplify k into k 1546856168.657 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546856168.657 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856168.657 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856168.657 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546856168.657 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546856168.657 * [misc]taylor: Taking taylor expansion of -2 in n 1546856168.657 * [misc]backup-simplify: Simplify -2 into -2 1546856168.657 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856168.657 * [misc]taylor: Taking taylor expansion of PI in n 1546856168.657 * [misc]backup-simplify: Simplify PI into PI 1546856168.657 * [misc]taylor: Taking taylor expansion of n in n 1546856168.657 * [misc]backup-simplify: Simplify 0 into 0 1546856168.657 * [misc]backup-simplify: Simplify 1 into 1 1546856168.657 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856168.658 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546856168.658 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546856168.658 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546856168.658 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546856168.658 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546856168.659 * [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))) 1546856168.659 * [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)))) 1546856168.659 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1546856168.659 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1546856168.659 * [misc]taylor: Taking taylor expansion of -1 in n 1546856168.659 * [misc]backup-simplify: Simplify -1 into -1 1546856168.659 * [misc]taylor: Taking taylor expansion of k in n 1546856168.659 * [misc]backup-simplify: Simplify k into k 1546856168.659 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1546856168.659 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1546856168.659 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1546856168.659 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1546856168.660 * [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))) 1546856168.660 * [misc]taylor: Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) in k 1546856168.660 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1546856168.660 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1546856168.660 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546856168.660 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546856168.660 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856168.660 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856168.660 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546856168.660 * [misc]taylor: Taking taylor expansion of k in k 1546856168.660 * [misc]backup-simplify: Simplify 0 into 0 1546856168.660 * [misc]backup-simplify: Simplify 1 into 1 1546856168.660 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546856168.660 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856168.660 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856168.660 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1546856168.660 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1546856168.660 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1546856168.660 * [misc]taylor: Taking taylor expansion of -2 in k 1546856168.660 * [misc]backup-simplify: Simplify -2 into -2 1546856168.660 * [misc]taylor: Taking taylor expansion of PI in k 1546856168.660 * [misc]backup-simplify: Simplify PI into PI 1546856168.661 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546856168.661 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546856168.661 * [misc]taylor: Taking taylor expansion of (log n) in k 1546856168.661 * [misc]taylor: Taking taylor expansion of n in k 1546856168.661 * [misc]backup-simplify: Simplify n into n 1546856168.661 * [misc]backup-simplify: Simplify (log n) into (log n) 1546856168.661 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546856168.661 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546856168.661 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1546856168.661 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1546856168.662 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1546856168.662 * [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)))) 1546856168.662 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1546856168.662 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1546856168.662 * [misc]taylor: Taking taylor expansion of -1 in k 1546856168.662 * [misc]backup-simplify: Simplify -1 into -1 1546856168.662 * [misc]taylor: Taking taylor expansion of k in k 1546856168.662 * [misc]backup-simplify: Simplify 0 into 0 1546856168.662 * [misc]backup-simplify: Simplify 1 into 1 1546856168.662 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1546856168.662 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546856168.663 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1546856168.663 * [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))))) 1546856168.664 * [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))))) 1546856168.665 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546856168.666 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1546856168.668 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1546856168.668 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546856168.669 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546856168.669 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856168.670 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546856168.670 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1546856168.672 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546856168.673 * [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 1546856168.673 * [misc]taylor: Taking taylor expansion of 0 in k 1546856168.673 * [misc]backup-simplify: Simplify 0 into 0 1546856168.673 * [misc]backup-simplify: Simplify 0 into 0 1546856168.673 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1546856168.674 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1546856168.675 * [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)))))) 1546856168.676 * [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)))))) 1546856168.677 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856168.678 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1546856168.684 * [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 1546856168.684 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546856168.684 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1546856168.685 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856168.686 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546856168.687 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1546856168.689 * [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 1546856168.690 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546856168.690 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 1546856168.691 * [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 1546856168.691 * [misc]taylor: Taking taylor expansion of 0 in k 1546856168.691 * [misc]backup-simplify: Simplify 0 into 0 1546856168.691 * [misc]backup-simplify: Simplify 0 into 0 1546856168.691 * [misc]backup-simplify: Simplify 0 into 0 1546856168.692 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856168.693 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1546856168.695 * [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)))))) 1546856168.696 * [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)))))) 1546856168.698 * [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))))))))))) 1546856168.698 * * * [misc]progress: simplifying candidates 1546856168.698 * * * * [misc]progress: [ 1 / 83 ] simplifiying candidate # 1546856168.698 * * * * [misc]progress: [ 2 / 83 ] simplifiying candidate # 1546856168.698 * * * * [misc]progress: [ 3 / 83 ] simplifiying candidate # 1546856168.699 * [enter]simplify: Simplifying (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) 1546856168.699 * * [misc]simplify: iters left: 6 (11 enodes) 1546856168.702 * * [misc]simplify: iters left: 5 (21 enodes) 1546856168.710 * * [misc]simplify: iters left: 4 (47 enodes) 1546856168.726 * * [misc]simplify: iters left: 3 (113 enodes) 1546856168.754 * * [misc]simplify: iters left: 2 (328 enodes) 1546856169.071 * [exit]simplify: Simplified to (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) 1546856169.071 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (exp (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI)))) (sqrt k))) 1546856169.071 * * * * [misc]progress: [ 4 / 83 ] simplifiying candidate # 1546856169.071 * * * * [misc]progress: [ 5 / 83 ] simplifiying candidate # 1546856169.071 * [enter]simplify: Simplifying (* PI (* n 2)) 1546856169.071 * * [misc]simplify: iters left: 4 (5 enodes) 1546856169.072 * * [misc]simplify: iters left: 3 (9 enodes) 1546856169.073 * * [misc]simplify: iters left: 2 (15 enodes) 1546856169.075 * * [misc]simplify: iters left: 1 (17 enodes) 1546856169.077 * [exit]simplify: Simplified to (* (* 2 n) PI) 1546856169.077 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* 2 n) PI) (* 1 (- 1/2 (/ k 2)))) (sqrt k))) 1546856169.077 * * * * [misc]progress: [ 6 / 83 ] simplifiying candidate # 1546856169.078 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (/ k 2)) 1546856169.078 * * [misc]simplify: iters left: 5 (8 enodes) 1546856169.079 * * [misc]simplify: iters left: 4 (12 enodes) 1546856169.081 * * [misc]simplify: iters left: 3 (18 enodes) 1546856169.083 * * [misc]simplify: iters left: 2 (20 enodes) 1546856169.086 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ k 2)) 1546856169.086 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (/ (pow (* PI (* n 2)) 1/2) (pow (* (* 2 n) PI) (/ k 2))) (sqrt k))) 1546856169.086 * * * * [misc]progress: [ 7 / 83 ] simplifiying candidate # 1546856169.086 * [enter]simplify: Simplifying (cbrt (- 1/2 (/ k 2))) 1546856169.086 * * [misc]simplify: iters left: 5 (6 enodes) 1546856169.087 * * [misc]simplify: iters left: 4 (8 enodes) 1546856169.090 * * [misc]simplify: iters left: 3 (11 enodes) 1546856169.092 * [exit]simplify: Simplified to (cbrt (- 1/2 (/ k 2))) 1546856169.092 * [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))) 1546856169.092 * * * * [misc]progress: [ 8 / 83 ] simplifiying candidate # 1546856169.092 * [enter]simplify: Simplifying (sqrt (- 1/2 (/ k 2))) 1546856169.092 * * [misc]simplify: iters left: 5 (6 enodes) 1546856169.093 * * [misc]simplify: iters left: 4 (8 enodes) 1546856169.094 * * [misc]simplify: iters left: 3 (11 enodes) 1546856169.097 * [exit]simplify: Simplified to (sqrt (- 1/2 (/ k 2))) 1546856169.097 * [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))) 1546856169.097 * * * * [misc]progress: [ 9 / 83 ] simplifiying candidate # 1546856169.097 * [enter]simplify: Simplifying (- 1/2 (/ k 2)) 1546856169.097 * * [misc]simplify: iters left: 4 (5 enodes) 1546856169.099 * * [misc]simplify: iters left: 3 (7 enodes) 1546856169.101 * * [misc]simplify: iters left: 2 (10 enodes) 1546856169.104 * [exit]simplify: Simplified to (- 1/2 (/ k 2)) 1546856169.104 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (pow (pow (* PI (* n 2)) 1) (- 1/2 (/ k 2))) (sqrt k))) 1546856169.104 * * * * [misc]progress: [ 10 / 83 ] simplifiying candidate # 1546856169.104 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1546856169.104 * * [misc]simplify: iters left: 5 (9 enodes) 1546856169.107 * * [misc]simplify: iters left: 4 (15 enodes) 1546856169.112 * * [misc]simplify: iters left: 3 (21 enodes) 1546856169.117 * * [misc]simplify: iters left: 2 (22 enodes) 1546856169.122 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1546856169.123 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2)))) (sqrt k))) 1546856169.123 * * * * [misc]progress: [ 11 / 83 ] simplifiying candidate # 1546856169.123 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1546856169.123 * * [misc]simplify: iters left: 5 (9 enodes) 1546856169.125 * * [misc]simplify: iters left: 4 (15 enodes) 1546856169.127 * * [misc]simplify: iters left: 3 (21 enodes) 1546856169.129 * * [misc]simplify: iters left: 2 (22 enodes) 1546856169.132 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1546856169.132 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2)))) (sqrt k))) 1546856169.132 * * * * [misc]progress: [ 12 / 83 ] simplifiying candidate # 1546856169.133 * [enter]simplify: Simplifying (pow PI (- 1/2 (/ k 2))) 1546856169.133 * * [misc]simplify: iters left: 5 (7 enodes) 1546856169.134 * * [misc]simplify: iters left: 4 (9 enodes) 1546856169.135 * * [misc]simplify: iters left: 3 (12 enodes) 1546856169.137 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1546856169.137 * [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))) 1546856169.137 * * * * [misc]progress: [ 13 / 83 ] simplifiying candidate # 1546856169.137 * * * * [misc]progress: [ 14 / 83 ] simplifiying candidate # 1546856169.137 * * * * [misc]progress: [ 15 / 83 ] simplifiying candidate # 1546856169.137 * * * * [misc]progress: [ 16 / 83 ] simplifiying candidate # 1546856169.137 * * * * [misc]progress: [ 17 / 83 ] simplifiying candidate # 1546856169.137 * * * * [misc]progress: [ 18 / 83 ] simplifiying candidate # 1546856169.137 * * * * [misc]progress: [ 19 / 83 ] simplifiying candidate # 1546856169.137 * * * * [misc]progress: [ 20 / 83 ] simplifiying candidate # 1546856169.137 * * * * [misc]progress: [ 21 / 83 ] simplifiying candidate # 1546856169.137 * * * * [misc]progress: [ 22 / 83 ] simplifiying candidate # 1546856169.137 * * * * [misc]progress: [ 23 / 83 ] simplifiying candidate # 1546856169.137 * * * * [misc]progress: [ 24 / 83 ] simplifiying candidate # 1546856169.137 * * * * [misc]progress: [ 25 / 83 ] simplifiying candidate # 1546856169.137 * * * * [misc]progress: [ 26 / 83 ] simplifiying candidate # 1546856169.137 * * * * [misc]progress: [ 27 / 83 ] simplifiying candidate # 1546856169.137 * * * * [misc]progress: [ 28 / 83 ] simplifiying candidate # 1546856169.137 * * * * [misc]progress: [ 29 / 83 ] simplifiying candidate # 1546856169.137 * * * * [misc]progress: [ 30 / 83 ] simplifiying candidate # 1546856169.137 * * * * [misc]progress: [ 31 / 83 ] simplifiying candidate # 1546856169.137 * * * * [misc]progress: [ 32 / 83 ] simplifiying candidate # 1546856169.138 * * * * [misc]progress: [ 33 / 83 ] simplifiying candidate # 1546856169.138 * * * * [misc]progress: [ 34 / 83 ] simplifiying candidate # 1546856169.138 * [enter]simplify: Simplifying (- (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) (log (sqrt k))) 1546856169.138 * * [misc]simplify: iters left: 6 (14 enodes) 1546856169.141 * * [misc]simplify: iters left: 5 (27 enodes) 1546856169.145 * * [misc]simplify: iters left: 4 (55 enodes) 1546856169.156 * * [misc]simplify: iters left: 3 (144 enodes) 1546856169.233 * [exit]simplify: Simplified to (fma (- 1/2 (/ k 2)) (log (* (* 2 n) PI)) (- (log (sqrt k)))) 1546856169.233 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (- 1/2 (/ k 2)) (log (* (* 2 n) PI)) (- (log (sqrt k)))))) 1546856169.233 * * * * [misc]progress: [ 35 / 83 ] simplifiying candidate # 1546856169.233 * [enter]simplify: Simplifying (- (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) (log (sqrt k))) 1546856169.233 * * [misc]simplify: iters left: 6 (14 enodes) 1546856169.238 * * [misc]simplify: iters left: 5 (27 enodes) 1546856169.246 * * [misc]simplify: iters left: 4 (55 enodes) 1546856169.268 * * [misc]simplify: iters left: 3 (144 enodes) 1546856169.347 * [exit]simplify: Simplified to (fma (- 1/2 (/ k 2)) (log (* (* 2 n) PI)) (- (log (sqrt k)))) 1546856169.348 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (- 1/2 (/ k 2)) (log (* (* 2 n) PI)) (- (log (sqrt k)))))) 1546856169.348 * * * * [misc]progress: [ 36 / 83 ] simplifiying candidate # 1546856169.348 * [enter]simplify: Simplifying (- (log (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (log (sqrt k))) 1546856169.348 * * [misc]simplify: iters left: 6 (14 enodes) 1546856169.350 * * [misc]simplify: iters left: 5 (24 enodes) 1546856169.354 * * [misc]simplify: iters left: 4 (43 enodes) 1546856169.361 * * [misc]simplify: iters left: 3 (73 enodes) 1546856169.394 * * [misc]simplify: iters left: 2 (220 enodes) 1546856169.626 * [exit]simplify: Simplified to (fma (log (* (* PI 2) n)) (- 1/2 (/ k 2)) (- (log (sqrt k)))) 1546856169.627 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (log (* (* PI 2) n)) (- 1/2 (/ k 2)) (- (log (sqrt k)))))) 1546856169.627 * * * * [misc]progress: [ 37 / 83 ] simplifiying candidate # 1546856169.627 * * * * [misc]progress: [ 38 / 83 ] simplifiying candidate # 1546856169.627 * * * * [misc]progress: [ 39 / 83 ] simplifiying candidate # 1546856169.627 * [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))) 1546856169.627 * * [misc]simplify: iters left: 6 (16 enodes) 1546856169.633 * * [misc]simplify: iters left: 5 (31 enodes) 1546856169.642 * * [misc]simplify: iters left: 4 (67 enodes) 1546856169.665 * * [misc]simplify: iters left: 3 (124 enodes) 1546856169.710 * * [misc]simplify: iters left: 2 (195 enodes) 1546856169.790 * * [misc]simplify: iters left: 1 (309 enodes) 1546856169.914 * [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)))) 1546856169.914 * [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)))))) 1546856169.914 * * * * [misc]progress: [ 40 / 83 ] simplifiying candidate # 1546856169.914 * * * * [misc]progress: [ 41 / 83 ] simplifiying candidate # 1546856169.914 * * * * [misc]progress: [ 42 / 83 ] simplifiying candidate # 1546856169.914 * * * * [misc]progress: [ 43 / 83 ] simplifiying candidate # 1546856169.915 * * * * [misc]progress: [ 44 / 83 ] simplifiying candidate # 1546856169.915 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1546856169.915 * * [misc]simplify: iters left: 6 (12 enodes) 1546856169.919 * * [misc]simplify: iters left: 5 (19 enodes) 1546856169.922 * * [misc]simplify: iters left: 4 (25 enodes) 1546856169.925 * * [misc]simplify: iters left: 3 (26 enodes) 1546856169.928 * [exit]simplify: Simplified to (/ (sqrt (* (* 2 n) PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1546856169.928 * [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))))) 1546856169.929 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (sqrt k))) 1546856169.929 * * [misc]simplify: iters left: 6 (12 enodes) 1546856169.930 * * [misc]simplify: iters left: 5 (18 enodes) 1546856169.933 * * [misc]simplify: iters left: 4 (24 enodes) 1546856169.936 * * [misc]simplify: iters left: 3 (25 enodes) 1546856169.939 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt k))) 1546856169.940 * [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))))) 1546856169.940 * * * * [misc]progress: [ 45 / 83 ] simplifiying candidate # 1546856169.940 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (sqrt (sqrt k))) 1546856169.940 * * [misc]simplify: iters left: 6 (11 enodes) 1546856169.942 * * [misc]simplify: iters left: 5 (16 enodes) 1546856169.944 * * [misc]simplify: iters left: 4 (22 enodes) 1546856169.947 * * [misc]simplify: iters left: 3 (24 enodes) 1546856169.949 * [exit]simplify: Simplified to (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) 1546856169.950 * [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))))) 1546856169.950 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k))) 1546856169.950 * * [misc]simplify: iters left: 6 (12 enodes) 1546856169.952 * * [misc]simplify: iters left: 5 (18 enodes) 1546856169.954 * * [misc]simplify: iters left: 4 (24 enodes) 1546856169.957 * * [misc]simplify: iters left: 3 (25 enodes) 1546856169.961 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k))) 1546856169.961 * [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))))) 1546856169.961 * * * * [misc]progress: [ 46 / 83 ] simplifiying candidate # 1546856169.961 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) 1) 1546856169.961 * * [misc]simplify: iters left: 6 (9 enodes) 1546856169.962 * * [misc]simplify: iters left: 5 (16 enodes) 1546856169.965 * * [misc]simplify: iters left: 4 (24 enodes) 1546856169.968 * * [misc]simplify: iters left: 3 (26 enodes) 1546856169.971 * [exit]simplify: Simplified to (sqrt (* (* PI 2) n)) 1546856169.971 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) 1546856169.971 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)) 1546856169.971 * * [misc]simplify: iters left: 6 (11 enodes) 1546856169.973 * * [misc]simplify: iters left: 5 (17 enodes) 1546856169.975 * * [misc]simplify: iters left: 4 (23 enodes) 1546856169.979 * * [misc]simplify: iters left: 3 (24 enodes) 1546856169.983 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)) 1546856169.983 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)))) 1546856169.983 * * * * [misc]progress: [ 47 / 83 ] simplifiying candidate # 1546856169.983 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1546856169.983 * * [misc]simplify: iters left: 6 (12 enodes) 1546856169.985 * * [misc]simplify: iters left: 5 (19 enodes) 1546856169.987 * * [misc]simplify: iters left: 4 (25 enodes) 1546856169.991 * * [misc]simplify: iters left: 3 (26 enodes) 1546856169.994 * [exit]simplify: Simplified to (/ (sqrt (* (* 2 n) PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1546856169.994 * [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))))) 1546856169.994 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (sqrt k))) 1546856169.994 * * [misc]simplify: iters left: 6 (12 enodes) 1546856169.996 * * [misc]simplify: iters left: 5 (18 enodes) 1546856169.998 * * [misc]simplify: iters left: 4 (24 enodes) 1546856170.001 * * [misc]simplify: iters left: 3 (25 enodes) 1546856170.005 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt k))) 1546856170.005 * [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))))) 1546856170.005 * * * * [misc]progress: [ 48 / 83 ] simplifiying candidate # 1546856170.005 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (sqrt (sqrt k))) 1546856170.005 * * [misc]simplify: iters left: 6 (11 enodes) 1546856170.006 * * [misc]simplify: iters left: 5 (16 enodes) 1546856170.009 * * [misc]simplify: iters left: 4 (22 enodes) 1546856170.012 * * [misc]simplify: iters left: 3 (24 enodes) 1546856170.015 * [exit]simplify: Simplified to (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) 1546856170.015 * [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))))) 1546856170.015 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k))) 1546856170.015 * * [misc]simplify: iters left: 6 (12 enodes) 1546856170.017 * * [misc]simplify: iters left: 5 (18 enodes) 1546856170.019 * * [misc]simplify: iters left: 4 (24 enodes) 1546856170.022 * * [misc]simplify: iters left: 3 (25 enodes) 1546856170.026 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k))) 1546856170.026 * [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))))) 1546856170.026 * * * * [misc]progress: [ 49 / 83 ] simplifiying candidate # 1546856170.026 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) 1) 1546856170.026 * * [misc]simplify: iters left: 6 (9 enodes) 1546856170.027 * * [misc]simplify: iters left: 5 (16 enodes) 1546856170.030 * * [misc]simplify: iters left: 4 (24 enodes) 1546856170.033 * * [misc]simplify: iters left: 3 (26 enodes) 1546856170.035 * [exit]simplify: Simplified to (sqrt (* (* PI 2) n)) 1546856170.035 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) 1546856170.035 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)) 1546856170.036 * * [misc]simplify: iters left: 6 (11 enodes) 1546856170.037 * * [misc]simplify: iters left: 5 (17 enodes) 1546856170.040 * * [misc]simplify: iters left: 4 (23 enodes) 1546856170.043 * * [misc]simplify: iters left: 3 (24 enodes) 1546856170.046 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)) 1546856170.046 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)))) 1546856170.046 * * * * [misc]progress: [ 50 / 83 ] simplifiying candidate # 1546856170.046 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1546856170.046 * * [misc]simplify: iters left: 6 (11 enodes) 1546856170.048 * * [misc]simplify: iters left: 5 (15 enodes) 1546856170.051 * * [misc]simplify: iters left: 4 (18 enodes) 1546856170.053 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1546856170.054 * [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))))) 1546856170.054 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1546856170.054 * * [misc]simplify: iters left: 6 (11 enodes) 1546856170.055 * * [misc]simplify: iters left: 5 (14 enodes) 1546856170.057 * * [misc]simplify: iters left: 4 (17 enodes) 1546856170.060 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1546856170.060 * [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))))) 1546856170.060 * * * * [misc]progress: [ 51 / 83 ] simplifiying candidate # 1546856170.060 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1546856170.060 * * [misc]simplify: iters left: 6 (10 enodes) 1546856170.062 * * [misc]simplify: iters left: 5 (12 enodes) 1546856170.063 * * [misc]simplify: iters left: 4 (15 enodes) 1546856170.065 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1546856170.065 * [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))))) 1546856170.065 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1546856170.065 * * [misc]simplify: iters left: 6 (11 enodes) 1546856170.067 * * [misc]simplify: iters left: 5 (14 enodes) 1546856170.069 * * [misc]simplify: iters left: 4 (17 enodes) 1546856170.071 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1546856170.071 * [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))))) 1546856170.071 * * * * [misc]progress: [ 52 / 83 ] simplifiying candidate # 1546856170.072 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) 1) 1546856170.072 * * [misc]simplify: iters left: 6 (9 enodes) 1546856170.073 * * [misc]simplify: iters left: 5 (13 enodes) 1546856170.075 * * [misc]simplify: iters left: 4 (18 enodes) 1546856170.077 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1546856170.077 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1546856170.077 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)) 1546856170.077 * * [misc]simplify: iters left: 6 (10 enodes) 1546856170.079 * * [misc]simplify: iters left: 5 (13 enodes) 1546856170.081 * * [misc]simplify: iters left: 4 (16 enodes) 1546856170.083 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)) 1546856170.083 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1546856170.083 * * * * [misc]progress: [ 53 / 83 ] simplifiying candidate # 1546856170.083 * [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)))) 1546856170.083 * * [misc]simplify: iters left: 6 (16 enodes) 1546856170.086 * * [misc]simplify: iters left: 5 (28 enodes) 1546856170.090 * * [misc]simplify: iters left: 4 (46 enodes) 1546856170.096 * * [misc]simplify: iters left: 3 (50 enodes) 1546856170.102 * * [misc]simplify: iters left: 2 (53 enodes) 1546856170.111 * [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)))) 1546856170.111 * [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))))) 1546856170.111 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1546856170.112 * * [misc]simplify: iters left: 6 (14 enodes) 1546856170.116 * * [misc]simplify: iters left: 5 (20 enodes) 1546856170.118 * * [misc]simplify: iters left: 4 (29 enodes) 1546856170.122 * * [misc]simplify: iters left: 3 (30 enodes) 1546856170.126 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1546856170.126 * [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))))) 1546856170.126 * * * * [misc]progress: [ 54 / 83 ] simplifiying candidate # 1546856170.126 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) 1546856170.126 * * [misc]simplify: iters left: 6 (15 enodes) 1546856170.130 * * [misc]simplify: iters left: 5 (23 enodes) 1546856170.133 * * [misc]simplify: iters left: 4 (34 enodes) 1546856170.138 * * [misc]simplify: iters left: 3 (37 enodes) 1546856170.142 * [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)))))) 1546856170.143 * [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))))) 1546856170.143 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1546856170.143 * * [misc]simplify: iters left: 6 (14 enodes) 1546856170.147 * * [misc]simplify: iters left: 5 (20 enodes) 1546856170.153 * * [misc]simplify: iters left: 4 (29 enodes) 1546856170.160 * * [misc]simplify: iters left: 3 (30 enodes) 1546856170.167 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1546856170.167 * [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))))) 1546856170.168 * * * * [misc]progress: [ 55 / 83 ] simplifiying candidate # 1546856170.168 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1) 1546856170.168 * * [misc]simplify: iters left: 6 (14 enodes) 1546856170.173 * * [misc]simplify: iters left: 5 (24 enodes) 1546856170.180 * * [misc]simplify: iters left: 4 (39 enodes) 1546856170.191 * * [misc]simplify: iters left: 3 (54 enodes) 1546856170.204 * * [misc]simplify: iters left: 2 (80 enodes) 1546856170.224 * [exit]simplify: Simplified to (* (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))) 1546856170.224 * [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)))) 1546856170.224 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt k)) 1546856170.225 * * [misc]simplify: iters left: 6 (13 enodes) 1546856170.229 * * [misc]simplify: iters left: 5 (19 enodes) 1546856170.234 * * [misc]simplify: iters left: 4 (28 enodes) 1546856170.240 * * [misc]simplify: iters left: 3 (30 enodes) 1546856170.244 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt k)) 1546856170.244 * [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)))) 1546856170.244 * * * * [misc]progress: [ 56 / 83 ] simplifiying candidate # 1546856170.244 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1546856170.245 * * [misc]simplify: iters left: 6 (15 enodes) 1546856170.247 * * [misc]simplify: iters left: 5 (23 enodes) 1546856170.251 * * [misc]simplify: iters left: 4 (32 enodes) 1546856170.256 * * [misc]simplify: iters left: 3 (34 enodes) 1546856170.260 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1546856170.260 * [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))))) 1546856170.260 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1546856170.260 * * [misc]simplify: iters left: 6 (14 enodes) 1546856170.262 * * [misc]simplify: iters left: 5 (20 enodes) 1546856170.265 * * [misc]simplify: iters left: 4 (29 enodes) 1546856170.269 * * [misc]simplify: iters left: 3 (30 enodes) 1546856170.273 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1546856170.273 * [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))))) 1546856170.273 * * * * [misc]progress: [ 57 / 83 ] simplifiying candidate # 1546856170.274 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1546856170.274 * * [misc]simplify: iters left: 6 (14 enodes) 1546856170.276 * * [misc]simplify: iters left: 5 (20 enodes) 1546856170.279 * * [misc]simplify: iters left: 4 (29 enodes) 1546856170.283 * * [misc]simplify: iters left: 3 (30 enodes) 1546856170.286 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1546856170.287 * [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))))) 1546856170.287 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1546856170.287 * * [misc]simplify: iters left: 6 (14 enodes) 1546856170.289 * * [misc]simplify: iters left: 5 (20 enodes) 1546856170.292 * * [misc]simplify: iters left: 4 (29 enodes) 1546856170.296 * * [misc]simplify: iters left: 3 (30 enodes) 1546856170.299 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1546856170.299 * [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))))) 1546856170.299 * * * * [misc]progress: [ 58 / 83 ] simplifiying candidate # 1546856170.300 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1) 1546856170.300 * * [misc]simplify: iters left: 6 (13 enodes) 1546856170.302 * * [misc]simplify: iters left: 5 (21 enodes) 1546856170.305 * * [misc]simplify: iters left: 4 (32 enodes) 1546856170.309 * * [misc]simplify: iters left: 3 (33 enodes) 1546856170.313 * [exit]simplify: Simplified to (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) 1546856170.313 * [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)))) 1546856170.313 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt k)) 1546856170.313 * * [misc]simplify: iters left: 6 (13 enodes) 1546856170.315 * * [misc]simplify: iters left: 5 (19 enodes) 1546856170.318 * * [misc]simplify: iters left: 4 (28 enodes) 1546856170.321 * * [misc]simplify: iters left: 3 (30 enodes) 1546856170.326 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt k)) 1546856170.326 * [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)))) 1546856170.326 * * * * [misc]progress: [ 59 / 83 ] simplifiying candidate # 1546856170.327 * [enter]simplify: Simplifying (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1546856170.327 * * [misc]simplify: iters left: 6 (6 enodes) 1546856170.328 * * [misc]simplify: iters left: 5 (10 enodes) 1546856170.329 * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) 1546856170.329 * [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))))) 1546856170.329 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1546856170.329 * * [misc]simplify: iters left: 6 (13 enodes) 1546856170.331 * * [misc]simplify: iters left: 5 (19 enodes) 1546856170.334 * * [misc]simplify: iters left: 4 (28 enodes) 1546856170.338 * * [misc]simplify: iters left: 3 (30 enodes) 1546856170.342 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1546856170.342 * [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))))) 1546856170.342 * * * * [misc]progress: [ 60 / 83 ] simplifiying candidate # 1546856170.342 * [enter]simplify: Simplifying (/ 1 (sqrt (sqrt k))) 1546856170.342 * * [misc]simplify: iters left: 4 (5 enodes) 1546856170.343 * * [misc]simplify: iters left: 3 (7 enodes) 1546856170.344 * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt k))) 1546856170.344 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) 1546856170.344 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1546856170.344 * * [misc]simplify: iters left: 6 (13 enodes) 1546856170.349 * * [misc]simplify: iters left: 5 (19 enodes) 1546856170.354 * * [misc]simplify: iters left: 4 (28 enodes) 1546856170.362 * * [misc]simplify: iters left: 3 (30 enodes) 1546856170.370 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1546856170.370 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) 1546856170.370 * * * * [misc]progress: [ 61 / 83 ] simplifiying candidate # 1546856170.370 * [enter]simplify: Simplifying (/ 1 1) 1546856170.370 * * [misc]simplify: iters left: 2 (2 enodes) 1546856170.371 * * [misc]simplify: iters left: 1 (4 enodes) 1546856170.371 * [exit]simplify: Simplified to 1 1546856170.371 * [misc]simplify: Simplified (2 1) to (λ (k n) (* 1 (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))) 1546856170.371 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)) 1546856170.372 * * [misc]simplify: iters left: 6 (12 enodes) 1546856170.373 * * [misc]simplify: iters left: 5 (18 enodes) 1546856170.376 * * [misc]simplify: iters left: 4 (27 enodes) 1546856170.379 * * [misc]simplify: iters left: 3 (29 enodes) 1546856170.383 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k)) 1546856170.383 * [misc]simplify: Simplified (2 2) to (λ (k n) (* 1 (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k)))) 1546856170.383 * * * * [misc]progress: [ 62 / 83 ] simplifiying candidate # 1546856170.383 * * * * [misc]progress: [ 63 / 83 ] simplifiying candidate # 1546856170.383 * * * * [misc]progress: [ 64 / 83 ] simplifiying candidate # 1546856170.383 * * * * [misc]progress: [ 65 / 83 ] simplifiying candidate # 1546856170.384 * [enter]simplify: Simplifying (cbrt (sqrt k)) 1546856170.384 * * [misc]simplify: iters left: 2 (3 enodes) 1546856170.384 * [exit]simplify: Simplified to (cbrt (sqrt k)) 1546856170.384 * [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)))) 1546856170.384 * * * * [misc]progress: [ 66 / 83 ] simplifiying candidate # 1546856170.384 * [enter]simplify: Simplifying (sqrt (sqrt k)) 1546856170.384 * * [misc]simplify: iters left: 2 (3 enodes) 1546856170.385 * [exit]simplify: Simplified to (sqrt (sqrt k)) 1546856170.385 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k)))) 1546856170.385 * * * * [misc]progress: [ 67 / 83 ] simplifiying candidate # 1546856170.385 * [enter]simplify: Simplifying (sqrt k) 1546856170.385 * * [misc]simplify: iters left: 1 (2 enodes) 1546856170.385 * [exit]simplify: Simplified to (sqrt k) 1546856170.385 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) 1) (sqrt k))) 1546856170.385 * * * * [misc]progress: [ 68 / 83 ] simplifiying candidate # 1546856170.385 * [enter]simplify: Simplifying (pow (* PI (* n 2)) 1/2) 1546856170.385 * * [misc]simplify: iters left: 5 (7 enodes) 1546856170.387 * * [misc]simplify: iters left: 4 (12 enodes) 1546856170.388 * * [misc]simplify: iters left: 3 (18 enodes) 1546856170.390 * * [misc]simplify: iters left: 2 (20 enodes) 1546856170.393 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1546856170.393 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2)))))) 1546856170.393 * * * * [misc]progress: [ 69 / 83 ] simplifiying candidate # 1546856170.393 * [enter]simplify: Simplifying (pow (* PI (* n 2)) 1/2) 1546856170.393 * * [misc]simplify: iters left: 5 (7 enodes) 1546856170.394 * * [misc]simplify: iters left: 4 (12 enodes) 1546856170.396 * * [misc]simplify: iters left: 3 (18 enodes) 1546856170.398 * * [misc]simplify: iters left: 2 (20 enodes) 1546856170.401 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1546856170.401 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2)))))) 1546856170.401 * * * * [misc]progress: [ 70 / 83 ] simplifiying candidate # 1546856170.402 * [enter]simplify: Simplifying (pow PI (- 1/2 (/ k 2))) 1546856170.402 * * [misc]simplify: iters left: 5 (7 enodes) 1546856170.404 * * [misc]simplify: iters left: 4 (9 enodes) 1546856170.406 * * [misc]simplify: iters left: 3 (12 enodes) 1546856170.410 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1546856170.410 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (pow PI (- 1/2 (/ k 2))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2)))))) 1546856170.410 * * * * [misc]progress: [ 71 / 83 ] simplifiying candidate # 1546856170.410 * [enter]simplify: Simplifying (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546856170.410 * * [misc]simplify: iters left: 6 (12 enodes) 1546856170.414 * * [misc]simplify: iters left: 5 (18 enodes) 1546856170.419 * * [misc]simplify: iters left: 4 (27 enodes) 1546856170.427 * * [misc]simplify: iters left: 3 (29 enodes) 1546856170.435 * [exit]simplify: Simplified to (* (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) 1546856170.436 * [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))))))) 1546856170.436 * * * * [misc]progress: [ 72 / 83 ] simplifiying candidate # 1546856170.436 * [enter]simplify: Simplifying (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1546856170.436 * * [misc]simplify: iters left: 6 (11 enodes) 1546856170.440 * * [misc]simplify: iters left: 5 (17 enodes) 1546856170.445 * * [misc]simplify: iters left: 4 (26 enodes) 1546856170.452 * * [misc]simplify: iters left: 3 (27 enodes) 1546856170.459 * [exit]simplify: Simplified to (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) 1546856170.459 * [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))))))) 1546856170.459 * * * * [misc]progress: [ 73 / 83 ] simplifiying candidate # 1546856170.459 * * * * [misc]progress: [ 74 / 83 ] simplifiying candidate # 1546856170.459 * [enter]simplify: Simplifying (pow (* PI (* n 2)) 1/2) 1546856170.459 * * [misc]simplify: iters left: 5 (7 enodes) 1546856170.461 * * [misc]simplify: iters left: 4 (12 enodes) 1546856170.465 * * [misc]simplify: iters left: 3 (18 enodes) 1546856170.470 * * [misc]simplify: iters left: 2 (20 enodes) 1546856170.474 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1546856170.474 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2))))) 1546856170.475 * * * * [misc]progress: [ 75 / 83 ] simplifiying candidate # 1546856170.475 * [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))))) 1546856170.475 * * [misc]simplify: iters left: 6 (37 enodes) 1546856170.484 * * [misc]simplify: iters left: 5 (108 enodes) 1546856170.506 * * [misc]simplify: iters left: 4 (368 enodes) 1546856170.753 * [exit]simplify: Simplified to (fma -1/2 (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) (fma (* (* (* k k) (log n)) (* (log (* PI 2)) 1/4)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (fma (* (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (log (* PI 2)) (log (* PI 2)))) (* (* k k) 1/8) (fma (* (* (* k k) (log n)) (* (log n) 1/8)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (pow n 1/2) (pow (* PI 2) 1/2)))))) 1546856170.753 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (fma -1/2 (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) (fma (* (* (* k k) (log n)) (* (log (* PI 2)) 1/4)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (fma (* (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (log (* PI 2)) (log (* PI 2)))) (* (* k k) 1/8) (fma (* (* (* k k) (log n)) (* (log n) 1/8)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (pow n 1/2) (pow (* PI 2) 1/2)))))) (sqrt k))) 1546856170.753 * * * * [misc]progress: [ 76 / 83 ] simplifiying candidate # 1546856170.753 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 1546856170.754 * * [misc]simplify: iters left: 6 (15 enodes) 1546856170.757 * * [misc]simplify: iters left: 5 (33 enodes) 1546856170.762 * * [misc]simplify: iters left: 4 (64 enodes) 1546856170.786 * * [misc]simplify: iters left: 3 (179 enodes) 1546856170.871 * [exit]simplify: Simplified to (* (pow (* 2 PI) (fma -1/2 k 1/2)) (pow n (fma -1/2 k 1/2))) 1546856170.871 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (* (pow (* 2 PI) (fma -1/2 k 1/2)) (pow n (fma -1/2 k 1/2))) (sqrt k))) 1546856170.871 * * * * [misc]progress: [ 77 / 83 ] simplifiying candidate # 1546856170.871 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 1546856170.871 * * [misc]simplify: iters left: 6 (15 enodes) 1546856170.874 * * [misc]simplify: iters left: 5 (30 enodes) 1546856170.879 * * [misc]simplify: iters left: 4 (65 enodes) 1546856170.893 * * [misc]simplify: iters left: 3 (208 enodes) 1546856171.013 * [exit]simplify: Simplified to (pow (exp (fma -1/2 k 1/2)) (- (log (* -2 PI)) (log (/ -1 n)))) 1546856171.013 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (pow (exp (fma -1/2 k 1/2)) (- (log (* -2 PI)) (log (/ -1 n)))) (sqrt k))) 1546856171.013 * * * * [misc]progress: [ 78 / 83 ] simplifiying candidate # 1546856171.013 * [enter]simplify: Simplifying (* 2 (* n PI)) 1546856171.013 * * [misc]simplify: iters left: 4 (5 enodes) 1546856171.014 * * [misc]simplify: iters left: 3 (9 enodes) 1546856171.016 * * [misc]simplify: iters left: 2 (15 enodes) 1546856171.020 * * [misc]simplify: iters left: 1 (17 enodes) 1546856171.024 * [exit]simplify: Simplified to (* (* PI n) 2) 1546856171.024 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt k))) 1546856171.024 * * * * [misc]progress: [ 79 / 83 ] simplifiying candidate # 1546856171.024 * [enter]simplify: Simplifying (* 2 (* n PI)) 1546856171.024 * * [misc]simplify: iters left: 4 (5 enodes) 1546856171.026 * * [misc]simplify: iters left: 3 (9 enodes) 1546856171.029 * * [misc]simplify: iters left: 2 (15 enodes) 1546856171.032 * * [misc]simplify: iters left: 1 (17 enodes) 1546856171.034 * [exit]simplify: Simplified to (* (* PI n) 2) 1546856171.034 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt k))) 1546856171.034 * * * * [misc]progress: [ 80 / 83 ] simplifiying candidate # 1546856171.034 * [enter]simplify: Simplifying (* 2 (* n PI)) 1546856171.034 * * [misc]simplify: iters left: 4 (5 enodes) 1546856171.035 * * [misc]simplify: iters left: 3 (9 enodes) 1546856171.036 * * [misc]simplify: iters left: 2 (15 enodes) 1546856171.038 * * [misc]simplify: iters left: 1 (17 enodes) 1546856171.040 * [exit]simplify: Simplified to (* (* PI n) 2) 1546856171.040 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt k))) 1546856171.040 * * * * [misc]progress: [ 81 / 83 ] simplifiying candidate # 1546856171.041 * [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)))))))))))))))))))))) 1546856171.041 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1546856171.041 * * * * [misc]progress: [ 82 / 83 ] simplifiying candidate # 1546856171.041 * [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)))))))) 1546856171.041 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1546856171.041 * * * * [misc]progress: [ 83 / 83 ] simplifiying candidate # 1546856171.041 * [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))))))))))) 1546856171.041 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1546856171.041 * * * [misc]progress: adding candidates to table 1546856172.046 * * [misc]progress: iteration 2 / 4 1546856172.046 * * * [misc]progress: picking best candidate 1546856172.078 * * * * [misc]pick: Picked # 1546856172.078 * * * [misc]progress: localizing error 1546856172.086 * * * [misc]progress: generating rewritten candidates 1546856172.086 * * * * [misc]progress: [ 1 / 4 ] rewriting at (2 2 2) 1546856172.088 * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 2 2 1) 1546856172.090 * * * * [misc]progress: [ 3 / 4 ] rewriting at (2 2) 1546856172.099 * * * * [misc]progress: [ 4 / 4 ] rewriting at (2) 1546856172.106 * * * [misc]progress: generating series expansions 1546856172.106 * * * * [misc]progress: [ 1 / 4 ] generating series at (2 2 2) 1546856172.106 * [misc]backup-simplify: Simplify (pow (* PI (* n 2)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 1546856172.106 * [misc]approximate: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 1546856172.107 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1546856172.107 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1546856172.107 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1546856172.107 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546856172.107 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856172.107 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.107 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546856172.107 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856172.107 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.107 * [misc]taylor: Taking taylor expansion of k in k 1546856172.107 * [misc]backup-simplify: Simplify 0 into 0 1546856172.107 * [misc]backup-simplify: Simplify 1 into 1 1546856172.107 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1546856172.107 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1546856172.107 * [misc]taylor: Taking taylor expansion of 2 in k 1546856172.107 * [misc]backup-simplify: Simplify 2 into 2 1546856172.107 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1546856172.107 * [misc]taylor: Taking taylor expansion of n in k 1546856172.107 * [misc]backup-simplify: Simplify n into n 1546856172.107 * [misc]taylor: Taking taylor expansion of PI in k 1546856172.107 * [misc]backup-simplify: Simplify PI into PI 1546856172.107 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1546856172.107 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1546856172.107 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1546856172.108 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546856172.108 * [misc]backup-simplify: Simplify (- 0) into 0 1546856172.108 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546856172.108 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1546856172.108 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1546856172.108 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546856172.109 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546856172.109 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546856172.109 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546856172.109 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856172.109 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.109 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546856172.109 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856172.109 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.109 * [misc]taylor: Taking taylor expansion of k in n 1546856172.109 * [misc]backup-simplify: Simplify k into k 1546856172.109 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546856172.109 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546856172.109 * [misc]taylor: Taking taylor expansion of 2 in n 1546856172.109 * [misc]backup-simplify: Simplify 2 into 2 1546856172.109 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546856172.109 * [misc]taylor: Taking taylor expansion of n in n 1546856172.109 * [misc]backup-simplify: Simplify 0 into 0 1546856172.109 * [misc]backup-simplify: Simplify 1 into 1 1546856172.109 * [misc]taylor: Taking taylor expansion of PI in n 1546856172.109 * [misc]backup-simplify: Simplify PI into PI 1546856172.110 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546856172.110 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546856172.110 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546856172.111 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546856172.112 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856172.112 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546856172.112 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546856172.112 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546856172.112 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546856172.113 * [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)))) 1546856172.114 * [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))))) 1546856172.114 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546856172.114 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546856172.114 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546856172.114 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546856172.114 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856172.114 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.114 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546856172.114 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856172.114 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.114 * [misc]taylor: Taking taylor expansion of k in n 1546856172.114 * [misc]backup-simplify: Simplify k into k 1546856172.115 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546856172.115 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546856172.115 * [misc]taylor: Taking taylor expansion of 2 in n 1546856172.115 * [misc]backup-simplify: Simplify 2 into 2 1546856172.115 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546856172.115 * [misc]taylor: Taking taylor expansion of n in n 1546856172.115 * [misc]backup-simplify: Simplify 0 into 0 1546856172.115 * [misc]backup-simplify: Simplify 1 into 1 1546856172.115 * [misc]taylor: Taking taylor expansion of PI in n 1546856172.115 * [misc]backup-simplify: Simplify PI into PI 1546856172.115 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546856172.115 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546856172.116 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546856172.116 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546856172.117 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856172.117 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546856172.117 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546856172.117 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546856172.118 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546856172.118 * [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)))) 1546856172.119 * [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))))) 1546856172.119 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1546856172.119 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1546856172.119 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546856172.119 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856172.119 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.119 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546856172.119 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856172.119 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.119 * [misc]taylor: Taking taylor expansion of k in k 1546856172.120 * [misc]backup-simplify: Simplify 0 into 0 1546856172.120 * [misc]backup-simplify: Simplify 1 into 1 1546856172.120 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1546856172.120 * [misc]taylor: Taking taylor expansion of (log n) in k 1546856172.120 * [misc]taylor: Taking taylor expansion of n in k 1546856172.120 * [misc]backup-simplify: Simplify n into n 1546856172.120 * [misc]backup-simplify: Simplify (log n) into (log n) 1546856172.120 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1546856172.120 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1546856172.120 * [misc]taylor: Taking taylor expansion of 2 in k 1546856172.120 * [misc]backup-simplify: Simplify 2 into 2 1546856172.120 * [misc]taylor: Taking taylor expansion of PI in k 1546856172.120 * [misc]backup-simplify: Simplify PI into PI 1546856172.120 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546856172.121 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856172.121 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546856172.121 * [misc]backup-simplify: Simplify (- 0) into 0 1546856172.121 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546856172.122 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546856172.122 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1546856172.123 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1546856172.123 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1546856172.124 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546856172.125 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1546856172.128 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546856172.128 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1546856172.129 * [misc]backup-simplify: Simplify (- 0) into 0 1546856172.129 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856172.129 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546856172.130 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1546856172.132 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1546856172.132 * [misc]taylor: Taking taylor expansion of 0 in k 1546856172.132 * [misc]backup-simplify: Simplify 0 into 0 1546856172.132 * [misc]backup-simplify: Simplify 0 into 0 1546856172.133 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1546856172.133 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546856172.136 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546856172.136 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856172.136 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1546856172.137 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546856172.137 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546856172.138 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1546856172.139 * [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))))))) 1546856172.140 * [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))))))) 1546856172.142 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1546856172.144 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1546856172.146 * [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 1546856172.147 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1546856172.147 * [misc]backup-simplify: Simplify (- 0) into 0 1546856172.147 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856172.147 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546856172.148 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1546856172.149 * [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 1546856172.149 * [misc]taylor: Taking taylor expansion of 0 in k 1546856172.149 * [misc]backup-simplify: Simplify 0 into 0 1546856172.149 * [misc]backup-simplify: Simplify 0 into 0 1546856172.149 * [misc]backup-simplify: Simplify 0 into 0 1546856172.150 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1546856172.151 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546856172.154 * [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 1546856172.154 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856172.154 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1546856172.154 * [misc]backup-simplify: Simplify (- 0) into 0 1546856172.154 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856172.155 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1546856172.156 * [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))))) 1546856172.158 * [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))))) 1546856172.161 * [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))))) 1546856172.161 * [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)))) 1546856172.161 * [misc]approximate: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 1546856172.161 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1546856172.161 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1546856172.161 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1546856172.161 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546856172.161 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856172.161 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.161 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546856172.161 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856172.161 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.161 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546856172.161 * [misc]taylor: Taking taylor expansion of k in k 1546856172.161 * [misc]backup-simplify: Simplify 0 into 0 1546856172.161 * [misc]backup-simplify: Simplify 1 into 1 1546856172.161 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546856172.161 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1546856172.161 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1546856172.161 * [misc]taylor: Taking taylor expansion of 2 in k 1546856172.161 * [misc]backup-simplify: Simplify 2 into 2 1546856172.161 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546856172.161 * [misc]taylor: Taking taylor expansion of PI in k 1546856172.161 * [misc]backup-simplify: Simplify PI into PI 1546856172.161 * [misc]taylor: Taking taylor expansion of n in k 1546856172.161 * [misc]backup-simplify: Simplify n into n 1546856172.161 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546856172.161 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1546856172.162 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1546856172.162 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546856172.162 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546856172.162 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546856172.162 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1546856172.162 * [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)))) 1546856172.162 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546856172.162 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546856172.162 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546856172.162 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546856172.162 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856172.162 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.162 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546856172.162 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856172.162 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.162 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546856172.162 * [misc]taylor: Taking taylor expansion of k in n 1546856172.162 * [misc]backup-simplify: Simplify k into k 1546856172.162 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546856172.162 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546856172.162 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546856172.162 * [misc]taylor: Taking taylor expansion of 2 in n 1546856172.162 * [misc]backup-simplify: Simplify 2 into 2 1546856172.162 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856172.162 * [misc]taylor: Taking taylor expansion of PI in n 1546856172.162 * [misc]backup-simplify: Simplify PI into PI 1546856172.162 * [misc]taylor: Taking taylor expansion of n in n 1546856172.162 * [misc]backup-simplify: Simplify 0 into 0 1546856172.162 * [misc]backup-simplify: Simplify 1 into 1 1546856172.163 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856172.163 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546856172.163 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856172.163 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546856172.163 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546856172.163 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546856172.164 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546856172.164 * [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))) 1546856172.164 * [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)))) 1546856172.165 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546856172.165 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546856172.165 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546856172.165 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546856172.165 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856172.165 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.165 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546856172.165 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856172.165 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.165 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546856172.165 * [misc]taylor: Taking taylor expansion of k in n 1546856172.165 * [misc]backup-simplify: Simplify k into k 1546856172.165 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546856172.165 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546856172.165 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546856172.165 * [misc]taylor: Taking taylor expansion of 2 in n 1546856172.165 * [misc]backup-simplify: Simplify 2 into 2 1546856172.165 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856172.165 * [misc]taylor: Taking taylor expansion of PI in n 1546856172.165 * [misc]backup-simplify: Simplify PI into PI 1546856172.165 * [misc]taylor: Taking taylor expansion of n in n 1546856172.165 * [misc]backup-simplify: Simplify 0 into 0 1546856172.165 * [misc]backup-simplify: Simplify 1 into 1 1546856172.165 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856172.165 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546856172.165 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856172.166 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546856172.166 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546856172.166 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546856172.166 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546856172.166 * [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))) 1546856172.167 * [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)))) 1546856172.167 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1546856172.167 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1546856172.167 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546856172.167 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856172.167 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.167 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546856172.167 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856172.167 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.167 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546856172.167 * [misc]taylor: Taking taylor expansion of k in k 1546856172.167 * [misc]backup-simplify: Simplify 0 into 0 1546856172.167 * [misc]backup-simplify: Simplify 1 into 1 1546856172.167 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546856172.167 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1546856172.167 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1546856172.167 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1546856172.167 * [misc]taylor: Taking taylor expansion of 2 in k 1546856172.167 * [misc]backup-simplify: Simplify 2 into 2 1546856172.167 * [misc]taylor: Taking taylor expansion of PI in k 1546856172.167 * [misc]backup-simplify: Simplify PI into PI 1546856172.168 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546856172.168 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856172.168 * [misc]taylor: Taking taylor expansion of (log n) in k 1546856172.168 * [misc]taylor: Taking taylor expansion of n in k 1546856172.168 * [misc]backup-simplify: Simplify n into n 1546856172.168 * [misc]backup-simplify: Simplify (log n) into (log n) 1546856172.168 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546856172.168 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546856172.168 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546856172.168 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1546856172.169 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1546856172.169 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1546856172.170 * [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)))) 1546856172.170 * [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)))) 1546856172.171 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546856172.171 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546856172.173 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546856172.173 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546856172.173 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546856172.173 * [misc]backup-simplify: Simplify (- 0) into 0 1546856172.173 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856172.173 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546856172.174 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1546856172.175 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546856172.175 * [misc]taylor: Taking taylor expansion of 0 in k 1546856172.175 * [misc]backup-simplify: Simplify 0 into 0 1546856172.175 * [misc]backup-simplify: Simplify 0 into 0 1546856172.175 * [misc]backup-simplify: Simplify 0 into 0 1546856172.176 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856172.176 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546856172.179 * [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 1546856172.179 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546856172.180 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1546856172.180 * [misc]backup-simplify: Simplify (- 0) into 0 1546856172.180 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856172.180 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546856172.181 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1546856172.182 * [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 1546856172.182 * [misc]taylor: Taking taylor expansion of 0 in k 1546856172.182 * [misc]backup-simplify: Simplify 0 into 0 1546856172.182 * [misc]backup-simplify: Simplify 0 into 0 1546856172.182 * [misc]backup-simplify: Simplify 0 into 0 1546856172.182 * [misc]backup-simplify: Simplify 0 into 0 1546856172.183 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856172.184 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546856172.190 * [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 1546856172.191 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546856172.191 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1546856172.191 * [misc]backup-simplify: Simplify (- 0) into 0 1546856172.191 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856172.192 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546856172.193 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1546856172.197 * [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 1546856172.197 * [misc]taylor: Taking taylor expansion of 0 in k 1546856172.197 * [misc]backup-simplify: Simplify 0 into 0 1546856172.197 * [misc]backup-simplify: Simplify 0 into 0 1546856172.198 * [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))))) 1546856172.198 * [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)) 1546856172.198 * [misc]approximate: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 1546856172.198 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1546856172.198 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1546856172.198 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1546856172.198 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546856172.198 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546856172.198 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856172.198 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.198 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546856172.198 * [misc]taylor: Taking taylor expansion of k in k 1546856172.198 * [misc]backup-simplify: Simplify 0 into 0 1546856172.198 * [misc]backup-simplify: Simplify 1 into 1 1546856172.198 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546856172.199 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856172.199 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.199 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1546856172.199 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1546856172.199 * [misc]taylor: Taking taylor expansion of -2 in k 1546856172.199 * [misc]backup-simplify: Simplify -2 into -2 1546856172.199 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546856172.199 * [misc]taylor: Taking