1547111147.835 * [misc]progress: [Phase 1 of 3] Setting up. 1547111147.836 * * * [misc]progress: [1/2] Preparing points 1547111147.836 * * * * [misc]points: Sampling 256 additional inputs, on iter 0 have 0 / 256 1547111147.894 * * * * [misc]points: Filtering points with unrepresentable outputs 1547111147.895 * * * * [misc]points: Sampling 192 additional inputs, on iter 1 have 64 / 256 1547111147.947 * * * * [misc]points: Filtering points with unrepresentable outputs 1547111147.948 * * * * [misc]points: Sampling 135 additional inputs, on iter 2 have 121 / 256 1547111147.984 * * * * [misc]points: Filtering points with unrepresentable outputs 1547111147.984 * * * * [misc]points: Sampling 106 additional inputs, on iter 3 have 150 / 256 1547111148.011 * * * * [misc]points: Filtering points with unrepresentable outputs 1547111148.012 * * * * [misc]points: Sampling 74 additional inputs, on iter 4 have 182 / 256 1547111148.024 * * * * [misc]points: Filtering points with unrepresentable outputs 1547111148.025 * * * * [misc]points: Sampling 57 additional inputs, on iter 5 have 199 / 256 1547111148.035 * * * * [misc]points: Filtering points with unrepresentable outputs 1547111148.035 * * * * [misc]points: Sampling 48 additional inputs, on iter 6 have 208 / 256 1547111148.044 * * * * [misc]points: Filtering points with unrepresentable outputs 1547111148.044 * * * * [misc]points: Sampling 34 additional inputs, on iter 7 have 222 / 256 1547111148.071 * * * * [misc]points: Filtering points with unrepresentable outputs 1547111148.071 * * * * [misc]points: Sampling 27 additional inputs, on iter 8 have 229 / 256 1547111148.077 * * * * [misc]points: Filtering points with unrepresentable outputs 1547111148.077 * * * * [misc]points: Sampling 21 additional inputs, on iter 9 have 235 / 256 1547111148.083 * * * * [misc]points: Filtering points with unrepresentable outputs 1547111148.083 * * * * [misc]points: Sampling 16 additional inputs, on iter 10 have 240 / 256 1547111148.090 * * * * [misc]points: Filtering points with unrepresentable outputs 1547111148.090 * * * * [misc]points: Sampling 14 additional inputs, on iter 11 have 242 / 256 1547111148.095 * * * * [misc]points: Filtering points with unrepresentable outputs 1547111148.095 * * * * [misc]points: Sampling 12 additional inputs, on iter 12 have 244 / 256 1547111148.100 * * * * [misc]points: Filtering points with unrepresentable outputs 1547111148.100 * * * * [misc]points: Sampling 11 additional inputs, on iter 13 have 245 / 256 1547111148.106 * * * * [misc]points: Filtering points with unrepresentable outputs 1547111148.106 * * * * [misc]points: Sampling 9 additional inputs, on iter 14 have 247 / 256 1547111148.114 * * * * [misc]points: Filtering points with unrepresentable outputs 1547111148.114 * * * * [misc]points: Sampling 7 additional inputs, on iter 15 have 249 / 256 1547111148.122 * * * * [misc]points: Filtering points with unrepresentable outputs 1547111148.122 * * * * [misc]points: Sampling 6 additional inputs, on iter 16 have 250 / 256 1547111148.130 * * * * [misc]points: Filtering points with unrepresentable outputs 1547111148.130 * * * * [misc]points: Sampling 6 additional inputs, on iter 17 have 250 / 256 1547111148.137 * * * * [misc]points: Filtering points with unrepresentable outputs 1547111148.137 * * * * [misc]points: Sampling 5 additional inputs, on iter 18 have 251 / 256 1547111148.145 * * * * [misc]points: Filtering points with unrepresentable outputs 1547111148.145 * * * * [misc]points: Sampling 4 additional inputs, on iter 19 have 252 / 256 1547111148.152 * * * * [misc]points: Filtering points with unrepresentable outputs 1547111148.152 * * * * [misc]points: Sampling 4 additional inputs, on iter 20 have 252 / 256 1547111148.159 * * * * [misc]points: Filtering points with unrepresentable outputs 1547111148.159 * * * * [misc]points: Sampling 4 additional inputs, on iter 21 have 252 / 256 1547111148.166 * * * * [misc]points: Filtering points with unrepresentable outputs 1547111148.166 * * * * [misc]points: Sampling 4 additional inputs, on iter 22 have 253 / 256 1547111148.173 * * * * [misc]points: Filtering points with unrepresentable outputs 1547111148.173 * * * * [misc]points: Sampling 4 additional inputs, on iter 23 have 254 / 256 1547111148.180 * * * * [misc]points: Filtering points with unrepresentable outputs 1547111148.180 * * * * [misc]points: Sampling 4 additional inputs, on iter 24 have 254 / 256 1547111148.187 * * * * [misc]points: Filtering points with unrepresentable outputs 1547111148.187 * * * * [exit]points: Sampled 256 points with exact outputs 1547111148.187 * * * [misc]progress: [2/2] Setting up program. 1547111148.193 * [misc]progress: [Phase 2 of 3] Improving. 1547111148.193 * * * * [misc]progress: [ 1 / 1 ] simplifiying candidate # 1547111148.194 * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) 1547111148.194 * * [misc]simplify: iters left: 6 (13 enodes) 1547111148.199 * * [misc]simplify: iters left: 5 (28 enodes) 1547111148.206 * * [misc]simplify: iters left: 4 (44 enodes) 1547111148.245 * * [misc]simplify: iters left: 3 (54 enodes) 1547111148.257 * * [misc]simplify: iters left: 2 (57 enodes) 1547111148.268 * * [misc]simplify: iters left: 1 (65 enodes) 1547111148.283 * [exit]simplify: Simplified to (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)) 1547111148.283 * [misc]simplify: Simplified (2) to (λ (k n) (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) 1547111148.296 * * [misc]progress: iteration 1 / 4 1547111148.296 * * * [misc]progress: picking best candidate 1547111148.306 * * * * [misc]pick: Picked # 1547111148.307 * * * [misc]progress: localizing error 1547111148.339 * * * [misc]progress: generating rewritten candidates 1547111148.339 * * * * [misc]progress: [ 1 / 3 ] rewriting at (2 1) 1547111148.341 * * * * [misc]progress: [ 2 / 3 ] rewriting at (2 1 1) 1547111148.342 * * * * [misc]progress: [ 3 / 3 ] rewriting at (2) 1547111148.347 * * * [misc]progress: generating series expansions 1547111148.347 * * * * [misc]progress: [ 1 / 3 ] generating series at (2 1) 1547111148.347 * [misc]backup-simplify: Simplify (pow (* PI (* n 2)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 1547111148.347 * [misc]approximate: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 1547111148.347 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1547111148.348 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1547111148.348 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1547111148.348 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1547111148.348 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111148.348 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111148.348 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1547111148.348 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111148.348 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111148.348 * [misc]taylor: Taking taylor expansion of k in k 1547111148.348 * [misc]backup-simplify: Simplify 0 into 0 1547111148.348 * [misc]backup-simplify: Simplify 1 into 1 1547111148.348 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1547111148.348 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1547111148.348 * [misc]taylor: Taking taylor expansion of 2 in k 1547111148.348 * [misc]backup-simplify: Simplify 2 into 2 1547111148.348 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1547111148.348 * [misc]taylor: Taking taylor expansion of n in k 1547111148.348 * [misc]backup-simplify: Simplify n into n 1547111148.348 * [misc]taylor: Taking taylor expansion of PI in k 1547111148.348 * [misc]backup-simplify: Simplify PI into PI 1547111148.348 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1547111148.348 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1547111148.348 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1547111148.348 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1547111148.348 * [misc]backup-simplify: Simplify (- 0) into 0 1547111148.348 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1547111148.348 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1547111148.349 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1547111148.349 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1547111148.349 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1547111148.349 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1547111148.349 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1547111148.349 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111148.349 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111148.349 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1547111148.349 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111148.349 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111148.349 * [misc]taylor: Taking taylor expansion of k in n 1547111148.349 * [misc]backup-simplify: Simplify k into k 1547111148.349 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1547111148.349 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1547111148.349 * [misc]taylor: Taking taylor expansion of 2 in n 1547111148.349 * [misc]backup-simplify: Simplify 2 into 2 1547111148.349 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547111148.349 * [misc]taylor: Taking taylor expansion of n in n 1547111148.349 * [misc]backup-simplify: Simplify 0 into 0 1547111148.349 * [misc]backup-simplify: Simplify 1 into 1 1547111148.349 * [misc]taylor: Taking taylor expansion of PI in n 1547111148.349 * [misc]backup-simplify: Simplify PI into PI 1547111148.349 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547111148.349 * [misc]backup-simplify: Simplify (* 2 0) into 0 1547111148.354 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547111148.355 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1547111148.355 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547111148.355 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1547111148.355 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1547111148.355 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1547111148.356 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547111148.356 * [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)))) 1547111148.356 * [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))))) 1547111148.356 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1547111148.356 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1547111148.356 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1547111148.357 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1547111148.357 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111148.357 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111148.357 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1547111148.357 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111148.357 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111148.357 * [misc]taylor: Taking taylor expansion of k in n 1547111148.357 * [misc]backup-simplify: Simplify k into k 1547111148.357 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1547111148.357 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1547111148.357 * [misc]taylor: Taking taylor expansion of 2 in n 1547111148.357 * [misc]backup-simplify: Simplify 2 into 2 1547111148.357 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547111148.357 * [misc]taylor: Taking taylor expansion of n in n 1547111148.357 * [misc]backup-simplify: Simplify 0 into 0 1547111148.357 * [misc]backup-simplify: Simplify 1 into 1 1547111148.357 * [misc]taylor: Taking taylor expansion of PI in n 1547111148.357 * [misc]backup-simplify: Simplify PI into PI 1547111148.357 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547111148.357 * [misc]backup-simplify: Simplify (* 2 0) into 0 1547111148.358 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547111148.358 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1547111148.358 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547111148.358 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1547111148.358 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1547111148.358 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1547111148.359 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547111148.359 * [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)))) 1547111148.360 * [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))))) 1547111148.360 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1547111148.360 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1547111148.360 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1547111148.360 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111148.360 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111148.360 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1547111148.360 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111148.360 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111148.360 * [misc]taylor: Taking taylor expansion of k in k 1547111148.360 * [misc]backup-simplify: Simplify 0 into 0 1547111148.360 * [misc]backup-simplify: Simplify 1 into 1 1547111148.360 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1547111148.360 * [misc]taylor: Taking taylor expansion of (log n) in k 1547111148.360 * [misc]taylor: Taking taylor expansion of n in k 1547111148.360 * [misc]backup-simplify: Simplify n into n 1547111148.360 * [misc]backup-simplify: Simplify (log n) into (log n) 1547111148.360 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1547111148.360 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1547111148.360 * [misc]taylor: Taking taylor expansion of 2 in k 1547111148.360 * [misc]backup-simplify: Simplify 2 into 2 1547111148.360 * [misc]taylor: Taking taylor expansion of PI in k 1547111148.360 * [misc]backup-simplify: Simplify PI into PI 1547111148.360 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547111148.360 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547111148.361 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1547111148.361 * [misc]backup-simplify: Simplify (- 0) into 0 1547111148.361 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1547111148.361 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547111148.361 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1547111148.362 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1547111148.362 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1547111148.363 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1547111148.363 