taylor expansion of PI in k 1546856172.199 * [misc]backup-simplify: Simplify PI into PI 1546856172.199 * [misc]taylor: Taking taylor expansion of n in k 1546856172.199 * [misc]backup-simplify: Simplify n into n 1546856172.199 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546856172.199 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1546856172.199 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1546856172.199 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546856172.199 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546856172.200 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1546856172.200 * [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))) 1546856172.200 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546856172.200 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546856172.200 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546856172.200 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546856172.200 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546856172.200 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856172.200 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.200 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546856172.200 * [misc]taylor: Taking taylor expansion of k in n 1546856172.200 * [misc]backup-simplify: Simplify k into k 1546856172.200 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546856172.200 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856172.200 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.200 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546856172.200 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546856172.200 * [misc]taylor: Taking taylor expansion of -2 in n 1546856172.200 * [misc]backup-simplify: Simplify -2 into -2 1546856172.200 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856172.200 * [misc]taylor: Taking taylor expansion of PI in n 1546856172.200 * [misc]backup-simplify: Simplify PI into PI 1546856172.200 * [misc]taylor: Taking taylor expansion of n in n 1546856172.200 * [misc]backup-simplify: Simplify 0 into 0 1546856172.200 * [misc]backup-simplify: Simplify 1 into 1 1546856172.201 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856172.201 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546856172.202 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546856172.202 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546856172.202 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546856172.202 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546856172.203 * [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))) 1546856172.206 * [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)))) 1546856172.206 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546856172.206 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546856172.206 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546856172.206 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546856172.206 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546856172.206 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856172.206 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.206 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546856172.207 * [misc]taylor: Taking taylor expansion of k in n 1546856172.207 * [misc]backup-simplify: Simplify k into k 1546856172.207 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546856172.207 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856172.207 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.207 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546856172.207 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546856172.207 * [misc]taylor: Taking taylor expansion of -2 in n 1546856172.207 * [misc]backup-simplify: Simplify -2 into -2 1546856172.207 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856172.207 * [misc]taylor: Taking taylor expansion of PI in n 1546856172.207 * [misc]backup-simplify: Simplify PI into PI 1546856172.207 * [misc]taylor: Taking taylor expansion of n in n 1546856172.207 * [misc]backup-simplify: Simplify 0 into 0 1546856172.207 * [misc]backup-simplify: Simplify 1 into 1 1546856172.207 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856172.208 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546856172.208 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546856172.208 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546856172.208 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546856172.209 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546856172.210 * [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))) 1546856172.210 * [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)))) 1546856172.210 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1546856172.210 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1546856172.210 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546856172.210 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546856172.210 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856172.211 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.211 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546856172.211 * [misc]taylor: Taking taylor expansion of k in k 1546856172.211 * [misc]backup-simplify: Simplify 0 into 0 1546856172.211 * [misc]backup-simplify: Simplify 1 into 1 1546856172.211 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546856172.211 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856172.211 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.211 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1546856172.211 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1546856172.211 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1546856172.211 * [misc]taylor: Taking taylor expansion of -2 in k 1546856172.211 * [misc]backup-simplify: Simplify -2 into -2 1546856172.211 * [misc]taylor: Taking taylor expansion of PI in k 1546856172.211 * [misc]backup-simplify: Simplify PI into PI 1546856172.211 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546856172.212 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546856172.212 * [misc]taylor: Taking taylor expansion of (log n) in k 1546856172.212 * [misc]taylor: Taking taylor expansion of n in k 1546856172.212 * [misc]backup-simplify: Simplify n into n 1546856172.212 * [misc]backup-simplify: Simplify (log n) into (log n) 1546856172.212 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546856172.212 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546856172.212 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1546856172.213 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1546856172.214 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1546856172.214 * [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)))) 1546856172.215 * [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)))) 1546856172.216 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546856172.217 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1546856172.220 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1546856172.220 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546856172.220 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546856172.220 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856172.221 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546856172.222 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1546856172.223 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546856172.223 * [misc]taylor: Taking taylor expansion of 0 in k 1546856172.223 * [misc]backup-simplify: Simplify 0 into 0 1546856172.224 * [misc]backup-simplify: Simplify 0 into 0 1546856172.224 * [misc]backup-simplify: Simplify 0 into 0 1546856172.225 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856172.226 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1546856172.232 * [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 1546856172.232 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546856172.232 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1546856172.232 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856172.233 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546856172.234 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1546856172.236 * [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 1546856172.236 * [misc]taylor: Taking taylor expansion of 0 in k 1546856172.237 * [misc]backup-simplify: Simplify 0 into 0 1546856172.237 * [misc]backup-simplify: Simplify 0 into 0 1546856172.237 * [misc]backup-simplify: Simplify 0 into 0 1546856172.237 * [misc]backup-simplify: Simplify 0 into 0 1546856172.239 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856172.240 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546856172.249 * [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 1546856172.249 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546856172.250 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1546856172.250 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856172.250 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546856172.251 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 1546856172.255 * [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 1546856172.255 * [misc]taylor: Taking taylor expansion of 0 in k 1546856172.255 * [misc]backup-simplify: Simplify 0 into 0 1546856172.255 * [misc]backup-simplify: Simplify 0 into 0 1546856172.256 * [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))))) 1546856172.256 * * * * [misc]progress: [ 2 / 4 ] generating series at (2 2 2 1) 1546856172.256 * [misc]backup-simplify: Simplify (* PI (* n 2)) into (* 2 (* n PI)) 1546856172.256 * [misc]approximate: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1546856172.256 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546856172.257 * [misc]taylor: Taking taylor expansion of 2 in n 1546856172.257 * [misc]backup-simplify: Simplify 2 into 2 1546856172.257 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546856172.257 * [misc]taylor: Taking taylor expansion of n in n 1546856172.257 * [misc]backup-simplify: Simplify 0 into 0 1546856172.257 * [misc]backup-simplify: Simplify 1 into 1 1546856172.257 * [misc]taylor: Taking taylor expansion of PI in n 1546856172.257 * [misc]backup-simplify: Simplify PI into PI 1546856172.257 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546856172.257 * [misc]taylor: Taking taylor expansion of 2 in n 1546856172.257 * [misc]backup-simplify: Simplify 2 into 2 1546856172.257 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546856172.257 * [misc]taylor: Taking taylor expansion of n in n 1546856172.257 * [misc]backup-simplify: Simplify 0 into 0 1546856172.257 * [misc]backup-simplify: Simplify 1 into 1 1546856172.257 * [misc]taylor: Taking taylor expansion of PI in n 1546856172.257 * [misc]backup-simplify: Simplify PI into PI 1546856172.257 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546856172.258 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546856172.258 * [misc]backup-simplify: Simplify 0 into 0 1546856172.258 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546856172.259 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546856172.259 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546856172.260 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546856172.261 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1546856172.261 * [misc]backup-simplify: Simplify 0 into 0 1546856172.263 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1546856172.265 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1546856172.265 * [misc]backup-simplify: Simplify 0 into 0 1546856172.267 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1546856172.269 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1546856172.269 * [misc]backup-simplify: Simplify 0 into 0 1546856172.272 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1546856172.275 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1546856172.275 * [misc]backup-simplify: Simplify 0 into 0 1546856172.279 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1546856172.283 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1546856172.283 * [misc]backup-simplify: Simplify 0 into 0 1546856172.287 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1546856172.291 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1546856172.291 * [misc]backup-simplify: Simplify 0 into 0 1546856172.292 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1546856172.292 * [misc]backup-simplify: Simplify (* PI (* (/ 1 n) 2)) into (* 2 (/ PI n)) 1546856172.292 * [misc]approximate: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1546856172.292 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546856172.292 * [misc]taylor: Taking taylor expansion of 2 in n 1546856172.292 * [misc]backup-simplify: Simplify 2 into 2 1546856172.292 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856172.292 * [misc]taylor: Taking taylor expansion of PI in n 1546856172.292 * [misc]backup-simplify: Simplify PI into PI 1546856172.292 * [misc]taylor: Taking taylor expansion of n in n 1546856172.292 * [misc]backup-simplify: Simplify 0 into 0 1546856172.292 * [misc]backup-simplify: Simplify 1 into 1 1546856172.292 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856172.292 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546856172.292 * [misc]taylor: Taking taylor expansion of 2 in n 1546856172.292 * [misc]backup-simplify: Simplify 2 into 2 1546856172.292 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856172.292 * [misc]taylor: Taking taylor expansion of PI in n 1546856172.293 * [misc]backup-simplify: Simplify PI into PI 1546856172.293 * [misc]taylor: Taking taylor expansion of n in n 1546856172.293 * [misc]backup-simplify: Simplify 0 into 0 1546856172.293 * [misc]backup-simplify: Simplify 1 into 1 1546856172.293 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856172.293 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546856172.293 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546856172.295 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546856172.295 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546856172.295 * [misc]backup-simplify: Simplify 0 into 0 1546856172.297 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856172.298 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546856172.298 * [misc]backup-simplify: Simplify 0 into 0 1546856172.299 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856172.301 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546856172.301 * [misc]backup-simplify: Simplify 0 into 0 1546856172.303 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856172.305 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1546856172.305 * [misc]backup-simplify: Simplify 0 into 0 1546856172.307 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856172.310 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1546856172.310 * [misc]backup-simplify: Simplify 0 into 0 1546856172.313 * [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 1546856172.316 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1546856172.316 * [misc]backup-simplify: Simplify 0 into 0 1546856172.317 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 1546856172.317 * [misc]backup-simplify: Simplify (* PI (* (/ 1 (- n)) 2)) into (* -2 (/ PI n)) 1546856172.317 * [misc]approximate: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1546856172.317 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546856172.317 * [misc]taylor: Taking taylor expansion of -2 in n 1546856172.317 * [misc]backup-simplify: Simplify -2 into -2 1546856172.317 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856172.317 * [misc]taylor: Taking taylor expansion of PI in n 1546856172.317 * [misc]backup-simplify: Simplify PI into PI 1546856172.317 * [misc]taylor: Taking taylor expansion of n in n 1546856172.317 * [misc]backup-simplify: Simplify 0 into 0 1546856172.317 * [misc]backup-simplify: Simplify 1 into 1 1546856172.318 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856172.318 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546856172.318 * [misc]taylor: Taking taylor expansion of -2 in n 1546856172.318 * [misc]backup-simplify: Simplify -2 into -2 1546856172.318 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856172.318 * [misc]taylor: Taking taylor expansion of PI in n 1546856172.318 * [misc]backup-simplify: Simplify PI into PI 1546856172.318 * [misc]taylor: Taking taylor expansion of n in n 1546856172.318 * [misc]backup-simplify: Simplify 0 into 0 1546856172.318 * [misc]backup-simplify: Simplify 1 into 1 1546856172.318 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856172.318 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546856172.319 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546856172.320 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546856172.321 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1546856172.321 * [misc]backup-simplify: Simplify 0 into 0 1546856172.322 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856172.323 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1546856172.323 * [misc]backup-simplify: Simplify 0 into 0 1546856172.325 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856172.327 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546856172.327 * [misc]backup-simplify: Simplify 0 into 0 1546856172.329 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856172.332 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1546856172.332 * [misc]backup-simplify: Simplify 0 into 0 1546856172.334 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856172.336 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1546856172.336 * [misc]backup-simplify: Simplify 0 into 0 1546856172.339 * [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 1546856172.342 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1546856172.342 * [misc]backup-simplify: Simplify 0 into 0 1546856172.343 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 1546856172.343 * * * * [misc]progress: [ 3 / 4 ] generating series at (2 2) 1546856172.343 * [misc]backup-simplify: Simplify (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) into (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) 1546856172.343 * [misc]approximate: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in (k n) around 0 1546856172.343 * [misc]taylor: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in n 1546856172.343 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 1546856172.343 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546856172.343 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546856172.343 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546856172.343 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546856172.343 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856172.343 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.343 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546856172.343 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856172.343 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.343 * [misc]taylor: Taking taylor expansion of k in n 1546856172.343 * [misc]backup-simplify: Simplify k into k 1546856172.343 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546856172.343 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546856172.343 * [misc]taylor: Taking taylor expansion of 2 in n 1546856172.344 * [misc]backup-simplify: Simplify 2 into 2 1546856172.344 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546856172.344 * [misc]taylor: Taking taylor expansion of n in n 1546856172.344 * [misc]backup-simplify: Simplify 0 into 0 1546856172.344 * [misc]backup-simplify: Simplify 1 into 1 1546856172.344 * [misc]taylor: Taking taylor expansion of PI in n 1546856172.344 * [misc]backup-simplify: Simplify PI into PI 1546856172.344 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546856172.344 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546856172.345 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546856172.346 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546856172.346 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856172.346 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546856172.346 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546856172.346 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546856172.347 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546856172.347 * [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)))) 1546856172.348 * [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))))) 1546856172.349 * [misc]backup-simplify: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (/ 1 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) 1546856172.349 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1546856172.349 * [misc]taylor: Taking taylor expansion of k in n 1546856172.349 * [misc]backup-simplify: Simplify k into k 1546856172.349 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1546856172.349 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1546856172.349 * [misc]taylor: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in k 1546856172.349 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 1546856172.349 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1546856172.349 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1546856172.349 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1546856172.349 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546856172.349 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856172.349 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.349 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546856172.349 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856172.349 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.349 * [misc]taylor: Taking taylor expansion of k in k 1546856172.349 * [misc]backup-simplify: Simplify 0 into 0 1546856172.349 * [misc]backup-simplify: Simplify 1 into 1 1546856172.349 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1546856172.349 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1546856172.349 * [misc]taylor: Taking taylor expansion of 2 in k 1546856172.350 * [misc]backup-simplify: Simplify 2 into 2 1546856172.350 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1546856172.350 * [misc]taylor: Taking taylor expansion of n in k 1546856172.350 * [misc]backup-simplify: Simplify n into n 1546856172.350 * [misc]taylor: Taking taylor expansion of PI in k 1546856172.350 * [misc]backup-simplify: Simplify PI into PI 1546856172.350 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1546856172.350 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1546856172.350 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1546856172.350 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546856172.350 * [misc]backup-simplify: Simplify (- 0) into 0 1546856172.350 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546856172.350 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1546856172.351 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1546856172.351 * [misc]backup-simplify: Simplify (/ 1 (pow (* 2 (* n PI)) 1/2)) into (sqrt (/ 1 (* PI (* n 2)))) 1546856172.351 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1546856172.351 * [misc]taylor: Taking taylor expansion of k in k 1546856172.351 * [misc]backup-simplify: Simplify 0 into 0 1546856172.351 * [misc]backup-simplify: Simplify 1 into 1 1546856172.351 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546856172.352 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546856172.352 * [misc]taylor: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in k 1546856172.352 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 1546856172.352 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1546856172.352 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1546856172.352 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1546856172.352 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546856172.352 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856172.352 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.352 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546856172.352 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856172.352 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.352 * [misc]taylor: Taking taylor expansion of k in k 1546856172.352 * [misc]backup-simplify: Simplify 0 into 0 1546856172.352 * [misc]backup-simplify: Simplify 1 into 1 1546856172.352 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1546856172.352 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1546856172.352 * [misc]taylor: Taking taylor expansion of 2 in k 1546856172.352 * [misc]backup-simplify: Simplify 2 into 2 1546856172.352 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1546856172.352 * [misc]taylor: Taking taylor expansion of n in k 1546856172.352 * [misc]backup-simplify: Simplify n into n 1546856172.352 * [misc]taylor: Taking taylor expansion of PI in k 1546856172.352 * [misc]backup-simplify: Simplify PI into PI 1546856172.352 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1546856172.352 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1546856172.352 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1546856172.353 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546856172.353 * [misc]backup-simplify: Simplify (- 0) into 0 1546856172.353 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546856172.353 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1546856172.353 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1546856172.353 * [misc]backup-simplify: Simplify (/ 1 (pow (* 2 (* n PI)) 1/2)) into (sqrt (/ 1 (* PI (* n 2)))) 1546856172.353 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1546856172.353 * [misc]taylor: Taking taylor expansion of k in k 1546856172.353 * [misc]backup-simplify: Simplify 0 into 0 1546856172.353 * [misc]backup-simplify: Simplify 1 into 1 1546856172.354 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546856172.354 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546856172.354 * [misc]backup-simplify: Simplify (* (sqrt (/ 1 (* PI (* n 2)))) 0) into 0 1546856172.354 * [misc]taylor: Taking taylor expansion of 0 in n 1546856172.354 * [misc]backup-simplify: Simplify 0 into 0 1546856172.354 * [misc]backup-simplify: Simplify 0 into 0 1546856172.355 * [misc]backup-simplify: Simplify (+ (* n 0) (* 0 PI)) into 0 1546856172.355 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0 1546856172.356 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 1546856172.356 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1546856172.356 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546856172.356 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546856172.357 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI))))) 1546856172.357 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1)))) into (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) 1546856172.358 * [misc]backup-simplify: Simplify (- (+ (* (sqrt (/ 1 (* PI (* n 2)))) (/ (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) (pow (* 2 (* n PI)) 1/2))))) into (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) 1546856172.359 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 (* PI (* n 2)))) +nan.0) (* (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) 0)) into (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))) 1546856172.359 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))) in n 1546856172.359 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))) in n 1546856172.359 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546856172.359 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546856172.359 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)) in n 1546856172.359 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n 1546856172.359 * [misc]taylor: Taking taylor expansion of (/ 1 (* n PI)) in n 1546856172.359 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546856172.359 * [misc]taylor: Taking taylor expansion of n in n 1546856172.359 * [misc]backup-simplify: Simplify 0 into 0 1546856172.359 * [misc]backup-simplify: Simplify 1 into 1 1546856172.359 * [misc]taylor: Taking taylor expansion of PI in n 1546856172.359 * [misc]backup-simplify: Simplify PI into PI 1546856172.359 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546856172.360 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546856172.360 * [misc]backup-simplify: Simplify (/ 1 PI) into (/ 1 PI) 1546856172.360 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546856172.361 * [misc]backup-simplify: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI) 1546856172.361 * [misc]taylor: Taking taylor expansion of (sqrt 1/2) in n 1546856172.361 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856172.361 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.361 * [misc]backup-simplify: Simplify (sqrt 1/2) into (sqrt 1/2) 1546856172.361 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 1/2))) into 0 1546856172.363 * [misc]backup-simplify: Simplify (+ (* 0 0) (* (/ +nan.0 PI) (sqrt 1/2))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 1546856172.363 * [misc]backup-simplify: Simplify (* 0 (sqrt 1/2)) into 0 1546856172.365 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (sqrt 1/2) PI)))) (* 0 0)) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 1546856172.366 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (/ (sqrt 1/2) PI)))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 1546856172.367 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (sqrt 1/2) PI))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 1546856172.367 * [misc]backup-simplify: Simplify 0 into 0 1546856172.368 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1546856172.369 * [misc]backup-simplify: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 1546856172.369 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 1546856172.372 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 1)))) 2) into 0 1546856172.372 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1546856172.373 * [misc]backup-simplify: Simplify (- 0) into 0 1546856172.373 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856172.373 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0 1546856172.374 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) 1546856172.377 * [misc]backup-simplify: Simplify (- (+ (* (sqrt (/ 1 (* PI (* n 2)))) (/ (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) (pow (* 2 (* n PI)) 1/2))) (* (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (/ (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) (pow (* 2 (* n PI)) 1/2))))) into (- (* 1/4 (* (* (pow (sqrt 2) 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 3))) (sqrt (/ 1 (* n PI))))) (* 1/8 (* (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI)))))) 1546856172.380 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 (* PI (* n 2)))) +nan.0) (+ (* (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) +nan.0) (* (- (* 1/4 (* (* (pow (sqrt 2) 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 3))) (sqrt (/ 1 (* n PI))))) (* 1/8 (* (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI)))))) 0))) into (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))))) 1546856172.380 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))))) in n 1546856172.380 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))))) in n 1546856172.380 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) in n 1546856172.380 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546856172.380 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546856172.380 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI)))) in n 1546856172.380 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) in n 1546856172.381 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1546856172.381 * [misc]taylor: Taking taylor expansion of 2 in n 1546856172.381 * [misc]backup-simplify: Simplify 2 into 2 1546856172.381 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1546856172.381 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1546856172.381 * [misc]taylor: Taking taylor expansion of (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2)) in n 1546856172.381 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546856172.381 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546856172.381 * [misc]taylor: Taking taylor expansion of 2 in n 1546856172.381 * [misc]backup-simplify: Simplify 2 into 2 1546856172.381 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546856172.381 * [misc]taylor: Taking taylor expansion of n in n 1546856172.381 * [misc]backup-simplify: Simplify 0 into 0 1546856172.381 * [misc]backup-simplify: Simplify 1 into 1 1546856172.381 * [misc]taylor: Taking taylor expansion of PI in n 1546856172.381 * [misc]backup-simplify: Simplify PI into PI 1546856172.382 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546856172.382 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546856172.383 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546856172.383 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546856172.384 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856172.384 * [misc]taylor: Taking taylor expansion of (pow (sqrt 1/2) 2) in n 1546856172.384 * [misc]taylor: Taking taylor expansion of (sqrt 1/2) in n 1546856172.384 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856172.384 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.384 * [misc]backup-simplify: Simplify (sqrt 1/2) into (sqrt 1/2) 1546856172.384 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 1/2))) into 0 1546856172.384 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n 1546856172.384 * [misc]taylor: Taking taylor expansion of (/ 1 (* n PI)) in n 1546856172.385 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546856172.385 * [misc]taylor: Taking taylor expansion of n in n 1546856172.385 * [misc]backup-simplify: Simplify 0 into 0 1546856172.385 * [misc]backup-simplify: Simplify 1 into 1 1546856172.385 * [misc]taylor: Taking taylor expansion of PI in n 1546856172.385 * [misc]backup-simplify: Simplify PI into PI 1546856172.385 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546856172.386 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546856172.386 * [misc]backup-simplify: Simplify (/ 1 PI) into (/ 1 PI) 1546856172.386 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546856172.387 * [misc]backup-simplify: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI) 1546856172.387 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))) in n 1546856172.387 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))) in n 1546856172.387 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546856172.387 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546856172.387 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)) in n 1546856172.387 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n 1546856172.387 * [misc]taylor: Taking taylor expansion of (/ 1 (* n PI)) in n 1546856172.387 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546856172.387 * [misc]taylor: Taking taylor expansion of n in n 1546856172.387 * [misc]backup-simplify: Simplify 0 into 0 1546856172.387 * [misc]backup-simplify: Simplify 1 into 1 1546856172.387 * [misc]taylor: Taking taylor expansion of PI in n 1546856172.387 * [misc]backup-simplify: Simplify PI into PI 1546856172.387 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546856172.388 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546856172.388 * [misc]backup-simplify: Simplify (/ 1 PI) into (/ 1 PI) 1546856172.388 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546856172.389 * [misc]backup-simplify: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI) 1546856172.389 * [misc]taylor: Taking taylor expansion of (sqrt 1/2) in n 1546856172.389 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856172.389 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.389 * [misc]backup-simplify: Simplify (sqrt 1/2) into (sqrt 1/2) 1546856172.390 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 1/2))) into 0 1546856172.390 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546856172.391 * [misc]backup-simplify: Simplify (* (sqrt 1/2) (sqrt 1/2)) into (pow (sqrt 1/2) 2) 1546856172.392 * [misc]backup-simplify: Simplify (* (+ (log n) (log (* 2 PI))) (pow (sqrt 1/2) 2)) into (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI)))) 1546856172.393 * [misc]backup-simplify: Simplify (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) into (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) 1546856172.394 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546856172.394 * [misc]backup-simplify: Simplify (+ (* (sqrt 1/2) 0) (* 0 (sqrt 1/2))) into 0 1546856172.395 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546856172.396 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1546856172.399 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546856172.400 * [misc]backup-simplify: Simplify (+ (* (+ (log n) (log (* 2 PI))) 0) (* 0 (pow (sqrt 1/2) 2))) into 0 1546856172.401 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI)))))) into 0 1546856172.403 * [misc]backup-simplify: Simplify (+ (* (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) (/ +nan.0 PI)) (* 0 0)) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))) 1546856172.404 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) 0) into 0 1546856172.409 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))) (* 0 0)) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))) 1546856172.410 * [misc]backup-simplify: Simplify (+ (* 0 0) (* (/ +nan.0 PI) (sqrt 1/2))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 1546856172.410 * [misc]backup-simplify: Simplify (* 0 (sqrt 1/2)) into 0 1546856172.412 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (sqrt 1/2) PI)))) (* 0 0)) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 1546856172.413 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (/ (sqrt 1/2) PI)))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 1546856172.418 * [misc]backup-simplify: Simplify (+ (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))) (- (* +nan.0 (/ (sqrt 1/2) PI)))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) 1546856172.425 * [misc]backup-simplify: Simplify (- (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) 1546856172.431 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) 1546856172.432 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1/2))) into 0 1546856172.433 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546856172.435 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 PI) (/ 0 PI)))) into 0 1546856172.436 * [misc]backup-simplify: Simplify (/ (- 0 (pow (/ +nan.0 PI) 2) (+)) (* 2 0)) into (/ +nan.0 (pow PI 2)) 1546856172.439 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* (/ +nan.0 PI) 0) (* (/ +nan.0 (pow PI 2)) (sqrt 1/2)))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) 1546856172.442 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2))))) (+ (* 0 (- (* +nan.0 (/ (sqrt 1/2) PI)))) (* 0 0))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) 1546856172.445 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2))))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) 1546856172.446 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) 1546856172.456 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) (* n k)) (+ (* (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) (pow (* 1 k) 2)) (* (- (* +nan.0 (/ (sqrt 1/2) PI))) (* 1 k)))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow k 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI))))) PI)) (- (+ (* +nan.0 (/ (* (sqrt 1/2) (pow k 2)) PI)) (- (+ (* +nan.0 (/ (* n (* (sqrt 1/2) k)) (pow PI 2))) (- (+ (* +nan.0 (/ (* (log n) (* (sqrt 2) (* (pow (sqrt 1/2) 2) (pow k 2)))) PI)) (- (* +nan.0 (/ (* (sqrt 1/2) k) PI))))))))))) 1546856172.456 * [misc]backup-simplify: Simplify (/ (sqrt (/ 1 k)) (pow (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2)))) into (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) 1546856172.456 * [misc]approximate: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in (k n) around 0 1546856172.457 * [misc]taylor: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in n 1546856172.457 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1546856172.457 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546856172.457 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546856172.457 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546856172.457 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546856172.457 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856172.457 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.457 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546856172.457 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856172.457 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.457 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546856172.457 * [misc]taylor: Taking taylor expansion of k in n 1546856172.457 * [misc]backup-simplify: Simplify k into k 1546856172.457 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546856172.457 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546856172.457 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546856172.457 * [misc]taylor: Taking taylor expansion of 2 in n 1546856172.457 * [misc]backup-simplify: Simplify 2 into 2 1546856172.457 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856172.457 * [misc]taylor: Taking taylor expansion of PI in n 1546856172.457 * [misc]backup-simplify: Simplify PI into PI 1546856172.457 * [misc]taylor: Taking taylor expansion of n in n 1546856172.457 * [misc]backup-simplify: Simplify 0 into 0 1546856172.457 * [misc]backup-simplify: Simplify 1 into 1 1546856172.458 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856172.458 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546856172.459 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856172.459 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546856172.459 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546856172.459 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546856172.460 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546856172.460 * [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))) 1546856172.461 * [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)))) 1546856172.462 * [misc]backup-simplify: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 1546856172.462 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1546856172.462 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546856172.462 * [misc]taylor: Taking taylor expansion of k in n 1546856172.462 * [misc]backup-simplify: Simplify k into k 1546856172.462 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546856172.462 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1546856172.462 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546856172.462 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1546856172.462 * [misc]taylor: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in k 1546856172.462 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 1546856172.462 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1546856172.462 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1546856172.462 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1546856172.462 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546856172.462 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856172.462 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.462 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546856172.462 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856172.463 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.463 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546856172.463 * [misc]taylor: Taking taylor expansion of k in k 1546856172.463 * [misc]backup-simplify: Simplify 0 into 0 1546856172.463 * [misc]backup-simplify: Simplify 1 into 1 1546856172.463 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546856172.463 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1546856172.463 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1546856172.463 * [misc]taylor: Taking taylor expansion of 2 in k 1546856172.463 * [misc]backup-simplify: Simplify 2 into 2 1546856172.463 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546856172.463 * [misc]taylor: Taking taylor expansion of PI in k 1546856172.463 * [misc]backup-simplify: Simplify PI into PI 1546856172.463 * [misc]taylor: Taking taylor expansion of n in k 1546856172.463 * [misc]backup-simplify: Simplify n into n 1546856172.463 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546856172.463 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1546856172.463 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1546856172.463 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546856172.464 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546856172.464 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546856172.464 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1546856172.464 * [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)))) 1546856172.464 * [misc]backup-simplify: Simplify (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) into (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 1546856172.464 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1546856172.464 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546856172.464 * [misc]taylor: Taking taylor expansion of k in k 1546856172.464 * [misc]backup-simplify: Simplify 0 into 0 1546856172.464 * [misc]backup-simplify: Simplify 1 into 1 1546856172.465 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546856172.465 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546856172.465 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546856172.465 * [misc]taylor: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in k 1546856172.465 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 1546856172.465 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1546856172.465 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1546856172.465 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1546856172.465 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546856172.465 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856172.465 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.465 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546856172.466 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856172.466 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.466 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546856172.466 * [misc]taylor: Taking taylor expansion of k in k 1546856172.466 * [misc]backup-simplify: Simplify 0 into 0 1546856172.466 * [misc]backup-simplify: Simplify 1 into 1 1546856172.466 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546856172.466 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1546856172.466 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1546856172.466 * [misc]taylor: Taking taylor expansion of 2 in k 1546856172.466 * [misc]backup-simplify: Simplify 2 into 2 1546856172.466 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546856172.466 * [misc]taylor: Taking taylor expansion of PI in k 1546856172.466 * [misc]backup-simplify: Simplify PI into PI 1546856172.466 * [misc]taylor: Taking taylor expansion of n in k 1546856172.466 * [misc]backup-simplify: Simplify n into n 1546856172.466 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546856172.466 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1546856172.466 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1546856172.466 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546856172.467 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546856172.467 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546856172.467 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1546856172.467 * [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)))) 1546856172.467 * [misc]backup-simplify: Simplify (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) into (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 1546856172.467 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1546856172.467 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546856172.467 * [misc]taylor: Taking taylor expansion of k in k 1546856172.467 * [misc]backup-simplify: Simplify 0 into 0 1546856172.467 * [misc]backup-simplify: Simplify 1 into 1 1546856172.467 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546856172.468 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546856172.468 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546856172.468 * [misc]backup-simplify: Simplify (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 0) into 0 1546856172.468 * [misc]taylor: Taking taylor expansion of 0 in n 1546856172.468 * [misc]backup-simplify: Simplify 0 into 0 1546856172.468 * [misc]backup-simplify: Simplify 0 into 0 1546856172.468 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 1546856172.468 * [misc]backup-simplify: Simplify (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (* 0 0)) into (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) 1546856172.469 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) in n 1546856172.469 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 1546856172.469 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546856172.469 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546856172.469 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1546856172.469 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546856172.469 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546856172.469 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546856172.469 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546856172.469 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856172.469 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.469 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546856172.469 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856172.469 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.469 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546856172.469 * [misc]taylor: Taking taylor expansion of k in n 1546856172.469 * [misc]backup-simplify: Simplify k into k 1546856172.469 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546856172.469 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546856172.469 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546856172.469 * [misc]taylor: Taking taylor expansion of 2 in n 1546856172.469 * [misc]backup-simplify: Simplify 2 into 2 1546856172.469 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856172.469 * [misc]taylor: Taking taylor expansion of PI in n 1546856172.469 * [misc]backup-simplify: Simplify PI into PI 1546856172.469 * [misc]taylor: Taking taylor expansion of n in n 1546856172.469 * [misc]backup-simplify: Simplify 0 into 0 1546856172.469 * [misc]backup-simplify: Simplify 1 into 1 1546856172.469 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856172.469 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546856172.470 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856172.470 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546856172.470 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546856172.470 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546856172.470 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546856172.471 * [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))) 1546856172.471 * [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)))) 1546856172.471 * [misc]backup-simplify: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 1546856172.472 * [misc]backup-simplify: Simplify (* +nan.0 (/ 1 (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))))) 1546856172.472 * [misc]backup-simplify: Simplify (- (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 1546856172.473 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 1546856172.473 * [misc]backup-simplify: Simplify 0 into 0 1546856172.473 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1546856172.473 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1546856172.474 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) (* 0 (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 1546856172.474 * [misc]backup-simplify: Simplify (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) 1546856172.474 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) in n 1546856172.474 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 1546856172.474 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546856172.474 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546856172.474 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1546856172.474 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546856172.474 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546856172.474 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546856172.474 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546856172.474 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856172.474 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.474 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546856172.474 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856172.474 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.474 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546856172.474 * [misc]taylor: Taking taylor expansion of k in n 1546856172.474 * [misc]backup-simplify: Simplify k into k 1546856172.474 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546856172.474 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546856172.474 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546856172.474 * [misc]taylor: Taking taylor expansion of 2 in n 1546856172.474 * [misc]backup-simplify: Simplify 2 into 2 1546856172.474 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856172.474 * [misc]taylor: Taking taylor expansion of PI in n 1546856172.474 * [misc]backup-simplify: Simplify PI into PI 1546856172.474 * [misc]taylor: Taking taylor expansion of n in n 1546856172.474 * [misc]backup-simplify: Simplify 0 into 0 1546856172.474 * [misc]backup-simplify: Simplify 1 into 1 1546856172.475 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856172.475 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546856172.475 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856172.475 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546856172.475 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546856172.475 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546856172.476 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546856172.476 * [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))) 1546856172.476 * [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)))) 1546856172.477 * [misc]backup-simplify: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 1546856172.477 * [misc]backup-simplify: Simplify (* +nan.0 (/ 1 (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))))) 1546856172.478 * [misc]backup-simplify: Simplify (- (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 1546856172.478 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 1546856172.479 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546856172.479 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546856172.481 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546856172.481 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546856172.481 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546856172.481 * [misc]backup-simplify: Simplify (- 0) into 0 1546856172.481 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856172.482 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546856172.482 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1546856172.483 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546856172.484 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (/ 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))) into 0 1546856172.485 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0 1546856172.485 * [misc]backup-simplify: Simplify (- 0) into 0 1546856172.485 * [misc]backup-simplify: Simplify 0 into 0 1546856172.485 * [misc]backup-simplify: Simplify 0 into 0 1546856172.485 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856172.486 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1546856172.486 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) (* 0 (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) (* 0 (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 1546856172.486 * [misc]backup-simplify: Simplify (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) 1546856172.486 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) in n 1546856172.486 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 1546856172.486 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546856172.486 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546856172.486 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1546856172.486 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546856172.486 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546856172.486 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546856172.486 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546856172.487 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856172.487 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.487 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546856172.487 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856172.487 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.487 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546856172.487 * [misc]taylor: Taking taylor expansion of k in n 1546856172.487 * [misc]backup-simplify: Simplify k into k 1546856172.487 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546856172.487 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546856172.487 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546856172.487 * [misc]taylor: Taking taylor expansion of 2 in n 1546856172.487 * [misc]backup-simplify: Simplify 2 into 2 1546856172.487 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856172.487 * [misc]taylor: Taking taylor expansion of PI in n 1546856172.487 * [misc]backup-simplify: Simplify PI into PI 1546856172.487 * [misc]taylor: Taking taylor expansion of n in n 1546856172.487 * [misc]backup-simplify: Simplify 0 into 0 1546856172.487 * [misc]backup-simplify: Simplify 1 into 1 1546856172.487 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856172.487 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546856172.487 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856172.487 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546856172.488 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546856172.488 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546856172.488 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546856172.488 * [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))) 1546856172.489 * [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)))) 1546856172.489 * [misc]backup-simplify: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 1546856172.490 * [misc]backup-simplify: Simplify (* +nan.0 (/ 1 (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))))) 1546856172.490 * [misc]backup-simplify: Simplify (- (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 1546856172.490 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 1546856172.492 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 2)) (+ (* (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (* 1 (/ 1 k))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))))))) into (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))))))))) 1546856172.492 * [misc]backup-simplify: Simplify (/ (sqrt (/ 1 (- k))) (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2)))) into (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) 1546856172.492 * [misc]approximate: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in (k n) around 0 1546856172.492 * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1546856172.492 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1546856172.492 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1546856172.492 * [misc]taylor: Taking taylor expansion of -1 in n 1546856172.492 * [misc]backup-simplify: Simplify -1 into -1 1546856172.492 * [misc]taylor: Taking taylor expansion of k in n 1546856172.492 * [misc]backup-simplify: Simplify k into k 1546856172.492 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1546856172.492 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1546856172.492 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1546856172.492 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1546856172.492 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546856172.492 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546856172.492 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546856172.493 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546856172.493 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546856172.493 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856172.493 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.493 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546856172.493 * [misc]taylor: Taking taylor expansion of k in n 1546856172.493 * [misc]backup-simplify: Simplify k into k 1546856172.493 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546856172.493 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856172.493 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.493 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546856172.493 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546856172.493 * [misc]taylor: Taking taylor expansion of -2 in n 1546856172.493 * [misc]backup-simplify: Simplify -2 into -2 1546856172.493 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856172.493 * [misc]taylor: Taking taylor expansion of PI in n 1546856172.493 * [misc]backup-simplify: Simplify PI into PI 1546856172.493 * [misc]taylor: Taking taylor expansion of n in n 1546856172.493 * [misc]backup-simplify: Simplify 0 into 0 1546856172.493 * [misc]backup-simplify: Simplify 1 into 1 1546856172.493 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856172.493 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546856172.494 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546856172.494 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546856172.494 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546856172.494 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546856172.495 * [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))) 1546856172.495 * [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)))) 1546856172.495 * [misc]backup-simplify: Simplify (/ (sqrt (/ -1 k)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ (sqrt (/ -1 k)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 1546856172.496 * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in k 1546856172.496 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1546856172.496 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1546856172.496 * [misc]taylor: Taking taylor expansion of -1 in k 1546856172.496 * [misc]backup-simplify: Simplify -1 into -1 1546856172.496 * [misc]taylor: Taking taylor expansion of k in k 1546856172.496 * [misc]backup-simplify: Simplify 0 into 0 1546856172.496 * [misc]backup-simplify: Simplify 1 into 1 1546856172.496 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1546856172.496 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546856172.496 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1546856172.496 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1546856172.496 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1546856172.496 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1546856172.496 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546856172.496 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546856172.496 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856172.496 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.496 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546856172.496 * [misc]taylor: Taking taylor expansion of k in k 1546856172.496 * [misc]backup-simplify: Simplify 0 into 0 1546856172.496 * [misc]backup-simplify: Simplify 1 into 1 1546856172.496 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546856172.496 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856172.496 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.496 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1546856172.496 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1546856172.496 * [misc]taylor: Taking taylor expansion of -2 in k 1546856172.496 * [misc]backup-simplify: Simplify -2 into -2 1546856172.497 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546856172.497 * [misc]taylor: Taking taylor expansion of PI in k 1546856172.497 * [misc]backup-simplify: Simplify PI into PI 1546856172.497 * [misc]taylor: Taking taylor expansion of n in k 1546856172.497 * [misc]backup-simplify: Simplify n into n 1546856172.497 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546856172.497 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1546856172.497 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1546856172.497 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546856172.497 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546856172.497 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1546856172.497 * [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))) 1546856172.497 * [misc]backup-simplify: Simplify (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) into (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) 1546856172.497 * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in k 1546856172.497 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1546856172.497 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1546856172.497 * [misc]taylor: Taking taylor expansion of -1 in k 1546856172.497 * [misc]backup-simplify: Simplify -1 into -1 1546856172.497 * [misc]taylor: Taking taylor expansion of k in k 1546856172.497 * [misc]backup-simplify: Simplify 0 into 0 1546856172.497 * [misc]backup-simplify: Simplify 1 into 1 1546856172.497 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1546856172.498 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546856172.498 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1546856172.498 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1546856172.498 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1546856172.498 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1546856172.498 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546856172.498 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546856172.498 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856172.498 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.498 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546856172.498 * [misc]taylor: Taking taylor expansion of k in k 1546856172.498 * [misc]backup-simplify: Simplify 0 into 0 1546856172.498 * [misc]backup-simplify: Simplify 1 into 1 1546856172.498 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546856172.498 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856172.498 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.498 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1546856172.498 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1546856172.498 * [misc]taylor: Taking taylor expansion of -2 in k 1546856172.498 * [misc]backup-simplify: Simplify -2 into -2 1546856172.498 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546856172.498 * [misc]taylor: Taking taylor expansion of PI in k 1546856172.498 * [misc]backup-simplify: Simplify PI into PI 1546856172.498 * [misc]taylor: Taking taylor expansion of n in k 1546856172.498 * [misc]backup-simplify: Simplify n into n 1546856172.498 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546856172.498 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1546856172.498 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1546856172.499 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546856172.499 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546856172.499 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1546856172.499 * [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))) 1546856172.499 * [misc]backup-simplify: Simplify (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) into (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) 1546856172.499 * [misc]taylor: Taking taylor expansion of (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1546856172.499 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546856172.499 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546856172.499 * [misc]taylor: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1546856172.499 * [misc]taylor: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546856172.499 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546856172.499 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546856172.499 * [misc]taylor: Taking taylor expansion of -2 in n 1546856172.499 * [misc]backup-simplify: Simplify -2 into -2 