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1547111148.365 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1547111148.365 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1547111148.365 * [misc]backup-simplify: Simplify (- 0) into 0 1547111148.365 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111148.366 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547111148.366 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1547111148.367 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1547111148.367 * [misc]taylor: Taking taylor expansion of 0 in k 1547111148.367 * [misc]backup-simplify: Simplify 0 into 0 1547111148.367 * [misc]backup-simplify: Simplify 0 into 0 1547111148.368 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1547111148.368 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1547111148.370 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1547111148.370 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111148.370 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1547111148.370 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1547111148.370 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1547111148.371 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1547111148.371 * [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))))))) 1547111148.372 * [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))))))) 1547111148.373 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1547111148.374 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1547111148.377 * [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 1547111148.377 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1547111148.377 * [misc]backup-simplify: Simplify (- 0) into 0 1547111148.377 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111148.378 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547111148.378 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1547111148.380 * [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 1547111148.380 * [misc]taylor: Taking taylor expansion of 0 in k 1547111148.380 * [misc]backup-simplify: Simplify 0 into 0 1547111148.380 * [misc]backup-simplify: Simplify 0 into 0 1547111148.380 * [misc]backup-simplify: Simplify 0 into 0 1547111148.381 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1547111148.381 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1547111148.384 * [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 1547111148.384 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111148.384 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1547111148.384 * [misc]backup-simplify: Simplify (- 0) into 0 1547111148.385 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111148.385 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1547111148.386 * [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))))) 1547111148.388 * [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))))) 1547111148.391 * [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))))) 1547111148.391 * [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)))) 1547111148.391 * [misc]approximate: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 1547111148.391 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1547111148.391 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1547111148.391 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1547111148.391 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1547111148.391 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111148.391 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111148.391 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1547111148.392 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111148.392 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111148.392 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547111148.392 * [misc]taylor: Taking taylor expansion of k in k 1547111148.392 * [misc]backup-simplify: Simplify 0 into 0 1547111148.392 * [misc]backup-simplify: Simplify 1 into 1 1547111148.392 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547111148.392 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1547111148.392 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1547111148.392 * [misc]taylor: Taking taylor expansion of 2 in k 1547111148.392 * [misc]backup-simplify: Simplify 2 into 2 1547111148.392 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1547111148.392 * [misc]taylor: Taking taylor expansion of PI in k 1547111148.392 * [misc]backup-simplify: Simplify PI into PI 1547111148.392 * [misc]taylor: Taking taylor expansion of n in k 1547111148.392 * [misc]backup-simplify: Simplify n into n 1547111148.392 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1547111148.392 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1547111148.392 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1547111148.392 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1547111148.392 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1547111148.392 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1547111148.392 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1547111148.393 * [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)))) 1547111148.393 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1547111148.393 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1547111148.393 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1547111148.393 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1547111148.393 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111148.393 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111148.393 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1547111148.393 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111148.393 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111148.393 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547111148.393 * [misc]taylor: Taking taylor expansion of k in n 1547111148.393 * [misc]backup-simplify: Simplify k into k 1547111148.393 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547111148.393 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1547111148.393 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1547111148.393 * [misc]taylor: Taking taylor expansion of 2 in n 1547111148.393 * [misc]backup-simplify: Simplify 2 into 2 1547111148.393 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547111148.393 * [misc]taylor: Taking taylor expansion of PI in n 1547111148.393 * [misc]backup-simplify: Simplify PI into PI 1547111148.393 * [misc]taylor: Taking taylor expansion of n in n 1547111148.393 * [misc]backup-simplify: Simplify 0 into 0 1547111148.393 * [misc]backup-simplify: Simplify 1 into 1 1547111148.393 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547111148.393 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547111148.394 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547111148.394 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1547111148.394 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1547111148.394 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1547111148.394 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547111148.395 * [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))) 1547111148.395 * [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)))) 1547111148.395 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1547111148.395 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1547111148.395 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1547111148.395 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1547111148.395 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111148.395 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111148.395 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1547111148.395 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111148.395 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111148.395 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547111148.395 * [misc]taylor: Taking taylor expansion of k in n 1547111148.395 * [misc]backup-simplify: Simplify k into k 1547111148.395 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547111148.395 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1547111148.395 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1547111148.395 * [misc]taylor: Taking taylor expansion of 2 in n 1547111148.395 * [misc]backup-simplify: Simplify 2 into 2 1547111148.395 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547111148.395 * [misc]taylor: Taking taylor expansion of PI in n 1547111148.395 * [misc]backup-simplify: Simplify PI into PI 1547111148.395 * [misc]taylor: Taking taylor expansion of n in n 1547111148.395 * [misc]backup-simplify: Simplify 0 into 0 1547111148.395 * [misc]backup-simplify: Simplify 1 into 1 1547111148.396 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547111148.396 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547111148.396 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547111148.396 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1547111148.396 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1547111148.396 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1547111148.397 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547111148.397 * [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))) 1547111148.397 * [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)))) 1547111148.397 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1547111148.397 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1547111148.398 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1547111148.398 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111148.398 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111148.398 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1547111148.398 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111148.398 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111148.398 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547111148.398 * [misc]taylor: Taking taylor expansion of k in k 1547111148.398 * [misc]backup-simplify: Simplify 0 into 0 1547111148.398 * [misc]backup-simplify: Simplify 1 into 1 1547111148.398 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547111148.398 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1547111148.398 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1547111148.398 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1547111148.398 * [misc]taylor: Taking taylor expansion of 2 in k 1547111148.398 * [misc]backup-simplify: Simplify 2 into 2 1547111148.398 * [misc]taylor: Taking taylor expansion of PI in k 1547111148.398 * [misc]backup-simplify: Simplify PI into PI 1547111148.398 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547111148.398 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547111148.398 * [misc]taylor: Taking taylor expansion of (log n) in k 1547111148.398 * [misc]taylor: Taking taylor expansion of n in k 1547111148.398 * [misc]backup-simplify: Simplify n into n 1547111148.398 * [misc]backup-simplify: Simplify (log n) into (log n) 1547111148.399 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1547111148.399 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1547111148.399 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1547111148.399 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1547111148.399 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1547111148.399 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1547111148.400 * [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)))) 1547111148.400 * [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)))) 1547111148.401 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1547111148.401 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1547111148.403 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1547111148.403 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1547111148.403 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1547111148.403 * [misc]backup-simplify: Simplify (- 0) into 0 1547111148.403 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111148.404 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547111148.404 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1547111148.405 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1547111148.405 * [misc]taylor: Taking taylor expansion of 0 in k 1547111148.405 * [misc]backup-simplify: Simplify 0 into 0 1547111148.405 * [misc]backup-simplify: Simplify 0 into 0 1547111148.405 * [misc]backup-simplify: Simplify 0 into 0 1547111148.406 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111148.407 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1547111148.410 * [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 1547111148.410 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1547111148.410 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1547111148.410 * [misc]backup-simplify: Simplify (- 0) into 0 1547111148.410 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111148.411 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547111148.411 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1547111148.412 * [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 1547111148.413 * [misc]taylor: Taking taylor expansion of 0 in k 1547111148.413 * [misc]backup-simplify: Simplify 0 into 0 1547111148.413 * [misc]backup-simplify: Simplify 0 into 0 1547111148.413 * [misc]backup-simplify: Simplify 0 into 0 1547111148.413 * [misc]backup-simplify: Simplify 0 into 0 1547111148.414 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111148.415 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1547111148.422 * [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 1547111148.423 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1547111148.423 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1547111148.423 * [misc]backup-simplify: Simplify (- 0) into 0 1547111148.424 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111148.424 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547111148.425 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1547111148.429 * [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 1547111148.429 * [misc]taylor: Taking taylor expansion of 0 in k 1547111148.429 * [misc]backup-simplify: Simplify 0 into 0 1547111148.429 * [misc]backup-simplify: Simplify 0 into 0 1547111148.430 * [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))))) 1547111148.430 * [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)) 1547111148.430 * [misc]approximate: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 1547111148.430 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1547111148.430 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1547111148.430 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1547111148.430 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1547111148.430 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1547111148.430 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111148.430 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111148.430 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547111148.430 * [misc]taylor: Taking taylor expansion of k in k 1547111148.430 * [misc]backup-simplify: Simplify 0 into 0 1547111148.430 * [misc]backup-simplify: Simplify 1 into 1 1547111148.430 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547111148.430 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111148.430 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111148.431 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1547111148.431 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1547111148.431 * [misc]taylor: Taking taylor expansion of -2 in k 1547111148.431 * [misc]backup-simplify: Simplify -2 into -2 1547111148.431 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1547111148.431 * [misc]taylor: Taking taylor expansion of PI in k 1547111148.431 * [misc]backup-simplify: Simplify PI into PI 1547111148.431 * [misc]taylor: Taking taylor expansion of n in k 1547111148.431 * [misc]backup-simplify: Simplify n into n 1547111148.431 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1547111148.431 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1547111148.431 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1547111148.431 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1547111148.431 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1547111148.431 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1547111148.432 * [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))) 1547111148.432 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1547111148.432 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1547111148.432 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1547111148.432 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1547111148.432 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1547111148.432 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111148.432 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111148.432 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547111148.432 * [misc]taylor: Taking taylor expansion of k in n 1547111148.432 * [misc]backup-simplify: Simplify k into k 1547111148.432 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547111148.432 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111148.432 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111148.432 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1547111148.432 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1547111148.432 * [misc]taylor: Taking taylor expansion of -2 in n 1547111148.432 * [misc]backup-simplify: Simplify -2 into -2 1547111148.432 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547111148.432 * [misc]taylor: Taking taylor expansion of PI in n 1547111148.432 * [misc]backup-simplify: Simplify PI into PI 1547111148.432 * [misc]taylor: Taking taylor expansion of n in n 1547111148.432 * [misc]backup-simplify: Simplify 0 into 0 1547111148.432 * [misc]backup-simplify: Simplify 1 into 1 1547111148.433 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547111148.433 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547111148.433 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1547111148.433 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1547111148.434 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1547111148.434 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547111148.435 * [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))) 1547111148.435 * [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)))) 1547111148.435 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1547111148.435 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1547111148.436 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1547111148.436 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1547111148.436 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1547111148.436 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111148.436 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111148.436 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547111148.436 * [misc]taylor: Taking taylor expansion of k in n 1547111148.436 * [misc]backup-simplify: Simplify k into k 1547111148.436 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547111148.436 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111148.436 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111148.436 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1547111148.436 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1547111148.436 * [misc]taylor: Taking taylor expansion of -2 in n 1547111148.436 * [misc]backup-simplify: Simplify -2 into -2 1547111148.436 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547111148.436 * [misc]taylor: Taking taylor expansion of PI in n 1547111148.436 * [misc]backup-simplify: Simplify PI into PI 1547111148.436 * [misc]taylor: Taking taylor expansion of n in n 1547111148.436 * [misc]backup-simplify: Simplify 0 into 0 1547111148.436 * [misc]backup-simplify: Simplify 1 into 1 1547111148.436 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547111148.437 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547111148.437 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1547111148.437 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1547111148.437 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1547111148.438 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547111148.438 * [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))) 1547111148.439 * [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)))) 1547111148.439 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1547111148.439 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1547111148.439 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1547111148.439 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1547111148.439 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111148.439 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111148.439 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547111148.439 * [misc]taylor: Taking taylor expansion of k in k 1547111148.439 * [misc]backup-simplify: Simplify 0 into 0 1547111148.439 * [misc]backup-simplify: Simplify 1 into 1 1547111148.440 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547111148.440 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111148.440 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111148.440 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1547111148.440 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1547111148.440 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1547111148.440 * [misc]taylor: Taking taylor expansion of -2 in k 1547111148.440 * [misc]backup-simplify: Simplify -2 into -2 1547111148.440 * [misc]taylor: Taking taylor expansion of PI in k 1547111148.440 * [misc]backup-simplify: Simplify PI into PI 1547111148.440 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547111148.441 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1547111148.441 * [misc]taylor: Taking taylor expansion of (log n) in k 1547111148.441 * [misc]taylor: Taking taylor expansion of n in k 1547111148.441 * [misc]backup-simplify: Simplify n into n 1547111148.441 * [misc]backup-simplify: Simplify (log n) into (log n) 1547111148.441 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1547111148.441 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1547111148.441 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1547111148.442 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1547111148.442 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1547111148.443 * [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)))) 1547111148.443 * [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)))) 1547111148.444 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1547111148.445 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1547111148.448 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1547111148.448 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1547111148.448 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1547111148.448 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111148.449 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547111148.450 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1547111148.451 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1547111148.451 * [misc]taylor: Taking taylor expansion of 0 in k 1547111148.451 * [misc]backup-simplify: Simplify 0 into 0 1547111148.451 * [misc]backup-simplify: Simplify 0 into 0 1547111148.451 * [misc]backup-simplify: Simplify 0 into 0 1547111148.453 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111148.454 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1547111148.459 * [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 1547111148.460 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1547111148.460 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1547111148.460 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111148.461 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547111148.462 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1547111148.464 * [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 1547111148.464 * [misc]taylor: Taking taylor expansion of 0 in k 1547111148.464 * [misc]backup-simplify: Simplify 0 into 0 1547111148.464 * [misc]backup-simplify: Simplify 0 into 0 1547111148.464 * [misc]backup-simplify: Simplify 0 into 0 1547111148.464 * [misc]backup-simplify: Simplify 0 into 0 1547111148.466 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111148.468 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1547111148.475 * [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 1547111148.475 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1547111148.476 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1547111148.476 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111148.477 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547111148.478 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 1547111148.483 * [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 1547111148.483 * [misc]taylor: Taking taylor expansion of 0 in k 1547111148.483 * [misc]backup-simplify: Simplify 0 into 0 1547111148.483 * [misc]backup-simplify: Simplify 0 into 0 1547111148.484 * [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))))) 1547111148.484 * * * * [misc]progress: [ 2 / 3 ] generating series at (2 1 1) 1547111148.484 * [misc]backup-simplify: Simplify (* PI (* n 2)) into (* 2 (* n PI)) 1547111148.484 * [misc]approximate: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1547111148.484 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1547111148.484 * [misc]taylor: Taking taylor expansion of 2 in n 1547111148.484 * [misc]backup-simplify: Simplify 2 into 2 1547111148.484 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547111148.484 * [misc]taylor: Taking taylor expansion of n in n 1547111148.484 * [misc]backup-simplify: Simplify 0 into 0 1547111148.484 * [misc]backup-simplify: Simplify 1 into 1 1547111148.484 * [misc]taylor: Taking taylor expansion of PI in n 1547111148.484 * [misc]backup-simplify: Simplify PI into PI 1547111148.484 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1547111148.484 * [misc]taylor: Taking taylor expansion of 2 in n 1547111148.484 * [misc]backup-simplify: Simplify 2 into 2 1547111148.485 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547111148.485 * [misc]taylor: Taking taylor expansion of n in n 1547111148.485 * [misc]backup-simplify: Simplify 0 into 0 1547111148.485 * [misc]backup-simplify: Simplify 1 into 1 1547111148.485 * [misc]taylor: Taking taylor expansion of PI in n 1547111148.485 * [misc]backup-simplify: Simplify PI into PI 1547111148.485 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547111148.485 * [misc]backup-simplify: Simplify (* 2 0) into 0 1547111148.485 * [misc]backup-simplify: Simplify 0 into 0 1547111148.486 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547111148.487 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1547111148.487 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547111148.488 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1547111148.489 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1547111148.489 * [misc]backup-simplify: Simplify 0 into 0 1547111148.490 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1547111148.492 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1547111148.492 * [misc]backup-simplify: Simplify 0 into 0 1547111148.494 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1547111148.496 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1547111148.496 * [misc]backup-simplify: Simplify 0 into 0 1547111148.499 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1547111148.501 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1547111148.501 * [misc]backup-simplify: Simplify 0 into 0 1547111148.504 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1547111148.508 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1547111148.508 * [misc]backup-simplify: Simplify 0 into 0 1547111148.512 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1547111148.516 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1547111148.517 * [misc]backup-simplify: Simplify 0 into 0 1547111148.517 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1547111148.517 * [misc]backup-simplify: Simplify (* PI (* (/ 1 n) 2)) into (* 2 (/ PI n)) 1547111148.517 * [misc]approximate: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1547111148.517 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1547111148.517 * [misc]taylor: Taking taylor expansion of 2 in n 1547111148.517 * [misc]backup-simplify: Simplify 2 into 2 1547111148.517 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547111148.517 * [misc]taylor: Taking taylor expansion of PI in n 1547111148.517 * [misc]backup-simplify: Simplify PI into PI 