1546856172.499 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856172.499 * [misc]taylor: Taking taylor expansion of PI in n 1546856172.499 * [misc]backup-simplify: Simplify PI into PI 1546856172.499 * [misc]taylor: Taking taylor expansion of n in n 1546856172.499 * [misc]backup-simplify: Simplify 0 into 0 1546856172.499 * [misc]backup-simplify: Simplify 1 into 1 1546856172.499 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856172.500 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546856172.500 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546856172.500 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546856172.500 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546856172.500 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856172.500 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.500 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546856172.500 * [misc]taylor: Taking taylor expansion of k in n 1546856172.500 * [misc]backup-simplify: Simplify k into k 1546856172.500 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546856172.500 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856172.500 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.500 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546856172.500 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546856172.501 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546856172.501 * [misc]backup-simplify: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1546856172.501 * [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)))) 1546856172.502 * [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))))) 1546856172.502 * [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))))) 1546856172.502 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1546856172.503 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1546856172.503 * [misc]backup-simplify: Simplify (- (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (+ (* (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ 0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))))) into (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) 1546856172.503 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) in n 1546856172.503 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 1546856172.503 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546856172.503 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546856172.503 * [misc]taylor: Taking taylor expansion of (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1546856172.503 * [misc]taylor: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1546856172.503 * [misc]taylor: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546856172.503 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546856172.503 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546856172.503 * [misc]taylor: Taking taylor expansion of -2 in n 1546856172.504 * [misc]backup-simplify: Simplify -2 into -2 1546856172.504 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856172.504 * [misc]taylor: Taking taylor expansion of PI in n 1546856172.504 * [misc]backup-simplify: Simplify PI into PI 1546856172.504 * [misc]taylor: Taking taylor expansion of n in n 1546856172.504 * [misc]backup-simplify: Simplify 0 into 0 1546856172.504 * [misc]backup-simplify: Simplify 1 into 1 1546856172.504 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856172.504 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546856172.504 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546856172.504 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546856172.504 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546856172.504 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856172.504 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.504 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546856172.504 * [misc]taylor: Taking taylor expansion of k in n 1546856172.504 * [misc]backup-simplify: Simplify k into k 1546856172.504 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546856172.504 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856172.504 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.505 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546856172.505 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546856172.505 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546856172.505 * [misc]backup-simplify: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1546856172.506 * [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)))) 1546856172.506 * [misc]backup-simplify: Simplify (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 1546856172.506 * [misc]backup-simplify: Simplify (* +nan.0 (/ 1 (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))))) 1546856172.507 * [misc]backup-simplify: Simplify (- (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) 1546856172.508 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) 1546856172.509 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546856172.509 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546856172.509 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546856172.509 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856172.510 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546856172.510 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1546856172.512 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1546856172.512 * [misc]backup-simplify: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0 1546856172.513 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546856172.514 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (+ (* (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))))) into 0 1546856172.514 * [misc]backup-simplify: Simplify 0 into 0 1546856172.514 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856172.515 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1546856172.516 * [misc]backup-simplify: Simplify (- (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (+ (* (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ 0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) (* (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) (/ 0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))))) into (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) 1546856172.516 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) in n 1546856172.516 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 1546856172.516 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546856172.516 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546856172.516 * [misc]taylor: Taking taylor expansion of (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1546856172.516 * [misc]taylor: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1546856172.516 * [misc]taylor: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546856172.516 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546856172.516 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546856172.516 * [misc]taylor: Taking taylor expansion of -2 in n 1546856172.516 * [misc]backup-simplify: Simplify -2 into -2 1546856172.516 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856172.516 * [misc]taylor: Taking taylor expansion of PI in n 1546856172.516 * [misc]backup-simplify: Simplify PI into PI 1546856172.516 * [misc]taylor: Taking taylor expansion of n in n 1546856172.516 * [misc]backup-simplify: Simplify 0 into 0 1546856172.516 * [misc]backup-simplify: Simplify 1 into 1 1546856172.516 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856172.516 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546856172.517 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546856172.517 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546856172.517 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546856172.517 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856172.517 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.517 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546856172.517 * [misc]taylor: Taking taylor expansion of k in n 1546856172.517 * [misc]backup-simplify: Simplify k into k 1546856172.517 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546856172.517 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856172.517 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.517 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546856172.517 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546856172.517 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546856172.518 * [misc]backup-simplify: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1546856172.518 * [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)))) 1546856172.519 * [misc]backup-simplify: Simplify (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 1546856172.519 * [misc]backup-simplify: Simplify (* +nan.0 (/ 1 (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))))) 1546856172.519 * [misc]backup-simplify: Simplify (- (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) 1546856172.520 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) 1546856172.521 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (* 1 (/ 1 (- k)))) (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) into (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))))))))) 1546856172.521 * * * * [misc]progress: [ 4 / 4 ] generating series at (2) 1546856172.522 * [misc]backup-simplify: Simplify (/ 1 (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) into (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) 1546856172.522 * [misc]approximate: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (k n) around 0 1546856172.522 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 1546856172.522 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1546856172.522 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546856172.522 * [misc]taylor: Taking taylor expansion of k in n 1546856172.522 * [misc]backup-simplify: Simplify k into k 1546856172.522 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546856172.522 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1546856172.522 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546856172.522 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1546856172.522 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546856172.522 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546856172.522 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546856172.522 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546856172.522 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856172.522 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.522 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546856172.522 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856172.522 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.522 * [misc]taylor: Taking taylor expansion of k in n 1546856172.522 * [misc]backup-simplify: Simplify k into k 1546856172.522 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546856172.522 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546856172.522 * [misc]taylor: Taking taylor expansion of 2 in n 1546856172.522 * [misc]backup-simplify: Simplify 2 into 2 1546856172.522 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546856172.522 * [misc]taylor: Taking taylor expansion of n in n 1546856172.522 * [misc]backup-simplify: Simplify 0 into 0 1546856172.522 * [misc]backup-simplify: Simplify 1 into 1 1546856172.522 * [misc]taylor: Taking taylor expansion of PI in n 1546856172.522 * [misc]backup-simplify: Simplify PI into PI 1546856172.522 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546856172.523 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546856172.523 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546856172.523 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546856172.524 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856172.524 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546856172.524 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546856172.524 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546856172.525 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546856172.525 * [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)))) 1546856172.526 * [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))))) 1546856172.526 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 1546856172.526 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1546856172.526 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546856172.526 * [misc]taylor: Taking taylor expansion of k in k 1546856172.526 * [misc]backup-simplify: Simplify 0 into 0 1546856172.526 * [misc]backup-simplify: Simplify 1 into 1 1546856172.526 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546856172.526 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546856172.527 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546856172.527 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1546856172.527 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1546856172.527 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1546856172.527 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546856172.527 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856172.527 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.527 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546856172.527 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856172.527 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.527 * [misc]taylor: Taking taylor expansion of k in k 1546856172.527 * [misc]backup-simplify: Simplify 0 into 0 1546856172.527 * [misc]backup-simplify: Simplify 1 into 1 1546856172.527 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1546856172.527 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1546856172.527 * [misc]taylor: Taking taylor expansion of 2 in k 1546856172.527 * [misc]backup-simplify: Simplify 2 into 2 1546856172.527 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1546856172.527 * [misc]taylor: Taking taylor expansion of n in k 1546856172.528 * [misc]backup-simplify: Simplify n into n 1546856172.528 * [misc]taylor: Taking taylor expansion of PI in k 1546856172.528 * [misc]backup-simplify: Simplify PI into PI 1546856172.528 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1546856172.528 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1546856172.528 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1546856172.528 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546856172.528 * [misc]backup-simplify: Simplify (- 0) into 0 1546856172.528 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546856172.528 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1546856172.529 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1546856172.529 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 1546856172.529 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1546856172.529 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546856172.529 * [misc]taylor: Taking taylor expansion of k in k 1546856172.529 * [misc]backup-simplify: Simplify 0 into 0 1546856172.529 * [misc]backup-simplify: Simplify 1 into 1 1546856172.529 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546856172.529 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546856172.529 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546856172.530 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1546856172.530 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1546856172.530 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1546856172.530 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546856172.530 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856172.530 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.530 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546856172.530 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856172.530 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.530 * [misc]taylor: Taking taylor expansion of k in k 1546856172.530 * [misc]backup-simplify: Simplify 0 into 0 1546856172.530 * [misc]backup-simplify: Simplify 1 into 1 1546856172.530 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1546856172.530 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1546856172.530 * [misc]taylor: Taking taylor expansion of 2 in k 1546856172.530 * [misc]backup-simplify: Simplify 2 into 2 1546856172.530 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1546856172.530 * [misc]taylor: Taking taylor expansion of n in k 1546856172.530 * [misc]backup-simplify: Simplify n into n 1546856172.530 * [misc]taylor: Taking taylor expansion of PI in k 1546856172.530 * [misc]backup-simplify: Simplify PI into PI 1546856172.530 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1546856172.530 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1546856172.530 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1546856172.530 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546856172.531 * [misc]backup-simplify: Simplify (- 0) into 0 1546856172.531 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546856172.531 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1546856172.531 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1546856172.531 * [misc]backup-simplify: Simplify (* 0 (pow (* 2 (* n PI)) 1/2)) into 0 1546856172.531 * [misc]taylor: Taking taylor expansion of 0 in n 1546856172.531 * [misc]backup-simplify: Simplify 0 into 0 1546856172.531 * [misc]backup-simplify: Simplify 0 into 0 1546856172.532 * [misc]backup-simplify: Simplify (+ (* n 0) (* 0 PI)) into 0 1546856172.532 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0 1546856172.532 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 1546856172.532 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1546856172.532 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546856172.533 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546856172.533 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI))))) 1546856172.533 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1)))) into (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) 1546856172.533 * [misc]backup-simplify: Simplify (+ (* 0 (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI)))))) (* +nan.0 (pow (* 2 (* n PI)) 1/2))) into (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) 1546856172.533 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 1546856172.533 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 1546856172.533 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546856172.533 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546856172.533 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1546856172.533 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1546856172.533 * [misc]taylor: Taking taylor expansion of 2 in n 1546856172.533 * [misc]backup-simplify: Simplify 2 into 2 1546856172.533 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1546856172.534 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1546856172.534 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1546856172.534 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546856172.534 * [misc]taylor: Taking taylor expansion of n in n 1546856172.534 * [misc]backup-simplify: Simplify 0 into 0 1546856172.534 * [misc]backup-simplify: Simplify 1 into 1 1546856172.534 * [misc]taylor: Taking taylor expansion of PI in n 1546856172.534 * [misc]backup-simplify: Simplify PI into PI 1546856172.534 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546856172.534 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546856172.534 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546856172.535 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1546856172.535 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1546856172.535 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1546856172.535 * [misc]backup-simplify: Simplify (- 0) into 0 1546856172.535 * [misc]backup-simplify: Simplify 0 into 0 1546856172.535 * [misc]backup-simplify: Simplify 0 into 0 1546856172.535 * [misc]backup-simplify: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 1546856172.536 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 1546856172.537 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 1)))) 2) into 0 1546856172.537 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1546856172.537 * [misc]backup-simplify: Simplify (- 0) into 0 1546856172.537 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856172.537 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0 1546856172.538 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) 1546856172.538 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1546856172.539 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1546856172.539 * [misc]backup-simplify: Simplify (+ (* 0 (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2)))) (+ (* +nan.0 (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI)))))) (* +nan.0 (pow (* 2 (* n PI)) 1/2)))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) 1546856172.539 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) in n 1546856172.539 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))) in n 1546856172.539 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n 1546856172.539 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546856172.539 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546856172.539 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n 1546856172.539 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n 1546856172.539 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1546856172.539 * [misc]taylor: Taking taylor expansion of 2 in n 1546856172.539 * [misc]backup-simplify: Simplify 2 into 2 1546856172.539 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1546856172.540 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1546856172.540 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546856172.540 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546856172.540 * [misc]taylor: Taking taylor expansion of 2 in n 1546856172.540 * [misc]backup-simplify: Simplify 2 into 2 1546856172.540 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546856172.540 * [misc]taylor: Taking taylor expansion of n in n 1546856172.540 * [misc]backup-simplify: Simplify 0 into 0 1546856172.540 * [misc]backup-simplify: Simplify 1 into 1 1546856172.540 * [misc]taylor: Taking taylor expansion of PI in n 1546856172.540 * [misc]backup-simplify: Simplify PI into PI 1546856172.540 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546856172.540 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546856172.540 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546856172.541 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546856172.541 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856172.541 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1546856172.541 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546856172.541 * [misc]taylor: Taking taylor expansion of n in n 1546856172.541 * [misc]backup-simplify: Simplify 0 into 0 1546856172.541 * [misc]backup-simplify: Simplify 1 into 1 1546856172.541 * [misc]taylor: Taking taylor expansion of PI in n 1546856172.541 * [misc]backup-simplify: Simplify PI into PI 1546856172.541 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546856172.542 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546856172.542 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546856172.542 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1546856172.542 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 1546856172.542 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 1546856172.542 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546856172.542 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546856172.542 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1546856172.542 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1546856172.542 * [misc]taylor: Taking taylor expansion of 2 in n 1546856172.542 * [misc]backup-simplify: Simplify 2 into 2 1546856172.543 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1546856172.543 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1546856172.543 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1546856172.543 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546856172.543 * [misc]taylor: Taking taylor expansion of n in n 1546856172.543 * [misc]backup-simplify: Simplify 0 into 0 1546856172.543 * [misc]backup-simplify: Simplify 1 into 1 1546856172.543 * [misc]taylor: Taking taylor expansion of PI in n 1546856172.543 * [misc]backup-simplify: Simplify PI into PI 1546856172.543 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546856172.544 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546856172.544 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546856172.544 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1546856172.544 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546856172.545 * [misc]backup-simplify: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 1546856172.545 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0 1546856172.545 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1546856172.545 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1546856172.546 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1546856172.546 * [misc]backup-simplify: Simplify (- 0) into 0 1546856172.546 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856172.546 * [misc]backup-simplify: Simplify (- 0) into 0 1546856172.546 * [misc]backup-simplify: Simplify 0 into 0 1546856172.547 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1546856172.548 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1546856172.548 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 1546856172.549 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI))) 1546856172.549 * [misc]backup-simplify: Simplify 0 into 0 1546856172.550 * [misc]backup-simplify: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546856172.550 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 1546856172.552 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 (* n PI)) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 (* n PI)) 1)))) 6) into 0 1546856172.552 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1546856172.552 * [misc]backup-simplify: Simplify (- 0) into 0 1546856172.553 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856172.553 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log (* 2 (* n PI))))))) into 0 1546856172.554 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 3) 6)) (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 3))) 1546856172.554 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856172.555 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1546856172.555 * [misc]backup-simplify: Simplify (+ (* 0 (* -1/48 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 3)))) (+ (* +nan.0 (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2)))) (+ (* +nan.0 (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI)))))) (* +nan.0 (pow (* 2 (* n PI)) 1/2))))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))))) 1546856172.556 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))))) in n 1546856172.556 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))))) in n 1546856172.556 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n 1546856172.556 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546856172.556 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546856172.556 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n 1546856172.556 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n 1546856172.556 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1546856172.556 * [misc]taylor: Taking taylor expansion of 2 in n 1546856172.556 * [misc]backup-simplify: Simplify 2 into 2 1546856172.556 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1546856172.556 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1546856172.556 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546856172.556 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546856172.556 * [misc]taylor: Taking taylor expansion of 2 in n 1546856172.556 * [misc]backup-simplify: Simplify 2 into 2 1546856172.556 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546856172.556 * [misc]taylor: Taking taylor expansion of n in n 1546856172.556 * [misc]backup-simplify: Simplify 0 into 0 1546856172.556 * [misc]backup-simplify: Simplify 1 into 1 1546856172.556 * [misc]taylor: Taking taylor expansion of PI in n 1546856172.556 * [misc]backup-simplify: Simplify PI into PI 1546856172.556 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546856172.556 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546856172.557 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546856172.557 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546856172.557 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856172.558 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1546856172.558 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546856172.558 * [misc]taylor: Taking taylor expansion of n in n 1546856172.558 * [misc]backup-simplify: Simplify 0 into 0 1546856172.558 * [misc]backup-simplify: Simplify 1 into 1 1546856172.558 * [misc]taylor: Taking taylor expansion of PI in n 1546856172.558 * [misc]backup-simplify: Simplify PI into PI 1546856172.558 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546856172.558 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546856172.558 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546856172.559 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1546856172.559 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) in n 1546856172.559 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))) in n 1546856172.559 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) in n 1546856172.559 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546856172.559 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546856172.559 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))) in n 1546856172.559 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) in n 1546856172.559 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1546856172.559 * [misc]taylor: Taking taylor expansion of 2 in n 1546856172.559 * [misc]backup-simplify: Simplify 2 into 2 1546856172.559 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1546856172.559 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1546856172.559 * [misc]taylor: Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n 1546856172.559 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546856172.559 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546856172.559 * [misc]taylor: Taking taylor expansion of 2 in n 1546856172.559 * [misc]backup-simplify: Simplify 2 into 2 1546856172.559 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546856172.559 * [misc]taylor: Taking taylor expansion of n in n 1546856172.559 * [misc]backup-simplify: Simplify 0 into 0 1546856172.559 * [misc]backup-simplify: Simplify 1 into 1 1546856172.559 * [misc]taylor: Taking taylor expansion of PI in n 1546856172.559 * [misc]backup-simplify: Simplify PI into PI 1546856172.560 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546856172.560 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546856172.560 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546856172.561 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546856172.561 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856172.562 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546856172.562 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1546856172.562 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546856172.562 * [misc]taylor: Taking taylor expansion of n in n 1546856172.562 * [misc]backup-simplify: Simplify 0 into 0 1546856172.562 * [misc]backup-simplify: Simplify 1 into 1 1546856172.562 * [misc]taylor: Taking taylor expansion of PI in n 1546856172.562 * [misc]backup-simplify: Simplify PI into PI 1546856172.563 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546856172.563 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546856172.564 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546856172.564 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1546856172.564 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 1546856172.564 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 1546856172.564 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546856172.564 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546856172.564 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1546856172.564 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1546856172.564 * [misc]taylor: Taking taylor expansion of 2 in n 1546856172.564 * [misc]backup-simplify: Simplify 2 into 2 1546856172.565 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1546856172.565 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1546856172.565 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1546856172.565 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546856172.565 * [misc]taylor: Taking taylor expansion of n in n 1546856172.565 * [misc]backup-simplify: Simplify 0 into 0 1546856172.565 * [misc]backup-simplify: Simplify 1 into 1 1546856172.565 * [misc]taylor: Taking taylor expansion of PI in n 1546856172.565 * [misc]backup-simplify: Simplify PI into PI 1546856172.565 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546856172.566 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546856172.566 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546856172.567 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1546856172.567 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546856172.568 * [misc]backup-simplify: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 1546856172.569 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0 1546856172.569 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1546856172.570 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546856172.570 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546856172.571 * [misc]backup-simplify: Simplify (* (+ (log n) (log (* 2 PI))) (+ (log n) (log (* 2 PI)))) into (pow (+ (log n) (log (* 2 PI))) 2) 1546856172.572 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) into (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 1546856172.573 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 0) into 0 1546856172.573 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1546856172.573 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1546856172.573 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1546856172.573 * [misc]backup-simplify: Simplify (- 0) into 0 1546856172.573 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856172.574 * [misc]backup-simplify: Simplify (- 0) into 0 1546856172.574 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856172.574 * [misc]backup-simplify: Simplify (- 0) into 0 1546856172.574 * [misc]backup-simplify: Simplify 0 into 0 1546856172.575 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546856172.576 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1546856172.579 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546856172.580 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546856172.580 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1546856172.581 * [misc]backup-simplify: Simplify (+ (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) (* +nan.0 PI)) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) 1546856172.584 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) 1546856172.585 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1546856172.587 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1546856172.589 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 1546856172.592 * [misc]backup-simplify: Simplify (+ (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) (- (* +nan.0 (* (sqrt 2) PI)))) into (- (+ (* +nan.0 (* (sqrt 2) PI)) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))))) 1546856172.596 * [misc]backup-simplify: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) PI)) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) 1546856172.599 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) 1546856172.601 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546856172.602 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 1546856172.603 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1546856172.606 * [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)))) 1546856172.610 * [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)))) 1546856172.612 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 1546856172.613 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 1546856172.619 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) (pow (* n 1) 2)) (+ (* (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) (* n k)) (* (- (* +nan.0 (* (sqrt 2) PI))) (* n 1)))) into (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))))))) 1546856172.619 * [misc]backup-simplify: Simplify (/ 1 (/ (sqrt (/ 1 k)) (pow (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2))))) into (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 1546856172.620 * [misc]approximate: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (k n) around 0 1546856172.620 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1546856172.620 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1546856172.620 * [misc]taylor: Taking taylor expansion of k in n 1546856172.620 * [misc]backup-simplify: Simplify k into k 1546856172.620 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1546856172.620 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1546856172.620 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546856172.620 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546856172.620 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546856172.620 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546856172.620 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856172.620 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.620 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546856172.620 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856172.620 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.620 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546856172.620 * [misc]taylor: Taking taylor expansion of k in n 1546856172.620 * [misc]backup-simplify: Simplify k into k 1546856172.620 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546856172.620 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546856172.620 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546856172.620 * [misc]taylor: Taking taylor expansion of 2 in n 1546856172.620 * [misc]backup-simplify: Simplify 2 into 2 1546856172.620 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856172.620 * [misc]taylor: Taking taylor expansion of PI in n 1546856172.620 * [misc]backup-simplify: Simplify PI into PI 1546856172.620 * [misc]taylor: Taking taylor expansion of n in n 1546856172.620 * [misc]backup-simplify: Simplify 0 into 0 1546856172.620 * [misc]backup-simplify: Simplify 1 into 1 1546856172.621 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856172.621 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546856172.622 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856172.622 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546856172.622 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546856172.622 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546856172.622 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546856172.623 * [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))) 1546856172.624 * [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)))) 1546856172.624 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 1546856172.624 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1546856172.624 * [misc]taylor: Taking taylor expansion of k in k 1546856172.624 * [misc]backup-simplify: Simplify 0 into 0 1546856172.624 * [misc]backup-simplify: Simplify 1 into 1 1546856172.624 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546856172.624 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546856172.624 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1546856172.625 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1546856172.625 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1546856172.625 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546856172.625 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856172.625 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.625 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546856172.625 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856172.625 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.625 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546856172.625 * [misc]taylor: Taking taylor expansion of k in k 1546856172.625 * [misc]backup-simplify: Simplify 0 into 0 1546856172.625 * [misc]backup-simplify: Simplify 1 into 1 1546856172.625 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546856172.625 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1546856172.625 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1546856172.625 * [misc]taylor: Taking taylor expansion of 2 in k 1546856172.625 * [misc]backup-simplify: Simplify 2 into 2 1546856172.625 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546856172.625 * [misc]taylor: Taking taylor expansion of PI in k 1546856172.625 * [misc]backup-simplify: Simplify PI into PI 1546856172.625 * [misc]taylor: Taking taylor expansion of n in k 1546856172.625 * [misc]backup-simplify: Simplify n into n 1546856172.625 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546856172.625 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1546856172.625 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1546856172.626 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546856172.626 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546856172.626 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546856172.626 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1546856172.626 * [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)))) 1546856172.626 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 1546856172.626 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1546856172.626 * [misc]taylor: Taking taylor expansion of k in k 1546856172.626 * [misc]backup-simplify: Simplify 0 into 0 1546856172.626 * [misc]backup-simplify: Simplify 1 into 1 1546856172.627 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546856172.627 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546856172.627 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1546856172.627 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1546856172.627 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1546856172.627 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546856172.627 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856172.627 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.627 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546856172.627 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856172.627 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.627 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546856172.627 * [misc]taylor: Taking taylor expansion of k in k 1546856172.627 * [misc]backup-simplify: Simplify 0 into 0 1546856172.627 * [misc]backup-simplify: Simplify 1 into 1 1546856172.628 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546856172.628 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1546856172.628 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1546856172.628 * [misc]taylor: Taking taylor expansion of 2 in k 1546856172.628 * [misc]backup-simplify: Simplify 2 into 2 1546856172.628 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546856172.628 * [misc]taylor: Taking taylor expansion of PI in k 1546856172.628 * [misc]backup-simplify: Simplify PI into PI 1546856172.628 * [misc]taylor: Taking taylor expansion of n in k 1546856172.628 * [misc]backup-simplify: Simplify n into n 1546856172.628 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546856172.628 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1546856172.628 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1546856172.628 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546856172.628 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546856172.628 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546856172.629 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1546856172.629 * [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)))) 1546856172.629 * [misc]backup-simplify: Simplify (* 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) into 0 1546856172.629 * [misc]taylor: Taking taylor expansion of 0 in n 1546856172.629 * [misc]backup-simplify: Simplify 0 into 0 1546856172.629 * [misc]backup-simplify: Simplify 0 into 0 1546856172.629 * [misc]backup-simplify: Simplify (+ (* 0 0) (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) into (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) 1546856172.630 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 1546856172.630 * [misc]taylor: Taking taylor expansion of (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1546856172.630 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546856172.630 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546856172.630 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546856172.630 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546856172.630 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546856172.630 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546856172.630 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856172.630 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.630 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546856172.630 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856172.630 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.630 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546856172.630 * [misc]taylor: Taking taylor expansion of k in n 1546856172.630 * [misc]backup-simplify: Simplify k into k 1546856172.630 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546856172.630 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546856172.630 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546856172.630 * [misc]taylor: Taking taylor expansion of 2 in n 1546856172.630 * [misc]backup-simplify: Simplify 2 into 2 1546856172.630 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856172.630 * [misc]taylor: Taking taylor expansion of PI in n 1546856172.630 * [misc]backup-simplify: Simplify PI into PI 1546856172.630 * [misc]taylor: Taking taylor expansion of n in n 1546856172.630 * [misc]backup-simplify: Simplify 0 into 0 1546856172.630 * [misc]backup-simplify: Simplify 1 into 1 1546856172.630 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856172.631 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546856172.631 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856172.631 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546856172.631 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546856172.632 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546856172.632 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546856172.633 * [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))) 1546856172.633 * [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)))) 1546856172.634 * [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))))) 1546856172.635 * [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)))))) 1546856172.635 * [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)))))) 1546856172.635 * [misc]backup-simplify: Simplify 0 into 0 1546856172.636 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1546856172.637 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* +nan.0 0) (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) into (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) 1546856172.637 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 1546856172.637 * [misc]taylor: Taking taylor expansion of (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1546856172.637 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546856172.637 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546856172.637 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546856172.637 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546856172.637 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546856172.637 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546856172.637 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856172.637 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.637 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546856172.637 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856172.637 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.637 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546856172.637 * [misc]taylor: Taking taylor expansion of k in n 1546856172.637 * [misc]backup-simplify: Simplify k into k 1546856172.637 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546856172.637 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546856172.637 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546856172.637 * [misc]taylor: Taking taylor expansion of 2 in n 1546856172.638 * [misc]backup-simplify: Simplify 2 into 2 1546856172.638 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856172.638 * [misc]taylor: Taking taylor expansion of PI in n 1546856172.638 * [misc]backup-simplify: Simplify PI into PI 1546856172.638 * [misc]taylor: Taking taylor expansion of n in n 1546856172.638 * [misc]backup-simplify: Simplify 0 into 0 1546856172.638 * [misc]backup-simplify: Simplify 1 into 1 1546856172.638 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856172.638 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546856172.639 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856172.639 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546856172.639 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546856172.639 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546856172.640 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546856172.640 * [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))) 1546856172.641 * [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)))) 1546856172.642 * [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))))) 1546856172.642 * [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)))))) 1546856172.643 * [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)))))) 1546856172.644 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546856172.646 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546856172.649 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546856172.649 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546856172.649 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546856172.649 * [misc]backup-simplify: Simplify (- 0) into 0 1546856172.650 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856172.651 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546856172.651 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1546856172.653 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546856172.654 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0 1546856172.654 * [misc]backup-simplify: Simplify (- 0) into 0 1546856172.654 * [misc]backup-simplify: Simplify 0 into 0 1546856172.654 * [misc]backup-simplify: Simplify 0 into 0 1546856172.656 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1546856172.656 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* +nan.0 0) (+ (* +nan.0 0) (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) 1546856172.656 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 1546856172.656 * [misc]taylor: Taking taylor expansion of (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1546856172.656 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546856172.656 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546856172.656 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546856172.656 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546856172.657 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546856172.657 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546856172.657 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856172.657 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.657 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546856172.657 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856172.657 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.657 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546856172.657 * [misc]taylor: Taking taylor expansion of k in n 1546856172.657 * [misc]backup-simplify: Simplify k into k 1546856172.657 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546856172.657 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546856172.657 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546856172.657 * [misc]taylor: Taking taylor expansion of 2 in n 1546856172.657 * [misc]backup-simplify: Simplify 2 into 2 1546856172.657 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856172.657 * [misc]taylor: Taking taylor expansion of PI in n 1546856172.657 * [misc]backup-simplify: Simplify PI into PI 1546856172.657 * [misc]taylor: Taking taylor expansion of n in n 1546856172.657 * [misc]backup-simplify: Simplify 0 into 0 1546856172.657 * [misc]backup-simplify: Simplify 1 into 1 1546856172.657 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856172.658 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546856172.658 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856172.658 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546856172.658 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546856172.658 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546856172.659 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546856172.660 * [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))) 1546856172.660 * [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)))) 1546856172.661 * [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))))) 1546856172.662 * [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)))))) 1546856172.663 * [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)))))) 1546856172.665 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (* 1 (/ 1 k))))) 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)))))))) 1546856172.666 * [misc]backup-simplify: Simplify (/ 1 (/ (sqrt (/ 1 (- k))) (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2))))) into (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) 1546856172.666 * [misc]approximate: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (k n) around 0 1546856172.666 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 1546856172.666 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546856172.666 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546856172.666 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546856172.666 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546856172.666 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546856172.666 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856172.666 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.666 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546856172.666 * [misc]taylor: Taking taylor expansion of k in n 1546856172.666 * [misc]backup-simplify: Simplify k into k 1546856172.666 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546856172.666 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856172.666 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.666 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546856172.666 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546856172.666 * [misc]taylor: Taking taylor expansion of -2 in n 1546856172.666 * [misc]backup-simplify: Simplify -2 into -2 1546856172.666 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856172.666 * [misc]taylor: Taking taylor expansion of PI in n 1546856172.666 * [misc]backup-simplify: Simplify PI into PI 1546856172.666 * [misc]taylor: Taking taylor expansion of n in n 1546856172.667 * [misc]backup-simplify: Simplify 0 into 0 1546856172.667 * [misc]backup-simplify: Simplify 1 into 1 1546856172.667 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856172.667 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546856172.668 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546856172.668 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546856172.668 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546856172.669 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546856172.669 * [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))) 1546856172.670 * [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)))) 1546856172.670 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1546856172.670 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1546856172.670 * [misc]taylor: Taking taylor expansion of -1 in n 1546856172.670 * [misc]backup-simplify: Simplify -1 into -1 1546856172.670 * [misc]taylor: Taking taylor expansion of k in n 1546856172.670 * [misc]backup-simplify: Simplify k into k 1546856172.670 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1546856172.670 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1546856172.670 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1546856172.671 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1546856172.671 * [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))) 1546856172.671 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 1546856172.671 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1546856172.671 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1546856172.671 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1546856172.672 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546856172.672 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546856172.672 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856172.672 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.672 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546856172.672 * [misc]taylor: Taking taylor expansion of k in k 1546856172.672 * [misc]backup-simplify: Simplify 0 into 0 1546856172.672 * [misc]backup-simplify: Simplify 1 into 1 1546856172.672 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546856172.672 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856172.672 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.672 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1546856172.672 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1546856172.672 * [misc]taylor: Taking taylor expansion of -2 in k 1546856172.672 * [misc]backup-simplify: Simplify -2 into -2 1546856172.672 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546856172.672 * [misc]taylor: Taking taylor expansion of PI in k 1546856172.672 * [misc]backup-simplify: Simplify PI into PI 1546856172.672 * [misc]taylor: Taking taylor expansion of n in k 1546856172.672 * [misc]backup-simplify: Simplify n into n 1546856172.672 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546856172.672 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1546856172.672 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1546856172.673 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546856172.673 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546856172.673 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1546856172.673 * [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))) 1546856172.673 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1546856172.673 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1546856172.673 * [misc]taylor: Taking taylor expansion of -1 in k 1546856172.673 * [misc]backup-simplify: Simplify -1 into -1 1546856172.673 * [misc]taylor: Taking taylor expansion of k in k 1546856172.673 * [misc]backup-simplify: Simplify 0 into 0 1546856172.673 * [misc]backup-simplify: Simplify 1 into 1 1546856172.674 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1546856172.674 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546856172.674 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1546856172.674 * [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)))) 1546856172.674 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 1546856172.674 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1546856172.675 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1546856172.675 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1546856172.675 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546856172.675 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546856172.675 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856172.675 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.675 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546856172.675 * [misc]taylor: Taking taylor expansion of k in k 1546856172.675 * [misc]backup-simplify: Simplify 0 into 0 1546856172.675 * [misc]backup-simplify: Simplify 1 into 1 1546856172.675 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546856172.675 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856172.675 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.675 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1546856172.675 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1546856172.675 * [misc]taylor: Taking taylor expansion of -2 in k 1546856172.675 * [misc]backup-simplify: Simplify -2 into -2 1546856172.675 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546856172.675 * [misc]taylor: Taking taylor expansion of PI in k 1546856172.675 * [misc]backup-simplify: Simplify PI into PI 1546856172.675 * [misc]taylor: Taking taylor expansion of n in k 1546856172.675 * [misc]backup-simplify: Simplify n into n 1546856172.675 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546856172.676 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1546856172.676 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1546856172.676 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546856172.676 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546856172.676 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1546856172.676 * [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))) 1546856172.676 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1546856172.676 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1546856172.676 * [misc]taylor: Taking taylor expansion of -1 in k 1546856172.676 * [misc]backup-simplify: Simplify -1 into -1 1546856172.676 * [misc]taylor: Taking taylor expansion of k in k 1546856172.676 * [misc]backup-simplify: Simplify 0 into 0 1546856172.677 * [misc]backup-simplify: Simplify 1 into 1 1546856172.677 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1546856172.677 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546856172.677 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1546856172.678 * [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)))) 1546856172.678 * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1546856172.678 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546856172.678 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546856172.678 * [misc]taylor: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1546856172.678 * [misc]taylor: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546856172.678 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546856172.678 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546856172.678 * [misc]taylor: Taking taylor expansion of -2 in n 1546856172.678 * [misc]backup-simplify: Simplify -2 into -2 1546856172.678 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856172.678 * [misc]taylor: Taking taylor expansion of PI in n 1546856172.678 * [misc]backup-simplify: Simplify PI into PI 1546856172.678 * [misc]taylor: Taking taylor expansion of n in n 1546856172.678 * [misc]backup-simplify: Simplify 0 into 0 1546856172.678 * [misc]backup-simplify: Simplify 1 into 1 1546856172.678 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856172.679 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546856172.679 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546856172.679 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546856172.679 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546856172.679 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856172.679 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.679 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546856172.679 * [misc]taylor: Taking taylor expansion of k in n 1546856172.679 * [misc]backup-simplify: Simplify k into k 1546856172.679 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546856172.679 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856172.679 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.680 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546856172.680 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546856172.680 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546856172.681 * [misc]backup-simplify: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1546856172.682 * [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)))) 1546856172.682 * [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))))) 1546856172.683 * [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))))) 1546856172.683 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1546856172.684 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1546856172.685 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) 1546856172.685 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 1546856172.685 * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1546856172.685 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546856172.685 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546856172.685 * [misc]taylor: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1546856172.685 * [misc]taylor: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546856172.685 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546856172.685 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546856172.685 * [misc]taylor: Taking taylor expansion of -2 in n 1546856172.685 * [misc]backup-simplify: Simplify -2 into -2 1546856172.686 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856172.686 * [misc]taylor: Taking taylor expansion of PI in n 1546856172.686 * [misc]backup-simplify: Simplify PI into PI 1546856172.686 * [misc]taylor: Taking taylor expansion of n in n 1546856172.686 * [misc]backup-simplify: Simplify 0 into 0 1546856172.686 * [misc]backup-simplify: Simplify 1 into 1 1546856172.686 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856172.686 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546856172.687 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546856172.687 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546856172.687 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546856172.687 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856172.687 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.687 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546856172.687 * [misc]taylor: Taking taylor expansion of k in n 1546856172.687 * [misc]backup-simplify: Simplify k into k 1546856172.687 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546856172.687 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856172.687 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.688 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546856172.688 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546856172.688 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546856172.688 * [misc]backup-simplify: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1546856172.689 * [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)))) 1546856172.690 * [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))))) 1546856172.690 * [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)))))) 1546856172.691 * [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)))))) 1546856172.692 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546856172.692 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546856172.692 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546856172.692 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856172.694 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546856172.694 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1546856172.697 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1546856172.698 * [misc]backup-simplify: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0 1546856172.699 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546856172.701 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into 0 1546856172.701 * [misc]backup-simplify: Simplify 0 into 0 1546856172.701 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856172.702 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1546856172.703 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) 1546856172.704 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 1546856172.704 * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1546856172.704 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546856172.704 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546856172.704 * [misc]taylor: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1546856172.704 * [misc]taylor: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546856172.704 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546856172.704 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546856172.704 * [misc]taylor: Taking taylor expansion of -2 in n 1546856172.704 * [misc]backup-simplify: Simplify -2 into -2 1546856172.704 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856172.704 * [misc]taylor: Taking taylor expansion of PI in n 1546856172.704 * [misc]backup-simplify: Simplify PI into PI 1546856172.704 * [misc]taylor: Taking taylor expansion of n in n 1546856172.704 * [misc]backup-simplify: Simplify 0 into 0 1546856172.704 * [misc]backup-simplify: Simplify 1 into 1 1546856172.704 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856172.705 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546856172.705 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546856172.705 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546856172.705 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546856172.705 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856172.705 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.705 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546856172.705 * [misc]taylor: Taking taylor expansion of k in n 1546856172.705 * [misc]backup-simplify: Simplify k into k 1546856172.705 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546856172.705 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856172.705 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856172.706 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546856172.706 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546856172.706 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546856172.707 * [misc]backup-simplify: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1546856172.707 * [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)))) 1546856172.708 * [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))))) 1546856172.709 * [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)))))) 1546856172.710 * [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)))))) 1546856172.712 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (* 1 (/ 1 (- k)))) (* +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))))))))))) 1546856172.712 * * * [misc]progress: simplifying candidates 1546856172.712 * * * * [misc]progress: [ 1 / 128 ] simplifiying candidate # 1546856172.713 * * * * [misc]progress: [ 2 / 128 ] simplifiying candidate # 1546856172.713 * * * * [misc]progress: [ 3 / 128 ] simplifiying candidate # 1546856172.713 * [enter]simplify: Simplifying (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) 1546856172.713 * * [misc]simplify: iters left: 6 (11 enodes) 1546856172.717 * * [misc]simplify: iters left: 5 (21 enodes) 1546856172.724 * * [misc]simplify: iters left: 4 (47 enodes) 1546856172.741 * * [misc]simplify: iters left: 3 (113 enodes) 1546856172.801 * * [misc]simplify: iters left: 2 (328 enodes) 1546856173.088 * [exit]simplify: Simplified to (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) 1546856173.088 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ 1 (/ (sqrt k) (exp (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))))))) 1546856173.088 * * * * [misc]progress: [ 4 / 128 ] simplifiying candidate # 1546856173.089 * * * * [misc]progress: [ 5 / 128 ] simplifiying candidate # 1546856173.089 * [enter]simplify: Simplifying (* PI (* n 2)) 1546856173.089 * * [misc]simplify: iters left: 4 (5 enodes) 1546856173.091 * * [misc]simplify: iters left: 3 (9 enodes) 1546856173.093 * * [misc]simplify: iters left: 2 (15 enodes) 1546856173.097 * * [misc]simplify: iters left: 1 (17 enodes) 1546856173.101 * [exit]simplify: Simplified to (* (* 2 n) PI) 1546856173.101 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* 2 n) PI) (* 1 (- 1/2 (/ k 2))))))) 1546856173.101 * * * * [misc]progress: [ 6 / 128 ] simplifiying candidate # 1546856173.101 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (/ k 2)) 1546856173.101 * * [misc]simplify: iters left: 5 (8 enodes) 1546856173.104 * * [misc]simplify: iters left: 4 (12 enodes) 1546856173.105 * * [misc]simplify: iters left: 3 (18 enodes) 1546856173.108 * * [misc]simplify: iters left: 2 (20 enodes) 1546856173.110 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ k 2)) 1546856173.110 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (/ (sqrt k) (/ (pow (* PI (* n 2)) 1/2) (pow (* (* 2 n) PI) (/ k 2)))))) 1546856173.110 * * * * [misc]progress: [ 7 / 128 ] simplifiying candidate # 1546856173.110 * [enter]simplify: Simplifying (cbrt (- 1/2 (/ k 2))) 1546856173.110 * * [misc]simplify: iters left: 5 (6 enodes) 1546856173.111 * * [misc]simplify: iters left: 4 (8 enodes) 1546856173.113 * * [misc]simplify: iters left: 3 (11 enodes) 1546856173.114 * [exit]simplify: Simplified to (cbrt (- 1/2 (/ k 2))) 1546856173.114 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* PI (* n 2)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2))))))) 1546856173.114 * * * * [misc]progress: [ 8 / 128 ] simplifiying candidate # 1546856173.114 * [enter]simplify: Simplifying (sqrt (- 1/2 (/ k 2))) 1546856173.114 * * [misc]simplify: iters left: 5 (6 enodes) 1546856173.115 * * [misc]simplify: iters left: 4 (8 enodes) 1546856173.116 * * [misc]simplify: iters left: 3 (11 enodes) 1546856173.118 * [exit]simplify: Simplified to (sqrt (- 1/2 (/ k 2))) 1546856173.118 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* PI (* n 2)) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2))))))) 1546856173.118 * * * * [misc]progress: [ 9 / 128 ] simplifiying candidate # 1546856173.118 * [enter]simplify: Simplifying (- 1/2 (/ k 2)) 1546856173.118 * * [misc]simplify: iters left: 4 (5 enodes) 1546856173.119 * * [misc]simplify: iters left: 3 (7 enodes) 1546856173.120 * * [misc]simplify: iters left: 2 (10 enodes) 1546856173.121 * [exit]simplify: Simplified to (- 1/2 (/ k 2)) 1546856173.121 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* PI (* n 2)) 1) (- 1/2 (/ k 2)))))) 1546856173.121 * * * * [misc]progress: [ 10 / 128 ] simplifiying candidate # 1546856173.121 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1546856173.121 * * [misc]simplify: iters left: 5 (9 enodes) 1546856173.123 * * [misc]simplify: iters left: 4 (15 enodes) 1546856173.125 * * [misc]simplify: iters left: 3 (21 enodes) 1546856173.128 * * [misc]simplify: iters left: 2 (22 enodes) 1546856173.131 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1546856173.131 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (/ (sqrt k) (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2))))))) 1546856173.131 * * * * [misc]progress: [ 11 / 128 ] simplifiying candidate # 1546856173.131 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1546856173.131 * * [misc]simplify: iters left: 5 (9 enodes) 1546856173.132 * * [misc]simplify: iters left: 4 (15 enodes) 1546856173.135 * * [misc]simplify: iters left: 3 (21 enodes) 1546856173.137 * * [misc]simplify: iters left: 2 (22 enodes) 1546856173.140 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1546856173.140 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (/ (sqrt k) (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2))))))) 1546856173.140 * * * * [misc]progress: [ 12 / 128 ] simplifiying candidate # 1546856173.140 * [enter]simplify: Simplifying (pow PI (- 1/2 (/ k 2))) 1546856173.140 * * [misc]simplify: iters left: 5 (7 enodes) 1546856173.141 * * [misc]simplify: iters left: 4 (9 enodes) 1546856173.143 * * [misc]simplify: iters left: 3 (12 enodes) 1546856173.144 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1546856173.144 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ 1 (/ (sqrt k) (* (pow PI (- 1/2 (/ k 2))) (pow (* n 2) (- 1/2 (/ k 2))))))) 1546856173.144 * * * * [misc]progress: [ 13 / 128 ] simplifiying candidate # 1546856173.144 * * * * [misc]progress: [ 14 / 128 ] simplifiying candidate # 1546856173.144 * * * * [misc]progress: [ 15 / 128 ] simplifiying candidate # 1546856173.145 * * * * [misc]progress: [ 16 / 128 ] simplifiying candidate # 1546856173.145 * * * * [misc]progress: [ 17 / 128 ] simplifiying candidate # 1546856173.145 * * * * [misc]progress: [ 18 / 128 ] simplifiying candidate # 1546856173.145 * * * * [misc]progress: [ 19 / 128 ] simplifiying candidate # 1546856173.145 * * * * [misc]progress: [ 20 / 128 ] simplifiying candidate # 1546856173.145 * * * * [misc]progress: [ 21 / 128 ] simplifiying candidate # 1546856173.145 * * * * [misc]progress: [ 22 / 128 ] simplifiying candidate # 1546856173.145 * * * * [misc]progress: [ 23 / 128 ] simplifiying candidate # 1546856173.145 * * * * [misc]progress: [ 24 / 128 ] simplifiying candidate # 1546856173.145 * * * * [misc]progress: [ 25 / 128 ] simplifiying candidate # 1546856173.145 * * * * [misc]progress: [ 26 / 128 ] simplifiying candidate # 1546856173.145 * * * * [misc]progress: [ 27 / 128 ] simplifiying candidate # 1546856173.145 * * * * [misc]progress: [ 28 / 128 ] simplifiying candidate # 1546856173.145 * * * * [misc]progress: [ 29 / 128 ] simplifiying candidate # 1546856173.145 * * * * [misc]progress: [ 30 / 128 ] simplifiying candidate # 1546856173.145 * * * * [misc]progress: [ 31 / 128 ] simplifiying candidate # 1546856173.145 * * * * [misc]progress: [ 32 / 128 ] simplifiying candidate # 1546856173.145 * * * * [misc]progress: [ 33 / 128 ] simplifiying candidate # 1546856173.145 * * * * [misc]progress: [ 34 / 128 ] simplifiying candidate # 1546856173.145 * [enter]simplify: Simplifying (- (log (sqrt k)) (* (log (* PI (* n 2))) (- 1/2 (/ k 2)))) 1546856173.145 * * [misc]simplify: iters left: 6 (14 enodes) 1546856173.148 * * [misc]simplify: iters left: 5 (26 enodes) 1546856173.156 * * [misc]simplify: iters left: 4 (59 enodes) 1546856173.169 * * [misc]simplify: iters left: 3 (172 enodes) 1546856173.247 * [exit]simplify: Simplified to (fma (+ (/ k 2) -1/2) (log (* (* PI 2) n)) (log (sqrt k))) 1546856173.247 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (exp (fma (+ (/ k 2) -1/2) (log (* (* PI 2) n)) (log (sqrt k)))))) 1546856173.247 * * * * [misc]progress: [ 35 / 128 ] simplifiying candidate # 1546856173.247 * [enter]simplify: Simplifying (- (log (sqrt k)) (* (log (* PI (* n 2))) (- 1/2 (/ k 2)))) 1546856173.248 * * [misc]simplify: iters left: 6 (14 enodes) 1546856173.252 * * [misc]simplify: iters left: 5 (26 enodes) 1546856173.261 * * [misc]simplify: iters left: 4 (59 enodes) 1546856173.287 * * [misc]simplify: iters left: 3 (172 enodes) 1546856173.344 * [exit]simplify: Simplified to (fma (+ (/ k 2) -1/2) (log (* (* PI 2) n)) (log (sqrt k))) 1546856173.344 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (exp (fma (+ (/ k 2) -1/2) (log (* (* PI 2) n)) (log (sqrt k)))))) 1546856173.344 * * * * [misc]progress: [ 36 / 128 ] simplifiying candidate # 1546856173.345 * [enter]simplify: Simplifying (- (log (sqrt k)) (log (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546856173.345 * * [misc]simplify: iters left: 6 (14 enodes) 1546856173.347 * * [misc]simplify: iters left: 5 (24 enodes) 1546856173.351 * * [misc]simplify: iters left: 4 (46 enodes) 1546856173.361 * * [misc]simplify: iters left: 3 (105 enodes) 1546856173.416 * * [misc]simplify: iters left: 2 (354 enodes) 1546856173.667 * [exit]simplify: Simplified to (fma (+ (/ k 2) -1/2) (log (* n (* PI 2))) (log (sqrt k))) 1546856173.668 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (exp (fma (+ (/ k 2) -1/2) (log (* n (* PI 2))) (log (sqrt k)))))) 1546856173.668 * * * * [misc]progress: [ 37 / 128 ] simplifiying candidate # 1546856173.668 * * * * [misc]progress: [ 38 / 128 ] simplifiying candidate # 1546856173.668 * * * * [misc]progress: [ 39 / 128 ] simplifiying candidate # 1546856173.668 * [enter]simplify: Simplifying (/ (* (* (sqrt k) (sqrt k)) (sqrt k)) (* (* (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546856173.668 * * [misc]simplify: iters left: 6 (16 enodes) 1546856173.671 * * [misc]simplify: iters left: 5 (31 enodes) 1546856173.676 * * [misc]simplify: iters left: 4 (70 enodes) 1546856173.689 * * [misc]simplify: iters left: 3 (130 enodes) 1546856173.726 * * [misc]simplify: iters left: 2 (206 enodes) 1546856173.815 * * [misc]simplify: iters left: 1 (288 enodes) 1546856173.959 * [exit]simplify: Simplified to (/ (/ (* k (sqrt k)) (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (* (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (pow (* (* 2 PI) n) (- 1/2 (/ k 2))))) 1546856173.959 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (cbrt (/ (/ (* k (sqrt k)) (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (* (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))))))) 1546856173.959 * * * * [misc]progress: [ 40 / 128 ] simplifiying candidate # 1546856173.959 * * * * [misc]progress: [ 41 / 128 ] simplifiying candidate # 1546856173.959 * * * * [misc]progress: [ 42 / 128 ] simplifiying candidate # 1546856173.959 * * * * [misc]progress: [ 43 / 128 ] simplifiying candidate # 1546856173.959 * * * * [misc]progress: [ 44 / 128 ] simplifiying candidate # 1546856173.959 * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* PI (* n 2)) 1/2)) 1546856173.959 * * [misc]simplify: iters left: 6 (12 enodes) 1546856173.963 * * [misc]simplify: iters left: 5 (19 enodes) 1546856173.969 * * [misc]simplify: iters left: 4 (27 enodes) 1546856173.976 * * [misc]simplify: iters left: 3 (29 enodes) 1546856173.984 * [exit]simplify: Simplified to (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (* (* n 2) PI))) 1546856173.984 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (* (* n 2) PI))) (/ (cbrt (sqrt k)) (pow (* PI (* n 2)) (- (/ k 2))))))) 1546856173.985 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (pow (* PI (* n 2)) (- (/ k 2)))) 1546856173.985 * * [misc]simplify: iters left: 6 (12 enodes) 1546856173.989 * * [misc]simplify: iters left: 5 (18 enodes) 1546856173.994 * * [misc]simplify: iters left: 4 (24 enodes) 1546856174.001 * * [misc]simplify: iters left: 3 (25 enodes) 1546856174.007 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2)))) 1546856174.008 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (* (* n 2) PI))) (/ (cbrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2))))))) 1546856174.008 * * * * [misc]progress: [ 45 / 128 ] simplifiying candidate # 1546856174.008 * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* PI (* n 2)) 1/2)) 1546856174.008 * * [misc]simplify: iters left: 6 (12 enodes) 1546856174.012 * * [misc]simplify: iters left: 5 (19 enodes) 1546856174.018 * * [misc]simplify: iters left: 4 (27 enodes) 1546856174.025 * * [misc]simplify: iters left: 3 (29 enodes) 1546856174.032 * [exit]simplify: Simplified to (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (* (* n 2) PI))) 1546856174.033 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (* (* n 2) PI))) (/ (cbrt (sqrt k)) (pow (* PI (* n 2)) (- (/ k 2))))))) 1546856174.033 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (pow (* PI (* n 2)) (- (/ k 2)))) 1546856174.033 * * [misc]simplify: iters left: 6 (12 enodes) 1546856174.037 * * [misc]simplify: iters left: 5 (18 enodes) 1546856174.042 * * [misc]simplify: iters left: 4 (24 enodes) 1546856174.049 * * [misc]simplify: iters left: 3 (25 enodes) 1546856174.055 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2)))) 1546856174.055 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (* (* n 2) PI))) (/ (cbrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2))))))) 1546856174.055 * * * * [misc]progress: [ 46 / 128 ] simplifiying candidate # 1546856174.055 * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow PI (- 1/2 (/ k 2)))) 1546856174.056 * * [misc]simplify: iters left: 6 (11 enodes) 1546856174.059 * * [misc]simplify: iters left: 5 (15 enodes) 1546856174.063 * * [misc]simplify: iters left: 4 (20 enodes) 1546856174.069 * * [misc]simplify: iters left: 3 (21 enodes) 1546856174.075 * [exit]simplify: Simplified to (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow PI (- 1/2 (/ k 2)))) 1546856174.075 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow PI (- 1/2 (/ k 2)))) (/ (cbrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2))))))) 1546856174.075 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))) 1546856174.075 * * [misc]simplify: iters left: 6 (11 enodes) 1546856174.078 * * [misc]simplify: iters left: 5 (14 enodes) 1546856174.082 * * [misc]simplify: iters left: 4 (17 enodes) 1546856174.089 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))) 1546856174.089 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow PI (- 1/2 (/ k 2)))) (/ (cbrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2))))))) 1546856174.089 * * * * [misc]progress: [ 47 / 128 ] simplifiying candidate # 1546856174.089 * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) 1546856174.090 * * [misc]simplify: iters left: 6 (16 enodes) 1546856174.095 * * [misc]simplify: iters left: 5 (28 enodes) 1546856174.103 * * [misc]simplify: iters left: 4 (46 enodes) 1546856174.116 * * [misc]simplify: iters left: 3 (50 enodes) 1546856174.128 * * [misc]simplify: iters left: 2 (53 enodes) 1546856174.142 * [exit]simplify: Simplified to (* (/ (cbrt (sqrt k)) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) (/ (cbrt (sqrt k)) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))))) 1546856174.142 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (* (/ (cbrt (sqrt k)) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) (/ (cbrt (sqrt k)) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))))) (/ (cbrt (sqrt k)) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))))) 1546856174.143 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546856174.143 * * [misc]simplify: iters left: 6 (14 enodes) 1546856174.148 * * [misc]simplify: iters left: 5 (20 enodes) 1546856174.154 * * [misc]simplify: iters left: 4 (29 enodes) 1546856174.161 * * [misc]simplify: iters left: 3 (30 enodes) 1546856174.169 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) 1546856174.169 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) (/ (cbrt (sqrt k)) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))))))) 1546856174.169 * * * * [misc]progress: [ 48 / 128 ] simplifiying candidate # 1546856174.170 * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546856174.170 * * [misc]simplify: iters left: 6 (15 enodes) 1546856174.175 * * [misc]simplify: iters left: 5 (23 enodes) 1546856174.182 * * [misc]simplify: iters left: 4 (34 enodes) 1546856174.192 * * [misc]simplify: iters left: 3 (36 enodes) 1546856174.201 * [exit]simplify: Simplified to (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) 1546856174.201 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 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)))))))) 1546856174.201 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546856174.202 * * [misc]simplify: iters left: 6 (14 enodes) 1546856174.206 * * [misc]simplify: iters left: 5 (20 enodes) 1546856174.212 * * [misc]simplify: iters left: 4 (29 enodes) 1546856174.219 * * [misc]simplify: iters left: 3 (30 enodes) 1546856174.227 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) 1546856174.227 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 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)))))))) 1546856174.227 * * * * [misc]progress: [ 49 / 128 ] simplifiying candidate # 1546856174.227 * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1) 1546856174.227 * * [misc]simplify: iters left: 6 (6 enodes) 1546856174.229 * * [misc]simplify: iters left: 5 (10 enodes) 1546856174.232 * * [misc]simplify: iters left: 4 (16 enodes) 1546856174.236 * * [misc]simplify: iters left: 3 (18 enodes) 1546856174.241 * * [misc]simplify: iters left: 2 (23 enodes) 1546856174.247 * [exit]simplify: Simplified to (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1546856174.247 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (cbrt (sqrt k)) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))) 1546856174.248 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1546856174.248 * * [misc]simplify: iters left: 6 (13 enodes) 1546856174.252 * * [misc]simplify: iters left: 5 (19 enodes) 1546856174.257 * * [misc]simplify: iters left: 4 (28 enodes) 1546856174.264 * * [misc]simplify: iters left: 3 (30 enodes) 1546856174.272 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (pow (* 2 (* PI n)) (- 1/2 (/ k 2)))) 1546856174.272 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (cbrt (sqrt k)) (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))))) 1546856174.272 * * * * [misc]progress: [ 50 / 128 ] simplifiying candidate # 1546856174.272 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (pow (* PI (* n 2)) 1/2)) 1546856174.272 * * [misc]simplify: iters left: 6 (11 enodes) 1546856174.276 * * [misc]simplify: iters left: 5 (16 enodes) 1546856174.280 * * [misc]simplify: iters left: 4 (22 enodes) 1546856174.285 * * [misc]simplify: iters left: 3 (23 enodes) 1546856174.291 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (sqrt (* (* PI n) 2))) 1546856174.291 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (sqrt (* (* PI n) 2))) (/ (sqrt (sqrt k)) (pow (* PI (* n 2)) (- (/ k 2))))))) 1546856174.292 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (pow (* PI (* n 2)) (- (/ k 2)))) 1546856174.292 * * [misc]simplify: iters left: 6 (12 enodes) 1546856174.295 * * [misc]simplify: iters left: 5 (18 enodes) 1546856174.300 * * [misc]simplify: iters left: 4 (24 enodes) 1546856174.307 * * [misc]simplify: iters left: 3 (25 enodes) 1546856174.313 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2)))) 1546856174.313 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (sqrt (* (* PI n) 2))) (/ (sqrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2))))))) 1546856174.313 * * * * [misc]progress: [ 51 / 128 ] simplifiying candidate # 1546856174.314 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (pow (* PI (* n 2)) 1/2)) 1546856174.314 * * [misc]simplify: iters left: 6 (11 enodes) 1546856174.316 * * [misc]simplify: iters left: 5 (16 enodes) 1546856174.318 * * [misc]simplify: iters left: 4 (22 enodes) 1546856174.321 * * [misc]simplify: iters left: 3 (23 enodes) 1546856174.324 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (sqrt (* (* PI n) 2))) 1546856174.324 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (sqrt (* (* PI n) 2))) (/ (sqrt (sqrt k)) (pow (* PI (* n 2)) (- (/ k 2))))))) 1546856174.324 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (pow (* PI (* n 2)) (- (/ k 2)))) 1546856174.324 * * [misc]simplify: iters left: 6 (12 enodes) 1546856174.326 * * [misc]simplify: iters left: 5 (18 enodes) 1546856174.329 * * [misc]simplify: iters left: 4 (24 enodes) 1546856174.332 * * [misc]simplify: iters left: 3 (25 enodes) 1546856174.335 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2)))) 1546856174.336 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (sqrt (* (* PI n) 2))) (/ (sqrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2))))))) 1546856174.336 * * * * [misc]progress: [ 52 / 128 ] simplifiying candidate # 1546856174.336 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (pow PI (- 1/2 (/ k 2)))) 1546856174.336 * * [misc]simplify: iters left: 6 (10 enodes) 1546856174.337 * * [misc]simplify: iters left: 5 (12 enodes) 1546856174.339 * * [misc]simplify: iters left: 4 (15 enodes) 1546856174.341 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (pow PI (- 1/2 (/ k 2)))) 1546856174.341 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (pow PI (- 1/2 (/ k 2)))) (/ (sqrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2))))))) 1546856174.341 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))) 1546856174.341 * * [misc]simplify: iters left: 6 (11 enodes) 1546856174.343 * * [misc]simplify: iters left: 5 (14 enodes) 1546856174.345 * * [misc]simplify: iters left: 4 (17 enodes) 1546856174.347 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))) 1546856174.347 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (pow PI (- 1/2 (/ k 2)))) (/ (sqrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2))))))) 1546856174.347 * * * * [misc]progress: [ 53 / 128 ] simplifiying candidate # 1546856174.347 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) 1546856174.347 * * [misc]simplify: iters left: 6 (15 enodes) 1546856174.350 * * [misc]simplify: iters left: 5 (23 enodes) 1546856174.354 * * [misc]simplify: iters left: 4 (32 enodes) 1546856174.358 * * [misc]simplify: iters left: 3 (34 enodes) 1546856174.362 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (* (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))))) 1546856174.362 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (* (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))))) (/ (sqrt (sqrt k)) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))))) 1546856174.362 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546856174.362 * * [misc]simplify: iters left: 6 (14 enodes) 1546856174.364 * * [misc]simplify: iters left: 5 (20 enodes) 1546856174.367 * * [misc]simplify: iters left: 4 (29 enodes) 1546856174.371 * * [misc]simplify: iters left: 3 (30 enodes) 1546856174.379 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) 1546856174.379 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) (/ (sqrt (sqrt k)) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))))))) 1546856174.379 * * * * [misc]progress: [ 54 / 128 ] simplifiying candidate # 1546856174.379 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546856174.380 * * [misc]simplify: iters left: 6 (14 enodes) 1546856174.384 * * [misc]simplify: iters left: 5 (20 enodes) 1546856174.390 * * [misc]simplify: iters left: 4 (29 enodes) 1546856174.398 * * [misc]simplify: iters left: 3 (30 enodes) 1546856174.402 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) 1546856174.402 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 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)))))))) 1546856174.403 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546856174.403 * * [misc]simplify: iters left: 6 (14 enodes) 1546856174.405 * * [misc]simplify: iters left: 5 (20 enodes) 1546856174.408 * * [misc]simplify: iters left: 4 (29 enodes) 1546856174.411 * * [misc]simplify: iters left: 3 (30 enodes) 1546856174.415 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) 1546856174.415 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 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)))))))) 1546856174.415 * * * * [misc]progress: [ 55 / 128 ] simplifiying candidate # 1546856174.415 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) 1) 1546856174.415 * * [misc]simplify: iters left: 4 (5 enodes) 1546856174.416 * * [misc]simplify: iters left: 3 (7 enodes) 1546856174.417 * * [misc]simplify: iters left: 2 (9 enodes) 1546856174.418 * [exit]simplify: Simplified to (sqrt (sqrt k)) 1546856174.418 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))) 1546856174.419 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1546856174.419 * * [misc]simplify: iters left: 6 (13 enodes) 1546856174.421 * * [misc]simplify: iters left: 5 (19 enodes) 1546856174.423 * * [misc]simplify: iters left: 4 (28 enodes) 1546856174.427 * * [misc]simplify: iters left: 3 (30 enodes) 1546856174.435 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (pow (* 2 (* PI n)) (- 1/2 (/ k 2)))) 1546856174.435 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))))) 1546856174.435 * * * * [misc]progress: [ 56 / 128 ] simplifiying candidate # 1546856174.435 * [enter]simplify: Simplifying (/ 1 (pow (* PI (* n 2)) 1/2)) 1546856174.435 * * [misc]simplify: iters left: 6 (9 enodes) 1546856174.438 * * [misc]simplify: iters left: 5 (16 enodes) 1546856174.443 * * [misc]simplify: iters left: 4 (22 enodes) 1546856174.448 * * [misc]simplify: iters left: 3 (23 enodes) 1546856174.455 * [exit]simplify: Simplified to (/ 1 (sqrt (* n (* 2 PI)))) 1546856174.455 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ 1 (sqrt (* n (* 2 PI)))) (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2))))))) 1546856174.456 * [enter]simplify: Simplifying (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2)))) 1546856174.456 * * [misc]simplify: iters left: 6 (11 enodes) 1546856174.459 * * [misc]simplify: iters left: 5 (17 enodes) 1546856174.464 * * [misc]simplify: iters left: 4 (23 enodes) 1546856174.471 * * [misc]simplify: iters left: 3 (24 enodes) 1546856174.477 * [exit]simplify: Simplified to (/ (sqrt k) (pow (* 2 (* PI n)) (- (/ k 2)))) 1546856174.477 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ 1 (sqrt (* n (* 2 PI)))) (/ (sqrt k) (pow (* 2 (* PI n)) (- (/ k 2))))))) 1546856174.477 * * * * [misc]progress: [ 57 / 128 ] simplifiying candidate # 1546856174.477 * [enter]simplify: Simplifying (/ 1 (pow (* PI (* n 2)) 1/2)) 1546856174.477 * * [misc]simplify: iters left: 6 (9 enodes) 1546856174.480 * * [misc]simplify: iters left: 5 (16 enodes) 1546856174.485 * * [misc]simplify: iters left: 4 (22 enodes) 1546856174.490 * * [misc]simplify: iters left: 3 (23 enodes) 1546856174.496 * [exit]simplify: Simplified to (/ 1 (sqrt (* n (* 2 PI)))) 1546856174.496 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ 1 (sqrt (* n (* 2 PI)))) (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2))))))) 1546856174.496 * [enter]simplify: Simplifying (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2)))) 1546856174.497 * * [misc]simplify: iters left: 6 (11 enodes) 1546856174.500 * * [misc]simplify: iters left: 5 (17 enodes) 1546856174.505 * * [misc]simplify: iters left: 4 (23 enodes) 1546856174.511 * * [misc]simplify: iters left: 3 (24 enodes) 1546856174.518 * [exit]simplify: Simplified to (/ (sqrt k) (pow (* 2 (* PI n)) (- (/ k 2)))) 1546856174.518 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ 1 (sqrt (* n (* 2 PI)))) (/ (sqrt k) (pow (* 2 (* PI n)) (- (/ k 2))))))) 1546856174.518 * * * * [misc]progress: [ 58 / 128 ] simplifiying candidate # 1546856174.518 * [enter]simplify: Simplifying (/ 1 (pow PI (- 1/2 (/ k 2)))) 1546856174.518 * * [misc]simplify: iters left: 6 (9 enodes) 1546856174.521 * * [misc]simplify: iters left: 5 (13 enodes) 1546856174.525 * * [misc]simplify: iters left: 4 (16 enodes) 1546856174.529 * [exit]simplify: Simplified to (/ 1 (pow PI (- 1/2 (/ k 2)))) 1546856174.529 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ 1 (pow PI (- 1/2 (/ k 2)))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))))) 1546856174.530 * [enter]simplify: Simplifying (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2)))) 1546856174.530 * * [misc]simplify: iters left: 6 (10 enodes) 1546856174.533 * * [misc]simplify: iters left: 5 (13 enodes) 1546856174.537 * * [misc]simplify: iters left: 4 (16 enodes) 1546856174.542 * [exit]simplify: Simplified to (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2)))) 1546856174.542 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ 1 (pow PI (- 1/2 (/ k 2)))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))))) 1546856174.542 * * * * [misc]progress: [ 59 / 128 ] simplifiying candidate # 1546856174.542 * [enter]simplify: Simplifying (/ 1 (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) 1546856174.542 * * [misc]simplify: iters left: 6 (14 enodes) 1546856174.547 * * [misc]simplify: iters left: 5 (24 enodes) 1546856174.554 * * [misc]simplify: iters left: 4 (33 enodes) 1546856174.563 * * [misc]simplify: iters left: 3 (34 enodes) 1546856174.572 * [exit]simplify: Simplified to (/ (/ 1 (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) 1546856174.572 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ (/ 1 (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)))))))) 1546856174.572 * [enter]simplify: Simplifying (/ (sqrt k) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546856174.572 * * [misc]simplify: iters left: 6 (13 enodes) 1546856174.574 * * [misc]simplify: iters left: 5 (19 enodes) 1546856174.577 * * [misc]simplify: iters left: 4 (28 enodes) 1546856174.581 * * [misc]simplify: iters left: 3 (30 enodes) 1546856174.584 * [exit]simplify: Simplified to (/ (sqrt k) (cbrt (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))) 1546856174.584 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ 1 (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) (/ (sqrt k) (cbrt (pow (* 2 (* PI n)) (- 1/2 (/ k 2)))))))) 1546856174.584 * * * * [misc]progress: [ 60 / 128 ] simplifiying candidate # 1546856174.585 * [enter]simplify: Simplifying (/ 1 (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546856174.585 * * [misc]simplify: iters left: 6 (13 enodes) 1546856174.587 * * [misc]simplify: iters left: 5 (21 enodes) 1546856174.591 * * [misc]simplify: iters left: 4 (30 enodes) 1546856174.594 * * [misc]simplify: iters left: 3 (31 enodes) 1546856174.598 * [exit]simplify: Simplified to (/ 1 (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2))))) 1546856174.598 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ 1 (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2))))) (/ (sqrt k) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))))) 1546856174.598 * [enter]simplify: Simplifying (/ (sqrt k) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546856174.598 * * [misc]simplify: iters left: 6 (13 enodes) 1546856174.601 * * [misc]simplify: iters left: 5 (19 enodes) 1546856174.603 * * [misc]simplify: iters left: 4 (28 enodes) 1546856174.607 * * [misc]simplify: iters left: 3 (30 enodes) 1546856174.611 * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))) 1546856174.611 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ 1 (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (/ (sqrt k) (sqrt (pow (* 2 (* PI n)) (- 1/2 (/ k 2)))))))) 1546856174.611 * * * * [misc]progress: [ 61 / 128 ] simplifiying candidate # 1546856174.611 * [enter]simplify: Simplifying (/ 1 1) 1546856174.611 * * [misc]simplify: iters left: 2 (2 enodes) 1546856174.611 * * [misc]simplify: iters left: 1 (4 enodes) 1546856174.612 * [exit]simplify: Simplified to 1 1546856174.612 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* 1 (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))) 1546856174.612 * [enter]simplify: Simplifying (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1546856174.612 * * [misc]simplify: iters left: 6 (12 enodes) 1546856174.614 * * [misc]simplify: iters left: 5 (18 enodes) 1546856174.617 * * [misc]simplify: iters left: 4 (27 enodes) 1546856174.620 * * [misc]simplify: iters left: 3 (29 enodes) 1546856174.624 * [exit]simplify: Simplified to (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1546856174.624 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* 1 (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))) 1546856174.624 * * * * [misc]progress: [ 62 / 128 ] simplifiying candidate # 1546856174.624 * * * * [misc]progress: [ 63 / 128 ] simplifiying candidate # 1546856174.624 * * * * [misc]progress: [ 64 / 128 ] simplifiying candidate # 1546856174.624 * * * * [misc]progress: [ 65 / 128 ] simplifiying candidate # 1546856174.625 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1546856174.625 * * [misc]simplify: iters left: 5 (9 enodes) 1546856174.626 * * [misc]simplify: iters left: 4 (15 enodes) 1546856174.628 * * [misc]simplify: iters left: 3 (21 enodes) 1546856174.631 * * [misc]simplify: iters left: 2 (22 enodes) 1546856174.634 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1546856174.634 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (/ (/ (sqrt k) (pow (* PI (* n 2)) 1/2)) (pow (* (* PI n) 2) (- (/ k 2)))))) 1546856174.634 * * * * [misc]progress: [ 66 / 128 ] simplifiying candidate # 1546856174.634 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1546856174.634 * * [misc]simplify: iters left: 5 (9 enodes) 1546856174.636 * * [misc]simplify: iters left: 4 (15 enodes) 1546856174.638 * * [misc]simplify: iters left: 3 (21 enodes) 1546856174.641 * * [misc]simplify: iters left: 2 (22 enodes) 1546856174.644 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1546856174.644 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (/ (/ (sqrt k) (pow (* PI (* n 2)) 1/2)) (pow (* (* PI n) 2) (- (/ k 2)))))) 1546856174.644 * * * * [misc]progress: [ 67 / 128 ] simplifiying candidate # 1546856174.644 * [enter]simplify: Simplifying (pow (* n 2) (- 1/2 (/ k 2))) 1546856174.644 * * [misc]simplify: iters left: 5 (8 enodes) 1546856174.645 * * [misc]simplify: iters left: 4 (11 enodes) 1546856174.647 * * [misc]simplify: iters left: 3 (14 enodes) 1546856174.649 * [exit]simplify: Simplified to (pow (* n 2) (- 1/2 (/ k 2))) 1546856174.649 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (/ (/ (sqrt k) (pow PI (- 1/2 (/ k 2)))) (pow (* n 2) (- 1/2 (/ k 2)))))) 1546856174.649 * * * * [misc]progress: [ 68 / 128 ] simplifiying candidate # 1546856174.649 * [enter]simplify: Simplifying (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1546856174.649 * * [misc]simplify: iters left: 6 (11 enodes) 1546856174.651 * * [misc]simplify: iters left: 5 (17 enodes) 1546856174.653 * * [misc]simplify: iters left: 4 (26 enodes) 1546856174.657 * * [misc]simplify: iters left: 3 (27 enodes) 1546856174.660 * [exit]simplify: Simplified to (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) 1546856174.660 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (/ (/ (sqrt k) (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))))) 1546856174.660 * * * * [misc]progress: [ 69 / 128 ] simplifiying candidate # 1546856174.660 * [enter]simplify: Simplifying (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1546856174.660 * * [misc]simplify: iters left: 6 (11 enodes) 1546856174.662 * * [misc]simplify: iters left: 5 (17 enodes) 1546856174.665 * * [misc]simplify: iters left: 4 (26 enodes) 1546856174.669 * * [misc]simplify: iters left: 3 (27 enodes) 1546856174.672 * [exit]simplify: Simplified to (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) 1546856174.672 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (/ (/ (sqrt k) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))))) 1546856174.672 * * * * [misc]progress: [ 70 / 128 ] simplifiying candidate # 1546856174.672 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- 1/2 (/ k 2))) 1546856174.673 * * [misc]simplify: iters left: 5 (10 enodes) 1546856174.674 * * [misc]simplify: iters left: 4 (16 enodes) 1546856174.677 * * [misc]simplify: iters left: 3 (25 enodes) 1546856174.681 * * [misc]simplify: iters left: 2 (26 enodes) 1546856174.687 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) 1546856174.687 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (/ (/ (sqrt k) 1) (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))))) 1546856174.687 * * * * [misc]progress: [ 71 / 128 ] simplifiying candidate # 1546856174.687 * [enter]simplify: Simplifying (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1546856174.687 * * [misc]simplify: iters left: 4 (4 enodes) 1546856174.689 * [exit]simplify: Simplified to (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1546856174.689 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (cbrt (sqrt k)))))) 1546856174.689 * * * * [misc]progress: [ 72 / 128 ] simplifiying candidate # 1546856174.689 * [enter]simplify: Simplifying (sqrt (sqrt k)) 1546856174.689 * * [misc]simplify: iters left: 2 (3 enodes) 1546856174.690 * [exit]simplify: Simplified to (sqrt (sqrt k)) 1546856174.690 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (/ (sqrt (sqrt k)) (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))) 1546856174.690 * * * * [misc]progress: [ 73 / 128 ] simplifiying candidate # 1546856174.690 * * * * [misc]progress: [ 74 / 128 ] simplifiying candidate # 1546856174.690 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (/ k 2)) 1546856174.690 * * [misc]simplify: iters left: 5 (8 enodes) 1546856174.693 * * [misc]simplify: iters left: 4 (12 enodes) 1546856174.696 * * [misc]simplify: iters left: 3 (18 enodes) 1546856174.701 * * [misc]simplify: iters left: 2 (20 enodes) 1546856174.706 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ k 2)) 1546856174.706 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (sqrt k) (pow (* PI (* n 2)) 1/2)) (pow (* (* 2 n) PI) (/ k 2))))) 1546856174.706 * * * * [misc]progress: [ 75 / 128 ] simplifiying candidate # 1546856174.706 * * * * [misc]progress: [ 76 / 128 ] simplifiying candidate # 1546856174.706 * * * * [misc]progress: [ 77 / 128 ] simplifiying candidate # 1546856174.706 * * * * [misc]progress: [ 78 / 128 ] simplifiying candidate # 1546856174.707 * [enter]simplify: Simplifying (- 1) 1546856174.707 * * [misc]simplify: iters left: 2 (2 enodes) 1546856174.708 * * [misc]simplify: iters left: 1 (5 enodes) 1546856174.709 * [exit]simplify: Simplified to -1 1546856174.709 * [misc]simplify: Simplified (2 2) to (λ (k n) (pow (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) -1)) 1546856174.709 * * * * [misc]progress: [ 79 / 128 ] simplifiying candidate # 1546856174.709 * * * * [misc]progress: [ 80 / 128 ] simplifiying candidate # 1546856174.709 * * * * [misc]progress: [ 81 / 128 ] simplifiying candidate # 1546856174.709 * * * * [misc]progress: [ 82 / 128 ] simplifiying candidate # 1546856174.710 * * * * [misc]progress: [ 83 / 128 ] simplifiying candidate # 1546856174.710 * * * * [misc]progress: [ 84 / 128 ] simplifiying candidate # 1546856174.710 * * * * [misc]progress: [ 85 / 128 ] simplifiying candidate # 1546856174.710 * * * * [misc]progress: [ 86 / 128 ] simplifiying candidate # 1546856174.710 * * * * [misc]progress: [ 87 / 128 ] simplifiying candidate # 1546856174.710 * * * * [misc]progress: [ 88 / 128 ] simplifiying candidate # 1546856174.710 * * * * [misc]progress: [ 89 / 128 ] simplifiying candidate # 1546856174.710 * * * * [misc]progress: [ 90 / 128 ] simplifiying candidate # 1546856174.710 * * * * [misc]progress: [ 91 / 128 ] simplifiying candidate # 1546856174.710 * * * * [misc]progress: [ 92 / 128 ] simplifiying candidate # 1546856174.710 * * * * [misc]progress: [ 93 / 128 ] simplifiying candidate # 1546856174.710 * [enter]simplify: Simplifying (cbrt (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546856174.710 * * [misc]simplify: iters left: 6 (13 enodes) 1546856174.714 * * [misc]simplify: iters left: 5 (19 enodes) 1546856174.720 * * [misc]simplify: iters left: 4 (28 enodes) 1546856174.727 * * [misc]simplify: iters left: 3 (30 enodes) 1546856174.735 * [exit]simplify: Simplified to (cbrt (/ (sqrt k) (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))) 1546856174.735 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (* (cbrt (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (cbrt (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))) (cbrt (/ (sqrt k) (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))))) 1546856174.735 * * * * [misc]progress: [ 94 / 128 ] simplifiying candidate # 1546856174.736 * [enter]simplify: Simplifying (sqrt (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546856174.736 * * [misc]simplify: iters left: 6 (13 enodes) 1546856174.740 * * [misc]simplify: iters left: 5 (19 enodes) 1546856174.745 * * [misc]simplify: iters left: 4 (28 enodes) 1546856174.753 * * [misc]simplify: iters left: 3 (30 enodes) 1546856174.760 * [exit]simplify: Simplified to (sqrt (/ (sqrt k) (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))) 1546856174.760 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (sqrt (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) (sqrt (/ (sqrt k) (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))))) 1546856174.760 * * * * [misc]progress: [ 95 / 128 ] simplifiying candidate # 1546856174.761 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (pow (* PI (* n 2)) (- (/ k 2)))) 1546856174.761 * * [misc]simplify: iters left: 6 (12 enodes) 1546856174.765 * * [misc]simplify: iters left: 5 (18 enodes) 1546856174.770 * * [misc]simplify: iters left: 4 (24 enodes) 1546856174.776 * * [misc]simplify: iters left: 3 (25 enodes) 1546856174.782 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2)))) 1546856174.783 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* PI (* n 2)) 1/2))) (/ (cbrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2)))))) 1546856174.783 * * * * [misc]progress: [ 96 / 128 ] simplifiying candidate # 1546856174.783 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (pow (* PI (* n 2)) (- (/ k 2)))) 1546856174.783 * * [misc]simplify: iters left: 6 (12 enodes) 1546856174.787 * * [misc]simplify: iters left: 5 (18 enodes) 1546856174.792 * * [misc]simplify: iters left: 4 (24 enodes) 1546856174.800 * * [misc]simplify: iters left: 3 (25 enodes) 1546856174.806 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2)))) 1546856174.806 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* PI (* n 2)) 1/2))) (/ (cbrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2)))))) 1546856174.806 * * * * [misc]progress: [ 97 / 128 ] simplifiying candidate # 1546856174.807 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))) 1546856174.807 * * [misc]simplify: iters left: 6 (11 enodes) 1546856174.810 * * [misc]simplify: iters left: 5 (14 enodes) 1546856174.814 * * [misc]simplify: iters left: 4 (17 enodes) 1546856174.819 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))) 1546856174.819 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow PI (- 1/2 (/ k 2))))) (/ (cbrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))))) 1546856174.819 * * * * [misc]progress: [ 98 / 128 ] simplifiying candidate # 1546856174.819 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546856174.819 * * [misc]simplify: iters left: 6 (14 enodes) 1546856174.824 * * [misc]simplify: iters left: 5 (20 enodes) 1546856174.830 * * [misc]simplify: iters left: 4 (29 enodes) 1546856174.837 * * [misc]simplify: iters left: 3 (30 enodes) 1546856174.846 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) 1546856174.846 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))) (/ (cbrt (sqrt k)) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))))) 1546856174.846 * * * * [misc]progress: [ 99 / 128 ] simplifiying candidate # 1546856174.846 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546856174.847 * * [misc]simplify: iters left: 6 (14 enodes) 1546856174.851 * * [misc]simplify: iters left: 5 (20 enodes) 1546856174.857 * * [misc]simplify: iters left: 4 (29 enodes) 1546856174.865 * * [misc]simplify: iters left: 3 (30 enodes) 1546856174.872 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) 1546856174.872 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 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))))))) 1546856174.872 * * * * [misc]progress: [ 100 / 128 ] simplifiying candidate # 1546856174.873 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1546856174.873 * * [misc]simplify: iters left: 6 (13 enodes) 1546856174.877 * * [misc]simplify: iters left: 5 (19 enodes) 1546856174.883 * * [misc]simplify: iters left: 4 (28 enodes) 1546856174.890 * * [misc]simplify: iters left: 3 (30 enodes) 1546856174.898 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (pow (* 2 (* PI n)) (- 1/2 (/ k 2)))) 1546856174.898 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1)) (/ (cbrt (sqrt k)) (pow (* 2 (* PI n)) (- 1/2 (/ k 2)))))) 1546856174.899 * * * * [misc]progress: [ 101 / 128 ] simplifiying candidate # 1546856174.899 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (pow (* PI (* n 2)) (- (/ k 2)))) 1546856174.899 * * [misc]simplify: iters left: 6 (12 enodes) 1546856174.903 * * [misc]simplify: iters left: 5 (18 enodes) 1546856174.908 * * [misc]simplify: iters left: 4 (24 enodes) 1546856174.914 * * [misc]simplify: iters left: 3 (25 enodes) 1546856174.921 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2)))) 1546856174.921 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (pow (* PI (* n 2)) 1/2))) (/ (sqrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2)))))) 1546856174.921 * * * * [misc]progress: [ 102 / 128 ] simplifiying candidate # 1546856174.921 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (pow (* PI (* n 2)) (- (/ k 2)))) 1546856174.921 * * [misc]simplify: iters left: 6 (12 enodes) 1546856174.925 * * [misc]simplify: iters left: 5 (18 enodes) 1546856174.931 * * [misc]simplify: iters left: 4 (24 enodes) 1546856174.937 * * [misc]simplify: iters left: 3 (25 enodes) 1546856174.944 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2)))) 1546856174.944 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (pow (* PI (* n 2)) 1/2))) (/ (sqrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2)))))) 1546856174.944 * * * * [misc]progress: [ 103 / 128 ] simplifiying candidate # 1546856174.944 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))) 1546856174.944 * * [misc]simplify: iters left: 6 (11 enodes) 1546856174.949 * * [misc]simplify: iters left: 5 (14 enodes) 1546856174.953 * * [misc]simplify: iters left: 4 (17 enodes) 1546856174.958 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))) 1546856174.958 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (pow PI (- 1/2 (/ k 2))))) (/ (sqrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))))) 1546856174.958 * * * * [misc]progress: [ 104 / 128 ] simplifiying candidate # 1546856174.958 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546856174.959 * * [misc]simplify: iters left: 6 (14 enodes) 1546856174.963 * * [misc]simplify: iters left: 5 (20 enodes) 1546856174.969 * * [misc]simplify: iters left: 4 (29 enodes) 1546856174.976 * * [misc]simplify: iters left: 3 (30 enodes) 1546856174.983 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) 1546856174.984 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))) (/ (sqrt (sqrt k)) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))))) 1546856174.984 * * * * [misc]progress: [ 105 / 128 ] simplifiying candidate # 1546856174.984 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546856174.984 * * [misc]simplify: iters left: 6 (14 enodes) 1546856174.989 * * [misc]simplify: iters left: 5 (20 enodes) 1546856174.995 * * [misc]simplify: iters left: 4 (29 enodes) 1546856175.002 * * [misc]simplify: iters left: 3 (30 enodes) 1546856175.011 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) 1546856175.011 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 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))))))) 1546856175.011 * * * * [misc]progress: [ 106 / 128 ] simplifiying candidate # 1546856175.011 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1546856175.011 * * [misc]simplify: iters left: 6 (13 enodes) 1546856175.015 * * [misc]simplify: iters left: 5 (19 enodes) 1546856175.021 * * [misc]simplify: iters left: 4 (28 enodes) 1546856175.028 * * [misc]simplify: iters left: 3 (30 enodes) 1546856175.036 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (pow (* 2 (* PI n)) (- 1/2 (/ k 2)))) 1546856175.036 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) 1)) (/ (sqrt (sqrt k)) (pow (* 2 (* PI n)) (- 1/2 (/ k 2)))))) 1546856175.036 * * * * [misc]progress: [ 107 / 128 ] simplifiying candidate # 1546856175.036 * [enter]simplify: Simplifying (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2)))) 1546856175.036 * * [misc]simplify: iters left: 6 (11 enodes) 1546856175.040 * * [misc]simplify: iters left: 5 (17 enodes) 1546856175.045 * * [misc]simplify: iters left: 4 (23 enodes) 1546856175.051 * * [misc]simplify: iters left: 3 (24 enodes) 1546856175.057 * [exit]simplify: Simplified to (/ (sqrt k) (pow (* 2 (* PI n)) (- (/ k 2)))) 1546856175.057 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ 1 (pow (* PI (* n 2)) 1/2))) (/ (sqrt k) (pow (* 2 (* PI n)) (- (/ k 2)))))) 1546856175.057 * * * * [misc]progress: [ 108 / 128 ] simplifiying candidate # 1546856175.057 * [enter]simplify: Simplifying (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2)))) 1546856175.058 * * [misc]simplify: iters left: 6 (11 enodes) 1546856175.060 * * [misc]simplify: iters left: 5 (17 enodes) 1546856175.063 * * [misc]simplify: iters left: 4 (23 enodes) 1546856175.066 * * [misc]simplify: iters left: 3 (24 enodes) 1546856175.069 * [exit]simplify: Simplified to (/ (sqrt k) (pow (* 2 (* PI n)) (- (/ k 2)))) 1546856175.069 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ 1 (pow (* PI (* n 2)) 1/2))) (/ (sqrt k) (pow (* 2 (* PI n)) (- (/ k 2)))))) 1546856175.069 * * * * [misc]progress: [ 109 / 128 ] simplifiying candidate # 1546856175.069 * [enter]simplify: Simplifying (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2)))) 1546856175.069 * * [misc]simplify: iters left: 6 (10 enodes) 1546856175.070 * * [misc]simplify: iters left: 5 (13 enodes) 1546856175.072 * * [misc]simplify: iters left: 4 (16 enodes) 1546856175.075 * [exit]simplify: Simplified to (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2)))) 1546856175.075 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ 1 (pow PI (- 1/2 (/ k 2))))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2)))))) 1546856175.075 * * * * [misc]progress: [ 110 / 128 ] simplifiying candidate # 1546856175.075 * [enter]simplify: Simplifying (/ (sqrt k) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546856175.075 * * [misc]simplify: iters left: 6 (13 enodes) 1546856175.077 * * [misc]simplify: iters left: 5 (19 enodes) 1546856175.080 * * [misc]simplify: iters left: 4 (28 enodes) 1546856175.084 * * [misc]simplify: iters left: 3 (30 enodes) 1546856175.088 * [exit]simplify: Simplified to (/ (sqrt k) (cbrt (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))) 1546856175.088 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ 1 (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))) (/ (sqrt k) (cbrt (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))))) 1546856175.088 * * * * [misc]progress: [ 111 / 128 ] simplifiying candidate # 1546856175.088 * [enter]simplify: Simplifying (/ (sqrt k) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546856175.088 * * [misc]simplify: iters left: 6 (13 enodes) 1546856175.090 * * [misc]simplify: iters left: 5 (19 enodes) 1546856175.093 * * [misc]simplify: iters left: 4 (28 enodes) 1546856175.097 * * [misc]simplify: iters left: 3 (30 enodes) 1546856175.101 * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))) 1546856175.101 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ 1 (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) (/ (sqrt k) (sqrt (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))))) 1546856175.101 * * * * [misc]progress: [ 112 / 128 ] simplifiying candidate # 1546856175.101 * [enter]simplify: Simplifying (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1546856175.101 * * [misc]simplify: iters left: 6 (12 enodes) 1546856175.103 * * [misc]simplify: iters left: 5 (18 enodes) 1546856175.105 * * [misc]simplify: iters left: 4 (27 enodes) 1546856175.109 * * [misc]simplify: iters left: 3 (29 enodes) 1546856175.115 * [exit]simplify: Simplified to (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1546856175.115 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ 1 1)) (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) 1546856175.115 * * * * [misc]progress: [ 113 / 128 ] simplifiying candidate # 1546856175.115 * [enter]simplify: Simplifying (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1546856175.115 * * [misc]simplify: iters left: 6 (12 enodes) 1546856175.119 * * [misc]simplify: iters left: 5 (18 enodes) 1546856175.124 * * [misc]simplify: iters left: 4 (27 enodes) 1546856175.132 * * [misc]simplify: iters left: 3 (29 enodes) 1546856175.139 * [exit]simplify: Simplified to (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1546856175.139 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 1) (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) 1546856175.139 * * * * [misc]progress: [ 114 / 128 ] simplifiying candidate # 1546856175.139 * [enter]simplify: Simplifying (/ 1 (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1546856175.139 * * [misc]simplify: iters left: 6 (12 enodes) 1546856175.143 * * [misc]simplify: iters left: 5 (20 enodes) 1546856175.149 * * [misc]simplify: iters left: 4 (29 enodes) 1546856175.157 * * [misc]simplify: iters left: 3 (30 enodes) 1546856175.164 * [exit]simplify: Simplified to (/ 1 (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) 1546856175.164 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (sqrt k)) (/ 1 (pow (* (* n PI) 2) (- 1/2 (/ k 2)))))) 1546856175.164 * * * * [misc]progress: [ 115 / 128 ] simplifiying candidate # 1546856175.164 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (/ k 2)) 1546856175.165 * * [misc]simplify: iters left: 5 (8 enodes) 1546856175.168 * * [misc]simplify: iters left: 4 (12 enodes) 1546856175.171 * * [misc]simplify: iters left: 3 (18 enodes) 1546856175.176 * * [misc]simplify: iters left: 2 (20 enodes) 1546856175.182 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ k 2)) 1546856175.182 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (sqrt k) (pow (* PI (* n 2)) 1/2))) (pow (* (* 2 n) PI) (/ k 2)))) 1546856175.182 * * * * [misc]progress: [ 116 / 128 ] simplifiying candidate # 1546856175.182 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- 1/2 (/ k 2))) 1546856175.182 * * [misc]simplify: iters left: 5 (10 enodes) 1546856175.185 * * [misc]simplify: iters left: 4 (16 enodes) 1546856175.190 * * [misc]simplify: iters left: 3 (25 enodes) 1546856175.198 * * [misc]simplify: iters left: 2 (26 enodes) 1546856175.204 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) 1546856175.205 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) 1546856175.206 * * * * [misc]progress: [ 117 / 128 ] simplifiying candidate # 1546856175.206 * [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))))) 1546856175.206 * * [misc]simplify: iters left: 6 (37 enodes) 1546856175.222 * * [misc]simplify: iters left: 5 (108 enodes) 1546856175.266 * * [misc]simplify: iters left: 4 (368 enodes) 1546856175.577 * [exit]simplify: Simplified to (fma -1/2 (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) (fma (* (* (* k k) (log n)) (* (log (* PI 2)) 1/4)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (fma (* (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (log (* PI 2)) (log (* PI 2)))) (* (* k k) 1/8) (fma (* (* (* k k) (log n)) (* (log n) 1/8)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (pow n 1/2) (pow (* PI 2) 1/2)))))) 1546856175.577 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (/ (sqrt k) (fma -1/2 (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) (fma (* (* (* k k) (log n)) (* (log (* PI 2)) 1/4)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (fma (* (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (log (* PI 2)) (log (* PI 2)))) (* (* k k) 1/8) (fma (* (* (* k k) (log n)) (* (log n) 1/8)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (pow n 1/2) (pow (* PI 2) 1/2))))))))) 1546856175.577 * * * * [misc]progress: [ 118 / 128 ] simplifiying candidate # 1546856175.577 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 1546856175.577 * * [misc]simplify: iters left: 6 (15 enodes) 1546856175.584 * * [misc]simplify: iters left: 5 (33 enodes) 1546856175.595 * * [misc]simplify: iters left: 4 (64 enodes) 1546856175.620 * * [misc]simplify: iters left: 3 (179 enodes) 1546856175.755 * [exit]simplify: Simplified to (* (pow (* 2 PI) (fma -1/2 k 1/2)) (pow n (fma -1/2 k 1/2))) 1546856175.755 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (/ (sqrt k) (* (pow (* 2 PI) (fma -1/2 k 1/2)) (pow n (fma -1/2 k 1/2)))))) 1546856175.755 * * * * [misc]progress: [ 119 / 128 ] simplifiying candidate # 1546856175.756 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 1546856175.756 * * [misc]simplify: iters left: 6 (15 enodes) 1546856175.762 * * [misc]simplify: iters left: 5 (30 enodes) 1546856175.772 * * [misc]simplify: iters left: 4 (65 enodes) 1546856175.800 * * [misc]simplify: iters left: 3 (208 enodes) 1546856175.955 * [exit]simplify: Simplified to (pow (exp (fma -1/2 k 1/2)) (- (log (* -2 PI)) (log (/ -1 n)))) 1546856175.955 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (/ (sqrt k) (pow (exp (fma -1/2 k 1/2)) (- (log (* -2 PI)) (log (/ -1 n))))))) 1546856175.955 * * * * [misc]progress: [ 120 / 128 ] simplifiying candidate # 1546856175.955 * [enter]simplify: Simplifying (* 2 (* n PI)) 1546856175.955 * * [misc]simplify: iters left: 4 (5 enodes) 1546856175.957 * * [misc]simplify: iters left: 3 (9 enodes) 1546856175.960 * * [misc]simplify: iters left: 2 (15 enodes) 1546856175.964 * * [misc]simplify: iters left: 1 (17 enodes) 1546856175.968 * [exit]simplify: Simplified to (* (* PI n) 2) 1546856175.968 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* PI n) 2) (- 1/2 (/ k 2)))))) 1546856175.968 * * * * [misc]progress: [ 121 / 128 ] simplifiying candidate # 1546856175.968 * [enter]simplify: Simplifying (* 2 (* n PI)) 1546856175.968 * * [misc]simplify: iters left: 4 (5 enodes) 1546856175.970 * * [misc]simplify: iters left: 3 (9 enodes) 1546856175.972 * * [misc]simplify: iters left: 2 (15 enodes) 1546856175.976 * * [misc]simplify: iters left: 1 (17 enodes) 1546856175.980 * [exit]simplify: Simplified to (* (* PI n) 2) 1546856175.980 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* PI n) 2) (- 1/2 (/ k 2)))))) 1546856175.980 * * * * [misc]progress: [ 122 / 128 ] simplifiying candidate # 1546856175.981 * [enter]simplify: Simplifying (* 2 (* n PI)) 1546856175.981 * * [misc]simplify: iters left: 4 (5 enodes) 1546856175.982 * * [misc]simplify: iters left: 3 (9 enodes) 1546856175.985 * * [misc]simplify: iters left: 2 (15 enodes) 1546856175.989 * * [misc]simplify: iters left: 1 (17 enodes) 1546856175.993 * [exit]simplify: Simplified to (* (* PI n) 2) 1546856175.993 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* PI n) 2) (- 1/2 (/ k 2)))))) 1546856175.994 * * * * [misc]progress: [ 123 / 128 ] simplifiying candidate # 1546856175.994 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow k 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI))))) PI)) (- (+ (* +nan.0 (/ (* (sqrt 1/2) (pow k 2)) PI)) (- (+ (* +nan.0 (/ (* n (* (sqrt 1/2) k)) (pow PI 2))) (- (+ (* +nan.0 (/ (* (log n) (* (sqrt 2) (* (pow (sqrt 1/2) 2) (pow k 2)))) PI)) (- (* +nan.0 (/ (* (sqrt 1/2) k) PI))))))))))) 1546856175.994 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ 1 +nan.0)) 1546856175.994 * * * * [misc]progress: [ 124 / 128 ] simplifiying candidate # 1546856175.994 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))))))))) 1546856175.994 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ 1 +nan.0)) 1546856175.994 * * * * [misc]progress: [ 125 / 128 ] simplifiying candidate # 1546856175.995 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))))))))) 1546856175.995 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ 1 +nan.0)) 1546856175.995 * * * * [misc]progress: [ 126 / 128 ] simplifiying candidate # 1546856175.995 * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))))))) 1546856175.995 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1546856175.995 * * * * [misc]progress: [ 127 / 128 ] simplifiying candidate # 1546856175.996 * [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)))))))) 1546856175.996 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1546856175.996 * * * * [misc]progress: [ 128 / 128 ] simplifiying candidate # 1546856175.996 * [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))))))))))) 1546856175.996 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1546856175.996 * * * [misc]progress: adding candidates to table 1546856178.073 * * [misc]progress: iteration 3 / 4 1546856178.073 * * * [misc]progress: picking best candidate 1546856178.119 * * * * [misc]pick: Picked # 1546856178.119 * * * [misc]progress: localizing error 1546856178.136 * * * [misc]progress: generating rewritten candidates 1546856178.136 * * * * [misc]progress: [ 1 / 4 ] rewriting at (2 2 2 2) 1546856178.140 * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 2 2 2 1) 1546856178.142 * * * * [misc]progress: [ 3 / 4 ] rewriting at (2 2) 1546856178.152 * * * * [misc]progress: [ 4 / 4 ] rewriting at (2 2 2) 1546856178.157 * * * [misc]progress: generating series expansions 1546856178.157 * * * * [misc]progress: [ 1 / 4 ] generating series at (2 2 2 2) 1546856178.157 * [misc]backup-simplify: Simplify (pow (* PI (* n 2)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 1546856178.157 * [misc]approximate: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 1546856178.158 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1546856178.158 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1546856178.158 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1546856178.158 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546856178.158 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856178.158 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.158 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546856178.158 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856178.158 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.158 * [misc]taylor: Taking taylor expansion of k in k 1546856178.158 * [misc]backup-simplify: Simplify 0 into 0 1546856178.158 * [misc]backup-simplify: Simplify 1 into 1 1546856178.158 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1546856178.158 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1546856178.158 * [misc]taylor: Taking taylor expansion of 2 in k 1546856178.158 * [misc]backup-simplify: Simplify 2 into 2 1546856178.158 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1546856178.158 * [misc]taylor: Taking taylor expansion of n in k 1546856178.158 * [misc]backup-simplify: Simplify n into n 1546856178.158 * [misc]taylor: Taking taylor expansion of PI in k 1546856178.158 * [misc]backup-simplify: Simplify PI into PI 1546856178.158 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1546856178.158 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1546856178.158 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1546856178.159 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546856178.159 * [misc]backup-simplify: Simplify (- 0) into 0 1546856178.159 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546856178.159 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1546856178.159 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1546856178.159 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546856178.159 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546856178.159 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546856178.159 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546856178.159 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856178.159 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.159 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546856178.159 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856178.159 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.159 * [misc]taylor: Taking taylor expansion of k in n 1546856178.159 * [misc]backup-simplify: Simplify k into k 1546856178.159 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546856178.160 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546856178.160 * [misc]taylor: Taking taylor expansion of 2 in n 1546856178.160 * [misc]backup-simplify: Simplify 2 into 2 1546856178.160 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546856178.160 * [misc]taylor: Taking taylor expansion of n in n 1546856178.160 * [misc]backup-simplify: Simplify 0 into 0 1546856178.160 * [misc]backup-simplify: Simplify 1 into 1 1546856178.160 * [misc]taylor: Taking taylor expansion of PI in n 1546856178.160 * [misc]backup-simplify: Simplify PI into PI 1546856178.160 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546856178.160 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546856178.161 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546856178.162 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546856178.162 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856178.162 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546856178.162 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546856178.162 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546856178.163 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546856178.164 * [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)))) 1546856178.164 * [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))))) 1546856178.168 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546856178.168 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546856178.168 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546856178.168 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546856178.168 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856178.168 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.168 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546856178.168 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856178.168 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.168 * [misc]taylor: Taking taylor expansion of k in n 1546856178.168 * [misc]backup-simplify: Simplify k into k 1546856178.168 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546856178.169 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546856178.169 * [misc]taylor: Taking taylor expansion of 2 in n 1546856178.169 * [misc]backup-simplify: Simplify 2 into 2 1546856178.169 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546856178.169 * [misc]taylor: Taking taylor expansion of n in n 1546856178.169 * [misc]backup-simplify: Simplify 0 into 0 1546856178.169 * [misc]backup-simplify: Simplify 1 into 1 1546856178.169 * [misc]taylor: Taking taylor expansion of PI in n 1546856178.169 * [misc]backup-simplify: Simplify PI into PI 1546856178.169 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546856178.169 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546856178.170 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546856178.171 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546856178.171 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856178.171 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546856178.171 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546856178.172 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546856178.172 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546856178.173 * [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)))) 1546856178.173 * [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))))) 1546856178.174 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1546856178.174 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1546856178.174 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546856178.174 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856178.174 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.174 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546856178.174 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856178.174 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.174 * [misc]taylor: Taking taylor expansion of k in k 1546856178.174 * [misc]backup-simplify: Simplify 0 into 0 1546856178.174 * [misc]backup-simplify: Simplify 1 into 1 1546856178.174 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1546856178.174 * [misc]taylor: Taking taylor expansion of (log n) in k 1546856178.174 * [misc]taylor: Taking taylor expansion of n in k 1546856178.174 * [misc]backup-simplify: Simplify n into n 1546856178.174 * [misc]backup-simplify: Simplify (log n) into (log n) 1546856178.174 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1546856178.174 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1546856178.174 * [misc]taylor: Taking taylor expansion of 2 in k 1546856178.174 * [misc]backup-simplify: Simplify 2 into 2 1546856178.174 * [misc]taylor: Taking taylor expansion of PI in k 1546856178.174 * [misc]backup-simplify: Simplify PI into PI 1546856178.175 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546856178.175 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856178.175 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546856178.175 * [misc]backup-simplify: Simplify (- 0) into 0 1546856178.176 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546856178.176 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546856178.177 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1546856178.177 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1546856178.178 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1546856178.179 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546856178.180 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1546856178.183 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546856178.183 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1546856178.183 * [misc]backup-simplify: Simplify (- 0) into 0 1546856178.184 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856178.184 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546856178.185 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1546856178.187 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1546856178.187 * [misc]taylor: Taking taylor expansion of 0 in k 1546856178.187 * [misc]backup-simplify: Simplify 0 into 0 1546856178.187 * [misc]backup-simplify: Simplify 0 into 0 1546856178.188 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1546856178.188 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546856178.192 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546856178.192 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856178.192 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1546856178.193 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546856178.193 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546856178.193 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1546856178.195 * [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))))))) 1546856178.196 * [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))))))) 1546856178.198 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1546856178.200 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1546856178.205 * [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 1546856178.205 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1546856178.206 * [misc]backup-simplify: Simplify (- 0) into 0 1546856178.206 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856178.206 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546856178.207 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1546856178.210 * [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 1546856178.210 * [misc]taylor: Taking taylor expansion of 0 in k 1546856178.210 * [misc]backup-simplify: Simplify 0 into 0 1546856178.210 * [misc]backup-simplify: Simplify 0 into 0 1546856178.210 * [misc]backup-simplify: Simplify 0 into 0 1546856178.212 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1546856178.213 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546856178.218 * [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 1546856178.218 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856178.219 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1546856178.219 * [misc]backup-simplify: Simplify (- 0) into 0 1546856178.219 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856178.220 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1546856178.222 * [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))))) 1546856178.225 * [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))))) 1546856178.230 * [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))))) 1546856178.231 * [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)))) 1546856178.231 * [misc]approximate: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 1546856178.231 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1546856178.231 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1546856178.231 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1546856178.231 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546856178.231 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856178.231 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.231 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546856178.231 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856178.231 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.231 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546856178.231 * [misc]taylor: Taking taylor expansion of k in k 1546856178.231 * [misc]backup-simplify: Simplify 0 into 0 1546856178.231 * [misc]backup-simplify: Simplify 1 into 1 1546856178.231 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546856178.231 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1546856178.231 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1546856178.231 * [misc]taylor: Taking taylor expansion of 2 in k 1546856178.231 * [misc]backup-simplify: Simplify 2 into 2 1546856178.231 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546856178.231 * [misc]taylor: Taking taylor expansion of PI in k 1546856178.231 * [misc]backup-simplify: Simplify PI into PI 1546856178.231 * [misc]taylor: Taking taylor expansion of n in k 1546856178.231 * [misc]backup-simplify: Simplify n into n 1546856178.232 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546856178.232 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1546856178.232 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1546856178.232 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546856178.232 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546856178.232 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546856178.232 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1546856178.233 * [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)))) 1546856178.233 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546856178.233 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546856178.233 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546856178.233 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546856178.233 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856178.233 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.233 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546856178.233 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856178.233 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.233 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546856178.233 * [misc]taylor: Taking taylor expansion of k in n 1546856178.233 * [misc]backup-simplify: Simplify k into k 1546856178.233 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546856178.233 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546856178.233 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546856178.233 * [misc]taylor: Taking taylor expansion of 2 in n 1546856178.233 * [misc]backup-simplify: Simplify 2 into 2 1546856178.233 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856178.233 * [misc]taylor: Taking taylor expansion of PI in n 1546856178.233 * [misc]backup-simplify: Simplify PI into PI 1546856178.233 * [misc]taylor: Taking taylor expansion of n in n 1546856178.233 * [misc]backup-simplify: Simplify 0 into 0 1546856178.233 * [misc]backup-simplify: Simplify 1 into 1 1546856178.234 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856178.234 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546856178.235 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856178.235 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546856178.235 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546856178.235 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546856178.236 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546856178.236 * [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))) 1546856178.237 * [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)))) 1546856178.237 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546856178.237 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546856178.237 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546856178.237 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546856178.237 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856178.237 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.237 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546856178.237 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856178.237 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.237 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546856178.237 * [misc]taylor: Taking taylor expansion of k in n 1546856178.237 * [misc]backup-simplify: Simplify k into k 1546856178.237 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546856178.237 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546856178.237 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546856178.237 * [misc]taylor: Taking taylor expansion of 2 in n 1546856178.237 * [misc]backup-simplify: Simplify 2 into 2 1546856178.237 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856178.237 * [misc]taylor: Taking taylor expansion of PI in n 1546856178.237 * [misc]backup-simplify: Simplify PI into PI 1546856178.237 * [misc]taylor: Taking taylor expansion of n in n 1546856178.237 * [misc]backup-simplify: Simplify 0 into 0 1546856178.238 * [misc]backup-simplify: Simplify 1 into 1 1546856178.238 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856178.238 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546856178.239 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856178.239 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546856178.239 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546856178.239 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546856178.240 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546856178.240 * [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))) 1546856178.241 * [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)))) 1546856178.241 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1546856178.241 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1546856178.241 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546856178.241 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856178.241 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.241 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546856178.241 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856178.241 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.241 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546856178.241 * [misc]taylor: Taking taylor expansion of k in k 1546856178.241 * [misc]backup-simplify: Simplify 0 into 0 1546856178.241 * [misc]backup-simplify: Simplify 1 into 1 1546856178.242 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546856178.242 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1546856178.242 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1546856178.242 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1546856178.242 * [misc]taylor: Taking taylor expansion of 2 in k 1546856178.242 * [misc]backup-simplify: Simplify 2 into 2 1546856178.242 * [misc]taylor: Taking taylor expansion of PI in k 1546856178.242 * [misc]backup-simplify: Simplify PI into PI 1546856178.242 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546856178.243 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856178.243 * [misc]taylor: Taking taylor expansion of (log n) in k 1546856178.243 * [misc]taylor: Taking taylor expansion of n in k 1546856178.243 * [misc]backup-simplify: Simplify n into n 1546856178.243 * [misc]backup-simplify: Simplify (log n) into (log n) 1546856178.243 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546856178.243 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546856178.243 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546856178.243 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1546856178.244 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1546856178.244 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1546856178.245 * [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)))) 1546856178.246 * [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)))) 1546856178.247 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546856178.247 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546856178.250 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546856178.250 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546856178.251 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546856178.251 * [misc]backup-simplify: Simplify (- 0) into 0 1546856178.251 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856178.252 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546856178.253 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1546856178.254 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546856178.254 * [misc]taylor: Taking taylor expansion of 0 in k 1546856178.254 * [misc]backup-simplify: Simplify 0 into 0 1546856178.254 * [misc]backup-simplify: Simplify 0 into 0 1546856178.255 * [misc]backup-simplify: Simplify 0 into 0 1546856178.256 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856178.257 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546856178.262 * [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 1546856178.262 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546856178.263 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1546856178.263 * [misc]backup-simplify: Simplify (- 0) into 0 1546856178.263 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856178.264 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546856178.265 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1546856178.267 * [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 1546856178.267 * [misc]taylor: Taking taylor expansion of 0 in k 1546856178.267 * [misc]backup-simplify: Simplify 0 into 0 1546856178.267 * [misc]backup-simplify: Simplify 0 into 0 1546856178.267 * [misc]backup-simplify: Simplify 0 into 0 1546856178.267 * [misc]backup-simplify: Simplify 0 into 0 1546856178.269 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856178.270 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546856178.278 * [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 1546856178.279 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546856178.279 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1546856178.279 * [misc]backup-simplify: Simplify (- 0) into 0 1546856178.280 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856178.280 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546856178.281 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1546856178.285 * [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 1546856178.285 * [misc]taylor: Taking taylor expansion of 0 in k 1546856178.285 * [misc]backup-simplify: Simplify 0 into 0 1546856178.286 * [misc]backup-simplify: Simplify 0 into 0 1546856178.286 * [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))))) 1546856178.286 * [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)) 1546856178.287 * [misc]approximate: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 1546856178.287 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1546856178.287 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1546856178.287 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1546856178.287 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546856178.287 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546856178.287 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856178.287 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.287 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546856178.287 * [misc]taylor: Taking taylor expansion of k in k 1546856178.287 * [misc]backup-simplify: Simplify 0 into 0 1546856178.287 * [misc]backup-simplify: Simplify 1 into 1 1546856178.287 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546856178.287 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856178.287 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.287 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1546856178.287 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1546856178.287 * [misc]taylor: Taking taylor expansion of -2 in k 1546856178.287 * [misc]backup-simplify: Simplify -2 into -2 1546856178.287 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546856178.287 * [misc]taylor: Taking taylor expansion of PI in k 1546856178.287 * [misc]backup-simplify: Simplify PI into PI 1546856178.287 * [misc]taylor: Taking taylor expansion of n in k 1546856178.287 * [misc]backup-simplify: Simplify n into n 1546856178.287 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546856178.288 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1546856178.288 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1546856178.288 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546856178.288 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546856178.288 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1546856178.288 * [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))) 1546856178.288 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546856178.288 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546856178.288 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546856178.288 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546856178.288 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546856178.288 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856178.289 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.289 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546856178.289 * [misc]taylor: Taking taylor expansion of k in n 1546856178.289 * [misc]backup-simplify: Simplify k into k 1546856178.289 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546856178.289 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856178.289 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.289 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546856178.289 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546856178.289 * [misc]taylor: Taking taylor expansion of -2 in n 1546856178.289 * [misc]backup-simplify: Simplify -2 into -2 1546856178.289 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856178.289 * [misc]taylor: Taking taylor expansion of PI in n 1546856178.289 * [misc]backup-simplify: Simplify PI into PI 1546856178.289 * [misc]taylor: Taking taylor expansion of n in n 1546856178.289 * [misc]backup-simplify: Simplify 0 into 0 1546856178.289 * [misc]backup-simplify: Simplify 1 into 1 1546856178.289 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856178.290 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546856178.290 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546856178.290 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546856178.290 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546856178.291 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546856178.292 * [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))) 1546856178.292 * [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)))) 1546856178.292 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546856178.293 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546856178.293 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546856178.293 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546856178.293 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546856178.293 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856178.293 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.293 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546856178.293 * [misc]taylor: Taking taylor expansion of k in n 1546856178.293 * [misc]backup-simplify: Simplify k into k 1546856178.293 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546856178.293 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856178.293 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.293 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546856178.293 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546856178.293 * [misc]taylor: Taking taylor expansion of -2 in n 1546856178.293 * [misc]backup-simplify: Simplify -2 into -2 1546856178.293 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856178.293 * [misc]taylor: Taking taylor expansion of PI in n 1546856178.293 * [misc]backup-simplify: Simplify PI into PI 1546856178.293 * [misc]taylor: Taking taylor expansion of n in n 1546856178.293 * [misc]backup-simplify: Simplify 0 into 0 1546856178.293 * [misc]backup-simplify: Simplify 1 into 1 1546856178.293 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856178.294 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546856178.294 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546856178.294 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546856178.294 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546856178.295 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546856178.296 * [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))) 1546856178.296 * [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)))) 1546856178.296 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1546856178.296 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1546856178.296 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546856178.296 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546856178.296 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856178.297 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.297 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546856178.297 * [misc]taylor: Taking taylor expansion of k in k 1546856178.297 * [misc]backup-simplify: Simplify 0 into 0 1546856178.297 * [misc]backup-simplify: Simplify 1 into 1 1546856178.297 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546856178.297 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856178.297 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.297 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1546856178.297 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1546856178.297 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1546856178.297 * [misc]taylor: Taking taylor expansion of -2 in k 1546856178.297 * [misc]backup-simplify: Simplify -2 into -2 1546856178.297 * [misc]taylor: Taking taylor expansion of PI in k 1546856178.297 * [misc]backup-simplify: Simplify PI into PI 1546856178.297 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546856178.298 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546856178.298 * [misc]taylor: Taking taylor expansion of (log n) in k 1546856178.298 * [misc]taylor: Taking taylor expansion of n in k 1546856178.298 * [misc]backup-simplify: Simplify n into n 1546856178.298 * [misc]backup-simplify: Simplify (log n) into (log n) 1546856178.298 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546856178.298 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546856178.298 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1546856178.299 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1546856178.299 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1546856178.300 * [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)))) 1546856178.301 * [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)))) 1546856178.302 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546856178.303 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1546856178.306 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1546856178.306 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546856178.306 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546856178.306 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856178.307 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546856178.308 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1546856178.309 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546856178.309 * [misc]taylor: Taking taylor expansion of 0 in k 1546856178.309 * [misc]backup-simplify: Simplify 0 into 0 1546856178.309 * [misc]backup-simplify: Simplify 0 into 0 1546856178.309 * [misc]backup-simplify: Simplify 0 into 0 1546856178.311 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856178.312 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1546856178.317 * [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 1546856178.317 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546856178.318 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1546856178.318 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856178.319 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546856178.320 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1546856178.322 * [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 1546856178.322 * [misc]taylor: Taking taylor expansion of 0 in k 1546856178.322 * [misc]backup-simplify: Simplify 0 into 0 1546856178.322 * [misc]backup-simplify: Simplify 0 into 0 1546856178.322 * [misc]backup-simplify: Simplify 0 into 0 1546856178.322 * [misc]backup-simplify: Simplify 0 into 0 1546856178.324 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856178.326 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546856178.334 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0 1546856178.334 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546856178.334 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1546856178.335 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856178.335 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546856178.336 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 1546856178.340 * [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 1546856178.340 * [misc]taylor: Taking taylor expansion of 0 in k 1546856178.340 * [misc]backup-simplify: Simplify 0 into 0 1546856178.340 * [misc]backup-simplify: Simplify 0 into 0 1546856178.341 * [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))))) 1546856178.341 * * * * [misc]progress: [ 2 / 4 ] generating series at (2 2 2 2 1) 1546856178.341 * [misc]backup-simplify: Simplify (* PI (* n 2)) into (* 2 (* n PI)) 1546856178.341 * [misc]approximate: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1546856178.341 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546856178.341 * [misc]taylor: Taking taylor expansion of 2 in n 1546856178.341 * [misc]backup-simplify: Simplify 2 into 2 1546856178.341 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546856178.341 * [misc]taylor: Taking taylor expansion of n in n 1546856178.341 * [misc]backup-simplify: Simplify 0 into 0 1546856178.341 * [misc]backup-simplify: Simplify 1 into 1 1546856178.342 * [misc]taylor: Taking taylor expansion of PI in n 1546856178.342 * [misc]backup-simplify: Simplify PI into PI 1546856178.342 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546856178.342 * [misc]taylor: Taking taylor expansion of 2 in n 1546856178.342 * [misc]backup-simplify: Simplify 2 into 2 1546856178.342 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546856178.342 * [misc]taylor: Taking taylor expansion of n in n 1546856178.342 * [misc]backup-simplify: Simplify 0 into 0 1546856178.342 * [misc]backup-simplify: Simplify 1 into 1 1546856178.342 * [misc]taylor: Taking taylor expansion of PI in n 1546856178.342 * [misc]backup-simplify: Simplify PI into PI 1546856178.342 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546856178.344 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546856178.344 * [misc]backup-simplify: Simplify 0 into 0 1546856178.345 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546856178.345 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546856178.345 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546856178.347 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546856178.348 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1546856178.348 * [misc]backup-simplify: Simplify 0 into 0 1546856178.349 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1546856178.351 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1546856178.351 * [misc]backup-simplify: Simplify 0 into 0 1546856178.353 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1546856178.355 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1546856178.355 * [misc]backup-simplify: Simplify 0 into 0 1546856178.358 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1546856178.361 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1546856178.361 * [misc]backup-simplify: Simplify 0 into 0 1546856178.364 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1546856178.368 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1546856178.368 * [misc]backup-simplify: Simplify 0 into 0 1546856178.372 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1546856178.376 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1546856178.376 * [misc]backup-simplify: Simplify 0 into 0 1546856178.377 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1546856178.377 * [misc]backup-simplify: Simplify (* PI (* (/ 1 n) 2)) into (* 2 (/ PI n)) 1546856178.377 * [misc]approximate: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1546856178.377 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546856178.377 * [misc]taylor: Taking taylor expansion of 2 in n 1546856178.377 * [misc]backup-simplify: Simplify 2 into 2 1546856178.377 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856178.377 * [misc]taylor: Taking taylor expansion of PI in n 1546856178.377 * [misc]backup-simplify: Simplify PI into PI 1546856178.377 * [misc]taylor: Taking taylor expansion of n in n 1546856178.377 * [misc]backup-simplify: Simplify 0 into 0 1546856178.377 * [misc]backup-simplify: Simplify 1 into 1 1546856178.378 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856178.378 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546856178.378 * [misc]taylor: Taking taylor expansion of 2 in n 1546856178.378 * [misc]backup-simplify: Simplify 2 into 2 1546856178.378 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856178.378 * [misc]taylor: Taking taylor expansion of PI in n 1546856178.378 * [misc]backup-simplify: Simplify PI into PI 1546856178.378 * [misc]taylor: Taking taylor expansion of n in n 1546856178.378 * [misc]backup-simplify: Simplify 0 into 0 1546856178.378 * [misc]backup-simplify: Simplify 1 into 1 1546856178.378 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856178.378 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546856178.379 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546856178.380 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546856178.380 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546856178.381 * [misc]backup-simplify: Simplify 0 into 0 1546856178.382 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856178.383 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546856178.383 * [misc]backup-simplify: Simplify 0 into 0 1546856178.385 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856178.386 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546856178.386 * [misc]backup-simplify: Simplify 0 into 0 1546856178.388 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856178.390 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1546856178.390 * [misc]backup-simplify: Simplify 0 into 0 1546856178.393 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856178.395 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1546856178.395 * [misc]backup-simplify: Simplify 0 into 0 1546856178.398 * [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 1546856178.401 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1546856178.402 * [misc]backup-simplify: Simplify 0 into 0 1546856178.402 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 1546856178.402 * [misc]backup-simplify: Simplify (* PI (* (/ 1 (- n)) 2)) into (* -2 (/ PI n)) 1546856178.402 * [misc]approximate: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1546856178.402 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546856178.402 * [misc]taylor: Taking taylor expansion of -2 in n 1546856178.402 * [misc]backup-simplify: Simplify -2 into -2 1546856178.402 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856178.402 * [misc]taylor: Taking taylor expansion of PI in n 1546856178.402 * [misc]backup-simplify: Simplify PI into PI 1546856178.402 * [misc]taylor: Taking taylor expansion of n in n 1546856178.402 * [misc]backup-simplify: Simplify 0 into 0 1546856178.402 * [misc]backup-simplify: Simplify 1 into 1 1546856178.403 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856178.403 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546856178.403 * [misc]taylor: Taking taylor expansion of -2 in n 1546856178.403 * [misc]backup-simplify: Simplify -2 into -2 1546856178.403 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856178.403 * [misc]taylor: Taking taylor expansion of PI in n 1546856178.403 * [misc]backup-simplify: Simplify PI into PI 1546856178.403 * [misc]taylor: Taking taylor expansion of n in n 1546856178.403 * [misc]backup-simplify: Simplify 0 into 0 1546856178.403 * [misc]backup-simplify: Simplify 1 into 1 1546856178.403 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856178.404 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546856178.404 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546856178.405 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546856178.406 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1546856178.406 * [misc]backup-simplify: Simplify 0 into 0 1546856178.407 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856178.408 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1546856178.408 * [misc]backup-simplify: Simplify 0 into 0 1546856178.410 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856178.411 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546856178.411 * [misc]backup-simplify: Simplify 0 into 0 1546856178.414 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856178.416 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1546856178.416 * [misc]backup-simplify: Simplify 0 into 0 1546856178.418 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856178.421 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1546856178.421 * [misc]backup-simplify: Simplify 0 into 0 1546856178.424 * [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 1546856178.427 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1546856178.427 * [misc]backup-simplify: Simplify 0 into 0 1546856178.428 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 1546856178.428 * * * * [misc]progress: [ 3 / 4 ] generating series at (2 2) 1546856178.428 * [misc]backup-simplify: Simplify (* (sqrt k) (/ 1 (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) into (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) 1546856178.428 * [misc]approximate: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in (k n) around 0 1546856178.428 * [misc]taylor: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in n 1546856178.428 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 1546856178.428 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546856178.428 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546856178.428 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546856178.428 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546856178.428 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856178.428 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.428 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546856178.428 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856178.428 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.428 * [misc]taylor: Taking taylor expansion of k in n 1546856178.429 * [misc]backup-simplify: Simplify k into k 1546856178.429 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546856178.429 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546856178.429 * [misc]taylor: Taking taylor expansion of 2 in n 1546856178.429 * [misc]backup-simplify: Simplify 2 into 2 1546856178.429 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546856178.429 * [misc]taylor: Taking taylor expansion of n in n 1546856178.429 * [misc]backup-simplify: Simplify 0 into 0 1546856178.429 * [misc]backup-simplify: Simplify 1 into 1 1546856178.429 * [misc]taylor: Taking taylor expansion of PI in n 1546856178.429 * [misc]backup-simplify: Simplify PI into PI 1546856178.429 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546856178.429 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546856178.430 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546856178.431 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546856178.431 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856178.431 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546856178.431 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546856178.431 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546856178.432 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546856178.432 * [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)))) 1546856178.432 * [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))))) 1546856178.433 * [misc]backup-simplify: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (/ 1 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) 1546856178.433 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1546856178.433 * [misc]taylor: Taking taylor expansion of k in n 1546856178.433 * [misc]backup-simplify: Simplify k into k 1546856178.433 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1546856178.433 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1546856178.433 * [misc]taylor: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in k 1546856178.433 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 1546856178.433 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1546856178.433 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1546856178.433 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1546856178.433 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546856178.433 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856178.433 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.433 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546856178.433 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856178.433 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.433 * [misc]taylor: Taking taylor expansion of k in k 1546856178.433 * [misc]backup-simplify: Simplify 0 into 0 1546856178.433 * [misc]backup-simplify: Simplify 1 into 1 1546856178.433 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1546856178.433 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1546856178.433 * [misc]taylor: Taking taylor expansion of 2 in k 1546856178.433 * [misc]backup-simplify: Simplify 2 into 2 1546856178.433 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1546856178.433 * [misc]taylor: Taking taylor expansion of n in k 1546856178.433 * [misc]backup-simplify: Simplify n into n 1546856178.433 * [misc]taylor: Taking taylor expansion of PI in k 1546856178.433 * [misc]backup-simplify: Simplify PI into PI 1546856178.433 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1546856178.433 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1546856178.433 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1546856178.434 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546856178.434 * [misc]backup-simplify: Simplify (- 0) into 0 1546856178.434 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546856178.434 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1546856178.434 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1546856178.434 * [misc]backup-simplify: Simplify (/ 1 (pow (* 2 (* n PI)) 1/2)) into (sqrt (/ 1 (* PI (* n 2)))) 1546856178.434 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1546856178.434 * [misc]taylor: Taking taylor expansion of k in k 1546856178.434 * [misc]backup-simplify: Simplify 0 into 0 1546856178.434 * [misc]backup-simplify: Simplify 1 into 1 1546856178.434 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546856178.434 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546856178.435 * [misc]taylor: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in k 1546856178.435 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 1546856178.435 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1546856178.435 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1546856178.435 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1546856178.435 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546856178.435 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856178.435 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.435 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546856178.435 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856178.435 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.435 * [misc]taylor: Taking taylor expansion of k in k 1546856178.435 * [misc]backup-simplify: Simplify 0 into 0 1546856178.435 * [misc]backup-simplify: Simplify 1 into 1 1546856178.435 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1546856178.435 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1546856178.435 * [misc]taylor: Taking taylor expansion of 2 in k 1546856178.435 * [misc]backup-simplify: Simplify 2 into 2 1546856178.435 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1546856178.435 * [misc]taylor: Taking taylor expansion of n in k 1546856178.435 * [misc]backup-simplify: Simplify n into n 1546856178.435 * [misc]taylor: Taking taylor expansion of PI in k 1546856178.435 * [misc]backup-simplify: Simplify PI into PI 1546856178.435 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1546856178.435 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1546856178.435 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1546856178.435 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546856178.435 * [misc]backup-simplify: Simplify (- 0) into 0 1546856178.435 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546856178.435 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1546856178.435 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1546856178.436 * [misc]backup-simplify: Simplify (/ 1 (pow (* 2 (* n PI)) 1/2)) into (sqrt (/ 1 (* PI (* n 2)))) 1546856178.436 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1546856178.436 * [misc]taylor: Taking taylor expansion of k in k 1546856178.436 * [misc]backup-simplify: Simplify 0 into 0 1546856178.436 * [misc]backup-simplify: Simplify 1 into 1 1546856178.436 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546856178.436 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546856178.436 * [misc]backup-simplify: Simplify (* (sqrt (/ 1 (* PI (* n 2)))) 0) into 0 1546856178.436 * [misc]taylor: Taking taylor expansion of 0 in n 1546856178.436 * [misc]backup-simplify: Simplify 0 into 0 1546856178.436 * [misc]backup-simplify: Simplify 0 into 0 1546856178.436 * [misc]backup-simplify: Simplify (+ (* n 0) (* 0 PI)) into 0 1546856178.437 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0 1546856178.437 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 1546856178.437 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1546856178.437 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546856178.437 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546856178.438 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI))))) 1546856178.438 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1)))) into (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) 1546856178.438 * [misc]backup-simplify: Simplify (- (+ (* (sqrt (/ 1 (* PI (* n 2)))) (/ (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) (pow (* 2 (* n PI)) 1/2))))) into (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) 1546856178.439 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 (* PI (* n 2)))) +nan.0) (* (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) 0)) into (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))) 1546856178.439 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))) in n 1546856178.439 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))) in n 1546856178.439 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546856178.439 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546856178.439 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)) in n 1546856178.439 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n 1546856178.439 * [misc]taylor: Taking taylor expansion of (/ 1 (* n PI)) in n 1546856178.439 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546856178.439 * [misc]taylor: Taking taylor expansion of n in n 1546856178.439 * [misc]backup-simplify: Simplify 0 into 0 1546856178.439 * [misc]backup-simplify: Simplify 1 into 1 1546856178.439 * [misc]taylor: Taking taylor expansion of PI in n 1546856178.439 * [misc]backup-simplify: Simplify PI into PI 1546856178.439 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546856178.440 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546856178.440 * [misc]backup-simplify: Simplify (/ 1 PI) into (/ 1 PI) 1546856178.440 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546856178.440 * [misc]backup-simplify: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI) 1546856178.440 * [misc]taylor: Taking taylor expansion of (sqrt 1/2) in n 1546856178.440 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856178.440 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.440 * [misc]backup-simplify: Simplify (sqrt 1/2) into (sqrt 1/2) 1546856178.441 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 1/2))) into 0 1546856178.441 * [misc]backup-simplify: Simplify (+ (* 0 0) (* (/ +nan.0 PI) (sqrt 1/2))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 1546856178.441 * [misc]backup-simplify: Simplify (* 0 (sqrt 1/2)) into 0 1546856178.442 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (sqrt 1/2) PI)))) (* 0 0)) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 1546856178.443 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (/ (sqrt 1/2) PI)))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 1546856178.444 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (sqrt 1/2) PI))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 1546856178.444 * [misc]backup-simplify: Simplify 0 into 0 1546856178.445 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1546856178.445 * [misc]backup-simplify: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 1546856178.445 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 1546856178.446 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 1)))) 2) into 0 1546856178.446 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1546856178.446 * [misc]backup-simplify: Simplify (- 0) into 0 1546856178.447 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856178.447 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0 1546856178.448 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) 1546856178.450 * [misc]backup-simplify: Simplify (- (+ (* (sqrt (/ 1 (* PI (* n 2)))) (/ (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) (pow (* 2 (* n PI)) 1/2))) (* (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (/ (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) (pow (* 2 (* n PI)) 1/2))))) into (- (* 1/4 (* (* (pow (sqrt 2) 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 3))) (sqrt (/ 1 (* n PI))))) (* 1/8 (* (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI)))))) 1546856178.453 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 (* PI (* n 2)))) +nan.0) (+ (* (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) +nan.0) (* (- (* 1/4 (* (* (pow (sqrt 2) 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 3))) (sqrt (/ 1 (* n PI))))) (* 1/8 (* (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI)))))) 0))) into (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))))) 1546856178.453 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))))) in n 1546856178.454 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))))) in n 1546856178.454 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) in n 1546856178.454 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546856178.454 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546856178.454 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI)))) in n 1546856178.454 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) in n 1546856178.454 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1546856178.454 * [misc]taylor: Taking taylor expansion of 2 in n 1546856178.454 * [misc]backup-simplify: Simplify 2 into 2 1546856178.454 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1546856178.454 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1546856178.454 * [misc]taylor: Taking taylor expansion of (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2)) in n 1546856178.454 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546856178.454 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546856178.454 * [misc]taylor: Taking taylor expansion of 2 in n 1546856178.454 * [misc]backup-simplify: Simplify 2 into 2 1546856178.454 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546856178.454 * [misc]taylor: Taking taylor expansion of n in n 1546856178.454 * [misc]backup-simplify: Simplify 0 into 0 1546856178.454 * [misc]backup-simplify: Simplify 1 into 1 1546856178.454 * [misc]taylor: Taking taylor expansion of PI in n 1546856178.454 * [misc]backup-simplify: Simplify PI into PI 1546856178.455 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546856178.455 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546856178.456 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546856178.456 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546856178.457 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856178.457 * [misc]taylor: Taking taylor expansion of (pow (sqrt 1/2) 2) in n 1546856178.457 * [misc]taylor: Taking taylor expansion of (sqrt 1/2) in n 1546856178.457 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856178.457 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.457 * [misc]backup-simplify: Simplify (sqrt 1/2) into (sqrt 1/2) 1546856178.457 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 1/2))) into 0 1546856178.457 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n 1546856178.457 * [misc]taylor: Taking taylor expansion of (/ 1 (* n PI)) in n 1546856178.457 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546856178.457 * [misc]taylor: Taking taylor expansion of n in n 1546856178.457 * [misc]backup-simplify: Simplify 0 into 0 1546856178.457 * [misc]backup-simplify: Simplify 1 into 1 1546856178.457 * [misc]taylor: Taking taylor expansion of PI in n 1546856178.457 * [misc]backup-simplify: Simplify PI into PI 1546856178.458 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546856178.458 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546856178.458 * [misc]backup-simplify: Simplify (/ 1 PI) into (/ 1 PI) 1546856178.459 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546856178.459 * [misc]backup-simplify: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI) 1546856178.459 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))) in n 1546856178.459 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))) in n 1546856178.459 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546856178.460 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546856178.460 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)) in n 1546856178.460 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n 1546856178.460 * [misc]taylor: Taking taylor expansion of (/ 1 (* n PI)) in n 1546856178.460 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546856178.460 * [misc]taylor: Taking taylor expansion of n in n 1546856178.460 * [misc]backup-simplify: Simplify 0 into 0 1546856178.460 * [misc]backup-simplify: Simplify 1 into 1 1546856178.460 * [misc]taylor: Taking taylor expansion of PI in n 1546856178.460 * [misc]backup-simplify: Simplify PI into PI 1546856178.460 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546856178.461 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546856178.461 * [misc]backup-simplify: Simplify (/ 1 PI) into (/ 1 PI) 1546856178.461 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546856178.462 * [misc]backup-simplify: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI) 1546856178.462 * [misc]taylor: Taking taylor expansion of (sqrt 1/2) in n 1546856178.462 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856178.462 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.462 * [misc]backup-simplify: Simplify (sqrt 1/2) into (sqrt 1/2) 1546856178.462 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 1/2))) into 0 1546856178.463 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546856178.463 * [misc]backup-simplify: Simplify (* (sqrt 1/2) (sqrt 1/2)) into (pow (sqrt 1/2) 2) 1546856178.464 * [misc]backup-simplify: Simplify (* (+ (log n) (log (* 2 PI))) (pow (sqrt 1/2) 2)) into (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI)))) 1546856178.465 * [misc]backup-simplify: Simplify (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) into (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) 1546856178.466 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546856178.466 * [misc]backup-simplify: Simplify (+ (* (sqrt 1/2) 0) (* 0 (sqrt 1/2))) into 0 1546856178.468 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546856178.469 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1546856178.472 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546856178.473 * [misc]backup-simplify: Simplify (+ (* (+ (log n) (log (* 2 PI))) 0) (* 0 (pow (sqrt 1/2) 2))) into 0 1546856178.474 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI)))))) into 0 1546856178.476 * [misc]backup-simplify: Simplify (+ (* (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) (/ +nan.0 PI)) (* 0 0)) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))) 1546856178.477 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) 0) into 0 1546856178.482 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))) (* 0 0)) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))) 1546856178.483 * [misc]backup-simplify: Simplify (+ (* 0 0) (* (/ +nan.0 PI) (sqrt 1/2))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 1546856178.483 * [misc]backup-simplify: Simplify (* 0 (sqrt 1/2)) into 0 1546856178.485 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (sqrt 1/2) PI)))) (* 0 0)) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 1546856178.486 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (/ (sqrt 1/2) PI)))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 1546856178.493 * [misc]backup-simplify: Simplify (+ (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))) (- (* +nan.0 (/ (sqrt 1/2) PI)))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) 1546856178.500 * [misc]backup-simplify: Simplify (- (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) 1546856178.506 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) 1546856178.508 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1/2))) into 0 1546856178.509 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546856178.510 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 PI) (/ 0 PI)))) into 0 1546856178.512 * [misc]backup-simplify: Simplify (/ (- 0 (pow (/ +nan.0 PI) 2) (+)) (* 2 0)) into (/ +nan.0 (pow PI 2)) 1546856178.514 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* (/ +nan.0 PI) 0) (* (/ +nan.0 (pow PI 2)) (sqrt 1/2)))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) 1546856178.518 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2))))) (+ (* 0 (- (* +nan.0 (/ (sqrt 1/2) PI)))) (* 0 0))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) 1546856178.521 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2))))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) 1546856178.522 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) 1546856178.532 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) (* n k)) (+ (* (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) (pow (* 1 k) 2)) (* (- (* +nan.0 (/ (sqrt 1/2) PI))) (* 1 k)))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow k 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI))))) PI)) (- (+ (* +nan.0 (/ (* (sqrt 1/2) (pow k 2)) PI)) (- (+ (* +nan.0 (/ (* n (* (sqrt 1/2) k)) (pow PI 2))) (- (+ (* +nan.0 (/ (* (log n) (* (sqrt 2) (* (pow (sqrt 1/2) 2) (pow k 2)))) PI)) (- (* +nan.0 (/ (* (sqrt 1/2) k) PI))))))))))) 1546856178.532 * [misc]backup-simplify: Simplify (* (sqrt (/ 1 k)) (/ 1 (pow (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2))))) into (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) 1546856178.533 * [misc]approximate: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in (k n) around 0 1546856178.533 * [misc]taylor: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in n 1546856178.533 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1546856178.533 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546856178.533 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546856178.533 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546856178.533 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546856178.533 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856178.533 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.533 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546856178.533 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856178.533 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.533 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546856178.533 * [misc]taylor: Taking taylor expansion of k in n 1546856178.533 * [misc]backup-simplify: Simplify k into k 1546856178.533 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546856178.533 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546856178.533 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546856178.533 * [misc]taylor: Taking taylor expansion of 2 in n 1546856178.533 * [misc]backup-simplify: Simplify 2 into 2 1546856178.533 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856178.533 * [misc]taylor: Taking taylor expansion of PI in n 1546856178.533 * [misc]backup-simplify: Simplify PI into PI 1546856178.533 * [misc]taylor: Taking taylor expansion of n in n 1546856178.533 * [misc]backup-simplify: Simplify 0 into 0 1546856178.533 * [misc]backup-simplify: Simplify 1 into 1 1546856178.534 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856178.534 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546856178.535 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856178.535 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546856178.535 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546856178.535 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546856178.536 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546856178.536 * [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))) 1546856178.537 * [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)))) 1546856178.537 * [misc]backup-simplify: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 1546856178.538 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1546856178.538 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546856178.538 * [misc]taylor: Taking taylor expansion of k in n 1546856178.538 * [misc]backup-simplify: Simplify k into k 1546856178.538 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546856178.538 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1546856178.538 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546856178.538 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1546856178.538 * [misc]taylor: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in k 1546856178.538 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 1546856178.538 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1546856178.538 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1546856178.538 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1546856178.538 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546856178.538 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856178.538 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.538 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546856178.538 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856178.538 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.538 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546856178.538 * [misc]taylor: Taking taylor expansion of k in k 1546856178.538 * [misc]backup-simplify: Simplify 0 into 0 1546856178.538 * [misc]backup-simplify: Simplify 1 into 1 1546856178.539 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546856178.539 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1546856178.539 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1546856178.539 * [misc]taylor: Taking taylor expansion of 2 in k 1546856178.539 * [misc]backup-simplify: Simplify 2 into 2 1546856178.539 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546856178.539 * [misc]taylor: Taking taylor expansion of PI in k 1546856178.539 * [misc]backup-simplify: Simplify PI into PI 1546856178.539 * [misc]taylor: Taking taylor expansion of n in k 1546856178.539 * [misc]backup-simplify: Simplify n into n 1546856178.539 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546856178.539 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1546856178.539 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1546856178.539 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546856178.539 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546856178.540 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546856178.540 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1546856178.540 * [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)))) 1546856178.540 * [misc]backup-simplify: Simplify (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) into (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 1546856178.540 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1546856178.540 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546856178.540 * [misc]taylor: Taking taylor expansion of k in k 1546856178.540 * [misc]backup-simplify: Simplify 0 into 0 1546856178.540 * [misc]backup-simplify: Simplify 1 into 1 1546856178.540 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546856178.540 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546856178.540 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546856178.540 * [misc]taylor: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in k 1546856178.540 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 1546856178.540 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1546856178.540 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1546856178.540 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1546856178.541 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546856178.541 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856178.541 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.541 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546856178.541 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856178.541 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.541 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546856178.541 * [misc]taylor: Taking taylor expansion of k in k 1546856178.541 * [misc]backup-simplify: Simplify 0 into 0 1546856178.541 * [misc]backup-simplify: Simplify 1 into 1 1546856178.541 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546856178.541 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1546856178.541 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1546856178.541 * [misc]taylor: Taking taylor expansion of 2 in k 1546856178.541 * [misc]backup-simplify: Simplify 2 into 2 1546856178.541 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546856178.541 * [misc]taylor: Taking taylor expansion of PI in k 1546856178.541 * [misc]backup-simplify: Simplify PI into PI 1546856178.541 * [misc]taylor: Taking taylor expansion of n in k 1546856178.541 * [misc]backup-simplify: Simplify n into n 1546856178.541 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546856178.541 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1546856178.541 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1546856178.541 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546856178.541 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546856178.541 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546856178.541 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1546856178.541 * [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)))) 1546856178.542 * [misc]backup-simplify: Simplify (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) into (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 1546856178.542 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1546856178.542 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546856178.542 * [misc]taylor: Taking taylor expansion of k in k 1546856178.542 * [misc]backup-simplify: Simplify 0 into 0 1546856178.542 * [misc]backup-simplify: Simplify 1 into 1 1546856178.542 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546856178.542 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546856178.542 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546856178.542 * [misc]backup-simplify: Simplify (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 0) into 0 1546856178.542 * [misc]taylor: Taking taylor expansion of 0 in n 1546856178.542 * [misc]backup-simplify: Simplify 0 into 0 1546856178.542 * [misc]backup-simplify: Simplify 0 into 0 1546856178.543 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 1546856178.543 * [misc]backup-simplify: Simplify (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (* 0 0)) into (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) 1546856178.543 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) in n 1546856178.543 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 1546856178.543 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546856178.543 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546856178.543 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1546856178.543 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546856178.543 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546856178.543 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546856178.543 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546856178.543 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856178.543 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.543 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546856178.543 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856178.543 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.543 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546856178.543 * [misc]taylor: Taking taylor expansion of k in n 1546856178.543 * [misc]backup-simplify: Simplify k into k 1546856178.543 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546856178.543 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546856178.543 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546856178.543 * [misc]taylor: Taking taylor expansion of 2 in n 1546856178.543 * [misc]backup-simplify: Simplify 2 into 2 1546856178.543 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856178.543 * [misc]taylor: Taking taylor expansion of PI in n 1546856178.543 * [misc]backup-simplify: Simplify PI into PI 1546856178.543 * [misc]taylor: Taking taylor expansion of n in n 1546856178.543 * [misc]backup-simplify: Simplify 0 into 0 1546856178.543 * [misc]backup-simplify: Simplify 1 into 1 1546856178.544 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856178.544 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546856178.544 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856178.544 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546856178.544 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546856178.544 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546856178.545 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546856178.545 * [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))) 1546856178.545 * [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)))) 1546856178.546 * [misc]backup-simplify: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 1546856178.546 * [misc]backup-simplify: Simplify (* +nan.0 (/ 1 (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))))) 1546856178.547 * [misc]backup-simplify: Simplify (- (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 1546856178.547 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 1546856178.547 * [misc]backup-simplify: Simplify 0 into 0 1546856178.547 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1546856178.548 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1546856178.548 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) (* 0 (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 1546856178.548 * [misc]backup-simplify: Simplify (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) 1546856178.548 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) in n 1546856178.549 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 1546856178.549 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546856178.549 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546856178.549 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1546856178.549 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546856178.549 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546856178.549 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546856178.549 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546856178.549 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856178.549 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.549 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546856178.549 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856178.549 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.549 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546856178.549 * [misc]taylor: Taking taylor expansion of k in n 1546856178.549 * [misc]backup-simplify: Simplify k into k 1546856178.549 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546856178.549 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546856178.549 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546856178.549 * [misc]taylor: Taking taylor expansion of 2 in n 1546856178.549 * [misc]backup-simplify: Simplify 2 into 2 1546856178.549 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856178.549 * [misc]taylor: Taking taylor expansion of PI in n 1546856178.549 * [misc]backup-simplify: Simplify PI into PI 1546856178.549 * [misc]taylor: Taking taylor expansion of n in n 1546856178.549 * [misc]backup-simplify: Simplify 0 into 0 1546856178.549 * [misc]backup-simplify: Simplify 1 into 1 1546856178.549 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856178.549 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546856178.550 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856178.550 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546856178.550 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546856178.550 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546856178.550 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546856178.551 * [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))) 1546856178.551 * [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)))) 1546856178.551 * [misc]backup-simplify: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 1546856178.552 * [misc]backup-simplify: Simplify (* +nan.0 (/ 1 (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))))) 1546856178.552 * [misc]backup-simplify: Simplify (- (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 1546856178.553 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 1546856178.553 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546856178.554 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546856178.555 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546856178.556 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546856178.556 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546856178.556 * [misc]backup-simplify: Simplify (- 0) into 0 1546856178.556 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856178.556 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546856178.557 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1546856178.558 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546856178.558 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (/ 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))) into 0 1546856178.559 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0 1546856178.559 * [misc]backup-simplify: Simplify (- 0) into 0 1546856178.559 * [misc]backup-simplify: Simplify 0 into 0 1546856178.559 * [misc]backup-simplify: Simplify 0 into 0 1546856178.559 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856178.561 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1546856178.561 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) (* 0 (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) (* 0 (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 1546856178.562 * [misc]backup-simplify: Simplify (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) 1546856178.562 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) in n 1546856178.562 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 1546856178.562 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546856178.562 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546856178.562 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1546856178.562 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546856178.562 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546856178.562 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546856178.562 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546856178.562 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856178.562 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.562 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546856178.562 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856178.562 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.562 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546856178.562 * [misc]taylor: Taking taylor expansion of k in n 1546856178.562 * [misc]backup-simplify: Simplify k into k 1546856178.562 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546856178.562 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546856178.562 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546856178.562 * [misc]taylor: Taking taylor expansion of 2 in n 1546856178.562 * [misc]backup-simplify: Simplify 2 into 2 1546856178.562 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856178.562 * [misc]taylor: Taking taylor expansion of PI in n 1546856178.562 * [misc]backup-simplify: Simplify PI into PI 1546856178.563 * [misc]taylor: Taking taylor expansion of n in n 1546856178.563 * [misc]backup-simplify: Simplify 0 into 0 1546856178.563 * [misc]backup-simplify: Simplify 1 into 1 1546856178.563 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856178.563 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546856178.564 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856178.564 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546856178.564 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546856178.564 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546856178.565 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546856178.565 * [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))) 1546856178.566 * [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)))) 1546856178.566 * [misc]backup-simplify: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 1546856178.567 * [misc]backup-simplify: Simplify (* +nan.0 (/ 1 (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))))) 1546856178.568 * [misc]backup-simplify: Simplify (- (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 1546856178.568 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 1546856178.571 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 2)) (+ (* (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (* 1 (/ 1 k))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))))))) into (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))))))))) 1546856178.571 * [misc]backup-simplify: Simplify (* (sqrt (/ 1 (- k))) (/ 1 (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2))))) into (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) 1546856178.571 * [misc]approximate: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in (k n) around 0 1546856178.571 * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1546856178.571 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1546856178.571 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1546856178.571 * [misc]taylor: Taking taylor expansion of -1 in n 1546856178.572 * [misc]backup-simplify: Simplify -1 into -1 1546856178.572 * [misc]taylor: Taking taylor expansion of k in n 1546856178.572 * [misc]backup-simplify: Simplify k into k 1546856178.572 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1546856178.572 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1546856178.572 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1546856178.572 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1546856178.572 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546856178.572 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546856178.572 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546856178.572 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546856178.572 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546856178.572 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856178.572 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.572 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546856178.572 * [misc]taylor: Taking taylor expansion of k in n 1546856178.572 * [misc]backup-simplify: Simplify k into k 1546856178.572 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546856178.572 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856178.572 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.572 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546856178.572 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546856178.572 * [misc]taylor: Taking taylor expansion of -2 in n 1546856178.572 * [misc]backup-simplify: Simplify -2 into -2 1546856178.572 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856178.572 * [misc]taylor: Taking taylor expansion of PI in n 1546856178.573 * [misc]backup-simplify: Simplify PI into PI 1546856178.573 * [misc]taylor: Taking taylor expansion of n in n 1546856178.573 * [misc]backup-simplify: Simplify 0 into 0 1546856178.573 * [misc]backup-simplify: Simplify 1 into 1 1546856178.573 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856178.573 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546856178.574 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546856178.574 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546856178.574 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546856178.575 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546856178.575 * [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))) 1546856178.576 * [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)))) 1546856178.577 * [misc]backup-simplify: Simplify (/ (sqrt (/ -1 k)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ (sqrt (/ -1 k)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 1546856178.577 * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in k 1546856178.577 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1546856178.577 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1546856178.577 * [misc]taylor: Taking taylor expansion of -1 in k 1546856178.577 * [misc]backup-simplify: Simplify -1 into -1 1546856178.577 * [misc]taylor: Taking taylor expansion of k in k 1546856178.577 * [misc]backup-simplify: Simplify 0 into 0 1546856178.577 * [misc]backup-simplify: Simplify 1 into 1 1546856178.577 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1546856178.577 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546856178.578 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1546856178.578 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1546856178.578 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1546856178.578 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1546856178.578 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546856178.578 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546856178.578 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856178.578 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.578 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546856178.578 * [misc]taylor: Taking taylor expansion of k in k 1546856178.578 * [misc]backup-simplify: Simplify 0 into 0 1546856178.578 * [misc]backup-simplify: Simplify 1 into 1 1546856178.578 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546856178.578 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856178.578 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.578 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1546856178.578 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1546856178.578 * [misc]taylor: Taking taylor expansion of -2 in k 1546856178.578 * [misc]backup-simplify: Simplify -2 into -2 1546856178.578 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546856178.579 * [misc]taylor: Taking taylor expansion of PI in k 1546856178.579 * [misc]backup-simplify: Simplify PI into PI 1546856178.579 * [misc]taylor: Taking taylor expansion of n in k 1546856178.579 * [misc]backup-simplify: Simplify n into n 1546856178.579 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546856178.579 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1546856178.579 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1546856178.579 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546856178.579 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546856178.579 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1546856178.579 * [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))) 1546856178.580 * [misc]backup-simplify: Simplify (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) into (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) 1546856178.580 * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in k 1546856178.580 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1546856178.580 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1546856178.580 * [misc]taylor: Taking taylor expansion of -1 in k 1546856178.580 * [misc]backup-simplify: Simplify -1 into -1 1546856178.580 * [misc]taylor: Taking taylor expansion of k in k 1546856178.580 * [misc]backup-simplify: Simplify 0 into 0 1546856178.580 * [misc]backup-simplify: Simplify 1 into 1 1546856178.580 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1546856178.580 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546856178.581 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1546856178.581 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1546856178.581 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1546856178.581 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1546856178.581 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546856178.581 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546856178.581 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856178.581 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.581 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546856178.581 * [misc]taylor: Taking taylor expansion of k in k 1546856178.581 * [misc]backup-simplify: Simplify 0 into 0 1546856178.581 * [misc]backup-simplify: Simplify 1 into 1 1546856178.581 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546856178.581 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856178.581 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.581 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1546856178.581 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1546856178.581 * [misc]taylor: Taking taylor expansion of -2 in k 1546856178.581 * [misc]backup-simplify: Simplify -2 into -2 1546856178.581 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546856178.582 * [misc]taylor: Taking taylor expansion of PI in k 1546856178.582 * [misc]backup-simplify: Simplify PI into PI 1546856178.582 * [misc]taylor: Taking taylor expansion of n in k 1546856178.582 * [misc]backup-simplify: Simplify n into n 1546856178.582 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546856178.582 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1546856178.582 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1546856178.582 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546856178.582 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546856178.582 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1546856178.583 * [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))) 1546856178.583 * [misc]backup-simplify: Simplify (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) into (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) 1546856178.583 * [misc]taylor: Taking taylor expansion of (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1546856178.583 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546856178.583 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546856178.583 * [misc]taylor: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1546856178.583 * [misc]taylor: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546856178.583 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546856178.583 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546856178.583 * [misc]taylor: Taking taylor expansion of -2 in n 1546856178.584 * [misc]backup-simplify: Simplify -2 into -2 1546856178.584 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856178.584 * [misc]taylor: Taking taylor expansion of PI in n 1546856178.584 * [misc]backup-simplify: Simplify PI into PI 1546856178.584 * [misc]taylor: Taking taylor expansion of n in n 1546856178.584 * [misc]backup-simplify: Simplify 0 into 0 1546856178.584 * [misc]backup-simplify: Simplify 1 into 1 1546856178.584 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856178.584 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546856178.585 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546856178.585 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546856178.585 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546856178.585 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856178.585 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.585 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546856178.585 * [misc]taylor: Taking taylor expansion of k in n 1546856178.585 * [misc]backup-simplify: Simplify k into k 1546856178.585 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546856178.585 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856178.585 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.586 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546856178.586 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546856178.586 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546856178.587 * [misc]backup-simplify: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1546856178.588 * [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)))) 1546856178.588 * [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))))) 1546856178.589 * [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))))) 1546856178.589 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1546856178.590 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1546856178.591 * [misc]backup-simplify: Simplify (- (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (+ (* (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ 0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))))) into (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) 1546856178.591 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) in n 1546856178.591 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 1546856178.591 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546856178.591 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546856178.591 * [misc]taylor: Taking taylor expansion of (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1546856178.591 * [misc]taylor: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1546856178.591 * [misc]taylor: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546856178.591 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546856178.591 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546856178.591 * [misc]taylor: Taking taylor expansion of -2 in n 1546856178.591 * [misc]backup-simplify: Simplify -2 into -2 1546856178.591 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856178.591 * [misc]taylor: Taking taylor expansion of PI in n 1546856178.591 * [misc]backup-simplify: Simplify PI into PI 1546856178.591 * [misc]taylor: Taking taylor expansion of n in n 1546856178.591 * [misc]backup-simplify: Simplify 0 into 0 1546856178.591 * [misc]backup-simplify: Simplify 1 into 1 1546856178.592 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856178.592 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546856178.592 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546856178.592 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546856178.592 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546856178.592 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856178.592 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.592 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546856178.592 * [misc]taylor: Taking taylor expansion of k in n 1546856178.592 * [misc]backup-simplify: Simplify k into k 1546856178.592 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546856178.592 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856178.592 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.593 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546856178.593 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546856178.593 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546856178.593 * [misc]backup-simplify: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1546856178.594 * [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)))) 1546856178.594 * [misc]backup-simplify: Simplify (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 1546856178.595 * [misc]backup-simplify: Simplify (* +nan.0 (/ 1 (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))))) 1546856178.595 * [misc]backup-simplify: Simplify (- (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) 1546856178.596 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) 1546856178.596 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546856178.596 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546856178.596 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546856178.596 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856178.597 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546856178.597 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1546856178.599 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1546856178.599 * [misc]backup-simplify: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0 1546856178.600 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546856178.602 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (+ (* (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))))) into 0 1546856178.602 * [misc]backup-simplify: Simplify 0 into 0 1546856178.602 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856178.602 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1546856178.603 * [misc]backup-simplify: Simplify (- (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (+ (* (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ 0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) (* (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) (/ 0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))))) into (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) 1546856178.603 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) in n 1546856178.603 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 1546856178.603 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546856178.603 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546856178.603 * [misc]taylor: Taking taylor expansion of (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1546856178.603 * [misc]taylor: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1546856178.603 * [misc]taylor: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546856178.603 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546856178.603 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546856178.603 * [misc]taylor: Taking taylor expansion of -2 in n 1546856178.603 * [misc]backup-simplify: Simplify -2 into -2 1546856178.603 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856178.603 * [misc]taylor: Taking taylor expansion of PI in n 1546856178.603 * [misc]backup-simplify: Simplify PI into PI 1546856178.603 * [misc]taylor: Taking taylor expansion of n in n 1546856178.603 * [misc]backup-simplify: Simplify 0 into 0 1546856178.603 * [misc]backup-simplify: Simplify 1 into 1 1546856178.604 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856178.604 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546856178.604 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546856178.604 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546856178.604 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546856178.604 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856178.604 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.604 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546856178.604 * [misc]taylor: Taking taylor expansion of k in n 1546856178.604 * [misc]backup-simplify: Simplify k into k 1546856178.604 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546856178.604 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856178.604 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.605 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546856178.605 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546856178.605 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546856178.605 * [misc]backup-simplify: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1546856178.605 * [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)))) 1546856178.606 * [misc]backup-simplify: Simplify (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 1546856178.606 * [misc]backup-simplify: Simplify (* +nan.0 (/ 1 (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))))) 1546856178.607 * [misc]backup-simplify: Simplify (- (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) 1546856178.607 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) 1546856178.609 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (* 1 (/ 1 (- k)))) (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) into (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))))))))) 1546856178.609 * * * * [misc]progress: [ 4 / 4 ] generating series at (2 2 2) 1546856178.609 * [misc]backup-simplify: Simplify (/ 1 (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) into (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) 1546856178.609 * [misc]approximate: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (n k) around 0 1546856178.609 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 1546856178.609 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1546856178.609 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1546856178.609 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1546856178.609 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546856178.609 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856178.609 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.609 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546856178.609 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856178.609 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.609 * [misc]taylor: Taking taylor expansion of k in k 1546856178.609 * [misc]backup-simplify: Simplify 0 into 0 1546856178.609 * [misc]backup-simplify: Simplify 1 into 1 1546856178.609 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1546856178.609 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1546856178.609 * [misc]taylor: Taking taylor expansion of 2 in k 1546856178.609 * [misc]backup-simplify: Simplify 2 into 2 1546856178.609 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1546856178.609 * [misc]taylor: Taking taylor expansion of n in k 1546856178.609 * [misc]backup-simplify: Simplify n into n 1546856178.609 * [misc]taylor: Taking taylor expansion of PI in k 1546856178.609 * [misc]backup-simplify: Simplify PI into PI 1546856178.609 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1546856178.609 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1546856178.609 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1546856178.609 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546856178.610 * [misc]backup-simplify: Simplify (- 0) into 0 1546856178.610 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546856178.610 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1546856178.610 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1546856178.610 * [misc]backup-simplify: Simplify (/ 1 (pow (* 2 (* n PI)) 1/2)) into (sqrt (/ 1 (* PI (* n 2)))) 1546856178.610 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 1546856178.610 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546856178.610 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546856178.610 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546856178.610 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546856178.610 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856178.610 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.610 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546856178.610 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856178.610 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.610 * [misc]taylor: Taking taylor expansion of k in n 1546856178.610 * [misc]backup-simplify: Simplify k into k 1546856178.610 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546856178.610 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546856178.610 * [misc]taylor: Taking taylor expansion of 2 in n 1546856178.610 * [misc]backup-simplify: Simplify 2 into 2 1546856178.610 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546856178.610 * [misc]taylor: Taking taylor expansion of n in n 1546856178.610 * [misc]backup-simplify: Simplify 0 into 0 1546856178.610 * [misc]backup-simplify: Simplify 1 into 1 1546856178.610 * [misc]taylor: Taking taylor expansion of PI in n 1546856178.610 * [misc]backup-simplify: Simplify PI into PI 1546856178.611 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546856178.611 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546856178.611 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546856178.612 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546856178.612 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856178.612 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546856178.612 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546856178.612 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546856178.612 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546856178.613 * [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)))) 1546856178.613 * [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))))) 1546856178.614 * [misc]backup-simplify: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (/ 1 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) 1546856178.614 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 1546856178.614 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546856178.614 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546856178.614 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546856178.614 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546856178.614 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856178.614 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.614 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546856178.614 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856178.614 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.614 * [misc]taylor: Taking taylor expansion of k in n 1546856178.614 * [misc]backup-simplify: Simplify k into k 1546856178.614 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546856178.614 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546856178.614 * [misc]taylor: Taking taylor expansion of 2 in n 1546856178.614 * [misc]backup-simplify: Simplify 2 into 2 1546856178.614 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546856178.614 * [misc]taylor: Taking taylor expansion of n in n 1546856178.614 * [misc]backup-simplify: Simplify 0 into 0 1546856178.614 * [misc]backup-simplify: Simplify 1 into 1 1546856178.614 * [misc]taylor: Taking taylor expansion of PI in n 1546856178.614 * [misc]backup-simplify: Simplify PI into PI 1546856178.614 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546856178.614 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546856178.615 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546856178.615 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546856178.615 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856178.615 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546856178.615 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546856178.615 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546856178.616 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546856178.616 * [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)))) 1546856178.617 * [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))))) 1546856178.617 * [misc]backup-simplify: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (/ 1 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) 1546856178.617 * [misc]taylor: Taking taylor expansion of (/ 1 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) in k 1546856178.617 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1546856178.617 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1546856178.617 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546856178.617 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856178.617 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.617 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546856178.617 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856178.617 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.617 * [misc]taylor: Taking taylor expansion of k in k 1546856178.617 * [misc]backup-simplify: Simplify 0 into 0 1546856178.617 * [misc]backup-simplify: Simplify 1 into 1 1546856178.617 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1546856178.617 * [misc]taylor: Taking taylor expansion of (log n) in k 1546856178.617 * [misc]taylor: Taking taylor expansion of n in k 1546856178.617 * [misc]backup-simplify: Simplify n into n 1546856178.617 * [misc]backup-simplify: Simplify (log n) into (log n) 1546856178.617 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1546856178.617 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1546856178.617 * [misc]taylor: Taking taylor expansion of 2 in k 1546856178.617 * [misc]backup-simplify: Simplify 2 into 2 1546856178.617 * [misc]taylor: Taking taylor expansion of PI in k 1546856178.617 * [misc]backup-simplify: Simplify PI into PI 1546856178.618 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546856178.618 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856178.618 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546856178.618 * [misc]backup-simplify: Simplify (- 0) into 0 1546856178.618 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546856178.618 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546856178.619 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1546856178.619 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1546856178.620 * [misc]backup-simplify: Simplify (/ 1 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) into (/ 1 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) 1546856178.620 * [misc]backup-simplify: Simplify (/ 1 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) into (/ 1 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) 1546856178.621 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546856178.621 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1546856178.623 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546856178.623 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1546856178.623 * [misc]backup-simplify: Simplify (- 0) into 0 1546856178.623 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856178.624 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546856178.624 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1546856178.625 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1546856178.627 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) (/ 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))))) into 0 1546856178.627 * [misc]taylor: Taking taylor expansion of 0 in k 1546856178.627 * [misc]backup-simplify: Simplify 0 into 0 1546856178.627 * [misc]backup-simplify: Simplify 0 into 0 1546856178.627 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1546856178.628 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546856178.631 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546856178.631 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856178.631 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1546856178.631 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546856178.632 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546856178.632 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1546856178.634 * [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))))))) 1546856178.637 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (/ (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) into (+ (* 1/2 (/ (log (* 2 PI)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* 1/2 (/ (log n) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))) 1546856178.638 * [misc]backup-simplify: Simplify (+ (* 1/2 (/ (log (* 2 PI)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* 1/2 (/ (log n) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))) into (+ (* 1/2 (/ (log (* 2 PI)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* 1/2 (/ (log n) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))) 1546856178.640 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1546856178.642 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1546856178.648 * [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 1546856178.648 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1546856178.648 * [misc]backup-simplify: Simplify (- 0) into 0 1546856178.649 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856178.649 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546856178.650 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1546856178.653 * [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 1546856178.655 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) (/ 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))) (* 0 (/ 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))))) into 0 1546856178.655 * [misc]taylor: Taking taylor expansion of 0 in k 1546856178.655 * [misc]backup-simplify: Simplify 0 into 0 1546856178.655 * [misc]backup-simplify: Simplify 0 into 0 1546856178.655 * [misc]backup-simplify: Simplify 0 into 0 1546856178.656 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1546856178.658 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546856178.662 * [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 1546856178.663 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856178.663 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1546856178.663 * [misc]backup-simplify: Simplify (- 0) into 0 1546856178.663 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856178.664 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1546856178.666 * [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))))) 1546856178.671 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (/ (* (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))))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* (+ (* 1/2 (/ (log (* 2 PI)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* 1/2 (/ (log n) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))) (/ (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) into (+ (* 1/4 (/ (* (log n) (log (* 2 PI))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/8 (/ (pow (log (* 2 PI)) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* 1/8 (/ (pow (log n) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) 1546856178.673 * [misc]backup-simplify: Simplify (+ (* 1/4 (/ (* (log n) (log (* 2 PI))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/8 (/ (pow (log (* 2 PI)) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* 1/8 (/ (pow (log n) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) into (+ (* 1/4 (/ (* (log n) (log (* 2 PI))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/8 (/ (pow (log (* 2 PI)) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* 1/8 (/ (pow (log n) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) 1546856178.677 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/4 (/ (* (log n) (log (* 2 PI))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/8 (/ (pow (log (* 2 PI)) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* 1/8 (/ (pow (log n) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) (pow (* k 1) 2)) (+ (* (+ (* 1/2 (/ (log (* 2 PI)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* 1/2 (/ (log n) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))) (* k 1)) (/ 1 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))) into (+ (* 1/8 (/ (* (pow (log (* 2 PI)) 2) (pow k 2)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/2 (/ (* k (log (* 2 PI))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/2 (/ (* (log n) k) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/4 (/ (* (log (* 2 PI)) (* (log n) (pow k 2))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (/ 1 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (* 1/8 (/ (* (pow (log n) 2) (pow k 2)) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))))))) 1546856178.677 * [misc]backup-simplify: Simplify (/ 1 (pow (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2)))) into (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 1546856178.677 * [misc]approximate: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0 1546856178.677 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 1546856178.677 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1546856178.677 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1546856178.677 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1546856178.677 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546856178.677 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856178.677 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.677 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546856178.677 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856178.677 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.677 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546856178.677 * [misc]taylor: Taking taylor expansion of k in k 1546856178.677 * [misc]backup-simplify: Simplify 0 into 0 1546856178.677 * [misc]backup-simplify: Simplify 1 into 1 1546856178.677 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546856178.677 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1546856178.677 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1546856178.678 * [misc]taylor: Taking taylor expansion of 2 in k 1546856178.678 * [misc]backup-simplify: Simplify 2 into 2 1546856178.678 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546856178.678 * [misc]taylor: Taking taylor expansion of PI in k 1546856178.678 * [misc]backup-simplify: Simplify PI into PI 1546856178.678 * [misc]taylor: Taking taylor expansion of n in k 1546856178.678 * [misc]backup-simplify: Simplify n into n 1546856178.678 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546856178.678 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1546856178.678 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1546856178.678 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546856178.678 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546856178.678 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546856178.678 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1546856178.678 * [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)))) 1546856178.678 * [misc]backup-simplify: Simplify (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) into (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 1546856178.678 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1546856178.678 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546856178.678 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546856178.678 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546856178.678 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546856178.678 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856178.678 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.678 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546856178.678 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856178.678 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.679 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546856178.679 * [misc]taylor: Taking taylor expansion of k in n 1546856178.679 * [misc]backup-simplify: Simplify k into k 1546856178.679 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546856178.679 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546856178.679 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546856178.679 * [misc]taylor: Taking taylor expansion of 2 in n 1546856178.679 * [misc]backup-simplify: Simplify 2 into 2 1546856178.679 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856178.679 * [misc]taylor: Taking taylor expansion of PI in n 1546856178.679 * [misc]backup-simplify: Simplify PI into PI 1546856178.679 * [misc]taylor: Taking taylor expansion of n in n 1546856178.679 * [misc]backup-simplify: Simplify 0 into 0 1546856178.679 * [misc]backup-simplify: Simplify 1 into 1 1546856178.679 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856178.679 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546856178.679 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856178.680 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546856178.680 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546856178.680 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546856178.680 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546856178.680 * [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))) 1546856178.681 * [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)))) 1546856178.681 * [misc]backup-simplify: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 1546856178.681 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1546856178.681 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546856178.681 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546856178.681 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546856178.681 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546856178.681 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856178.681 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.681 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546856178.681 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856178.681 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.681 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546856178.681 * [misc]taylor: Taking taylor expansion of k in n 1546856178.681 * [misc]backup-simplify: Simplify k into k 1546856178.681 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546856178.681 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546856178.681 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546856178.681 * [misc]taylor: Taking taylor expansion of 2 in n 1546856178.682 * [misc]backup-simplify: Simplify 2 into 2 1546856178.682 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856178.682 * [misc]taylor: Taking taylor expansion of PI in n 1546856178.682 * [misc]backup-simplify: Simplify PI into PI 1546856178.682 * [misc]taylor: Taking taylor expansion of n in n 1546856178.682 * [misc]backup-simplify: Simplify 0 into 0 1546856178.682 * [misc]backup-simplify: Simplify 1 into 1 1546856178.682 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856178.682 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546856178.682 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856178.682 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546856178.682 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546856178.682 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546856178.683 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546856178.683 * [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))) 1546856178.684 * [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)))) 1546856178.684 * [misc]backup-simplify: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 1546856178.684 * [misc]taylor: Taking taylor expansion of (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) in k 1546856178.684 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1546856178.684 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1546856178.684 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546856178.684 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856178.684 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.684 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546856178.684 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856178.684 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.684 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546856178.684 * [misc]taylor: Taking taylor expansion of k in k 1546856178.684 * [misc]backup-simplify: Simplify 0 into 0 1546856178.684 * [misc]backup-simplify: Simplify 1 into 1 1546856178.684 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546856178.684 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1546856178.684 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1546856178.684 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1546856178.684 * [misc]taylor: Taking taylor expansion of 2 in k 1546856178.684 * [misc]backup-simplify: Simplify 2 into 2 1546856178.684 * [misc]taylor: Taking taylor expansion of PI in k 1546856178.684 * [misc]backup-simplify: Simplify PI into PI 1546856178.685 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546856178.685 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856178.685 * [misc]taylor: Taking taylor expansion of (log n) in k 1546856178.685 * [misc]taylor: Taking taylor expansion of n in k 1546856178.685 * [misc]backup-simplify: Simplify n into n 1546856178.685 * [misc]backup-simplify: Simplify (log n) into (log n) 1546856178.685 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546856178.685 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546856178.685 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546856178.685 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1546856178.686 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1546856178.686 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1546856178.686 * [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)))) 1546856178.687 * [misc]backup-simplify: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 1546856178.687 * [misc]backup-simplify: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 1546856178.688 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546856178.688 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546856178.690 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546856178.690 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546856178.690 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546856178.690 * [misc]backup-simplify: Simplify (- 0) into 0 1546856178.690 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856178.691 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546856178.691 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1546856178.692 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546856178.693 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (/ 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))) into 0 1546856178.693 * [misc]taylor: Taking taylor expansion of 0 in k 1546856178.693 * [misc]backup-simplify: Simplify 0 into 0 1546856178.693 * [misc]backup-simplify: Simplify 0 into 0 1546856178.694 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (/ 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))) into 0 1546856178.694 * [misc]backup-simplify: Simplify 0 into 0 1546856178.695 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856178.695 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546856178.699 * [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 1546856178.699 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546856178.699 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1546856178.699 * [misc]backup-simplify: Simplify (- 0) into 0 1546856178.699 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856178.700 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546856178.701 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1546856178.703 * [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 1546856178.705 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (/ 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) (* 0 (/ 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))) into 0 1546856178.705 * [misc]taylor: Taking taylor expansion of 0 in k 1546856178.705 * [misc]backup-simplify: Simplify 0 into 0 1546856178.705 * [misc]backup-simplify: Simplify 0 into 0 1546856178.705 * [misc]backup-simplify: Simplify 0 into 0 1546856178.707 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (/ 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) (* 0 (/ 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))) into 0 1546856178.707 * [misc]backup-simplify: Simplify 0 into 0 1546856178.709 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856178.711 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546856178.719 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 1546856178.719 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546856178.720 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1546856178.720 * [misc]backup-simplify: Simplify (- 0) into 0 1546856178.720 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856178.721 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546856178.722 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1546856178.725 * [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 1546856178.728 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (/ 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) (* 0 (/ 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) (* 0 (/ 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))) into 0 1546856178.728 * [misc]taylor: Taking taylor expansion of 0 in k 1546856178.728 * [misc]backup-simplify: Simplify 0 into 0 1546856178.728 * [misc]backup-simplify: Simplify 0 into 0 1546856178.729 * [misc]backup-simplify: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))) 1546856178.729 * [misc]backup-simplify: Simplify (/ 1 (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2)))) into (/ 1 (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) 1546856178.729 * [misc]approximate: Taking taylor expansion of (/ 1 (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in (n k) around 0 1546856178.729 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in k 1546856178.729 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1546856178.729 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1546856178.729 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1546856178.729 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546856178.729 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546856178.730 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856178.730 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.730 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546856178.730 * [misc]taylor: Taking taylor expansion of k in k 1546856178.730 * [misc]backup-simplify: Simplify 0 into 0 1546856178.730 * [misc]backup-simplify: Simplify 1 into 1 1546856178.730 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546856178.730 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856178.730 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.730 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1546856178.730 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1546856178.730 * [misc]taylor: Taking taylor expansion of -2 in k 1546856178.730 * [misc]backup-simplify: Simplify -2 into -2 1546856178.730 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546856178.730 * [misc]taylor: Taking taylor expansion of PI in k 1546856178.730 * [misc]backup-simplify: Simplify PI into PI 1546856178.730 * [misc]taylor: Taking taylor expansion of n in k 1546856178.730 * [misc]backup-simplify: Simplify n into n 1546856178.730 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546856178.730 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1546856178.730 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1546856178.731 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546856178.731 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546856178.731 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1546856178.731 * [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))) 1546856178.731 * [misc]backup-simplify: Simplify (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) into (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) 1546856178.731 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1546856178.731 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546856178.731 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546856178.731 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546856178.731 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546856178.731 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546856178.732 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856178.732 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.732 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546856178.732 * [misc]taylor: Taking taylor expansion of k in n 1546856178.732 * [misc]backup-simplify: Simplify k into k 1546856178.732 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546856178.732 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856178.732 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.732 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546856178.732 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546856178.732 * [misc]taylor: Taking taylor expansion of -2 in n 1546856178.732 * [misc]backup-simplify: Simplify -2 into -2 1546856178.732 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856178.732 * [misc]taylor: Taking taylor expansion of PI in n 1546856178.732 * [misc]backup-simplify: Simplify PI into PI 1546856178.732 * [misc]taylor: Taking taylor expansion of n in n 1546856178.732 * [misc]backup-simplify: Simplify 0 into 0 1546856178.732 * [misc]backup-simplify: Simplify 1 into 1 1546856178.732 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856178.733 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546856178.733 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546856178.733 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546856178.733 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546856178.734 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546856178.735 * [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))) 1546856178.735 * [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)))) 1546856178.736 * [misc]backup-simplify: Simplify (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 1546856178.736 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1546856178.736 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546856178.736 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546856178.736 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546856178.736 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546856178.736 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546856178.736 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856178.736 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.736 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546856178.736 * [misc]taylor: Taking taylor expansion of k in n 1546856178.736 * [misc]backup-simplify: Simplify k into k 1546856178.736 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546856178.736 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856178.736 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.736 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546856178.737 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546856178.737 * [misc]taylor: Taking taylor expansion of -2 in n 1546856178.737 * [misc]backup-simplify: Simplify -2 into -2 1546856178.737 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856178.737 * [misc]taylor: Taking taylor expansion of PI in n 1546856178.737 * [misc]backup-simplify: Simplify PI into PI 1546856178.737 * [misc]taylor: Taking taylor expansion of n in n 1546856178.737 * [misc]backup-simplify: Simplify 0 into 0 1546856178.737 * [misc]backup-simplify: Simplify 1 into 1 1546856178.737 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856178.737 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546856178.738 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546856178.738 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546856178.738 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546856178.739 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546856178.739 * [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))) 1546856178.740 * [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)))) 1546856178.740 * [misc]backup-simplify: Simplify (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 1546856178.741 * [misc]taylor: Taking taylor expansion of (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) in k 1546856178.741 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1546856178.741 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1546856178.741 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546856178.741 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546856178.741 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856178.741 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.741 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546856178.741 * [misc]taylor: Taking taylor expansion of k in k 1546856178.741 * [misc]backup-simplify: Simplify 0 into 0 1546856178.741 * [misc]backup-simplify: Simplify 1 into 1 1546856178.741 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546856178.741 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856178.741 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856178.741 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1546856178.741 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1546856178.741 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1546856178.741 * [misc]taylor: Taking taylor expansion of -2 in k 1546856178.741 * [misc]backup-simplify: Simplify -2 into -2 1546856178.741 * [misc]taylor: Taking taylor expansion of PI in k 1546856178.741 * [misc]backup-simplify: Simplify PI into PI 1546856178.742 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546856178.742 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546856178.742 * [misc]taylor: Taking taylor expansion of (log n) in k 1546856178.742 * [misc]taylor: Taking taylor expansion of n in k 1546856178.742 * [misc]backup-simplify: Simplify n into n 1546856178.742 * [misc]backup-simplify: Simplify (log n) into (log n) 1546856178.742 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546856178.743 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546856178.743 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1546856178.743 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1546856178.744 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1546856178.744 * [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)))) 1546856178.745 * [misc]backup-simplify: Simplify (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 1546856178.746 * [misc]backup-simplify: Simplify (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 1546856178.747 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546856178.748 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1546856178.750 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1546856178.751 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546856178.751 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546856178.751 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856178.752 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546856178.753 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1546856178.755 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546856178.756 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))))) into 0 1546856178.756 * [misc]taylor: Taking taylor expansion of 0 in k 1546856178.756 * [misc]backup-simplify: Simplify 0 into 0 1546856178.756 * [misc]backup-simplify: Simplify 0 into 0 1546856178.757 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))))) into 0 1546856178.757 * [misc]backup-simplify: Simplify 0 into 0 1546856178.759 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856178.760 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1546856178.765 * [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 1546856178.766 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546856178.766 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1546856178.766 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856178.767 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546856178.768 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1546856178.770 * [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 1546856178.772 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) (* 0 (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))))) into 0 1546856178.772 * [misc]taylor: Taking taylor expansion of 0 in k 1546856178.772 * [misc]backup-simplify: Simplify 0 into 0 1546856178.772 * [misc]backup-simplify: Simplify 0 into 0 1546856178.772 * [misc]backup-simplify: Simplify 0 into 0 1546856178.775 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) (* 0 (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))))) into 0 1546856178.775 * [misc]backup-simplify: Simplify 0 into 0 1546856178.777 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856178.779 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546856178.787 * [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 1546856178.787 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546856178.787 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1546856178.787 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856178.788 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546856178.788 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 1546856178.791 * [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 1546856178.792 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) (* 0 (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) (* 0 (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))))) into 0 1546856178.792 * [misc]taylor: Taking taylor expansion of 0 in k 1546856178.792 * [misc]backup-simplify: Simplify 0 into 0 1546856178.792 * [misc]backup-simplify: Simplify 0 into 0 1546856178.793 * [misc]backup-simplify: Simplify (/ 1 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))) 1546856178.793 * * * [misc]progress: simplifying candidates 1546856178.793 * * * * [misc]progress: [ 1 / 92 ] simplifiying candidate # 1546856178.793 * * * * [misc]progress: [ 2 / 92 ] simplifiying candidate # 1546856178.793 * * * * [misc]progress: [ 3 / 92 ] simplifiying candidate # 1546856178.793 * [enter]simplify: Simplifying (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) 1546856178.793 * * [misc]simplify: iters left: 6 (11 enodes) 1546856178.795 * * [misc]simplify: iters left: 5 (21 enodes) 1546856178.799 * * [misc]simplify: iters left: 4 (47 enodes) 1546856178.808 * * [misc]simplify: iters left: 3 (113 enodes) 1546856178.855 * * [misc]simplify: iters left: 2 (328 enodes) 1546856179.130 * [exit]simplify: Simplified to (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) 1546856179.130 * [misc]simplify: Simplified (2 2 2 2 1) to (λ (k n) (/ 1 (* (sqrt k) (/ 1 (exp (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI)))))))) 1546856179.130 * * * * [misc]progress: [ 4 / 92 ] simplifiying candidate # 1546856179.130 * * * * [misc]progress: [ 5 / 92 ] simplifiying candidate # 1546856179.131 * [enter]simplify: Simplifying (* PI (* n 2)) 1546856179.131 * * [misc]simplify: iters left: 4 (5 enodes) 1546856179.133 * * [misc]simplify: iters left: 3 (9 enodes) 1546856179.135 * * [misc]simplify: iters left: 2 (15 enodes) 1546856179.139 * * [misc]simplify: iters left: 1 (17 enodes) 1546856179.143 * [exit]simplify: Simplified to (* (* 2 n) PI) 1546856179.143 * [misc]simplify: Simplified (2 2 2 2 1) to (λ (k n) (/ 1 (* (sqrt k) (/ 1 (pow (* (* 2 n) PI) (* 1 (- 1/2 (/ k 2)))))))) 1546856179.143 * * * * [misc]progress: [ 6 / 92 ] simplifiying candidate # 1546856179.144 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (/ k 2)) 1546856179.144 * * [misc]simplify: iters left: 5 (8 enodes) 1546856179.145 * * [misc]simplify: iters left: 4 (12 enodes) 1546856179.147 * * [misc]simplify: iters left: 3 (18 enodes) 1546856179.152 * * [misc]simplify: iters left: 2 (20 enodes) 1546856179.154 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ k 2)) 1546856179.154 * [misc]simplify: Simplified (2 2 2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (/ 1 (/ (pow (* PI (* n 2)) 1/2) (pow (* (* 2 n) PI) (/ k 2))))))) 1546856179.154 * * * * [misc]progress: [ 7 / 92 ] simplifiying candidate # 1546856179.155 * [enter]simplify: Simplifying (cbrt (- 1/2 (/ k 2))) 1546856179.155 * * [misc]simplify: iters left: 5 (6 enodes) 1546856179.156 * * [misc]simplify: iters left: 4 (8 enodes) 1546856179.157 * * [misc]simplify: iters left: 3 (11 enodes) 1546856179.158 * [exit]simplify: Simplified to (cbrt (- 1/2 (/ k 2))) 1546856179.158 * [misc]simplify: Simplified (2 2 2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (/ 1 (pow (pow (* PI (* n 2)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))))))) 1546856179.158 * * * * [misc]progress: [ 8 / 92 ] simplifiying candidate # 1546856179.159 * [enter]simplify: Simplifying (sqrt (- 1/2 (/ k 2))) 1546856179.159 * * [misc]simplify: iters left: 5 (6 enodes) 1546856179.160 * * [misc]simplify: iters left: 4 (8 enodes) 1546856179.161 * * [misc]simplify: iters left: 3 (11 enodes) 1546856179.162 * [exit]simplify: Simplified to (sqrt (- 1/2 (/ k 2))) 1546856179.162 * [misc]simplify: Simplified (2 2 2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (/ 1 (pow (pow (* PI (* n 2)) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))))))) 1546856179.162 * * * * [misc]progress: [ 9 / 92 ] simplifiying candidate # 1546856179.163 * [enter]simplify: Simplifying (- 1/2 (/ k 2)) 1546856179.163 * * [misc]simplify: iters left: 4 (5 enodes) 1546856179.163 * * [misc]simplify: iters left: 3 (7 enodes) 1546856179.164 * * [misc]simplify: iters left: 2 (10 enodes) 1546856179.166 * [exit]simplify: Simplified to (- 1/2 (/ k 2)) 1546856179.166 * [misc]simplify: Simplified (2 2 2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (/ 1 (pow (pow (* PI (* n 2)) 1) (- 1/2 (/ k 2))))))) 1546856179.166 * * * * [misc]progress: [ 10 / 92 ] simplifiying candidate # 1546856179.166 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1546856179.166 * * [misc]simplify: iters left: 5 (9 enodes) 1546856179.167 * * [misc]simplify: iters left: 4 (15 enodes) 1546856179.170 * * [misc]simplify: iters left: 3 (21 enodes) 1546856179.172 * * [misc]simplify: iters left: 2 (22 enodes) 1546856179.175 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1546856179.175 * [misc]simplify: Simplified (2 2 2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (/ 1 (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2)))))))) 1546856179.175 * * * * [misc]progress: [ 11 / 92 ] simplifiying candidate # 1546856179.175 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1546856179.175 * * [misc]simplify: iters left: 5 (9 enodes) 1546856179.177 * * [misc]simplify: iters left: 4 (15 enodes) 1546856179.179 * * [misc]simplify: iters left: 3 (21 enodes) 1546856179.181 * * [misc]simplify: iters left: 2 (22 enodes) 1546856179.185 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1546856179.185 * [misc]simplify: Simplified (2 2 2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (/ 1 (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2)))))))) 1546856179.185 * * * * [misc]progress: [ 12 / 92 ] simplifiying candidate # 1546856179.185 * [enter]simplify: Simplifying (pow PI (- 1/2 (/ k 2))) 1546856179.185 * * [misc]simplify: iters left: 5 (7 enodes) 1546856179.188 * * [misc]simplify: iters left: 4 (9 enodes) 1546856179.191 * * [misc]simplify: iters left: 3 (12 enodes) 1546856179.194 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1546856179.194 * [misc]simplify: Simplified (2 2 2 2 1) to (λ (k n) (/ 1 (* (sqrt k) (/ 1 (* (pow PI (- 1/2 (/ k 2))) (pow (* n 2) (- 1/2 (/ k 2)))))))) 1546856179.194 * * * * [misc]progress: [ 13 / 92 ] simplifiying candidate # 1546856179.194 * * * * [misc]progress: [ 14 / 92 ] simplifiying candidate # 1546856179.194 * * * * [misc]progress: [ 15 / 92 ] simplifiying candidate # 1546856179.194 * * * * [misc]progress: [ 16 / 92 ] simplifiying candidate # 1546856179.195 * * * * [misc]progress: [ 17 / 92 ] simplifiying candidate # 1546856179.195 * * * * [misc]progress: [ 18 / 92 ] simplifiying candidate # 1546856179.195 * * * * [misc]progress: [ 19 / 92 ] simplifiying candidate # 1546856179.195 * * * * [misc]progress: [ 20 / 92 ] simplifiying candidate # 1546856179.195 * * * * [misc]progress: [ 21 / 92 ] simplifiying candidate # 1546856179.195 * * * * [misc]progress: [ 22 / 92 ] simplifiying candidate # 1546856179.195 * * * * [misc]progress: [ 23 / 92 ] simplifiying candidate # 1546856179.195 * * * * [misc]progress: [ 24 / 92 ] simplifiying candidate # 1546856179.195 * * * * [misc]progress: [ 25 / 92 ] simplifiying candidate # 1546856179.195 * * * * [misc]progress: [ 26 / 92 ] simplifiying candidate # 1546856179.195 * * * * [misc]progress: [ 27 / 92 ] simplifiying candidate # 1546856179.195 * * * * [misc]progress: [ 28 / 92 ] simplifiying candidate # 1546856179.195 * * * * [misc]progress: [ 29 / 92 ] simplifiying candidate # 1546856179.195 * * * * [misc]progress: [ 30 / 92 ] simplifiying candidate # 1546856179.195 * * * * [misc]progress: [ 31 / 92 ] simplifiying candidate # 1546856179.195 * * * * [misc]progress: [ 32 / 92 ] simplifiying candidate # 1546856179.196 * * * * [misc]progress: [ 33 / 92 ] simplifiying candidate # 1546856179.196 * [enter]simplify: Simplifying (* (sqrt k) (/ 1 (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546856179.196 * * [misc]simplify: iters left: 6 (14 enodes) 1546856179.201 * * [misc]simplify: iters left: 5 (25 enodes) 1546856179.208 * * [misc]simplify: iters left: 4 (41 enodes) 1546856179.220 * * [misc]simplify: iters left: 3 (49 enodes) 1546856179.232 * * [misc]simplify: iters left: 2 (65 enodes) 1546856179.248 * * [misc]simplify: iters left: 1 (66 enodes) 1546856179.258 * [exit]simplify: Simplified to (/ (sqrt k) (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) 1546856179.258 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (pow (/ (sqrt k) (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) 1))) 1546856179.258 * * * * [misc]progress: [ 34 / 92 ] simplifiying candidate # 1546856179.258 * * * * [misc]progress: [ 35 / 92 ] simplifiying candidate # 1546856179.259 * [enter]simplify: Simplifying (+ (log (sqrt k)) (- (* (log (* PI (* n 2))) (- 1/2 (/ k 2))))) 1546856179.259 * * [misc]simplify: iters left: 6 (15 enodes) 1546856179.264 * * [misc]simplify: iters left: 5 (31 enodes) 1546856179.276 * * [misc]simplify: iters left: 4 (74 enodes) 1546856179.306 * * [misc]simplify: iters left: 3 (218 enodes) 1546856179.424 * [exit]simplify: Simplified to (fma (+ -1/2 (/ k 2)) (log (* (* PI n) 2)) (log (sqrt k))) 1546856179.424 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (exp (fma (+ -1/2 (/ k 2)) (log (* (* PI n) 2)) (log (sqrt k)))))) 1546856179.424 * * * * [misc]progress: [ 36 / 92 ] simplifiying candidate # 1546856179.424 * [enter]simplify: Simplifying (+ (log (sqrt k)) (- (* (log (* PI (* n 2))) (- 1/2 (/ k 2))))) 1546856179.424 * * [misc]simplify: iters left: 6 (15 enodes) 1546856179.427 * * [misc]simplify: iters left: 5 (31 enodes) 1546856179.432 * * [misc]simplify: iters left: 4 (74 enodes) 1546856179.452 * * [misc]simplify: iters left: 3 (218 enodes) 1546856179.541 * [exit]simplify: Simplified to (fma (+ -1/2 (/ k 2)) (log (* (* PI n) 2)) (log (sqrt k))) 1546856179.541 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (exp (fma (+ -1/2 (/ k 2)) (log (* (* PI n) 2)) (log (sqrt k)))))) 1546856179.541 * * * * [misc]progress: [ 37 / 92 ] simplifiying candidate # 1546856179.542 * [enter]simplify: Simplifying (+ (log (sqrt k)) (- (log (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) 1546856179.542 * * [misc]simplify: iters left: 6 (15 enodes) 1546856179.544 * * [misc]simplify: iters left: 5 (25 enodes) 1546856179.548 * * [misc]simplify: iters left: 4 (46 enodes) 1546856179.556 * * [misc]simplify: iters left: 3 (106 enodes) 1546856179.590 * * [misc]simplify: iters left: 2 (355 enodes) 1546856179.863 * [exit]simplify: Simplified to (fma (log (* (* PI 2) n)) (+ (/ k 2) -1/2) (log (sqrt k))) 1546856179.863 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (exp (fma (log (* (* PI 2) n)) (+ (/ k 2) -1/2) (log (sqrt k)))))) 1546856179.863 * * * * [misc]progress: [ 38 / 92 ] simplifiying candidate # 1546856179.863 * [enter]simplify: Simplifying (+ (log (sqrt k)) (log (/ 1 (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) 1546856179.863 * * [misc]simplify: iters left: 6 (16 enodes) 1546856179.866 * * [misc]simplify: iters left: 5 (29 enodes) 1546856179.870 * * [misc]simplify: iters left: 4 (41 enodes) 1546856179.876 * * [misc]simplify: iters left: 3 (65 enodes) 1546856179.888 * * [misc]simplify: iters left: 2 (168 enodes) 1546856179.980 * [exit]simplify: Simplified to (fma (+ (/ k 2) -1/2) (log (* (* n 2) PI)) (log (sqrt k))) 1546856179.980 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (exp (fma (+ (/ k 2) -1/2) (log (* (* n 2) PI)) (log (sqrt k)))))) 1546856179.980 * * * * [misc]progress: [ 39 / 92 ] simplifiying candidate # 1546856179.980 * * * * [misc]progress: [ 40 / 92 ] simplifiying candidate # 1546856179.980 * * * * [misc]progress: [ 41 / 92 ] simplifiying candidate # 1546856179.980 * [enter]simplify: Simplifying (* (* (* (sqrt k) (sqrt k)) (sqrt k)) (* (* (/ 1 (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (/ 1 (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (/ 1 (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) 1546856179.980 * * [misc]simplify: iters left: 6 (18 enodes) 1546856179.983 * * [misc]simplify: iters left: 5 (39 enodes) 1546856179.990 * * [misc]simplify: iters left: 4 (88 enodes) 1546856180.012 * * [misc]simplify: iters left: 3 (159 enodes) 1546856180.049 * * [misc]simplify: iters left: 2 (281 enodes) 1546856180.196 * * [misc]simplify: iters left: 1 (424 enodes) 1546856180.328 * [exit]simplify: Simplified to (/ (/ (* (sqrt k) k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (* (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) 1546856180.328 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (cbrt (/ (/ (* (sqrt k) k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (* (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))) 1546856180.328 * * * * [misc]progress: [ 42 / 92 ] simplifiying candidate # 1546856180.328 * * * * [misc]progress: [ 43 / 92 ] simplifiying candidate # 1546856180.328 * * * * [misc]progress: [ 44 / 92 ] simplifiying candidate # 1546856180.328 * * * * [misc]progress: [ 45 / 92 ] simplifiying candidate # 1546856180.328 * * * * [misc]progress: [ 46 / 92 ] simplifiying candidate # 1546856180.329 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- 1/2 (/ k 2))) 1546856180.329 * * [misc]simplify: iters left: 5 (10 enodes) 1546856180.330 * * [misc]simplify: iters left: 4 (16 enodes) 1546856180.333 * * [misc]simplify: iters left: 3 (25 enodes) 1546856180.336 * * [misc]simplify: iters left: 2 (26 enodes) 1546856180.339 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) 1546856180.339 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))))) 1546856180.339 * * * * [misc]progress: [ 47 / 92 ] simplifiying candidate # 1546856180.339 * [enter]simplify: Simplifying (cbrt (/ 1 (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546856180.339 * * [misc]simplify: iters left: 6 (13 enodes) 1546856180.343 * * [misc]simplify: iters left: 5 (21 enodes) 1546856180.349 * * [misc]simplify: iters left: 4 (30 enodes) 1546856180.357 * * [misc]simplify: iters left: 3 (31 enodes) 1546856180.365 * [exit]simplify: Simplified to (cbrt (/ 1 (pow (* (* n PI) 2) (- 1/2 (/ k 2))))) 1546856180.365 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (* (sqrt k) (* (cbrt (/ 1 (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (cbrt (/ 1 (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))) (cbrt (/ 1 (pow (* (* n PI) 2) (- 1/2 (/ k 2)))))))) 1546856180.365 * * * * [misc]progress: [ 48 / 92 ] simplifiying candidate # 1546856180.365 * [enter]simplify: Simplifying (sqrt (/ 1 (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546856180.365 * * [misc]simplify: iters left: 6 (13 enodes) 1546856180.369 * * [misc]simplify: iters left: 5 (21 enodes) 1546856180.375 * * [misc]simplify: iters left: 4 (30 enodes) 1546856180.383 * * [misc]simplify: iters left: 3 (31 enodes) 1546856180.387 * [exit]simplify: Simplified to (sqrt (/ 1 (pow (* (* n PI) 2) (- 1/2 (/ k 2))))) 1546856180.387 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (* (sqrt k) (sqrt (/ 1 (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) (sqrt (/ 1 (pow (* (* n PI) 2) (- 1/2 (/ k 2)))))))) 1546856180.387 * * * * [misc]progress: [ 49 / 92 ] simplifiying candidate # 1546856180.387 * [enter]simplify: Simplifying (/ 1 (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1546856180.387 * * [misc]simplify: iters left: 6 (12 enodes) 1546856180.389 * * [misc]simplify: iters left: 5 (20 enodes) 1546856180.392 * * [misc]simplify: iters left: 4 (29 enodes) 1546856180.396 * * [misc]simplify: iters left: 3 (30 enodes) 1546856180.399 * [exit]simplify: Simplified to (/ 1 (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) 1546856180.399 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (* (sqrt k) 1) (/ 1 (pow (* (* n PI) 2) (- 1/2 (/ k 2))))))) 1546856180.399 * * * * [misc]progress: [ 50 / 92 ] simplifiying candidate # 1546856180.400 * [enter]simplify: Simplifying (/ 1 (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1546856180.400 * * [misc]simplify: iters left: 6 (12 enodes) 1546856180.401 * * [misc]simplify: iters left: 5 (20 enodes) 1546856180.404 * * [misc]simplify: iters left: 4 (29 enodes) 1546856180.408 * * [misc]simplify: iters left: 3 (30 enodes) 1546856180.412 * [exit]simplify: Simplified to (/ 1 (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) 1546856180.412 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (* (sqrt k) 1) (/ 1 (pow (* (* n PI) 2) (- 1/2 (/ k 2))))))) 1546856180.412 * * * * [misc]progress: [ 51 / 92 ] simplifiying candidate # 1546856180.412 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (/ k 2)) 1546856180.412 * * [misc]simplify: iters left: 5 (8 enodes) 1546856180.413 * * [misc]simplify: iters left: 4 (12 enodes) 1546856180.415 * * [misc]simplify: iters left: 3 (18 enodes) 1546856180.419 * * [misc]simplify: iters left: 2 (20 enodes) 1546856180.421 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ k 2)) 1546856180.421 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (* (sqrt k) (/ 1 (pow (* PI (* n 2)) 1/2))) (pow (* (* 2 n) PI) (/ k 2))))) 1546856180.421 * * * * [misc]progress: [ 52 / 92 ] simplifiying candidate # 1546856180.421 * [enter]simplify: Simplifying (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1546856180.421 * * [misc]simplify: iters left: 4 (4 enodes) 1546856180.422 * [exit]simplify: Simplified to (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1546856180.422 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (sqrt k)) (/ 1 (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))))) 1546856180.422 * * * * [misc]progress: [ 53 / 92 ] simplifiying candidate # 1546856180.422 * [enter]simplify: Simplifying (sqrt (sqrt k)) 1546856180.422 * * [misc]simplify: iters left: 2 (3 enodes) 1546856180.423 * [exit]simplify: Simplified to (sqrt (sqrt k)) 1546856180.423 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (sqrt (sqrt k)) (* (sqrt (sqrt k)) (/ 1 (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))))) 1546856180.423 * * * * [misc]progress: [ 54 / 92 ] simplifiying candidate # 1546856180.423 * * * * [misc]progress: [ 55 / 92 ] simplifiying candidate # 1546856180.423 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- 1/2 (/ k 2))) 1546856180.423 * * [misc]simplify: iters left: 5 (10 enodes) 1546856180.425 * * [misc]simplify: iters left: 4 (16 enodes) 1546856180.427 * * [misc]simplify: iters left: 3 (25 enodes) 1546856180.430 * * [misc]simplify: iters left: 2 (26 enodes) 1546856180.433 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) 1546856180.433 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (/ (* (sqrt k) 1) (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))))) 1546856180.433 * * * * [misc]progress: [ 56 / 92 ] simplifiying candidate # 1546856180.433 * * * * [misc]progress: [ 57 / 92 ] simplifiying candidate # 1546856180.433 * * * * [misc]progress: [ 58 / 92 ] simplifiying candidate # 1546856180.433 * * * * [misc]progress: [ 59 / 92 ] simplifiying candidate # 1546856180.433 * * * * [misc]progress: [ 60 / 92 ] simplifiying candidate # 1546856180.434 * [enter]simplify: Simplifying (- (- 1/2 (/ k 2))) 1546856180.434 * * [misc]simplify: iters left: 6 (6 enodes) 1546856180.434 * * [misc]simplify: iters left: 5 (8 enodes) 1546856180.436 * * [misc]simplify: iters left: 4 (15 enodes) 1546856180.438 * * [misc]simplify: iters left: 3 (21 enodes) 1546856180.441 * * [misc]simplify: iters left: 2 (23 enodes) 1546856180.443 * [exit]simplify: Simplified to (+ -1/2 (/ k 2)) 1546856180.443 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (pow (* PI (* n 2)) (+ -1/2 (/ k 2)))))) 1546856180.443 * * * * [misc]progress: [ 61 / 92 ] simplifiying candidate # 1546856180.443 * * * * [misc]progress: [ 62 / 92 ] simplifiying candidate # 1546856180.443 * * * * [misc]progress: [ 63 / 92 ] simplifiying candidate # 1546856180.443 * * * * [misc]progress: [ 64 / 92 ] simplifiying candidate # 1546856180.443 * * * * [misc]progress: [ 65 / 92 ] simplifiying candidate # 1546856180.443 * * * * [misc]progress: [ 66 / 92 ] simplifiying candidate # 1546856180.443 * * * * [misc]progress: [ 67 / 92 ] simplifiying candidate # 1546856180.443 * * * * [misc]progress: [ 68 / 92 ] simplifiying candidate # 1546856180.443 * * * * [misc]progress: [ 69 / 92 ] simplifiying candidate # 1546856180.443 * * * * [misc]progress: [ 70 / 92 ] simplifiying candidate # 1546856180.443 * * * * [misc]progress: [ 71 / 92 ] simplifiying candidate # 1546856180.443 * * * * [misc]progress: [ 72 / 92 ] simplifiying candidate # 1546856180.443 * * * * [misc]progress: [ 73 / 92 ] simplifiying candidate # 1546856180.443 * * * * [misc]progress: [ 74 / 92 ] simplifiying candidate # 1546856180.443 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1546856180.443 * * [misc]simplify: iters left: 5 (9 enodes) 1546856180.445 * * [misc]simplify: iters left: 4 (15 enodes) 1546856180.447 * * [misc]simplify: iters left: 3 (21 enodes) 1546856180.452 * * [misc]simplify: iters left: 2 (22 enodes) 1546856180.458 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1546856180.458 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (/ (/ 1 (pow (* PI (* n 2)) 1/2)) (pow (* (* PI n) 2) (- (/ k 2))))))) 1546856180.458 * * * * [misc]progress: [ 75 / 92 ] simplifiying candidate # 1546856180.458 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1546856180.458 * * [misc]simplify: iters left: 5 (9 enodes) 1546856180.461 * * [misc]simplify: iters left: 4 (15 enodes) 1546856180.466 * * [misc]simplify: iters left: 3 (21 enodes) 1546856180.471 * * [misc]simplify: iters left: 2 (22 enodes) 1546856180.476 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1546856180.477 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (/ (/ 1 (pow (* PI (* n 2)) 1/2)) (pow (* (* PI n) 2) (- (/ k 2))))))) 1546856180.477 * * * * [misc]progress: [ 76 / 92 ] simplifiying candidate # 1546856180.477 * [enter]simplify: Simplifying (pow (* n 2) (- 1/2 (/ k 2))) 1546856180.477 * * [misc]simplify: iters left: 5 (8 enodes) 1546856180.479 * * [misc]simplify: iters left: 4 (11 enodes) 1546856180.483 * * [misc]simplify: iters left: 3 (14 enodes) 1546856180.487 * [exit]simplify: Simplified to (pow (* n 2) (- 1/2 (/ k 2))) 1546856180.487 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (/ (/ 1 (pow PI (- 1/2 (/ k 2)))) (pow (* n 2) (- 1/2 (/ k 2))))))) 1546856180.487 * * * * [misc]progress: [ 77 / 92 ] simplifiying candidate # 1546856180.487 * [enter]simplify: Simplifying (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1546856180.487 * * [misc]simplify: iters left: 6 (11 enodes) 1546856180.489 * * [misc]simplify: iters left: 5 (17 enodes) 1546856180.491 * * [misc]simplify: iters left: 4 (26 enodes) 1546856180.495 * * [misc]simplify: iters left: 3 (27 enodes) 1546856180.498 * [exit]simplify: Simplified to (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) 1546856180.498 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (/ (/ 1 (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))))))) 1546856180.498 * * * * [misc]progress: [ 78 / 92 ] simplifiying candidate # 1546856180.498 * [enter]simplify: Simplifying (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1546856180.498 * * [misc]simplify: iters left: 6 (11 enodes) 1546856180.500 * * [misc]simplify: iters left: 5 (17 enodes) 1546856180.502 * * [misc]simplify: iters left: 4 (26 enodes) 1546856180.506 * * [misc]simplify: iters left: 3 (27 enodes) 1546856180.509 * [exit]simplify: Simplified to (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) 1546856180.509 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (/ (/ 1 (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))))))) 1546856180.509 * * * * [misc]progress: [ 79 / 92 ] simplifiying candidate # 1546856180.509 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- 1/2 (/ k 2))) 1546856180.509 * * [misc]simplify: iters left: 5 (10 enodes) 1546856180.511 * * [misc]simplify: iters left: 4 (16 enodes) 1546856180.514 * * [misc]simplify: iters left: 3 (25 enodes) 1546856180.520 * * [misc]simplify: iters left: 2 (26 enodes) 1546856180.526 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) 1546856180.526 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (/ (/ 1 1) (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))))) 1546856180.526 * * * * [misc]progress: [ 80 / 92 ] simplifiying candidate # 1546856180.526 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (/ k 2)) 1546856180.526 * * [misc]simplify: iters left: 5 (8 enodes) 1546856180.529 * * [misc]simplify: iters left: 4 (12 enodes) 1546856180.532 * * [misc]simplify: iters left: 3 (18 enodes) 1546856180.537 * * [misc]simplify: iters left: 2 (20 enodes) 1546856180.542 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ k 2)) 1546856180.542 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (* (/ 1 (pow (* PI (* n 2)) 1/2)) (pow (* (* 2 n) PI) (/ k 2)))))) 1546856180.542 * * * * [misc]progress: [ 81 / 92 ] simplifiying candidate # 1546856180.542 * [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))))) 1546856180.543 * * [misc]simplify: iters left: 6 (37 enodes) 1546856180.553 * * [misc]simplify: iters left: 5 (108 enodes) 1546856180.577 * * [misc]simplify: iters left: 4 (368 enodes) 1546856180.793 * [exit]simplify: Simplified to (fma -1/2 (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) (fma (* (* (* k k) (log n)) (* (log (* PI 2)) 1/4)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (fma (* (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (log (* PI 2)) (log (* PI 2)))) (* (* k k) 1/8) (fma (* (* (* k k) (log n)) (* (log n) 1/8)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (pow n 1/2) (pow (* PI 2) 1/2)))))) 1546856180.793 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (/ 1 (fma -1/2 (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) (fma (* (* (* k k) (log n)) (* (log (* PI 2)) 1/4)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (fma (* (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (log (* PI 2)) (log (* PI 2)))) (* (* k k) 1/8) (fma (* (* (* k k) (log n)) (* (log n) 1/8)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (pow n 1/2) (pow (* PI 2) 1/2)))))))))) 1546856180.793 * * * * [misc]progress: [ 82 / 92 ] simplifiying candidate # 1546856180.793 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 1546856180.793 * * [misc]simplify: iters left: 6 (15 enodes) 1546856180.796 * * [misc]simplify: iters left: 5 (33 enodes) 1546856180.802 * * [misc]simplify: iters left: 4 (64 enodes) 1546856180.814 * * [misc]simplify: iters left: 3 (179 enodes) 1546856180.912 * [exit]simplify: Simplified to (* (pow (* 2 PI) (fma -1/2 k 1/2)) (pow n (fma -1/2 k 1/2))) 1546856180.912 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (/ 1 (* (pow (* 2 PI) (fma -1/2 k 1/2)) (pow n (fma -1/2 k 1/2))))))) 1546856180.912 * * * * [misc]progress: [ 83 / 92 ] simplifiying candidate # 1546856180.912 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 1546856180.912 * * [misc]simplify: iters left: 6 (15 enodes) 1546856180.918 * * [misc]simplify: iters left: 5 (30 enodes) 1546856180.929 * * [misc]simplify: iters left: 4 (65 enodes) 1546856180.956 * * [misc]simplify: iters left: 3 (208 enodes) 1546856181.135 * [exit]simplify: Simplified to (pow (exp (fma -1/2 k 1/2)) (- (log (* -2 PI)) (log (/ -1 n)))) 1546856181.135 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (/ 1 (pow (exp (fma -1/2 k 1/2)) (- (log (* -2 PI)) (log (/ -1 n)))))))) 1546856181.135 * * * * [misc]progress: [ 84 / 92 ] simplifiying candidate # 1546856181.135 * [enter]simplify: Simplifying (* 2 (* n PI)) 1546856181.135 * * [misc]simplify: iters left: 4 (5 enodes) 1546856181.136 * * [misc]simplify: iters left: 3 (9 enodes) 1546856181.138 * * [misc]simplify: iters left: 2 (15 enodes) 1546856181.140 * * [misc]simplify: iters left: 1 (17 enodes) 1546856181.141 * [exit]simplify: Simplified to (* (* PI n) 2) 1546856181.142 * [misc]simplify: Simplified (2 2 2 2 1) to (λ (k n) (/ 1 (* (sqrt k) (/ 1 (pow (* (* PI n) 2) (- 1/2 (/ k 2))))))) 1546856181.142 * * * * [misc]progress: [ 85 / 92 ] simplifiying candidate # 1546856181.142 * [enter]simplify: Simplifying (* 2 (* n PI)) 1546856181.142 * * [misc]simplify: iters left: 4 (5 enodes) 1546856181.143 * * [misc]simplify: iters left: 3 (9 enodes) 1546856181.144 * * [misc]simplify: iters left: 2 (15 enodes) 1546856181.146 * * [misc]simplify: iters left: 1 (17 enodes) 1546856181.148 * [exit]simplify: Simplified to (* (* PI n) 2) 1546856181.148 * [misc]simplify: Simplified (2 2 2 2 1) to (λ (k n) (/ 1 (* (sqrt k) (/ 1 (pow (* (* PI n) 2) (- 1/2 (/ k 2))))))) 1546856181.148 * * * * [misc]progress: [ 86 / 92 ] simplifiying candidate # 1546856181.148 * [enter]simplify: Simplifying (* 2 (* n PI)) 1546856181.148 * * [misc]simplify: iters left: 4 (5 enodes) 1546856181.149 * * [misc]simplify: iters left: 3 (9 enodes) 1546856181.150 * * [misc]simplify: iters left: 2 (15 enodes) 1546856181.152 * * [misc]simplify: iters left: 1 (17 enodes) 1546856181.154 * [exit]simplify: Simplified to (* (* PI n) 2) 1546856181.154 * [misc]simplify: Simplified (2 2 2 2 1) to (λ (k n) (/ 1 (* (sqrt k) (/ 1 (pow (* (* PI n) 2) (- 1/2 (/ k 2))))))) 1546856181.154 * * * * [misc]progress: [ 87 / 92 ] simplifiying candidate # 1546856181.155 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow k 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI))))) PI)) (- (+ (* +nan.0 (/ (* (sqrt 1/2) (pow k 2)) PI)) (- (+ (* +nan.0 (/ (* n (* (sqrt 1/2) k)) (pow PI 2))) (- (+ (* +nan.0 (/ (* (log n) (* (sqrt 2) (* (pow (sqrt 1/2) 2) (pow k 2)))) PI)) (- (* +nan.0 (/ (* (sqrt 1/2) k) PI))))))))))) 1546856181.155 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ 1 +nan.0)) 1546856181.155 * * * * [misc]progress: [ 88 / 92 ] simplifiying candidate # 1546856181.155 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))))))))) 1546856181.155 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ 1 +nan.0)) 1546856181.155 * * * * [misc]progress: [ 89 / 92 ] simplifiying candidate # 1546856181.155 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))))))))) 1546856181.155 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ 1 +nan.0)) 1546856181.155 * * * * [misc]progress: [ 90 / 92 ] simplifiying candidate # 1546856181.155 * [enter]simplify: Simplifying (+ (* 1/8 (/ (* (pow (log (* 2 PI)) 2) (pow k 2)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/2 (/ (* k (log (* 2 PI))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/2 (/ (* (log n) k) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/4 (/ (* (log (* 2 PI)) (* (log n) (pow k 2))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (/ 1 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (* 1/8 (/ (* (pow (log n) 2) (pow k 2)) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))))))) 1546856181.155 * * [misc]simplify: iters left: 6 (39 enodes) 1546856181.164 * * [misc]simplify: iters left: 5 (109 enodes) 1546856181.187 * * [misc]simplify: iters left: 4 (317 enodes) 1546856181.357 * [exit]simplify: Simplified to (+ (+ (fma 1/4 (* (/ (* (log n) (* k k)) (pow n 1/2)) (/ (log (* PI 2)) (pow (* PI 2) 1/2))) (/ (/ 1 (pow n 1/2)) (pow (* PI 2) 1/2))) (/ (* (* (log n) (* k k)) (* (log n) 1/8)) (* (pow (* PI 2) 1/2) (pow n 1/2)))) (fma 1/8 (/ (* (* (* k k) (log (* PI 2))) (log (* PI 2))) (* (pow (* PI 2) 1/2) (pow n 1/2))) (fma 1/2 (* (/ (/ k (pow n 1/2)) (pow (* PI 2) 1/2)) (log (* PI 2))) (* (/ (* (log n) 1/2) (pow n 1/2)) (/ k (pow (* PI 2) 1/2)))))) 1546856181.358 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (+ (+ (fma 1/4 (* (/ (* (log n) (* k k)) (pow n 1/2)) (/ (log (* PI 2)) (pow (* PI 2) 1/2))) (/ (/ 1 (pow n 1/2)) (pow (* PI 2) 1/2))) (/ (* (* (log n) (* k k)) (* (log n) 1/8)) (* (pow (* PI 2) 1/2) (pow n 1/2)))) (fma 1/8 (/ (* (* (* k k) (log (* PI 2))) (log (* PI 2))) (* (pow (* PI 2) 1/2) (pow n 1/2))) (fma 1/2 (* (/ (/ k (pow n 1/2)) (pow (* PI 2) 1/2)) (log (* PI 2))) (* (/ (* (log n) 1/2) (pow n 1/2)) (/ k (pow (* PI 2) 1/2))))))))) 1546856181.358 * * * * [misc]progress: [ 91 / 92 ] simplifiying candidate # 1546856181.358 * [enter]simplify: Simplifying (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))) 1546856181.358 * * [misc]simplify: iters left: 6 (16 enodes) 1546856181.361 * * [misc]simplify: iters left: 5 (36 enodes) 1546856181.368 * * [misc]simplify: iters left: 4 (73 enodes) 1546856181.383 * * [misc]simplify: iters left: 3 (244 enodes) 1546856181.573 * [exit]simplify: Simplified to (pow (exp (- -1/2 (* -1/2 k))) (+ (log (* 2 PI)) (log n))) 1546856181.573 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (pow (exp (- -1/2 (* -1/2 k))) (+ (log (* 2 PI)) (log n)))))) 1546856181.573 * * * * [misc]progress: [ 92 / 92 ] simplifiying candidate # 1546856181.574 * [enter]simplify: Simplifying (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))) 1546856181.574 * * [misc]simplify: iters left: 6 (17 enodes) 1546856181.580 * * [misc]simplify: iters left: 5 (36 enodes) 1546856181.592 * * [misc]simplify: iters left: 4 (77 enodes) 1546856181.625 * * [misc]simplify: iters left: 3 (284 enodes) 1546856181.850 * [exit]simplify: Simplified to (pow (exp (- -1/2 (* k -1/2))) (- (log (* -2 PI)) (log (/ -1 n)))) 1546856181.850 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (pow (exp (- -1/2 (* k -1/2))) (- (log (* -2 PI)) (log (/ -1 n))))))) 1546856181.850 * * * [misc]progress: adding candidates to table 1546856182.938 * * [misc]progress: iteration 4 / 4 1546856182.938 * * * [misc]progress: picking best candidate 1546856182.977 * * * * [misc]pick: Picked # 1546856182.978 * * * [misc]progress: localizing error 1546856182.984 * * * [misc]progress: generating rewritten candidates 1546856182.984 * * * * [misc]progress: [ 1 / 4 ] rewriting at (2 2 1 1) 1546856182.986 * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 1 1 1) 1546856182.988 * * * * [misc]progress: [ 3 / 4 ] rewriting at (2 2 1 1 1) 1546856182.989 * * * * [misc]progress: [ 4 / 4 ] rewriting at (2 1 1 1 1) 1546856182.992 * * * [misc]progress: generating series expansions 1546856182.992 * * * * [misc]progress: [ 1 / 4 ] generating series at (2 2 1 1) 1546856182.992 * [misc]backup-simplify: Simplify (pow (* PI (* n 2)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 1546856182.992 * [misc]approximate: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 1546856182.992 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1546856182.992 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1546856182.992 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1546856182.992 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546856182.992 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856182.992 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856182.992 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546856182.992 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856182.992 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856182.992 * [misc]taylor: Taking taylor expansion of k in k 1546856182.992 * [misc]backup-simplify: Simplify 0 into 0 1546856182.992 * [misc]backup-simplify: Simplify 1 into 1 1546856182.992 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1546856182.992 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1546856182.993 * [misc]taylor: Taking taylor expansion of 2 in k 1546856182.993 * [misc]backup-simplify: Simplify 2 into 2 1546856182.993 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1546856182.993 * [misc]taylor: Taking taylor expansion of n in k 1546856182.993 * [misc]backup-simplify: Simplify n into n 1546856182.993 * [misc]taylor: Taking taylor expansion of PI in k 1546856182.993 * [misc]backup-simplify: Simplify PI into PI 1546856182.993 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1546856182.993 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1546856182.993 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1546856182.993 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546856182.993 * [misc]backup-simplify: Simplify (- 0) into 0 1546856182.994 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546856182.994 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1546856182.994 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1546856182.994 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546856182.994 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546856182.994 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546856182.994 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546856182.994 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856182.994 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856182.994 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546856182.994 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856182.994 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856182.994 * [misc]taylor: Taking taylor expansion of k in n 1546856182.994 * [misc]backup-simplify: Simplify k into k 1546856182.994 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546856182.994 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546856182.994 * [misc]taylor: Taking taylor expansion of 2 in n 1546856182.994 * [misc]backup-simplify: Simplify 2 into 2 1546856182.994 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546856182.994 * [misc]taylor: Taking taylor expansion of n in n 1546856182.994 * [misc]backup-simplify: Simplify 0 into 0 1546856182.994 * [misc]backup-simplify: Simplify 1 into 1 1546856182.994 * [misc]taylor: Taking taylor expansion of PI in n 1546856182.994 * [misc]backup-simplify: Simplify PI into PI 1546856182.995 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546856182.995 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546856182.996 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546856182.996 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546856182.997 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856182.997 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546856182.997 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546856182.997 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546856182.998 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546856182.998 * [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)))) 1546856182.999 * [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))))) 1546856182.999 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546856182.999 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546856182.999 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546856182.999 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546856182.999 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856182.999 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856182.999 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546856182.999 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856182.999 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856182.999 * [misc]taylor: Taking taylor expansion of k in n 1546856182.999 * [misc]backup-simplify: Simplify k into k 1546856182.999 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546856182.999 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546856182.999 * [misc]taylor: Taking taylor expansion of 2 in n 1546856182.999 * [misc]backup-simplify: Simplify 2 into 2 1546856182.999 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546856182.999 * [misc]taylor: Taking taylor expansion of n in n 1546856182.999 * [misc]backup-simplify: Simplify 0 into 0 1546856182.999 * [misc]backup-simplify: Simplify 1 into 1 1546856182.999 * [misc]taylor: Taking taylor expansion of PI in n 1546856182.999 * [misc]backup-simplify: Simplify PI into PI 1546856183.000 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546856183.000 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546856183.001 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546856183.001 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546856183.002 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856183.002 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546856183.002 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546856183.002 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546856183.003 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546856183.003 * [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)))) 1546856183.004 * [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))))) 1546856183.004 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1546856183.004 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1546856183.004 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546856183.004 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856183.004 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856183.004 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546856183.004 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856183.004 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856183.004 * [misc]taylor: Taking taylor expansion of k in k 1546856183.004 * [misc]backup-simplify: Simplify 0 into 0 1546856183.004 * [misc]backup-simplify: Simplify 1 into 1 1546856183.004 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1546856183.004 * [misc]taylor: Taking taylor expansion of (log n) in k 1546856183.004 * [misc]taylor: Taking taylor expansion of n in k 1546856183.004 * [misc]backup-simplify: Simplify n into n 1546856183.004 * [misc]backup-simplify: Simplify (log n) into (log n) 1546856183.004 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1546856183.004 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1546856183.004 * [misc]taylor: Taking taylor expansion of 2 in k 1546856183.004 * [misc]backup-simplify: Simplify 2 into 2 1546856183.004 * [misc]taylor: Taking taylor expansion of PI in k 1546856183.004 * [misc]backup-simplify: Simplify PI into PI 1546856183.004 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546856183.005 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856183.005 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546856183.005 * [misc]backup-simplify: Simplify (- 0) into 0 1546856183.005 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546856183.005 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546856183.006 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1546856183.006 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1546856183.006 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1546856183.007 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546856183.007 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1546856183.009 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546856183.009 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1546856183.009 * [misc]backup-simplify: Simplify (- 0) into 0 1546856183.009 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856183.010 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546856183.010 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1546856183.011 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1546856183.011 * [misc]taylor: Taking taylor expansion of 0 in k 1546856183.011 * [misc]backup-simplify: Simplify 0 into 0 1546856183.011 * [misc]backup-simplify: Simplify 0 into 0 1546856183.012 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1546856183.012 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546856183.014 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546856183.014 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856183.014 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1546856183.014 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546856183.014 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546856183.017 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1546856183.018 * [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))))))) 1546856183.019 * [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))))))) 1546856183.020 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1546856183.021 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1546856183.024 * [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 1546856183.024 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1546856183.024 * [misc]backup-simplify: Simplify (- 0) into 0 1546856183.025 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856183.025 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546856183.025 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1546856183.027 * [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 1546856183.027 * [misc]taylor: Taking taylor expansion of 0 in k 1546856183.027 * [misc]backup-simplify: Simplify 0 into 0 1546856183.027 * [misc]backup-simplify: Simplify 0 into 0 1546856183.027 * [misc]backup-simplify: Simplify 0 into 0 1546856183.028 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1546856183.028 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546856183.031 * [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 1546856183.031 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856183.032 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1546856183.032 * [misc]backup-simplify: Simplify (- 0) into 0 1546856183.032 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856183.032 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1546856183.034 * [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))))) 1546856183.036 * [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))))) 1546856183.040 * [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))))) 1546856183.041 * [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)))) 1546856183.041 * [misc]approximate: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 1546856183.041 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1546856183.041 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1546856183.041 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1546856183.041 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546856183.041 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856183.041 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856183.041 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546856183.041 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856183.041 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856183.041 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546856183.041 * [misc]taylor: Taking taylor expansion of k in k 1546856183.041 * [misc]backup-simplify: Simplify 0 into 0 1546856183.041 * [misc]backup-simplify: Simplify 1 into 1 1546856183.041 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546856183.041 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1546856183.041 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1546856183.042 * [misc]taylor: Taking taylor expansion of 2 in k 1546856183.042 * [misc]backup-simplify: Simplify 2 into 2 1546856183.042 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546856183.042 * [misc]taylor: Taking taylor expansion of PI in k 1546856183.042 * [misc]backup-simplify: Simplify PI into PI 1546856183.042 * [misc]taylor: Taking taylor expansion of n in k 1546856183.042 * [misc]backup-simplify: Simplify n into n 1546856183.042 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546856183.042 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1546856183.042 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1546856183.042 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546856183.042 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546856183.042 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546856183.043 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1546856183.043 * [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)))) 1546856183.043 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546856183.043 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546856183.043 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546856183.043 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546856183.043 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856183.043 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856183.043 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546856183.043 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856183.043 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856183.043 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546856183.043 * [misc]taylor: Taking taylor expansion of k in n 1546856183.043 * [misc]backup-simplify: Simplify k into k 1546856183.043 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546856183.043 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546856183.043 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546856183.043 * [misc]taylor: Taking taylor expansion of 2 in n 1546856183.043 * [misc]backup-simplify: Simplify 2 into 2 1546856183.043 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856183.043 * [misc]taylor: Taking taylor expansion of PI in n 1546856183.043 * [misc]backup-simplify: Simplify PI into PI 1546856183.044 * [misc]taylor: Taking taylor expansion of n in n 1546856183.044 * [misc]backup-simplify: Simplify 0 into 0 1546856183.044 * [misc]backup-simplify: Simplify 1 into 1 1546856183.044 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856183.044 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546856183.045 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856183.045 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546856183.045 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546856183.045 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546856183.046 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546856183.046 * [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))) 1546856183.047 * [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)))) 1546856183.047 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546856183.047 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546856183.047 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546856183.047 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546856183.047 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856183.047 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856183.047 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546856183.047 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856183.047 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856183.047 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546856183.047 * [misc]taylor: Taking taylor expansion of k in n 1546856183.047 * [misc]backup-simplify: Simplify k into k 1546856183.047 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546856183.047 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546856183.047 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546856183.048 * [misc]taylor: Taking taylor expansion of 2 in n 1546856183.048 * [misc]backup-simplify: Simplify 2 into 2 1546856183.048 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856183.048 * [misc]taylor: Taking taylor expansion of PI in n 1546856183.048 * [misc]backup-simplify: Simplify PI into PI 1546856183.048 * [misc]taylor: Taking taylor expansion of n in n 1546856183.048 * [misc]backup-simplify: Simplify 0 into 0 1546856183.048 * [misc]backup-simplify: Simplify 1 into 1 1546856183.048 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856183.048 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546856183.049 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856183.049 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546856183.049 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546856183.049 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546856183.050 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546856183.050 * [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))) 1546856183.051 * [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)))) 1546856183.051 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1546856183.051 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1546856183.051 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546856183.051 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856183.051 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856183.051 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546856183.051 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856183.051 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856183.051 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546856183.051 * [misc]taylor: Taking taylor expansion of k in k 1546856183.051 * [misc]backup-simplify: Simplify 0 into 0 1546856183.051 * [misc]backup-simplify: Simplify 1 into 1 1546856183.052 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546856183.052 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1546856183.052 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1546856183.052 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1546856183.052 * [misc]taylor: Taking taylor expansion of 2 in k 1546856183.052 * [misc]backup-simplify: Simplify 2 into 2 1546856183.052 * [misc]taylor: Taking taylor expansion of PI in k 1546856183.052 * [misc]backup-simplify: Simplify PI into PI 1546856183.052 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546856183.053 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856183.053 * [misc]taylor: Taking taylor expansion of (log n) in k 1546856183.053 * [misc]taylor: Taking taylor expansion of n in k 1546856183.053 * [misc]backup-simplify: Simplify n into n 1546856183.053 * [misc]backup-simplify: Simplify (log n) into (log n) 1546856183.053 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546856183.053 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546856183.053 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546856183.053 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1546856183.054 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1546856183.054 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1546856183.055 * [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)))) 1546856183.056 * [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)))) 1546856183.057 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546856183.057 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546856183.060 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546856183.060 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546856183.061 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546856183.061 * [misc]backup-simplify: Simplify (- 0) into 0 1546856183.061 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856183.062 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546856183.062 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1546856183.064 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546856183.064 * [misc]taylor: Taking taylor expansion of 0 in k 1546856183.064 * [misc]backup-simplify: Simplify 0 into 0 1546856183.064 * [misc]backup-simplify: Simplify 0 into 0 1546856183.064 * [misc]backup-simplify: Simplify 0 into 0 1546856183.065 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856183.066 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546856183.071 * [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 1546856183.072 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546856183.072 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1546856183.072 * [misc]backup-simplify: Simplify (- 0) into 0 1546856183.072 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856183.073 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546856183.074 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1546856183.076 * [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 1546856183.076 * [misc]taylor: Taking taylor expansion of 0 in k 1546856183.076 * [misc]backup-simplify: Simplify 0 into 0 1546856183.076 * [misc]backup-simplify: Simplify 0 into 0 1546856183.076 * [misc]backup-simplify: Simplify 0 into 0 1546856183.077 * [misc]backup-simplify: Simplify 0 into 0 1546856183.078 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856183.080 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546856183.089 * [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 1546856183.089 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546856183.089 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1546856183.089 * [misc]backup-simplify: Simplify (- 0) into 0 1546856183.090 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856183.090 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546856183.091 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1546856183.095 * [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 1546856183.095 * [misc]taylor: Taking taylor expansion of 0 in k 1546856183.095 * [misc]backup-simplify: Simplify 0 into 0 1546856183.095 * [misc]backup-simplify: Simplify 0 into 0 1546856183.096 * [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))))) 1546856183.096 * [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)) 1546856183.096 * [misc]approximate: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 1546856183.096 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1546856183.096 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1546856183.096 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1546856183.096 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546856183.096 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546856183.096 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856183.096 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856183.097 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546856183.097 * [misc]taylor: Taking taylor expansion of k in k 1546856183.097 * [misc]backup-simplify: Simplify 0 into 0 1546856183.097 * [misc]backup-simplify: Simplify 1 into 1 1546856183.097 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546856183.097 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856183.097 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856183.097 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1546856183.097 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1546856183.097 * [misc]taylor: Taking taylor expansion of -2 in k 1546856183.097 * [misc]backup-simplify: Simplify -2 into -2 1546856183.097 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546856183.097 * [misc]taylor: Taking taylor expansion of PI in k 1546856183.097 * [misc]backup-simplify: Simplify PI into PI 1546856183.097 * [misc]taylor: Taking taylor expansion of n in k 1546856183.097 * [misc]backup-simplify: Simplify n into n 1546856183.097 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546856183.097 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1546856183.097 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1546856183.097 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546856183.098 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546856183.098 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1546856183.098 * [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))) 1546856183.098 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546856183.098 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546856183.098 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546856183.098 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546856183.098 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546856183.098 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856183.098 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856183.098 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546856183.098 * [misc]taylor: Taking taylor expansion of k in n 1546856183.098 * [misc]backup-simplify: Simplify k into k 1546856183.098 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546856183.098 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856183.098 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856183.098 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546856183.098 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546856183.099 * [misc]taylor: Taking taylor expansion of -2 in n 1546856183.099 * [misc]backup-simplify: Simplify -2 into -2 1546856183.099 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856183.099 * [misc]taylor: Taking taylor expansion of PI in n 1546856183.099 * [misc]backup-simplify: Simplify PI into PI 1546856183.099 * [misc]taylor: Taking taylor expansion of n in n 1546856183.099 * [misc]backup-simplify: Simplify 0 into 0 1546856183.099 * [misc]backup-simplify: Simplify 1 into 1 1546856183.099 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856183.099 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546856183.100 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546856183.100 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546856183.100 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546856183.100 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546856183.101 * [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))) 1546856183.101 * [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)))) 1546856183.101 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546856183.101 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546856183.101 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546856183.101 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546856183.101 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546856183.101 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856183.101 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856183.101 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546856183.101 * [misc]taylor: Taking taylor expansion of k in n 1546856183.101 * [misc]backup-simplify: Simplify k into k 1546856183.101 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546856183.101 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856183.101 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856183.101 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546856183.101 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546856183.101 * [misc]taylor: Taking taylor expansion of -2 in n 1546856183.101 * [misc]backup-simplify: Simplify -2 into -2 1546856183.101 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856183.101 * [misc]taylor: Taking taylor expansion of PI in n 1546856183.101 * [misc]backup-simplify: Simplify PI into PI 1546856183.101 * [misc]taylor: Taking taylor expansion of n in n 1546856183.101 * [misc]backup-simplify: Simplify 0 into 0 1546856183.102 * [misc]backup-simplify: Simplify 1 into 1 1546856183.102 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856183.102 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546856183.102 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546856183.102 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546856183.102 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546856183.103 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546856183.103 * [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))) 1546856183.104 * [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)))) 1546856183.104 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1546856183.104 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1546856183.104 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546856183.104 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546856183.104 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856183.104 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856183.104 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546856183.104 * [misc]taylor: Taking taylor expansion of k in k 1546856183.104 * [misc]backup-simplify: Simplify 0 into 0 1546856183.104 * [misc]backup-simplify: Simplify 1 into 1 1546856183.104 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546856183.104 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856183.104 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856183.104 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1546856183.104 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1546856183.104 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1546856183.104 * [misc]taylor: Taking taylor expansion of -2 in k 1546856183.104 * [misc]backup-simplify: Simplify -2 into -2 1546856183.104 * [misc]taylor: Taking taylor expansion of PI in k 1546856183.104 * [misc]backup-simplify: Simplify PI into PI 1546856183.104 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546856183.105 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546856183.105 * [misc]taylor: Taking taylor expansion of (log n) in k 1546856183.105 * [misc]taylor: Taking taylor expansion of n in k 1546856183.105 * [misc]backup-simplify: Simplify n into n 1546856183.105 * [misc]backup-simplify: Simplify (log n) into (log n) 1546856183.105 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546856183.105 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546856183.105 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1546856183.105 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1546856183.106 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1546856183.106 * [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)))) 1546856183.106 * [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)))) 1546856183.107 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546856183.108 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1546856183.110 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1546856183.110 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546856183.110 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546856183.110 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856183.110 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546856183.111 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1546856183.112 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546856183.112 * [misc]taylor: Taking taylor expansion of 0 in k 1546856183.112 * [misc]backup-simplify: Simplify 0 into 0 1546856183.112 * [misc]backup-simplify: Simplify 0 into 0 1546856183.112 * [misc]backup-simplify: Simplify 0 into 0 1546856183.113 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856183.114 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1546856183.117 * [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 1546856183.117 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546856183.117 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1546856183.117 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856183.117 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546856183.118 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1546856183.119 * [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 1546856183.119 * [misc]taylor: Taking taylor expansion of 0 in k 1546856183.119 * [misc]backup-simplify: Simplify 0 into 0 1546856183.119 * [misc]backup-simplify: Simplify 0 into 0 1546856183.119 * [misc]backup-simplify: Simplify 0 into 0 1546856183.120 * [misc]backup-simplify: Simplify 0 into 0 1546856183.121 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856183.123 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546856183.131 * [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 1546856183.131 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546856183.131 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1546856183.131 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856183.132 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546856183.133 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 1546856183.137 * [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 1546856183.137 * [misc]taylor: Taking taylor expansion of 0 in k 1546856183.137 * [misc]backup-simplify: Simplify 0 into 0 1546856183.137 * [misc]backup-simplify: Simplify 0 into 0 1546856183.138 * [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))))) 1546856183.138 * * * * [misc]progress: [ 2 / 4 ] generating series at (2 1 1 1) 1546856183.138 * [misc]backup-simplify: Simplify (pow (* PI (* n 2)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 1546856183.138 * [misc]approximate: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 1546856183.138 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1546856183.138 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1546856183.138 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1546856183.138 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546856183.138 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856183.138 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856183.138 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546856183.138 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856183.138 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856183.138 * [misc]taylor: Taking taylor expansion of k in k 1546856183.138 * [misc]backup-simplify: Simplify 0 into 0 1546856183.138 * [misc]backup-simplify: Simplify 1 into 1 1546856183.138 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1546856183.138 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1546856183.138 * [misc]taylor: Taking taylor expansion of 2 in k 1546856183.138 * [misc]backup-simplify: Simplify 2 into 2 1546856183.138 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1546856183.138 * [misc]taylor: Taking taylor expansion of n in k 1546856183.138 * [misc]backup-simplify: Simplify n into n 1546856183.138 * [misc]taylor: Taking taylor expansion of PI in k 1546856183.138 * [misc]backup-simplify: Simplify PI into PI 1546856183.139 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1546856183.139 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1546856183.139 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1546856183.139 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546856183.139 * [misc]backup-simplify: Simplify (- 0) into 0 1546856183.139 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546856183.139 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1546856183.139 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1546856183.139 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546856183.139 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546856183.140 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546856183.140 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546856183.140 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856183.140 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856183.140 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546856183.140 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856183.140 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856183.140 * [misc]taylor: Taking taylor expansion of k in n 1546856183.140 * [misc]backup-simplify: Simplify k into k 1546856183.140 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546856183.140 