1547111148.517 * [misc]taylor: Taking taylor expansion of n in n 1547111148.517 * [misc]backup-simplify: Simplify 0 into 0 1547111148.517 * [misc]backup-simplify: Simplify 1 into 1 1547111148.518 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547111148.518 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1547111148.518 * [misc]taylor: Taking taylor expansion of 2 in n 1547111148.518 * [misc]backup-simplify: Simplify 2 into 2 1547111148.518 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547111148.518 * [misc]taylor: Taking taylor expansion of PI in n 1547111148.518 * [misc]backup-simplify: Simplify PI into PI 1547111148.518 * [misc]taylor: Taking taylor expansion of n in n 1547111148.518 * [misc]backup-simplify: Simplify 0 into 0 1547111148.518 * [misc]backup-simplify: Simplify 1 into 1 1547111148.518 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547111148.519 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547111148.519 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547111148.520 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1547111148.521 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1547111148.521 * [misc]backup-simplify: Simplify 0 into 0 1547111148.522 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111148.523 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1547111148.523 * [misc]backup-simplify: Simplify 0 into 0 1547111148.525 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111148.526 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1547111148.526 * [misc]backup-simplify: Simplify 0 into 0 1547111148.528 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111148.530 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1547111148.530 * [misc]backup-simplify: Simplify 0 into 0 1547111148.532 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111148.535 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1547111148.535 * [misc]backup-simplify: Simplify 0 into 0 1547111148.537 * [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 1547111148.541 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1547111148.541 * [misc]backup-simplify: Simplify 0 into 0 1547111148.541 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 1547111148.541 * [misc]backup-simplify: Simplify (* PI (* (/ 1 (- n)) 2)) into (* -2 (/ PI n)) 1547111148.541 * [misc]approximate: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1547111148.541 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1547111148.541 * [misc]taylor: Taking taylor expansion of -2 in n 1547111148.542 * [misc]backup-simplify: Simplify -2 into -2 1547111148.542 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547111148.542 * [misc]taylor: Taking taylor expansion of PI in n 1547111148.542 * [misc]backup-simplify: Simplify PI into PI 1547111148.542 * [misc]taylor: Taking taylor expansion of n in n 1547111148.542 * [misc]backup-simplify: Simplify 0 into 0 1547111148.542 * [misc]backup-simplify: Simplify 1 into 1 1547111148.542 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547111148.542 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1547111148.542 * [misc]taylor: Taking taylor expansion of -2 in n 1547111148.542 * [misc]backup-simplify: Simplify -2 into -2 1547111148.542 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547111148.542 * [misc]taylor: Taking taylor expansion of PI in n 1547111148.542 * [misc]backup-simplify: Simplify PI into PI 1547111148.542 * [misc]taylor: Taking taylor expansion of n in n 1547111148.542 * [misc]backup-simplify: Simplify 0 into 0 1547111148.542 * [misc]backup-simplify: Simplify 1 into 1 1547111148.542 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547111148.543 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547111148.543 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547111148.544 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1547111148.545 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1547111148.545 * [misc]backup-simplify: Simplify 0 into 0 1547111148.546 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111148.547 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1547111148.547 * [misc]backup-simplify: Simplify 0 into 0 1547111148.548 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111148.549 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1547111148.549 * [misc]backup-simplify: Simplify 0 into 0 1547111148.550 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111148.551 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1547111148.551 * [misc]backup-simplify: Simplify 0 into 0 1547111148.553 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111148.554 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1547111148.554 * [misc]backup-simplify: Simplify 0 into 0 1547111148.555 * [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 1547111148.557 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1547111148.557 * [misc]backup-simplify: Simplify 0 into 0 1547111148.557 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 1547111148.558 * * * * [misc]progress: [ 3 / 3 ] generating series at (2) 1547111148.558 * [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)))) 1547111148.558 * [misc]approximate: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (n k) around 0 1547111148.558 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 1547111148.558 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1547111148.558 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547111148.558 * [misc]taylor: Taking taylor expansion of k in k 1547111148.558 * [misc]backup-simplify: Simplify 0 into 0 1547111148.558 * [misc]backup-simplify: Simplify 1 into 1 1547111148.558 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547111148.558 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547111148.558 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1547111148.559 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1547111148.559 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1547111148.559 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1547111148.559 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1547111148.559 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111148.559 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111148.559 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1547111148.559 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111148.559 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111148.559 * [misc]taylor: Taking taylor expansion of k in k 1547111148.559 * [misc]backup-simplify: Simplify 0 into 0 1547111148.559 * [misc]backup-simplify: Simplify 1 into 1 1547111148.559 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1547111148.559 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1547111148.559 * [misc]taylor: Taking taylor expansion of 2 in k 1547111148.559 * [misc]backup-simplify: Simplify 2 into 2 1547111148.559 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1547111148.559 * [misc]taylor: Taking taylor expansion of n in k 1547111148.559 * [misc]backup-simplify: Simplify n into n 1547111148.559 * [misc]taylor: Taking taylor expansion of PI in k 1547111148.559 * [misc]backup-simplify: Simplify PI into PI 1547111148.559 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1547111148.559 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1547111148.559 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1547111148.559 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1547111148.559 * [misc]backup-simplify: Simplify (- 0) into 0 1547111148.559 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1547111148.559 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1547111148.559 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1547111148.559 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 1547111148.559 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1547111148.559 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547111148.559 * [misc]taylor: Taking taylor expansion of k in n 1547111148.560 * [misc]backup-simplify: Simplify k into k 1547111148.560 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547111148.560 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1547111148.560 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1547111148.560 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1547111148.560 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1547111148.560 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1547111148.560 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1547111148.560 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1547111148.560 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111148.560 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111148.560 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1547111148.560 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111148.560 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111148.560 * [misc]taylor: Taking taylor expansion of k in n 1547111148.560 * [misc]backup-simplify: Simplify k into k 1547111148.560 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1547111148.560 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1547111148.560 * [misc]taylor: Taking taylor expansion of 2 in n 1547111148.560 * [misc]backup-simplify: Simplify 2 into 2 1547111148.560 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547111148.560 * [misc]taylor: Taking taylor expansion of n in n 1547111148.560 * [misc]backup-simplify: Simplify 0 into 0 1547111148.560 * [misc]backup-simplify: Simplify 1 into 1 1547111148.560 * [misc]taylor: Taking taylor expansion of PI in n 1547111148.560 * [misc]backup-simplify: Simplify PI into PI 1547111148.560 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547111148.560 * [misc]backup-simplify: Simplify (* 2 0) into 0 1547111148.561 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547111148.561 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1547111148.561 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547111148.561 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1547111148.561 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1547111148.562 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1547111148.562 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547111148.562 * [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)))) 1547111148.563 * [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))))) 1547111148.563 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 1547111148.563 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1547111148.563 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547111148.563 * [misc]taylor: Taking taylor expansion of k in n 1547111148.563 * [misc]backup-simplify: Simplify k into k 1547111148.563 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547111148.563 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1547111148.563 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1547111148.563 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1547111148.563 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1547111148.563 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1547111148.563 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1547111148.563 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1547111148.563 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111148.563 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111148.563 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1547111148.563 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111148.563 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111148.563 * [misc]taylor: Taking taylor expansion of k in n 1547111148.563 * [misc]backup-simplify: Simplify k into k 1547111148.563 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1547111148.563 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1547111148.563 * [misc]taylor: Taking taylor expansion of 2 in n 1547111148.563 * [misc]backup-simplify: Simplify 2 into 2 1547111148.563 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547111148.563 * [misc]taylor: Taking taylor expansion of n in n 1547111148.563 * [misc]backup-simplify: Simplify 0 into 0 1547111148.563 * [misc]backup-simplify: Simplify 1 into 1 1547111148.563 * [misc]taylor: Taking taylor expansion of PI in n 1547111148.563 * [misc]backup-simplify: Simplify PI into PI 1547111148.563 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547111148.564 * [misc]backup-simplify: Simplify (* 2 0) into 0 1547111148.564 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547111148.564 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1547111148.565 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547111148.565 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1547111148.565 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1547111148.565 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1547111148.565 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547111148.566 * [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)))) 1547111148.566 * [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))))) 1547111148.566 * [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))) 1547111148.566 * [misc]taylor: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k))) in k 1547111148.566 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1547111148.566 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1547111148.566 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1547111148.566 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111148.567 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111148.567 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1547111148.567 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111148.567 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111148.567 * [misc]taylor: Taking taylor expansion of k in k 1547111148.567 * [misc]backup-simplify: Simplify 0 into 0 1547111148.567 * [misc]backup-simplify: Simplify 1 into 1 1547111148.567 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1547111148.567 * [misc]taylor: Taking taylor expansion of (log n) in k 1547111148.567 * [misc]taylor: Taking taylor expansion of n in k 1547111148.567 * [misc]backup-simplify: Simplify n into n 1547111148.567 * [misc]backup-simplify: Simplify (log n) into (log n) 1547111148.567 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1547111148.567 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1547111148.567 * [misc]taylor: Taking taylor expansion of 2 in k 1547111148.567 * [misc]backup-simplify: Simplify 2 into 2 1547111148.567 * [misc]taylor: Taking taylor expansion of PI in k 1547111148.567 * [misc]backup-simplify: Simplify PI into PI 1547111148.567 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547111148.567 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547111148.567 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1547111148.567 * [misc]backup-simplify: Simplify (- 0) into 0 1547111148.568 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1547111148.568 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547111148.568 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1547111148.569 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1547111148.569 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1547111148.569 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547111148.569 * [misc]taylor: Taking taylor expansion of k in k 1547111148.569 * [misc]backup-simplify: Simplify 0 into 0 1547111148.569 * [misc]backup-simplify: Simplify 1 into 1 1547111148.569 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547111148.569 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547111148.569 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1547111148.570 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) into 0 1547111148.570 * [misc]backup-simplify: Simplify 0 into 0 1547111148.571 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1547111148.571 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1547111148.573 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1547111148.573 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1547111148.573 * [misc]backup-simplify: Simplify (- 0) into 0 1547111148.573 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111148.574 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547111148.574 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1547111148.575 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1547111148.576 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 k)) 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))) into 0 1547111148.576 * [misc]taylor: Taking taylor expansion of 0 in k 1547111148.576 * [misc]backup-simplify: Simplify 0 into 0 1547111148.576 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1547111148.576 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1547111148.578 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1547111148.578 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111148.578 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1547111148.578 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1547111148.578 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1547111148.579 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1547111148.580 * [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))))))) 1547111148.581 * [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))))))) 1547111148.581 * [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))))))) 1547111148.582 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1547111148.583 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1547111148.588 * [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 1547111148.588 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1547111148.588 * [misc]backup-simplify: Simplify (- 0) into 0 1547111148.589 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111148.589 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547111148.590 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1547111148.592 * [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 1547111148.592 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1547111148.593 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 1547111148.594 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))))) into 0 1547111148.594 * [misc]taylor: Taking taylor expansion of 0 in k 1547111148.594 * [misc]backup-simplify: Simplify 0 into 0 1547111148.594 * [misc]backup-simplify: Simplify 0 into 0 1547111148.594 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1547111148.596 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1547111148.597 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1547111148.598 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1547111148.603 * [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 1547111148.603 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111148.603 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1547111148.603 * [misc]backup-simplify: Simplify (- 0) into 0 1547111148.604 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111148.604 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1547111148.607 * [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))))) 1547111148.611 * [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)))))))) 1547111148.615 * [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)))))))) 1547111148.618 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1547111148.620 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1547111148.628 * [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 1547111148.628 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 1547111148.629 * [misc]backup-simplify: Simplify (- 0) into 0 1547111148.629 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111148.629 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547111148.630 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 1547111148.634 * [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 1547111148.634 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1547111148.635 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 1547111148.636 * [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 1547111148.636 * [misc]taylor: Taking taylor expansion of 0 in k 1547111148.636 * [misc]backup-simplify: Simplify 0 into 0 1547111148.636 * [misc]backup-simplify: Simplify 0 into 0 1547111148.636 * [misc]backup-simplify: Simplify 0 into 0 1547111148.636 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111148.638 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1547111148.640 * [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 1547111148.642 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1547111148.650 * [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 1547111148.650 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111148.650 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1547111148.651 * [misc]backup-simplify: Simplify (- 0) into 0 1547111148.651 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111148.652 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 1547111148.654 * [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))))))) 1547111148.659 * [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)))))))))))))) 1547111148.663 * [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)))))))))))))) 1547111148.669 * [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)))))))))))))))))))))) 1547111148.669 * [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))))) 1547111148.669 * [misc]approximate: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0 1547111148.669 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 1547111148.669 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1547111148.669 * [misc]taylor: Taking taylor expansion of k in k 1547111148.669 * [misc]backup-simplify: Simplify 0 into 0 1547111148.669 * [misc]backup-simplify: Simplify 1 into 1 1547111148.670 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547111148.670 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1547111148.670 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1547111148.670 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1547111148.670 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1547111148.670 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1547111148.670 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111148.670 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111148.670 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1547111148.670 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111148.670 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111148.670 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547111148.670 * [misc]taylor: Taking taylor expansion of k in k 1547111148.670 * [misc]backup-simplify: Simplify 0 into 0 1547111148.670 * [misc]backup-simplify: Simplify 1 into 1 1547111148.670 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547111148.670 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1547111148.670 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1547111148.670 * [misc]taylor: Taking taylor expansion of 2 in k 1547111148.670 * [misc]backup-simplify: Simplify 2 into 2 1547111148.670 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1547111148.670 * [misc]taylor: Taking taylor expansion of PI in k 1547111148.670 * [misc]backup-simplify: Simplify PI into PI 1547111148.670 * [misc]taylor: Taking taylor expansion of n in k 1547111148.670 * [misc]backup-simplify: Simplify n into n 1547111148.671 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1547111148.671 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1547111148.671 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1547111148.671 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1547111148.671 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1547111148.671 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1547111148.671 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1547111148.671 * [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)))) 1547111148.671 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1547111148.671 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1547111148.671 * [misc]taylor: Taking taylor expansion of k in n 1547111148.671 * [misc]backup-simplify: Simplify k into k 1547111148.671 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1547111148.671 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1547111148.671 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1547111148.671 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1547111148.671 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1547111148.671 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1547111148.671 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111148.671 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111148.671 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1547111148.671 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111148.671 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111148.671 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547111148.671 * [misc]taylor: Taking taylor expansion of k in n 1547111148.671 * [misc]backup-simplify: Simplify k into k 1547111148.672 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547111148.672 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1547111148.672 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1547111148.672 * [misc]taylor: Taking taylor expansion of 2 in n 1547111148.672 * [misc]backup-simplify: Simplify 2 into 2 1547111148.672 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547111148.672 * [misc]taylor: Taking taylor expansion of PI in n 1547111148.672 * [misc]backup-simplify: Simplify PI into PI 1547111148.672 * [misc]taylor: Taking taylor expansion of n in n 1547111148.672 * [misc]backup-simplify: Simplify 0 into 0 1547111148.672 * [misc]backup-simplify: Simplify 1 into 1 1547111148.672 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547111148.672 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547111148.672 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547111148.672 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1547111148.672 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1547111148.673 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1547111148.673 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547111148.673 * [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))) 1547111148.674 * [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)))) 1547111148.674 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1547111148.674 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1547111148.674 * [misc]taylor: Taking taylor expansion of k in n 1547111148.674 * [misc]backup-simplify: Simplify k into k 1547111148.674 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1547111148.674 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1547111148.674 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1547111148.674 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1547111148.674 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1547111148.674 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1547111148.674 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111148.674 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111148.674 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1547111148.674 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111148.674 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111148.674 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547111148.674 * [misc]taylor: Taking taylor expansion of k in n 1547111148.674 * [misc]backup-simplify: Simplify k into k 1547111148.674 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547111148.674 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1547111148.674 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1547111148.674 * [misc]taylor: Taking taylor expansion of 2 in n 1547111148.674 * [misc]backup-simplify: Simplify 2 into 2 1547111148.674 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547111148.674 * [misc]taylor: Taking taylor expansion of PI in n 1547111148.674 * [misc]backup-simplify: Simplify PI into PI 1547111148.674 * [misc]taylor: Taking taylor expansion of n in n 1547111148.674 * [misc]backup-simplify: Simplify 0 into 0 1547111148.674 * [misc]backup-simplify: Simplify 1 into 1 1547111148.674 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547111148.675 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547111148.675 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547111148.675 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1547111148.675 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1547111148.675 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1547111148.675 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547111148.676 * [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))) 1547111148.676 * [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)))) 1547111148.677 * [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)) 1547111148.677 * [misc]taylor: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) in k 1547111148.677 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1547111148.677 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1547111148.677 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1547111148.677 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111148.677 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111148.677 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1547111148.677 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111148.677 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111148.677 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547111148.677 * [misc]taylor: Taking taylor expansion of k in k 1547111148.677 * [misc]backup-simplify: Simplify 0 into 0 1547111148.677 * [misc]backup-simplify: Simplify 1 into 1 1547111148.677 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547111148.677 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1547111148.677 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1547111148.677 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1547111148.677 * [misc]taylor: Taking taylor expansion of 2 in k 1547111148.677 * [misc]backup-simplify: Simplify 2 into 2 1547111148.677 * [misc]taylor: Taking taylor expansion of PI in k 1547111148.677 * [misc]backup-simplify: Simplify PI into PI 1547111148.677 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547111148.678 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547111148.678 * [misc]taylor: Taking taylor expansion of (log n) in k 1547111148.678 * [misc]taylor: Taking taylor expansion of n in k 1547111148.678 * [misc]backup-simplify: Simplify n into n 1547111148.678 * [misc]backup-simplify: Simplify (log n) into (log n) 1547111148.678 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1547111148.678 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1547111148.678 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1547111148.678 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1547111148.678 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1547111148.679 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1547111148.680 * [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)))) 1547111148.680 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1547111148.680 * [misc]taylor: Taking taylor expansion of k in k 1547111148.680 * [misc]backup-simplify: Simplify 0 into 0 1547111148.680 * [misc]backup-simplify: Simplify 1 into 1 1547111148.680 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547111148.680 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1547111148.681 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) into 0 1547111148.681 * [misc]backup-simplify: Simplify 0 into 0 1547111148.681 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1547111148.682 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1547111148.683 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1547111148.683 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1547111148.683 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1547111148.684 * [misc]backup-simplify: Simplify (- 0) into 0 1547111148.684 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111148.684 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547111148.684 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1547111148.685 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1547111148.686 * [misc]backup-simplify: Simplify (+ (* (sqrt k) 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0 1547111148.686 * [misc]taylor: Taking taylor expansion of 0 in k 1547111148.686 * [misc]backup-simplify: Simplify 0 into 0 1547111148.686 * [misc]backup-simplify: Simplify 0 into 0 1547111148.686 * [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)))))) 1547111148.687 * [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)))))) 1547111148.688 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111148.689 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1547111148.694 * [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 1547111148.694 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1547111148.694 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1547111148.694 * [misc]backup-simplify: Simplify (- 0) into 0 1547111148.695 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111148.695 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547111148.696 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1547111148.698 * [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 1547111148.699 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 1547111148.700 * [misc]backup-simplify: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0 1547111148.700 * [misc]taylor: Taking taylor expansion of 0 in k 1547111148.700 * [misc]backup-simplify: Simplify 0 into 0 1547111148.700 * [misc]backup-simplify: Simplify 0 into 0 1547111148.700 * [misc]backup-simplify: Simplify 0 into 0 1547111148.701 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1547111148.702 * [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)))))) 1547111148.703 * [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)))))) 1547111148.704 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111148.706 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1547111148.714 * [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 1547111148.714 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1547111148.715 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1547111148.715 * [misc]backup-simplify: Simplify (- 0) into 0 1547111148.715 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111148.716 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547111148.717 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1547111148.720 * [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 1547111148.720 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 1547111148.721 * [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 1547111148.721 * [misc]taylor: Taking taylor expansion of 0 in k 1547111148.721 * [misc]backup-simplify: Simplify 0 into 0 1547111148.721 * [misc]backup-simplify: Simplify 0 into 0 1547111148.721 * [misc]backup-simplify: Simplify 0 into 0 1547111148.721 * [misc]backup-simplify: Simplify 0 into 0 1547111148.722 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1547111148.722 * [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)))))) 1547111148.723 * [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)))))) 1547111148.724 * [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)))))))) 1547111148.725 * [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))) 1547111148.725 * [misc]approximate: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (n k) around 0 1547111148.725 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 1547111148.725 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1547111148.725 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1547111148.725 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1547111148.725 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1547111148.725 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1547111148.725 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111148.725 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111148.725 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547111148.725 * [misc]taylor: Taking taylor expansion of k in k 1547111148.725 * [misc]backup-simplify: Simplify 0 into 0 1547111148.725 * [misc]backup-simplify: Simplify 1 into 1 1547111148.725 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547111148.725 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111148.725 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111148.725 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1547111148.725 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1547111148.725 * [misc]taylor: Taking taylor expansion of -2 in k 1547111148.725 * [misc]backup-simplify: Simplify -2 into -2 1547111148.725 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1547111148.725 * [misc]taylor: Taking taylor expansion of PI in k 1547111148.725 * [misc]backup-simplify: Simplify PI into PI 1547111148.725 * [misc]taylor: Taking taylor expansion of n in k 1547111148.725 * [misc]backup-simplify: Simplify n into n 1547111148.725 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1547111148.725 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1547111148.725 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1547111148.725 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1547111148.726 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1547111148.726 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1547111148.726 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) 1547111148.726 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1547111148.726 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1547111148.726 * [misc]taylor: Taking taylor expansion of -1 in k 1547111148.726 * [misc]backup-simplify: Simplify -1 into -1 1547111148.726 * [misc]taylor: Taking taylor expansion of k in k 1547111148.726 * [misc]backup-simplify: Simplify 0 into 0 1547111148.726 * [misc]backup-simplify: Simplify 1 into 1 1547111148.726 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1547111148.726 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547111148.726 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1547111148.727 * [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)))) 1547111148.727 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 1547111148.727 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1547111148.727 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1547111148.727 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1547111148.727 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1547111148.727 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1547111148.727 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111148.727 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111148.727 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547111148.727 * [misc]taylor: Taking taylor expansion of k in n 1547111148.727 * [misc]backup-simplify: Simplify k into k 1547111148.727 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547111148.727 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111148.727 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111148.727 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1547111148.727 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1547111148.727 * [misc]taylor: Taking taylor expansion of -2 in n 1547111148.727 * [misc]backup-simplify: Simplify -2 into -2 1547111148.727 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547111148.727 * [misc]taylor: Taking taylor expansion of PI in n 1547111148.727 * [misc]backup-simplify: Simplify PI into PI 1547111148.727 * [misc]taylor: Taking taylor expansion of n in n 1547111148.727 * [misc]backup-simplify: Simplify 0 into 0 1547111148.727 * [misc]backup-simplify: Simplify 1 into 1 1547111148.727 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547111148.727 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547111148.728 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1547111148.728 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1547111148.728 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1547111148.728 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547111148.729 * [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))) 1547111148.729 * [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)))) 1547111148.729 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1547111148.729 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1547111148.729 * [misc]taylor: Taking taylor expansion of -1 in n 1547111148.729 * [misc]backup-simplify: Simplify -1 into -1 1547111148.729 * [misc]taylor: Taking taylor expansion of k in n 1547111148.729 * [misc]backup-simplify: Simplify k into k 1547111148.729 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1547111148.730 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1547111148.730 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1547111148.730 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1547111148.730 * [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))) 1547111148.730 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 1547111148.730 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1547111148.730 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1547111148.730 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1547111148.730 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1547111148.730 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1547111148.730 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111148.730 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111148.730 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547111148.730 * [misc]taylor: Taking taylor expansion of k in n 1547111148.730 * [misc]backup-simplify: Simplify k into k 1547111148.730 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547111148.730 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111148.731 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111148.731 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1547111148.731 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1547111148.731 * [misc]taylor: Taking taylor expansion of -2 in n 1547111148.731 * [misc]backup-simplify: Simplify -2 into -2 1547111148.731 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547111148.731 * [misc]taylor: Taking taylor expansion of PI in n 1547111148.731 * [misc]backup-simplify: Simplify PI into PI 1547111148.731 * [misc]taylor: Taking taylor expansion of n in n 1547111148.731 * [misc]backup-simplify: Simplify 0 into 0 1547111148.731 * [misc]backup-simplify: Simplify 1 into 1 1547111148.731 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547111148.731 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547111148.731 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1547111148.731 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1547111148.731 