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546856183.140 * [misc]taylor: Taking taylor expansion of 2 in n 1546856183.140 * [misc]backup-simplify: Simplify 2 into 2 1546856183.140 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546856183.140 * [misc]taylor: Taking taylor expansion of n in n 1546856183.140 * [misc]backup-simplify: Simplify 0 into 0 1546856183.140 * [misc]backup-simplify: Simplify 1 into 1 1546856183.140 * [misc]taylor: Taking taylor expansion of PI in n 1546856183.140 * [misc]backup-simplify: Simplify PI into PI 1546856183.140 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546856183.141 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546856183.141 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546856183.142 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546856183.142 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856183.142 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546856183.142 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546856183.143 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546856183.143 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546856183.144 * [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)))) 1546856183.145 * [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))))) 1546856183.145 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546856183.145 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546856183.145 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546856183.145 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546856183.145 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856183.145 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856183.145 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546856183.145 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856183.145 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856183.145 * [misc]taylor: Taking taylor expansion of k in n 1546856183.145 * [misc]backup-simplify: Simplify k into k 1546856183.145 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546856183.145 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546856183.145 * [misc]taylor: Taking taylor expansion of 2 in n 1546856183.145 * [misc]backup-simplify: Simplify 2 into 2 1546856183.145 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546856183.145 * [misc]taylor: Taking taylor expansion of n in n 1546856183.145 * [misc]backup-simplify: Simplify 0 into 0 1546856183.145 * [misc]backup-simplify: Simplify 1 into 1 1546856183.145 * [misc]taylor: Taking taylor expansion of PI in n 1546856183.145 * [misc]backup-simplify: Simplify PI into PI 1546856183.146 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546856183.146 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546856183.146 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546856183.147 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546856183.147 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856183.147 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546856183.148 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546856183.148 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546856183.148 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546856183.148 * [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)))) 1546856183.149 * [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))))) 1546856183.149 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1546856183.149 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1546856183.149 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546856183.149 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856183.149 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856183.149 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546856183.149 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856183.149 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856183.149 * [misc]taylor: Taking taylor expansion of k in k 1546856183.149 * [misc]backup-simplify: Simplify 0 into 0 1546856183.149 * [misc]backup-simplify: Simplify 1 into 1 1546856183.149 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1546856183.149 * [misc]taylor: Taking taylor expansion of (log n) in k 1546856183.149 * [misc]taylor: Taking taylor expansion of n in k 1546856183.149 * [misc]backup-simplify: Simplify n into n 1546856183.149 * [misc]backup-simplify: Simplify (log n) into (log n) 1546856183.149 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1546856183.149 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1546856183.149 * [misc]taylor: Taking taylor expansion of 2 in k 1546856183.149 * [misc]backup-simplify: Simplify 2 into 2 1546856183.149 * [misc]taylor: Taking taylor expansion of PI in k 1546856183.149 * [misc]backup-simplify: Simplify PI into PI 1546856183.149 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546856183.150 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856183.150 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546856183.150 * [misc]backup-simplify: Simplify (- 0) into 0 1546856183.150 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546856183.150 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546856183.151 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1546856183.151 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1546856183.151 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1546856183.152 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546856183.153 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1546856183.154 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546856183.154 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1546856183.154 * [misc]backup-simplify: Simplify (- 0) into 0 1546856183.155 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856183.155 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546856183.155 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1546856183.157 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1546856183.157 * [misc]taylor: Taking taylor expansion of 0 in k 1546856183.157 * [misc]backup-simplify: Simplify 0 into 0 1546856183.157 * [misc]backup-simplify: Simplify 0 into 0 1546856183.158 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1546856183.158 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546856183.160 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546856183.160 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856183.160 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1546856183.160 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546856183.160 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546856183.161 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1546856183.162 * [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))))))) 1546856183.163 * [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))))))) 1546856183.164 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1546856183.164 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1546856183.167 * [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 1546856183.168 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1546856183.168 * [misc]backup-simplify: Simplify (- 0) into 0 1546856183.168 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856183.168 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546856183.169 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1546856183.170 * [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 1546856183.170 * [misc]taylor: Taking taylor expansion of 0 in k 1546856183.170 * [misc]backup-simplify: Simplify 0 into 0 1546856183.170 * [misc]backup-simplify: Simplify 0 into 0 1546856183.170 * [misc]backup-simplify: Simplify 0 into 0 1546856183.171 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1546856183.172 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546856183.175 * [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 1546856183.175 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856183.175 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1546856183.175 * [misc]backup-simplify: Simplify (- 0) into 0 1546856183.176 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856183.176 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1546856183.177 * [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))))) 1546856183.179 * [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))))) 1546856183.183 * [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))))) 1546856183.184 * [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)))) 1546856183.184 * [misc]approximate: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 1546856183.184 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1546856183.184 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1546856183.184 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1546856183.184 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546856183.184 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856183.184 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856183.184 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546856183.184 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856183.184 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856183.184 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546856183.184 * [misc]taylor: Taking taylor expansion of k in k 1546856183.184 * [misc]backup-simplify: Simplify 0 into 0 1546856183.184 * [misc]backup-simplify: Simplify 1 into 1 1546856183.184 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546856183.185 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1546856183.185 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1546856183.185 * [misc]taylor: Taking taylor expansion of 2 in k 1546856183.185 * [misc]backup-simplify: Simplify 2 into 2 1546856183.185 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546856183.185 * [misc]taylor: Taking taylor expansion of PI in k 1546856183.185 * [misc]backup-simplify: Simplify PI into PI 1546856183.185 * [misc]taylor: Taking taylor expansion of n in k 1546856183.185 * [misc]backup-simplify: Simplify n into n 1546856183.185 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546856183.185 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1546856183.185 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1546856183.185 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546856183.185 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546856183.185 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546856183.186 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1546856183.186 * [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)))) 1546856183.186 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546856183.186 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546856183.186 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546856183.186 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546856183.186 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856183.186 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856183.186 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546856183.186 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856183.186 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856183.186 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546856183.186 * [misc]taylor: Taking taylor expansion of k in n 1546856183.186 * [misc]backup-simplify: Simplify k into k 1546856183.186 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546856183.186 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546856183.186 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546856183.186 * [misc]taylor: Taking taylor expansion of 2 in n 1546856183.186 * [misc]backup-simplify: Simplify 2 into 2 1546856183.186 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856183.186 * [misc]taylor: Taking taylor expansion of PI in n 1546856183.186 * [misc]backup-simplify: Simplify PI into PI 1546856183.186 * [misc]taylor: Taking taylor expansion of n in n 1546856183.186 * [misc]backup-simplify: Simplify 0 into 0 1546856183.186 * [misc]backup-simplify: Simplify 1 into 1 1546856183.187 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856183.187 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546856183.188 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856183.188 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546856183.188 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546856183.188 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546856183.189 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546856183.189 * [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))) 1546856183.190 * [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)))) 1546856183.190 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546856183.190 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546856183.190 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546856183.190 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546856183.190 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856183.190 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856183.190 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546856183.190 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856183.190 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856183.190 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546856183.190 * [misc]taylor: Taking taylor expansion of k in n 1546856183.190 * [misc]backup-simplify: Simplify k into k 1546856183.190 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546856183.190 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546856183.190 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546856183.190 * [misc]taylor: Taking taylor expansion of 2 in n 1546856183.190 * [misc]backup-simplify: Simplify 2 into 2 1546856183.190 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856183.190 * [misc]taylor: Taking taylor expansion of PI in n 1546856183.190 * [misc]backup-simplify: Simplify PI into PI 1546856183.190 * [misc]taylor: Taking taylor expansion of n in n 1546856183.190 * [misc]backup-simplify: Simplify 0 into 0 1546856183.190 * [misc]backup-simplify: Simplify 1 into 1 1546856183.191 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856183.191 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546856183.191 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856183.192 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546856183.192 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546856183.192 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546856183.192 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546856183.193 * [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))) 1546856183.194 * [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)))) 1546856183.194 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1546856183.194 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1546856183.194 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546856183.194 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856183.194 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856183.194 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546856183.194 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856183.194 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856183.194 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546856183.194 * [misc]taylor: Taking taylor expansion of k in k 1546856183.194 * [misc]backup-simplify: Simplify 0 into 0 1546856183.194 * [misc]backup-simplify: Simplify 1 into 1 1546856183.195 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546856183.195 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1546856183.195 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1546856183.195 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1546856183.195 * [misc]taylor: Taking taylor expansion of 2 in k 1546856183.195 * [misc]backup-simplify: Simplify 2 into 2 1546856183.195 * [misc]taylor: Taking taylor expansion of PI in k 1546856183.195 * [misc]backup-simplify: Simplify PI into PI 1546856183.195 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546856183.196 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546856183.196 * [misc]taylor: Taking taylor expansion of (log n) in k 1546856183.196 * [misc]taylor: Taking taylor expansion of n in k 1546856183.196 * [misc]backup-simplify: Simplify n into n 1546856183.196 * [misc]backup-simplify: Simplify (log n) into (log n) 1546856183.196 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546856183.196 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546856183.196 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546856183.197 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1546856183.197 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1546856183.198 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1546856183.198 * [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)))) 1546856183.199 * [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)))) 1546856183.200 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546856183.201 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546856183.204 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546856183.204 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546856183.204 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546856183.204 * [misc]backup-simplify: Simplify (- 0) into 0 1546856183.204 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856183.205 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546856183.206 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1546856183.207 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546856183.207 * [misc]taylor: Taking taylor expansion of 0 in k 1546856183.207 * [misc]backup-simplify: Simplify 0 into 0 1546856183.207 * [misc]backup-simplify: Simplify 0 into 0 1546856183.207 * [misc]backup-simplify: Simplify 0 into 0 1546856183.208 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856183.209 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546856183.212 * [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 1546856183.212 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546856183.212 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1546856183.212 * [misc]backup-simplify: Simplify (- 0) into 0 1546856183.212 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856183.213 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546856183.213 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1546856183.215 * [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 1546856183.215 * [misc]taylor: Taking taylor expansion of 0 in k 1546856183.215 * [misc]backup-simplify: Simplify 0 into 0 1546856183.215 * [misc]backup-simplify: Simplify 0 into 0 1546856183.215 * [misc]backup-simplify: Simplify 0 into 0 1546856183.215 * [misc]backup-simplify: Simplify 0 into 0 1546856183.216 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856183.217 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546856183.221 * [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 1546856183.221 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546856183.222 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1546856183.222 * [misc]backup-simplify: Simplify (- 0) into 0 1546856183.222 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856183.222 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546856183.223 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1546856183.225 * [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 1546856183.225 * [misc]taylor: Taking taylor expansion of 0 in k 1546856183.225 * [misc]backup-simplify: Simplify 0 into 0 1546856183.225 * [misc]backup-simplify: Simplify 0 into 0 1546856183.226 * [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))))) 1546856183.226 * [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)) 1546856183.226 * [misc]approximate: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 1546856183.226 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1546856183.226 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1546856183.226 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1546856183.226 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546856183.226 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546856183.226 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856183.226 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856183.226 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546856183.226 * [misc]taylor: Taking taylor expansion of k in k 1546856183.226 * [misc]backup-simplify: Simplify 0 into 0 1546856183.226 * [misc]backup-simplify: Simplify 1 into 1 1546856183.226 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546856183.226 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856183.226 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856183.226 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1546856183.226 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1546856183.226 * [misc]taylor: Taking taylor expansion of -2 in k 1546856183.226 * [misc]backup-simplify: Simplify -2 into -2 1546856183.226 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546856183.226 * [misc]taylor: Taking taylor expansion of PI in k 1546856183.226 * [misc]backup-simplify: Simplify PI into PI 1546856183.226 * [misc]taylor: Taking taylor expansion of n in k 1546856183.226 * [misc]backup-simplify: Simplify n into n 1546856183.226 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546856183.226 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1546856183.226 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1546856183.226 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546856183.227 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546856183.227 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1546856183.227 * [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))) 1546856183.227 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546856183.227 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546856183.227 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546856183.227 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546856183.227 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546856183.227 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856183.227 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856183.227 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546856183.227 * [misc]taylor: Taking taylor expansion of k in n 1546856183.227 * [misc]backup-simplify: Simplify k into k 1546856183.227 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546856183.227 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856183.227 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856183.227 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546856183.227 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546856183.227 * [misc]taylor: Taking taylor expansion of -2 in n 1546856183.227 * [misc]backup-simplify: Simplify -2 into -2 1546856183.227 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856183.227 * [misc]taylor: Taking taylor expansion of PI in n 1546856183.227 * [misc]backup-simplify: Simplify PI into PI 1546856183.227 * [misc]taylor: Taking taylor expansion of n in n 1546856183.227 * [misc]backup-simplify: Simplify 0 into 0 1546856183.227 * [misc]backup-simplify: Simplify 1 into 1 1546856183.227 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856183.227 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546856183.228 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546856183.228 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546856183.228 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546856183.228 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546856183.229 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1546856183.229 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 1546856183.229 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546856183.229 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546856183.229 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546856183.229 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546856183.229 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546856183.229 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856183.229 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856183.229 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546856183.229 * [misc]taylor: Taking taylor expansion of k in n 1546856183.229 * [misc]backup-simplify: Simplify k into k 1546856183.229 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546856183.229 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546856183.229 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856183.229 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546856183.229 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546856183.229 * [misc]taylor: Taking taylor expansion of -2 in n 1546856183.229 * [misc]backup-simplify: Simplify -2 into -2 1546856183.229 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856183.229 * [misc]taylor: Taking taylor expansion of PI in n 1546856183.229 * [misc]backup-simplify: Simplify PI into PI 1546856183.229 * [misc]taylor: Taking taylor expansion of n in n 1546856183.229 * [misc]backup-simplify: Simplify 0 into 0 1546856183.229 * [misc]backup-simplify: Simplify 1 into 1 1546856183.230 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856183.230 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546856183.230 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546856183.230 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546856183.230 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546856183.231 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546856183.231 * [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))) 1546856183.231 * [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)))) 1546856183.231 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1546856183.231 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1546856183.232 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546856183.232 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546856183.232 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856183.232 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856183.232 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546856183.232 * [misc]taylor: Taking taylor expansion of k in k 1546856183.232 * [misc]backup-simplify: Simplify 0 into 0 1546856183.232 * [misc]backup-simplify: Simplify 1 into 1 1546856183.232 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546856183.232 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546856183.232 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546856183.232 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1546856183.232 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1546856183.232 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1546856183.232 * [misc]taylor: Taking taylor expansion of -2 in k 1546856183.232 * [misc]backup-simplify: Simplify -2 into -2 1546856183.232 * [misc]taylor: Taking taylor expansion of PI in k 1546856183.232 * [misc]backup-simplify: Simplify PI into PI 1546856183.232 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546856183.232 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546856183.232 * [misc]taylor: Taking taylor expansion of (log n) in k 1546856183.232 * [misc]taylor: Taking taylor expansion of n in k 1546856183.232 * [misc]backup-simplify: Simplify n into n 1546856183.232 * [misc]backup-simplify: Simplify (log n) into (log n) 1546856183.233 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546856183.233 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546856183.233 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1546856183.233 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1546856183.233 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1546856183.234 * [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)))) 1546856183.234 * [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)))) 1546856183.235 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546856183.235 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1546856183.237 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1546856183.237 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546856183.237 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546856183.237 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856183.238 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546856183.238 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1546856183.239 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546856183.239 * [misc]taylor: Taking taylor expansion of 0 in k 1546856183.239 * [misc]backup-simplify: Simplify 0 into 0 1546856183.239 * [misc]backup-simplify: Simplify 0 into 0 1546856183.239 * [misc]backup-simplify: Simplify 0 into 0 1546856183.240 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856183.241 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1546856183.244 * [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 1546856183.244 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546856183.244 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1546856183.244 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856183.245 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546856183.246 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1546856183.248 * [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 1546856183.249 * [misc]taylor: Taking taylor expansion of 0 in k 1546856183.249 * [misc]backup-simplify: Simplify 0 into 0 1546856183.249 * [misc]backup-simplify: Simplify 0 into 0 1546856183.249 * [misc]backup-simplify: Simplify 0 into 0 1546856183.249 * [misc]backup-simplify: Simplify 0 into 0 1546856183.251 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856183.252 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546856183.260 * [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 1546856183.260 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546856183.261 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1546856183.261 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546856183.262 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546856183.263 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 1546856183.266 * [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 1546856183.266 * [misc]taylor: Taking taylor expansion of 0 in k 1546856183.267 * [misc]backup-simplify: Simplify 0 into 0 1546856183.267 * [misc]backup-simplify: Simplify 0 into 0 1546856183.267 * [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))))) 1546856183.267 * * * * [misc]progress: [ 3 / 4 ] generating series at (2 2 1 1 1) 1546856183.267 * [misc]backup-simplify: Simplify (* PI (* n 2)) into (* 2 (* n PI)) 1546856183.267 * [misc]approximate: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1546856183.267 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546856183.267 * [misc]taylor: Taking taylor expansion of 2 in n 1546856183.267 * [misc]backup-simplify: Simplify 2 into 2 1546856183.267 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546856183.267 * [misc]taylor: Taking taylor expansion of n in n 1546856183.267 * [misc]backup-simplify: Simplify 0 into 0 1546856183.267 * [misc]backup-simplify: Simplify 1 into 1 1546856183.267 * [misc]taylor: Taking taylor expansion of PI in n 1546856183.267 * [misc]backup-simplify: Simplify PI into PI 1546856183.268 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546856183.268 * [misc]taylor: Taking taylor expansion of 2 in n 1546856183.268 * [misc]backup-simplify: Simplify 2 into 2 1546856183.268 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546856183.268 * [misc]taylor: Taking taylor expansion of n in n 1546856183.268 * [misc]backup-simplify: Simplify 0 into 0 1546856183.268 * [misc]backup-simplify: Simplify 1 into 1 1546856183.268 * [misc]taylor: Taking taylor expansion of PI in n 1546856183.268 * [misc]backup-simplify: Simplify PI into PI 1546856183.268 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546856183.268 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546856183.268 * [misc]backup-simplify: Simplify 0 into 0 1546856183.268 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546856183.269 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546856183.269 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546856183.270 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546856183.270 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1546856183.270 * [misc]backup-simplify: Simplify 0 into 0 1546856183.271 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1546856183.272 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1546856183.272 * [misc]backup-simplify: Simplify 0 into 0 1546856183.273 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1546856183.274 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1546856183.275 * [misc]backup-simplify: Simplify 0 into 0 1546856183.276 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1546856183.278 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1546856183.278 * [misc]backup-simplify: Simplify 0 into 0 1546856183.280 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1546856183.282 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1546856183.282 * [misc]backup-simplify: Simplify 0 into 0 1546856183.285 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1546856183.287 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1546856183.287 * [misc]backup-simplify: Simplify 0 into 0 1546856183.287 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1546856183.287 * [misc]backup-simplify: Simplify (* PI (* (/ 1 n) 2)) into (* 2 (/ PI n)) 1546856183.287 * [misc]approximate: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1546856183.288 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546856183.288 * [misc]taylor: Taking taylor expansion of 2 in n 1546856183.288 * [misc]backup-simplify: Simplify 2 into 2 1546856183.288 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856183.288 * [misc]taylor: Taking taylor expansion of PI in n 1546856183.288 * [misc]backup-simplify: Simplify PI into PI 1546856183.288 * [misc]taylor: Taking taylor expansion of n in n 1546856183.288 * [misc]backup-simplify: Simplify 0 into 0 1546856183.288 * [misc]backup-simplify: Simplify 1 into 1 1546856183.288 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856183.288 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546856183.288 * [misc]taylor: Taking taylor expansion of 2 in n 1546856183.288 * [misc]backup-simplify: Simplify 2 into 2 1546856183.288 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856183.288 * [misc]taylor: Taking taylor expansion of PI in n 1546856183.288 * [misc]backup-simplify: Simplify PI into PI 1546856183.288 * [misc]taylor: Taking taylor expansion of n in n 1546856183.288 * [misc]backup-simplify: Simplify 0 into 0 1546856183.288 * [misc]backup-simplify: Simplify 1 into 1 1546856183.288 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856183.288 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546856183.289 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546856183.289 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546856183.290 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546856183.290 * [misc]backup-simplify: Simplify 0 into 0 1546856183.290 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856183.291 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546856183.291 * [misc]backup-simplify: Simplify 0 into 0 1546856183.292 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856183.293 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546856183.293 * [misc]backup-simplify: Simplify 0 into 0 1546856183.294 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856183.296 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1546856183.296 * [misc]backup-simplify: Simplify 0 into 0 1546856183.297 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856183.298 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1546856183.299 * [misc]backup-simplify: Simplify 0 into 0 1546856183.301 * [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 1546856183.304 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1546856183.304 * [misc]backup-simplify: Simplify 0 into 0 1546856183.304 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 1546856183.304 * [misc]backup-simplify: Simplify (* PI (* (/ 1 (- n)) 2)) into (* -2 (/ PI n)) 1546856183.304 * [misc]approximate: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1546856183.304 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546856183.304 * [misc]taylor: Taking taylor expansion of -2 in n 1546856183.304 * [misc]backup-simplify: Simplify -2 into -2 1546856183.304 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856183.304 * [misc]taylor: Taking taylor expansion of PI in n 1546856183.304 * [misc]backup-simplify: Simplify PI into PI 1546856183.304 * [misc]taylor: Taking taylor expansion of n in n 1546856183.304 * [misc]backup-simplify: Simplify 0 into 0 1546856183.304 * [misc]backup-simplify: Simplify 1 into 1 1546856183.305 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856183.305 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546856183.305 * [misc]taylor: Taking taylor expansion of -2 in n 1546856183.305 * [misc]backup-simplify: Simplify -2 into -2 1546856183.305 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856183.305 * [misc]taylor: Taking taylor expansion of PI in n 1546856183.305 * [misc]backup-simplify: Simplify PI into PI 1546856183.305 * [misc]taylor: Taking taylor expansion of n in n 1546856183.305 * [misc]backup-simplify: Simplify 0 into 0 1546856183.305 * [misc]backup-simplify: Simplify 1 into 1 1546856183.305 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856183.306 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546856183.306 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546856183.307 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546856183.308 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1546856183.308 * [misc]backup-simplify: Simplify 0 into 0 1546856183.309 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856183.310 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1546856183.310 * [misc]backup-simplify: Simplify 0 into 0 1546856183.312 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856183.313 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546856183.313 * [misc]backup-simplify: Simplify 0 into 0 1546856183.315 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856183.317 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1546856183.317 * [misc]backup-simplify: Simplify 0 into 0 1546856183.318 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856183.320 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1546856183.320 * [misc]backup-simplify: Simplify 0 into 0 1546856183.321 * [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 1546856183.323 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1546856183.323 * [misc]backup-simplify: Simplify 0 into 0 1546856183.323 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 1546856183.323 * * * * [misc]progress: [ 4 / 4 ] generating series at (2 1 1 1 1) 1546856183.324 * [misc]backup-simplify: Simplify (* PI (* n 2)) into (* 2 (* n PI)) 1546856183.324 * [misc]approximate: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1546856183.324 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546856183.324 * [misc]taylor: Taking taylor expansion of 2 in n 1546856183.324 * [misc]backup-simplify: Simplify 2 into 2 1546856183.324 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546856183.324 * [misc]taylor: Taking taylor expansion of n in n 1546856183.324 * [misc]backup-simplify: Simplify 0 into 0 1546856183.324 * [misc]backup-simplify: Simplify 1 into 1 1546856183.324 * [misc]taylor: Taking taylor expansion of PI in n 1546856183.324 * [misc]backup-simplify: Simplify PI into PI 1546856183.324 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546856183.324 * [misc]taylor: Taking taylor expansion of 2 in n 1546856183.324 * [misc]backup-simplify: Simplify 2 into 2 1546856183.324 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546856183.324 * [misc]taylor: Taking taylor expansion of n in n 1546856183.324 * [misc]backup-simplify: Simplify 0 into 0 1546856183.324 * [misc]backup-simplify: Simplify 1 into 1 1546856183.324 * [misc]taylor: Taking taylor expansion of PI in n 1546856183.324 * [misc]backup-simplify: Simplify PI into PI 1546856183.324 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546856183.324 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546856183.324 * [misc]backup-simplify: Simplify 0 into 0 1546856183.325 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546856183.325 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546856183.325 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546856183.326 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546856183.326 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1546856183.327 * [misc]backup-simplify: Simplify 0 into 0 1546856183.327 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1546856183.328 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1546856183.328 * [misc]backup-simplify: Simplify 0 into 0 1546856183.330 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1546856183.331 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1546856183.331 * [misc]backup-simplify: Simplify 0 into 0 1546856183.332 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1546856183.334 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1546856183.334 * [misc]backup-simplify: Simplify 0 into 0 1546856183.336 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1546856183.338 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1546856183.338 * [misc]backup-simplify: Simplify 0 into 0 1546856183.340 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1546856183.343 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1546856183.343 * [misc]backup-simplify: Simplify 0 into 0 1546856183.343 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1546856183.343 * [misc]backup-simplify: Simplify (* PI (* (/ 1 n) 2)) into (* 2 (/ PI n)) 1546856183.343 * [misc]approximate: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1546856183.343 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546856183.343 * [misc]taylor: Taking taylor expansion of 2 in n 1546856183.343 * [misc]backup-simplify: Simplify 2 into 2 1546856183.343 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856183.343 * [misc]taylor: Taking taylor expansion of PI in n 1546856183.343 * [misc]backup-simplify: Simplify PI into PI 1546856183.343 * [misc]taylor: Taking taylor expansion of n in n 1546856183.343 * [misc]backup-simplify: Simplify 0 into 0 1546856183.343 * [misc]backup-simplify: Simplify 1 into 1 1546856183.343 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856183.343 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546856183.343 * [misc]taylor: Taking taylor expansion of 2 in n 1546856183.343 * [misc]backup-simplify: Simplify 2 into 2 1546856183.344 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856183.344 * [misc]taylor: Taking taylor expansion of PI in n 1546856183.344 * [misc]backup-simplify: Simplify PI into PI 1546856183.344 * [misc]taylor: Taking taylor expansion of n in n 1546856183.344 * [misc]backup-simplify: Simplify 0 into 0 1546856183.344 * [misc]backup-simplify: Simplify 1 into 1 1546856183.344 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856183.344 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546856183.344 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546856183.346 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546856183.347 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546856183.347 * [misc]backup-simplify: Simplify 0 into 0 1546856183.348 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856183.349 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546856183.349 * [misc]backup-simplify: Simplify 0 into 0 1546856183.351 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856183.352 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546856183.352 * [misc]backup-simplify: Simplify 0 into 0 1546856183.354 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856183.356 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1546856183.356 * [misc]backup-simplify: Simplify 0 into 0 1546856183.358 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856183.361 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1546856183.361 * [misc]backup-simplify: Simplify 0 into 0 1546856183.364 * [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 1546856183.367 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1546856183.367 * [misc]backup-simplify: Simplify 0 into 0 1546856183.368 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 1546856183.368 * [misc]backup-simplify: Simplify (* PI (* (/ 1 (- n)) 2)) into (* -2 (/ PI n)) 1546856183.368 * [misc]approximate: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1546856183.368 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546856183.368 * [misc]taylor: Taking taylor expansion of -2 in n 1546856183.368 * [misc]backup-simplify: Simplify -2 into -2 1546856183.368 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856183.368 * [misc]taylor: Taking taylor expansion of PI in n 1546856183.368 * [misc]backup-simplify: Simplify PI into PI 1546856183.368 * [misc]taylor: Taking taylor expansion of n in n 1546856183.368 * [misc]backup-simplify: Simplify 0 into 0 1546856183.368 * [misc]backup-simplify: Simplify 1 into 1 1546856183.368 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856183.369 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546856183.369 * [misc]taylor: Taking taylor expansion of -2 in n 1546856183.369 * [misc]backup-simplify: Simplify -2 into -2 1546856183.369 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546856183.369 * [misc]taylor: Taking taylor expansion of PI in n 1546856183.369 * [misc]backup-simplify: Simplify PI into PI 1546856183.369 * [misc]taylor: Taking taylor expansion of n in n 1546856183.369 * [misc]backup-simplify: Simplify 0 into 0 1546856183.369 * [misc]backup-simplify: Simplify 1 into 1 1546856183.369 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546856183.369 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546856183.370 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546856183.371 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546856183.371 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1546856183.371 * [misc]backup-simplify: Simplify 0 into 0 1546856183.373 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856183.374 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1546856183.374 * [misc]backup-simplify: Simplify 0 into 0 1546856183.375 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856183.377 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546856183.377 * [misc]backup-simplify: Simplify 0 into 0 1546856183.379 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856183.381 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1546856183.381 * [misc]backup-simplify: Simplify 0 into 0 1546856183.383 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546856183.386 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1546856183.386 * [misc]backup-simplify: Simplify 0 into 0 1546856183.389 * [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 1546856183.392 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1546856183.392 * [misc]backup-simplify: Simplify 0 into 0 1546856183.392 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 1546856183.392 * * * [misc]progress: simplifying candidates 1546856183.392 * * * * [misc]progress: [ 1 / 72 ] simplifiying candidate # 1546856183.393 * * * * [misc]progress: [ 2 / 72 ] simplifiying candidate # 1546856183.393 * * * * [misc]progress: [ 3 / 72 ] simplifiying candidate # 1546856183.393 * [enter]simplify: Simplifying (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) 1546856183.393 * * [misc]simplify: iters left: 6 (11 enodes) 1546856183.398 * * [misc]simplify: iters left: 5 (21 enodes) 1546856183.405 * * [misc]simplify: iters left: 4 (47 enodes) 1546856183.415 * * [misc]simplify: iters left: 3 (113 enodes) 1546856183.467 * * [misc]simplify: iters left: 2 (328 enodes) 1546856183.745 * [exit]simplify: Simplified to (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) 1546856183.746 * [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))))) 1546856183.746 * * * * [misc]progress: [ 4 / 72 ] simplifiying candidate # 1546856183.746 * * * * [misc]progress: [ 5 / 72 ] simplifiying candidate # 1546856183.746 * [enter]simplify: Simplifying (* PI (* n 2)) 1546856183.746 * * [misc]simplify: iters left: 4 (5 enodes) 1546856183.748 * * [misc]simplify: iters left: 3 (9 enodes) 1546856183.750 * * [misc]simplify: iters left: 2 (15 enodes) 1546856183.754 * * [misc]simplify: iters left: 1 (17 enodes) 1546856183.758 * [exit]simplify: Simplified to (* (* 2 n) PI) 1546856183.758 * [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))))) 1546856183.758 * * * * [misc]progress: [ 6 / 72 ] simplifiying candidate # 1546856183.759 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (/ k 2)) 1546856183.759 * * [misc]simplify: iters left: 5 (8 enodes) 1546856183.761 * * [misc]simplify: iters left: 4 (12 enodes) 1546856183.765 * * [misc]simplify: iters left: 3 (18 enodes) 1546856183.770 * * [misc]simplify: iters left: 2 (20 enodes) 1546856183.774 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ k 2)) 1546856183.775 * [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))))) 1546856183.775 * * * * [misc]progress: [ 7 / 72 ] simplifiying candidate # 1546856183.775 * [enter]simplify: Simplifying (cbrt (- 1/2 (/ k 2))) 1546856183.775 * * [misc]simplify: iters left: 5 (6 enodes) 1546856183.776 * * [misc]simplify: iters left: 4 (8 enodes) 1546856183.777 * * [misc]simplify: iters left: 3 (11 enodes) 1546856183.779 * [exit]simplify: Simplified to (cbrt (- 1/2 (/ k 2))) 1546856183.779 * [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))))) 1546856183.779 * * * * [misc]progress: [ 8 / 72 ] simplifiying candidate # 1546856183.779 * [enter]simplify: Simplifying (sqrt (- 1/2 (/ k 2))) 1546856183.779 * * [misc]simplify: iters left: 5 (6 enodes) 1546856183.780 * * [misc]simplify: iters left: 4 (8 enodes) 1546856183.781 * * [misc]simplify: iters left: 3 (11 enodes) 1546856183.783 * [exit]simplify: Simplified to (sqrt (- 1/2 (/ k 2))) 1546856183.783 * [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))))) 1546856183.783 * * * * [misc]progress: [ 9 / 72 ] simplifiying candidate # 1546856183.783 * [enter]simplify: Simplifying (- 1/2 (/ k 2)) 1546856183.783 * * [misc]simplify: iters left: 4 (5 enodes) 1546856183.786 * * [misc]simplify: iters left: 3 (7 enodes) 1546856183.787 * * [misc]simplify: iters left: 2 (10 enodes) 1546856183.789 * [exit]simplify: Simplified to (- 1/2 (/ k 2)) 1546856183.789 * [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))))) 1546856183.789 * * * * [misc]progress: [ 10 / 72 ] simplifiying candidate # 1546856183.789 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1546856183.789 * * [misc]simplify: iters left: 5 (9 enodes) 1546856183.790 * * [misc]simplify: iters left: 4 (15 enodes) 1546856183.793 * * [misc]simplify: iters left: 3 (21 enodes) 1546856183.795 * * [misc]simplify: iters left: 2 (22 enodes) 1546856183.798 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1546856183.798 * [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))))) 1546856183.798 * * * * [misc]progress: [ 11 / 72 ] simplifiying candidate # 1546856183.798 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1546856183.798 * * [misc]simplify: iters left: 5 (9 enodes) 1546856183.800 * * [misc]simplify: iters left: 4 (15 enodes) 1546856183.802 * * [misc]simplify: iters left: 3 (21 enodes) 1546856183.804 * * [misc]simplify: iters left: 2 (22 enodes) 1546856183.807 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1546856183.807 * [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))))) 1546856183.807 * * * * [misc]progress: [ 12 / 72 ] simplifiying candidate # 1546856183.807 * [enter]simplify: Simplifying (pow PI (- 1/2 (/ k 2))) 1546856183.808 * * [misc]simplify: iters left: 5 (7 enodes) 1546856183.809 * * [misc]simplify: iters left: 4 (9 enodes) 1546856183.810 * * [misc]simplify: iters left: 3 (12 enodes) 1546856183.812 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1546856183.812 * [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))))) 1546856183.812 * * * * [misc]progress: [ 13 / 72 ] simplifiying candidate # 1546856183.812 * * * * [misc]progress: [ 14 / 72 ] simplifiying candidate # 1546856183.812 * * * * [misc]progress: [ 15 / 72 ] simplifiying candidate # 1546856183.812 * * * * [misc]progress: [ 16 / 72 ] simplifiying candidate # 1546856183.812 * * * * [misc]progress: [ 17 / 72 ] simplifiying candidate # 1546856183.812 * * * * [misc]progress: [ 18 / 72 ] simplifiying candidate # 1546856183.812 * * * * [misc]progress: [ 19 / 72 ] simplifiying candidate # 1546856183.812 * * * * [misc]progress: [ 20 / 72 ] simplifiying candidate # 1546856183.812 * * * * [misc]progress: [ 21 / 72 ] simplifiying candidate # 1546856183.812 * * * * [misc]progress: [ 22 / 72 ] simplifiying candidate # 1546856183.813 * [enter]simplify: Simplifying (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) 1546856183.813 * * [misc]simplify: iters left: 6 (11 enodes) 1546856183.816 * * [misc]simplify: iters left: 5 (21 enodes) 1546856183.823 * * [misc]simplify: iters left: 4 (47 enodes) 1546856183.840 * * [misc]simplify: iters left: 3 (113 enodes) 1546856183.880 * * [misc]simplify: iters left: 2 (328 enodes) 1546856184.170 * [exit]simplify: Simplified to (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) 1546856184.170 * [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))))) 1546856184.171 * * * * [misc]progress: [ 23 / 72 ] simplifiying candidate # 1546856184.171 * * * * [misc]progress: [ 24 / 72 ] simplifiying candidate # 1546856184.171 * [enter]simplify: Simplifying (* PI (* n 2)) 1546856184.171 * * [misc]simplify: iters left: 4 (5 enodes) 1546856184.172 * * [misc]simplify: iters left: 3 (9 enodes) 1546856184.173 * * [misc]simplify: iters left: 2 (15 enodes) 1546856184.175 * * [misc]simplify: iters left: 1 (17 enodes) 1546856184.177 * [exit]simplify: Simplified to (* (* 2 n) PI) 1546856184.177 * [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))))) 1546856184.177 * * * * [misc]progress: [ 25 / 72 ] simplifiying candidate # 1546856184.177 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (/ k 2)) 1546856184.178 * * [misc]simplify: iters left: 5 (8 enodes) 1546856184.179 * * [misc]simplify: iters left: 4 (12 enodes) 1546856184.180 * * [misc]simplify: iters left: 3 (18 enodes) 1546856184.183 * * [misc]simplify: iters left: 2 (20 enodes) 1546856184.185 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ k 2)) 1546856184.185 * [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))))) 1546856184.185 * * * * [misc]progress: [ 26 / 72 ] simplifiying candidate # 1546856184.186 * [enter]simplify: Simplifying (cbrt (- 1/2 (/ k 2))) 1546856184.186 * * [misc]simplify: iters left: 5 (6 enodes) 1546856184.187 * * [misc]simplify: iters left: 4 (8 enodes) 1546856184.188 * * [misc]simplify: iters left: 3 (11 enodes) 1546856184.189 * [exit]simplify: Simplified to (cbrt (- 1/2 (/ k 2))) 1546856184.189 * [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))))) 1546856184.189 * * * * [misc]progress: [ 27 / 72 ] simplifiying candidate # 1546856184.189 * [enter]simplify: Simplifying (sqrt (- 1/2 (/ k 2))) 1546856184.189 * * [misc]simplify: iters left: 5 (6 enodes) 1546856184.190 * * [misc]simplify: iters left: 4 (8 enodes) 1546856184.192 * * [misc]simplify: iters left: 3 (11 enodes) 1546856184.193 * [exit]simplify: Simplified to (sqrt (- 1/2 (/ k 2))) 1546856184.193 * [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))))) 1546856184.193 * * * * [misc]progress: [ 28 / 72 ] simplifiying candidate # 1546856184.193 * [enter]simplify: Simplifying (- 1/2 (/ k 2)) 1546856184.193 * * [misc]simplify: iters left: 4 (5 enodes) 1546856184.194 * * [misc]simplify: iters left: 3 (7 enodes) 1546856184.195 * * [misc]simplify: iters left: 2 (10 enodes) 1546856184.196 * [exit]simplify: Simplified to (- 1/2 (/ k 2)) 1546856184.196 * [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))))) 1546856184.196 * * * * [misc]progress: [ 29 / 72 ] simplifiying candidate # 1546856184.196 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1546856184.197 * * [misc]simplify: iters left: 5 (9 enodes) 1546856184.198 * * [misc]simplify: iters left: 4 (15 enodes) 1546856184.200 * * [misc]simplify: iters left: 3 (21 enodes) 1546856184.203 * * [misc]simplify: iters left: 2 (22 enodes) 1546856184.207 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1546856184.207 * [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))))) 1546856184.208 * * * * [misc]progress: [ 30 / 72 ] simplifiying candidate # 1546856184.208 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1546856184.208 * * [misc]simplify: iters left: 5 (9 enodes) 1546856184.211 * * [misc]simplify: iters left: 4 (15 enodes) 1546856184.215 * * [misc]simplify: iters left: 3 (21 enodes) 1546856184.220 * * [misc]simplify: iters left: 2 (22 enodes) 1546856184.226 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1546856184.226 * [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))))) 1546856184.226 * * * * [misc]progress: [ 31 / 72 ] simplifiying candidate # 1546856184.226 * [enter]simplify: Simplifying (pow PI (- 1/2 (/ k 2))) 1546856184.226 * * [misc]simplify: iters left: 5 (7 enodes) 1546856184.228 * * [misc]simplify: iters left: 4 (9 enodes) 1546856184.231 * * [misc]simplify: iters left: 3 (12 enodes) 1546856184.235 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1546856184.235 * [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))))) 1546856184.235 * * * * [misc]progress: [ 32 / 72 ] simplifiying candidate # 1546856184.235 * * * * [misc]progress: [ 33 / 72 ] simplifiying candidate # 1546856184.235 * * * * [misc]progress: [ 34 / 72 ] simplifiying candidate # 1546856184.235 * * * * [misc]progress: [ 35 / 72 ] simplifiying candidate # 1546856184.235 * * * * [misc]progress: [ 36 / 72 ] simplifiying candidate # 1546856184.235 * * * * [misc]progress: [ 37 / 72 ] simplifiying candidate # 1546856184.235 * * * * [misc]progress: [ 38 / 72 ] simplifiying candidate # 1546856184.235 * * * * [misc]progress: [ 39 / 72 ] simplifiying candidate # 1546856184.235 * * * * [misc]progress: [ 40 / 72 ] simplifiying candidate # 1546856184.235 * * * * [misc]progress: [ 41 / 72 ] simplifiying candidate # 1546856184.235 * * * * [misc]progress: [ 42 / 72 ] simplifiying candidate # 1546856184.236 * * * * [misc]progress: [ 43 / 72 ] simplifiying candidate # 1546856184.236 * * * * [misc]progress: [ 44 / 72 ] simplifiying candidate # 1546856184.236 * * * * [misc]progress: [ 45 / 72 ] simplifiying candidate # 1546856184.236 * * * * [misc]progress: [ 46 / 72 ] simplifiying candidate # 1546856184.236 * * * * [misc]progress: [ 47 / 72 ] simplifiying candidate # 1546856184.236 * * * * [misc]progress: [ 48 / 72 ] simplifiying candidate # 1546856184.236 * * * * [misc]progress: [ 49 / 72 ] simplifiying candidate # 1546856184.236 * * * * [misc]progress: [ 50 / 72 ] simplifiying candidate # 1546856184.236 * * * * [misc]progress: [ 51 / 72 ] simplifiying candidate # 1546856184.236 * * * * [misc]progress: [ 52 / 72 ] simplifiying candidate # 1546856184.236 * * * * [misc]progress: [ 53 / 72 ] simplifiying candidate # 1546856184.236 * * * * [misc]progress: [ 54 / 72 ] simplifiying candidate # 1546856184.236 * * * * [misc]progress: [ 55 / 72 ] simplifiying candidate # 1546856184.236 * * * * [misc]progress: [ 56 / 72 ] simplifiying candidate # 1546856184.236 * * * * [misc]progress: [ 57 / 72 ] simplifiying candidate # 1546856184.236 * * * * [misc]progress: [ 58 / 72 ] simplifiying candidate # 1546856184.237 * * * * [misc]progress: [ 59 / 72 ] simplifiying candidate # 1546856184.237 * * * * [misc]progress: [ 60 / 72 ] simplifiying candidate # 1546856184.237 * * * * [misc]progress: [ 61 / 72 ] simplifiying candidate # 1546856184.237 * [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))))) 1546856184.237 * * [misc]simplify: iters left: 6 (37 enodes) 1546856184.246 * * [misc]simplify: iters left: 5 (108 enodes) 1546856184.271 * * [misc]simplify: iters left: 4 (368 enodes) 1546856184.505 * [exit]simplify: Simplified to (fma -1/2 (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) (fma (* (* (* k k) (log n)) (* (log (* PI 2)) 1/4)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (fma (* (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (log (* PI 2)) (log (* PI 2)))) (* (* k k) 1/8) (fma (* (* (* k k) (log n)) (* (log n) 1/8)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (pow n 1/2) (pow (* PI 2) 1/2)))))) 1546856184.505 * [misc]simplify: Simplified (2 2 1 1) to (λ (k n) (* (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (fma -1/2 (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) (fma (* (* (* k k) (log n)) (* (log (* PI 2)) 1/4)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (fma (* (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (log (* PI 2)) (log (* PI 2)))) (* (* k k) 1/8) (fma (* (* (* k k) (log n)) (* (log n) 1/8)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (pow n 1/2) (pow (* PI 2) 1/2)))))) (sqrt k))))) 1546856184.505 * * * * [misc]progress: [ 62 / 72 ] simplifiying candidate # 1546856184.505 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 1546856184.506 * * [misc]simplify: iters left: 6 (15 enodes) 1546856184.509 * * [misc]simplify: iters left: 5 (33 enodes) 1546856184.514 * * [misc]simplify: iters left: 4 (64 enodes) 1546856184.535 * * [misc]simplify: iters left: 3 (179 enodes) 1546856184.672 * [exit]simplify: Simplified to (* (pow (* 2 PI) (fma -1/2 k 1/2)) (pow n (fma -1/2 k 1/2))) 1546856184.672 * [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) (fma -1/2 k 1/2)) (pow n (fma -1/2 k 1/2))) (sqrt k))))) 1546856184.673 * * * * [misc]progress: [ 63 / 72 ] simplifiying candidate # 1546856184.673 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 1546856184.673 * * [misc]simplify: iters left: 6 (15 enodes) 1546856184.679 * * [misc]simplify: iters left: 5 (30 enodes) 1546856184.691 * * [misc]simplify: iters left: 4 (65 enodes) 1546856184.718 * * [misc]simplify: iters left: 3 (208 enodes) 1546856184.893 * [exit]simplify: Simplified to (pow (exp (fma -1/2 k 1/2)) (- (log (* -2 PI)) (log (/ -1 n)))) 1546856184.893 * [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 (fma -1/2 k 1/2)) (- (log (* -2 PI)) (log (/ -1 n)))) (sqrt k))))) 1546856184.893 * * * * [misc]progress: [ 64 / 72 ] simplifiying candidate # 1546856184.893 * [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))))) 1546856184.894 * * [misc]simplify: iters left: 6 (37 enodes) 1546856184.909 * * [misc]simplify: iters left: 5 (108 enodes) 1546856184.958 * * [misc]simplify: iters left: 4 (368 enodes) 1546856185.206 * [exit]simplify: Simplified to (fma -1/2 (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) (fma (* (* (* k k) (log n)) (* (log (* PI 2)) 1/4)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (fma (* (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (log (* PI 2)) (log (* PI 2)))) (* (* k k) 1/8) (fma (* (* (* k k) (log n)) (* (log n) 1/8)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (pow n 1/2) (pow (* PI 2) 1/2)))))) 1546856185.206 * [misc]simplify: Simplified (2 1 1 1) to (λ (k n) (* (sqrt (/ (fma -1/2 (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) (fma (* (* (* k k) (log n)) (* (log (* PI 2)) 1/4)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (fma (* (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (log (* PI 2)) (log (* PI 2)))) (* (* k k) 1/8) (fma (* (* (* k k) (log n)) (* (log n) 1/8)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (pow n 1/2) (pow (* PI 2) 1/2)))))) (sqrt k))) (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))))) 1546856185.206 * * * * [misc]progress: [ 65 / 72 ] simplifiying candidate # 1546856185.206 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 1546856185.206 * * [misc]simplify: iters left: 6 (15 enodes) 1546856185.209 * * [misc]simplify: iters left: 5 (33 enodes) 1546856185.215 * * [misc]simplify: iters left: 4 (64 enodes) 1546856185.228 * * [misc]simplify: iters left: 3 (179 enodes) 1546856185.347 * [exit]simplify: Simplified to (* (pow (* 2 PI) (fma -1/2 k 1/2)) (pow n (fma -1/2 k 1/2))) 1546856185.347 * [misc]simplify: Simplified (2 1 1 1) to (λ (k n) (* (sqrt (/ (* (pow (* 2 PI) (fma -1/2 k 1/2)) (pow n (fma -1/2 k 1/2))) (sqrt k))) (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))))) 1546856185.347 * * * * [misc]progress: [ 66 / 72 ] simplifiying candidate # 1546856185.347 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 1546856185.347 * * [misc]simplify: iters left: 6 (15 enodes) 1546856185.350 * * [misc]simplify: iters left: 5 (30 enodes) 1546856185.355 * * [misc]simplify: iters left: 4 (65 enodes) 1546856185.374 * * [misc]simplify: iters left: 3 (208 enodes) 1546856185.522 * [exit]simplify: Simplified to (pow (exp (fma -1/2 k 1/2)) (- (log (* -2 PI)) (log (/ -1 n)))) 1546856185.522 * [misc]simplify: Simplified (2 1 1 1) to (λ (k n) (* (sqrt (/ (pow (exp (fma -1/2 k 1/2)) (- (log (* -2 PI)) (log (/ -1 n)))) (sqrt k))) (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))))) 1546856185.522 * * * * [misc]progress: [ 67 / 72 ] simplifiying candidate # 1546856185.522 * [enter]simplify: Simplifying (* 2 (* n PI)) 1546856185.523 * * [misc]simplify: iters left: 4 (5 enodes) 1546856185.524 * * [misc]simplify: iters left: 3 (9 enodes) 1546856185.527 * * [misc]simplify: iters left: 2 (15 enodes) 1546856185.531 * * [misc]simplify: iters left: 1 (17 enodes) 1546856185.535 * [exit]simplify: Simplified to (* (* PI n) 2) 1546856185.535 * [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))))) 1546856185.535 * * * * [misc]progress: [ 68 / 72 ] simplifiying candidate # 1546856185.535 * [enter]simplify: Simplifying (* 2 (* n PI)) 1546856185.535 * * [misc]simplify: iters left: 4 (5 enodes) 1546856185.537 * * [misc]simplify: iters left: 3 (9 enodes) 1546856185.540 * * [misc]simplify: iters left: 2 (15 enodes) 1546856185.544 * * [misc]simplify: iters left: 1 (17 enodes) 1546856185.548 * [exit]simplify: Simplified to (* (* PI n) 2) 1546856185.548 * [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))))) 1546856185.548 * * * * [misc]progress: [ 69 / 72 ] simplifiying candidate # 1546856185.548 * [enter]simplify: Simplifying (* 2 (* n PI)) 1546856185.548 * * [misc]simplify: iters left: 4 (5 enodes) 1546856185.550 * * [misc]simplify: iters left: 3 (9 enodes) 1546856185.553 * * [misc]simplify: iters left: 2 (15 enodes) 1546856185.557 * * [misc]simplify: iters left: 1 (17 enodes) 1546856185.565 * [exit]simplify: Simplified to (* (* PI n) 2) 1546856185.565 * [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))))) 1546856185.565 * * * * [misc]progress: [ 70 / 72 ] simplifiying candidate # 1546856185.566 * [enter]simplify: Simplifying (* 2 (* n PI)) 1546856185.566 * * [misc]simplify: iters left: 4 (5 enodes) 1546856185.567 * * [misc]simplify: iters left: 3 (9 enodes) 1546856185.569 * * [misc]simplify: iters left: 2 (15 enodes) 1546856185.571 * * [misc]simplify: iters left: 1 (17 enodes) 1546856185.573 * [exit]simplify: Simplified to (* (* PI n) 2) 1546856185.573 * [misc]simplify: Simplified (2 1 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))))) 1546856185.573 * * * * [misc]progress: [ 71 / 72 ] simplifiying candidate # 1546856185.573 * [enter]simplify: Simplifying (* 2 (* n PI)) 1546856185.573 * * [misc]simplify: iters left: 4 (5 enodes) 1546856185.574 * * [misc]simplify: iters left: 3 (9 enodes) 1546856185.575 * * [misc]simplify: iters left: 2 (15 enodes) 1546856185.577 * * [misc]simplify: iters left: 1 (17 enodes) 1546856185.579 * [exit]simplify: Simplified to (* (* PI n) 2) 1546856185.579 * [misc]simplify: Simplified (2 1 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))))) 1546856185.579 * * * * [misc]progress: [ 72 / 72 ] simplifiying candidate # 1546856185.579 * [enter]simplify: Simplifying (* 2 (* n PI)) 1546856185.579 * * [misc]simplify: iters left: 4 (5 enodes) 1546856185.580 * * [misc]simplify: iters left: 3 (9 enodes) 1546856185.581 * * [misc]simplify: iters left: 2 (15 enodes) 1546856185.583 * * [misc]simplify: iters left: 1 (17 enodes) 1546856185.585 * [exit]simplify: Simplified to (* (* PI n) 2) 1546856185.585 * [misc]simplify: Simplified (2 1 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))))) 1546856185.586 * * * [misc]progress: adding candidates to table 1546856186.685 * [misc]progress: [Phase 3 of 3] Extracting. 1546856186.686 * * [misc]regime: Finding splitpoints for: (# # # # # # # #) 1546856186.688 * * * [misc]regime-changes: Trying 2 branch expressions: (n k) 1546856186.688 * * * * [misc]regimes: Trying to branch on n from (# # # # # # # #) 1546856186.785 * * * * [misc]regimes: Trying to branch on k from (# # # # # # # #) 1546856186.871 * * * [misc]regime: Found split indices: #