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1547111148.732 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547111148.732 * [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))) 1547111148.733 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 1547111148.733 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1547111148.733 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1547111148.733 * [misc]taylor: Taking taylor expansion of -1 in n 1547111148.733 * [misc]backup-simplify: Simplify -1 into -1 1547111148.733 * [misc]taylor: Taking taylor expansion of k in n 1547111148.733 * [misc]backup-simplify: Simplify k into k 1547111148.733 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1547111148.733 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1547111148.733 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1547111148.733 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1547111148.734 * [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))) 1547111148.734 * [misc]taylor: Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) in k 1547111148.734 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1547111148.734 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1547111148.734 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1547111148.734 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1547111148.734 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111148.734 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111148.734 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547111148.734 * [misc]taylor: Taking taylor expansion of k in k 1547111148.734 * [misc]backup-simplify: Simplify 0 into 0 1547111148.734 * [misc]backup-simplify: Simplify 1 into 1 1547111148.734 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547111148.734 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111148.734 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111148.734 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1547111148.734 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1547111148.734 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1547111148.734 * [misc]taylor: Taking taylor expansion of -2 in k 1547111148.734 * [misc]backup-simplify: Simplify -2 into -2 1547111148.734 * [misc]taylor: Taking taylor expansion of PI in k 1547111148.734 * [misc]backup-simplify: Simplify PI into PI 1547111148.734 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547111148.735 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1547111148.735 * [misc]taylor: Taking taylor expansion of (log n) in k 1547111148.735 * [misc]taylor: Taking taylor expansion of n in k 1547111148.735 * [misc]backup-simplify: Simplify n into n 1547111148.735 * [misc]backup-simplify: Simplify (log n) into (log n) 1547111148.735 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1547111148.735 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1547111148.735 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1547111148.735 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1547111148.736 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1547111148.736 * [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)))) 1547111148.736 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1547111148.736 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1547111148.736 * [misc]taylor: Taking taylor expansion of -1 in k 1547111148.736 * [misc]backup-simplify: Simplify -1 into -1 1547111148.736 * [misc]taylor: Taking taylor expansion of k in k 1547111148.736 * [misc]backup-simplify: Simplify 0 into 0 1547111148.736 * [misc]backup-simplify: Simplify 1 into 1 1547111148.736 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1547111148.736 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547111148.737 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1547111148.737 * [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))))) 1547111148.737 * [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))))) 1547111148.738 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1547111148.738 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1547111148.741 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1547111148.741 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1547111148.741 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1547111148.741 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111148.742 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547111148.742 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1547111148.743 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1547111148.743 * [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 1547111148.743 * [misc]taylor: Taking taylor expansion of 0 in k 1547111148.743 * [misc]backup-simplify: Simplify 0 into 0 1547111148.744 * [misc]backup-simplify: Simplify 0 into 0 1547111148.744 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1547111148.744 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1547111148.745 * [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)))))) 1547111148.745 * [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)))))) 1547111148.746 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111148.747 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1547111148.752 * [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 1547111148.752 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1547111148.752 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1547111148.752 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111148.753 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547111148.754 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1547111148.756 * [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 1547111148.756 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1547111148.757 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 1547111148.758 * [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 1547111148.758 * [misc]taylor: Taking taylor expansion of 0 in k 1547111148.758 * [misc]backup-simplify: Simplify 0 into 0 1547111148.758 * [misc]backup-simplify: Simplify 0 into 0 1547111148.758 * [misc]backup-simplify: Simplify 0 into 0 1547111148.759 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111148.760 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1547111148.761 * [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)))))) 1547111148.761 * [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)))))) 1547111148.763 * [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))))))))))) 1547111148.763 * * * [misc]progress: simplifying candidates 1547111148.763 * * * * [misc]progress: [ 1 / 77 ] simplifiying candidate # 1547111148.763 * [enter]simplify: Simplifying (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) 1547111148.763 * * [misc]simplify: iters left: 6 (11 enodes) 1547111148.765 * * [misc]simplify: iters left: 5 (21 enodes) 1547111148.768 * * [misc]simplify: iters left: 4 (47 enodes) 1547111148.777 * * [misc]simplify: iters left: 3 (109 enodes) 1547111148.818 * * [misc]simplify: iters left: 2 (300 enodes) 1547111149.006 * [exit]simplify: Simplified to (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) 1547111149.007 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (exp (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI)))) (sqrt k))) 1547111149.007 * * * * [misc]progress: [ 2 / 77 ] simplifiying candidate # 1547111149.007 * * * * [misc]progress: [ 3 / 77 ] simplifiying candidate # 1547111149.007 * [enter]simplify: Simplifying (* PI (* n 2)) 1547111149.007 * * [misc]simplify: iters left: 4 (5 enodes) 1547111149.008 * * [misc]simplify: iters left: 3 (9 enodes) 1547111149.009 * * [misc]simplify: iters left: 2 (15 enodes) 1547111149.011 * * [misc]simplify: iters left: 1 (17 enodes) 1547111149.013 * [exit]simplify: Simplified to (* (* 2 n) PI) 1547111149.013 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* 2 n) PI) (* 1 (- 1/2 (/ k 2)))) (sqrt k))) 1547111149.013 * * * * [misc]progress: [ 4 / 77 ] simplifiying candidate # 1547111149.013 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (/ k 2)) 1547111149.013 * * [misc]simplify: iters left: 5 (8 enodes) 1547111149.015 * * [misc]simplify: iters left: 4 (12 enodes) 1547111149.018 * * [misc]simplify: iters left: 3 (18 enodes) 1547111149.023 * * [misc]simplify: iters left: 2 (20 enodes) 1547111149.028 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ k 2)) 1547111149.028 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (/ (pow (* PI (* n 2)) 1/2) (pow (* (* 2 n) PI) (/ k 2))) (sqrt k))) 1547111149.028 * * * * [misc]progress: [ 5 / 77 ] simplifiying candidate # 1547111149.028 * [enter]simplify: Simplifying (cbrt (- 1/2 (/ k 2))) 1547111149.028 * * [misc]simplify: iters left: 5 (6 enodes) 1547111149.030 * * [misc]simplify: iters left: 4 (8 enodes) 1547111149.033 * * [misc]simplify: iters left: 3 (11 enodes) 1547111149.035 * [exit]simplify: Simplified to (cbrt (- 1/2 (/ k 2))) 1547111149.036 * [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))) 1547111149.036 * * * * [misc]progress: [ 6 / 77 ] simplifiying candidate # 1547111149.036 * [enter]simplify: Simplifying (sqrt (- 1/2 (/ k 2))) 1547111149.036 * * [misc]simplify: iters left: 5 (6 enodes) 1547111149.037 * * [misc]simplify: iters left: 4 (8 enodes) 1547111149.038 * * [misc]simplify: iters left: 3 (11 enodes) 1547111149.039 * [exit]simplify: Simplified to (sqrt (- 1/2 (/ k 2))) 1547111149.039 * [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))) 1547111149.040 * * * * [misc]progress: [ 7 / 77 ] simplifiying candidate # 1547111149.040 * [enter]simplify: Simplifying (- 1/2 (/ k 2)) 1547111149.040 * * [misc]simplify: iters left: 4 (5 enodes) 1547111149.040 * * [misc]simplify: iters left: 3 (7 enodes) 1547111149.041 * * [misc]simplify: iters left: 2 (10 enodes) 1547111149.043 * [exit]simplify: Simplified to (- 1/2 (/ k 2)) 1547111149.043 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (pow (pow (* PI (* n 2)) 1) (- 1/2 (/ k 2))) (sqrt k))) 1547111149.043 * * * * [misc]progress: [ 8 / 77 ] simplifiying candidate # 1547111149.043 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1547111149.043 * * [misc]simplify: iters left: 5 (9 enodes) 1547111149.044 * * [misc]simplify: iters left: 4 (15 enodes) 1547111149.046 * * [misc]simplify: iters left: 3 (21 enodes) 1547111149.049 * * [misc]simplify: iters left: 2 (22 enodes) 1547111149.052 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1547111149.052 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2)))) (sqrt k))) 1547111149.052 * * * * [misc]progress: [ 9 / 77 ] simplifiying candidate # 1547111149.052 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1547111149.052 * * [misc]simplify: iters left: 5 (9 enodes) 1547111149.053 * * [misc]simplify: iters left: 4 (15 enodes) 1547111149.055 * * [misc]simplify: iters left: 3 (21 enodes) 1547111149.058 * * [misc]simplify: iters left: 2 (22 enodes) 1547111149.061 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1547111149.061 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2)))) (sqrt k))) 1547111149.061 * * * * [misc]progress: [ 10 / 77 ] simplifiying candidate # 1547111149.061 * [enter]simplify: Simplifying (pow PI (- 1/2 (/ k 2))) 1547111149.061 * * [misc]simplify: iters left: 5 (7 enodes) 1547111149.062 * * [misc]simplify: iters left: 4 (9 enodes) 1547111149.063 * * [misc]simplify: iters left: 3 (12 enodes) 1547111149.066 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1547111149.066 * [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))) 1547111149.067 * * * * [misc]progress: [ 11 / 77 ] simplifiying candidate # 1547111149.067 * * * * [misc]progress: [ 12 / 77 ] simplifiying candidate # 1547111149.067 * * * * [misc]progress: [ 13 / 77 ] simplifiying candidate # 1547111149.067 * * * * [misc]progress: [ 14 / 77 ] simplifiying candidate # 1547111149.067 * * * * [misc]progress: [ 15 / 77 ] simplifiying candidate # 1547111149.067 * * * * [misc]progress: [ 16 / 77 ] simplifiying candidate # 1547111149.067 * * * * [misc]progress: [ 17 / 77 ] simplifiying candidate # 1547111149.067 * * * * [misc]progress: [ 18 / 77 ] simplifiying candidate # 1547111149.067 * * * * [misc]progress: [ 19 / 77 ] simplifiying candidate # 1547111149.067 * * * * [misc]progress: [ 20 / 77 ] simplifiying candidate # 1547111149.067 * * * * [misc]progress: [ 21 / 77 ] simplifiying candidate # 1547111149.067 * * * * [misc]progress: [ 22 / 77 ] simplifiying candidate # 1547111149.067 * * * * [misc]progress: [ 23 / 77 ] simplifiying candidate # 1547111149.067 * * * * [misc]progress: [ 24 / 77 ] simplifiying candidate # 1547111149.067 * * * * [misc]progress: [ 25 / 77 ] simplifiying candidate # 1547111149.068 * * * * [misc]progress: [ 26 / 77 ] simplifiying candidate # 1547111149.068 * * * * [misc]progress: [ 27 / 77 ] simplifiying candidate # 1547111149.068 * * * * [misc]progress: [ 28 / 77 ] simplifiying candidate # 1547111149.068 * [enter]simplify: Simplifying (- (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) (log (sqrt k))) 1547111149.068 * * [misc]simplify: iters left: 6 (14 enodes) 1547111149.072 * * [misc]simplify: iters left: 5 (26 enodes) 1547111149.078 * * [misc]simplify: iters left: 4 (53 enodes) 1547111149.088 * * [misc]simplify: iters left: 3 (137 enodes) 1547111149.157 * * [misc]simplify: iters left: 2 (487 enodes) 1547111149.710 * [exit]simplify: Simplified to (- (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) (log (sqrt k))) 1547111149.710 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) (log (sqrt k))))) 1547111149.710 * * * * [misc]progress: [ 29 / 77 ] simplifiying candidate # 1547111149.710 * [enter]simplify: Simplifying (- (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) (log (sqrt k))) 1547111149.710 * * [misc]simplify: iters left: 6 (14 enodes) 1547111149.712 * * [misc]simplify: iters left: 5 (26 enodes) 1547111149.718 * * [misc]simplify: iters left: 4 (53 enodes) 1547111149.734 * * [misc]simplify: iters left: 3 (137 enodes) 1547111149.773 * * [misc]simplify: iters left: 2 (487 enodes) 1547111150.332 * [exit]simplify: Simplified to (- (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) (log (sqrt k))) 1547111150.332 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) (log (sqrt k))))) 1547111150.332 * * * * [misc]progress: [ 30 / 77 ] simplifiying candidate # 1547111150.333 * [enter]simplify: Simplifying (- (log (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (log (sqrt k))) 1547111150.333 * * [misc]simplify: iters left: 6 (14 enodes) 1547111150.335 * * [misc]simplify: iters left: 5 (24 enodes) 1547111150.338 * * [misc]simplify: iters left: 4 (42 enodes) 1547111150.344 * * [misc]simplify: iters left: 3 (71 enodes) 1547111150.359 * * [misc]simplify: iters left: 2 (208 enodes) 1547111150.487 * [exit]simplify: Simplified to (- (* (log (* (* 2 n) PI)) (- 1/2 (/ k 2))) (log (sqrt k))) 1547111150.487 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (log (* (* 2 n) PI)) (- 1/2 (/ k 2))) (log (sqrt k))))) 1547111150.487 * * * * [misc]progress: [ 31 / 77 ] simplifiying candidate # 1547111150.487 * * * * [misc]progress: [ 32 / 77 ] simplifiying candidate # 1547111150.487 * * * * [misc]progress: [ 33 / 77 ] simplifiying candidate # 1547111150.487 * [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))) 1547111150.487 * * [misc]simplify: iters left: 6 (16 enodes) 1547111150.493 * * [misc]simplify: iters left: 5 (31 enodes) 1547111150.503 * * [misc]simplify: iters left: 4 (67 enodes) 1547111150.524 * * [misc]simplify: iters left: 3 (124 enodes) 1547111150.557 * * [misc]simplify: iters left: 2 (195 enodes) 1547111150.609 * * [misc]simplify: iters left: 1 (309 enodes) 1547111150.725 * [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)))) 1547111150.725 * [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)))))) 1547111150.725 * * * * [misc]progress: [ 34 / 77 ] simplifiying candidate # 1547111150.725 * * * * [misc]progress: [ 35 / 77 ] simplifiying candidate # 1547111150.725 * * * * [misc]progress: [ 36 / 77 ] simplifiying candidate # 1547111150.725 * * * * [misc]progress: [ 37 / 77 ] simplifiying candidate # 1547111150.725 * * * * [misc]progress: [ 38 / 77 ] simplifiying candidate # 1547111150.726 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1547111150.726 * * [misc]simplify: iters left: 6 (12 enodes) 1547111150.728 * * [misc]simplify: iters left: 5 (19 enodes) 1547111150.730 * * [misc]simplify: iters left: 4 (25 enodes) 1547111150.736 * * [misc]simplify: iters left: 3 (26 enodes) 1547111150.742 * [exit]simplify: Simplified to (/ (sqrt (* (* 2 n) PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1547111150.742 * [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))))) 1547111150.742 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (sqrt k))) 1547111150.743 * * [misc]simplify: iters left: 6 (12 enodes) 1547111150.746 * * [misc]simplify: iters left: 5 (18 enodes) 1547111150.749 * * [misc]simplify: iters left: 4 (24 enodes) 1547111150.752 * * [misc]simplify: iters left: 3 (25 enodes) 1547111150.755 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt k))) 1547111150.756 * [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))))) 1547111150.756 * * * * [misc]progress: [ 39 / 77 ] simplifiying candidate # 1547111150.756 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (sqrt (sqrt k))) 1547111150.756 * * [misc]simplify: iters left: 6 (11 enodes) 1547111150.757 * * [misc]simplify: iters left: 5 (16 enodes) 1547111150.759 * * [misc]simplify: iters left: 4 (22 enodes) 1547111150.762 * * [misc]simplify: iters left: 3 (24 enodes) 1547111150.765 * [exit]simplify: Simplified to (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) 1547111150.765 * [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))))) 1547111150.765 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k))) 1547111150.765 * * [misc]simplify: iters left: 6 (12 enodes) 1547111150.767 * * [misc]simplify: iters left: 5 (18 enodes) 1547111150.769 * * [misc]simplify: iters left: 4 (24 enodes) 1547111150.773 * * [misc]simplify: iters left: 3 (25 enodes) 1547111150.776 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k))) 1547111150.776 * [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))))) 1547111150.776 * * * * [misc]progress: [ 40 / 77 ] simplifiying candidate # 1547111150.776 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) 1) 1547111150.776 * * [misc]simplify: iters left: 6 (9 enodes) 1547111150.777 * * [misc]simplify: iters left: 5 (16 enodes) 1547111150.780 * * [misc]simplify: iters left: 4 (24 enodes) 1547111150.786 * * [misc]simplify: iters left: 3 (26 enodes) 1547111150.791 * [exit]simplify: Simplified to (sqrt (* (* PI 2) n)) 1547111150.791 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) 1547111150.791 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)) 1547111150.792 * * [misc]simplify: iters left: 6 (11 enodes) 1547111150.795 * * [misc]simplify: iters left: 5 (17 enodes) 1547111150.800 * * [misc]simplify: iters left: 4 (23 enodes) 1547111150.807 * * [misc]simplify: iters left: 3 (24 enodes) 1547111150.813 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)) 1547111150.813 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)))) 1547111150.813 * * * * [misc]progress: [ 41 / 77 ] simplifiying candidate # 1547111150.813 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1547111150.813 * * [misc]simplify: iters left: 6 (12 enodes) 1547111150.818 * * [misc]simplify: iters left: 5 (19 enodes) 1547111150.825 * * [misc]simplify: iters left: 4 (25 enodes) 1547111150.831 * * [misc]simplify: iters left: 3 (26 enodes) 1547111150.838 * [exit]simplify: Simplified to (/ (sqrt (* (* 2 n) PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1547111150.838 * [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))))) 1547111150.838 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (sqrt k))) 1547111150.838 * * [misc]simplify: iters left: 6 (12 enodes) 1547111150.842 * * [misc]simplify: iters left: 5 (18 enodes) 1547111150.847 * * [misc]simplify: iters left: 4 (24 enodes) 1547111150.853 * * [misc]simplify: iters left: 3 (25 enodes) 1547111150.860 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt k))) 1547111150.860 * [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))))) 1547111150.860 * * * * [misc]progress: [ 42 / 77 ] simplifiying candidate # 1547111150.860 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (sqrt (sqrt k))) 1547111150.860 * * [misc]simplify: iters left: 6 (11 enodes) 1547111150.864 * * [misc]simplify: iters left: 5 (16 enodes) 1547111150.868 * * [misc]simplify: iters left: 4 (22 enodes) 1547111150.873 * * [misc]simplify: iters left: 3 (24 enodes) 1547111150.876 * [exit]simplify: Simplified to (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) 1547111150.876 * [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))))) 1547111150.876 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k))) 1547111150.876 * * [misc]simplify: iters left: 6 (12 enodes) 1547111150.878 * * [misc]simplify: iters left: 5 (18 enodes) 1547111150.880 * * [misc]simplify: iters left: 4 (24 enodes) 1547111150.883 * * [misc]simplify: iters left: 3 (25 enodes) 1547111150.886 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k))) 1547111150.886 * [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))))) 1547111150.886 * * * * [misc]progress: [ 43 / 77 ] simplifiying candidate # 1547111150.886 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) 1) 1547111150.886 * * [misc]simplify: iters left: 6 (9 enodes) 1547111150.888 * * [misc]simplify: iters left: 5 (16 enodes) 1547111150.890 * * [misc]simplify: iters left: 4 (24 enodes) 1547111150.893 * * [misc]simplify: iters left: 3 (26 enodes) 1547111150.896 * [exit]simplify: Simplified to (sqrt (* (* PI 2) n)) 1547111150.896 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) 1547111150.896 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)) 1547111150.896 * * [misc]simplify: iters left: 6 (11 enodes) 1547111150.898 * * [misc]simplify: iters left: 5 (17 enodes) 1547111150.900 * * [misc]simplify: iters left: 4 (23 enodes) 1547111150.903 * * [misc]simplify: iters left: 3 (24 enodes) 1547111150.906 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)) 1547111150.906 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)))) 1547111150.906 * * * * [misc]progress: [ 44 / 77 ] simplifiying candidate # 1547111150.907 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1547111150.907 * * [misc]simplify: iters left: 6 (11 enodes) 1547111150.908 * * [misc]simplify: iters left: 5 (15 enodes) 1547111150.910 * * [misc]simplify: iters left: 4 (18 enodes) 1547111150.913 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1547111150.913 * [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))))) 1547111150.913 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1547111150.913 * * [misc]simplify: iters left: 6 (11 enodes) 1547111150.914 * * [misc]simplify: iters left: 5 (14 enodes) 1547111150.917 * * [misc]simplify: iters left: 4 (17 enodes) 1547111150.922 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1547111150.922 * [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))))) 1547111150.922 * * * * [misc]progress: [ 45 / 77 ] simplifiying candidate # 1547111150.922 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1547111150.923 * * [misc]simplify: iters left: 6 (10 enodes) 1547111150.925 * * [misc]simplify: iters left: 5 (12 enodes) 1547111150.930 * * [misc]simplify: iters left: 4 (15 enodes) 1547111150.934 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1547111150.934 * [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))))) 1547111150.934 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1547111150.934 * * [misc]simplify: iters left: 6 (11 enodes) 1547111150.938 * * [misc]simplify: iters left: 5 (14 enodes) 1547111150.941 * * [misc]simplify: iters left: 4 (17 enodes) 1547111150.946 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1547111150.946 * [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))))) 1547111150.946 * * * * [misc]progress: [ 46 / 77 ] simplifiying candidate # 1547111150.947 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) 1) 1547111150.947 * * [misc]simplify: iters left: 6 (9 enodes) 1547111150.949 * * [misc]simplify: iters left: 5 (13 enodes) 1547111150.953 * * [misc]simplify: iters left: 4 (18 enodes) 1547111150.954 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1547111150.955 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1547111150.955 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)) 1547111150.955 * * [misc]simplify: iters left: 6 (10 enodes) 1547111150.956 * * [misc]simplify: iters left: 5 (13 enodes) 1547111150.958 * * [misc]simplify: iters left: 4 (16 enodes) 1547111150.961 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)) 1547111150.961 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1547111150.961 * * * * [misc]progress: [ 47 / 77 ] simplifiying candidate # 1547111150.961 * [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)))) 1547111150.961 * * [misc]simplify: iters left: 6 (16 enodes) 1547111150.964 * * [misc]simplify: iters left: 5 (28 enodes) 1547111150.968 * * [misc]simplify: iters left: 4 (46 enodes) 1547111150.974 * * [misc]simplify: iters left: 3 (50 enodes) 1547111150.980 * * [misc]simplify: iters left: 2 (53 enodes) 1547111150.993 * [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)))) 1547111150.993 * [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))))) 1547111150.993 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1547111150.993 * * [misc]simplify: iters left: 6 (14 enodes) 1547111150.998 * * [misc]simplify: iters left: 5 (20 enodes) 1547111151.001 * * [misc]simplify: iters left: 4 (29 enodes) 1547111151.005 * * [misc]simplify: iters left: 3 (30 enodes) 1547111151.009 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1547111151.009 * [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))))) 1547111151.009 * * * * [misc]progress: [ 48 / 77 ] simplifiying candidate # 1547111151.009 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) 1547111151.009 * * [misc]simplify: iters left: 6 (15 enodes) 1547111151.011 * * [misc]simplify: iters left: 5 (23 enodes) 1547111151.015 * * [misc]simplify: iters left: 4 (34 enodes) 1547111151.019 * * [misc]simplify: iters left: 3 (37 enodes) 1547111151.024 * [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)))))) 1547111151.024 * [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))))) 1547111151.024 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1547111151.024 * * [misc]simplify: iters left: 6 (14 enodes) 1547111151.027 * * [misc]simplify: iters left: 5 (20 enodes) 1547111151.032 * * [misc]simplify: iters left: 4 (29 enodes) 1547111151.039 * * [misc]simplify: iters left: 3 (30 enodes) 1547111151.046 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1547111151.046 * [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))))) 1547111151.046 * * * * [misc]progress: [ 49 / 77 ] simplifiying candidate # 1547111151.047 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1) 1547111151.047 * * [misc]simplify: iters left: 6 (14 enodes) 1547111151.051 * * [misc]simplify: iters left: 5 (24 enodes) 1547111151.059 * * [misc]simplify: iters left: 4 (39 enodes) 1547111151.069 * * [misc]simplify: iters left: 3 (54 enodes) 1547111151.083 * * [misc]simplify: iters left: 2 (80 enodes) 1547111151.103 * [exit]simplify: Simplified to (* (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))) 1547111151.103 * [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)))) 1547111151.103 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt k)) 1547111151.104 * * [misc]simplify: iters left: 6 (13 enodes) 1547111151.108 * * [misc]simplify: iters left: 5 (19 enodes) 1547111151.113 * * [misc]simplify: iters left: 4 (28 enodes) 1547111151.121 * * [misc]simplify: iters left: 3 (30 enodes) 1547111151.129 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt k)) 1547111151.129 * [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)))) 1547111151.129 * * * * [misc]progress: [ 50 / 77 ] simplifiying candidate # 1547111151.129 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1547111151.129 * * [misc]simplify: iters left: 6 (15 enodes) 1547111151.134 * * [misc]simplify: iters left: 5 (23 enodes) 1547111151.141 * * [misc]simplify: iters left: 4 (32 enodes) 1547111151.149 * * [misc]simplify: iters left: 3 (34 enodes) 1547111151.158 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1547111151.158 * [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))))) 1547111151.158 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1547111151.159 * * [misc]simplify: iters left: 6 (14 enodes) 1547111151.163 * * [misc]simplify: iters left: 5 (20 enodes) 1547111151.169 * * [misc]simplify: iters left: 4 (29 enodes) 1547111151.178 * * [misc]simplify: iters left: 3 (30 enodes) 1547111151.182 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1547111151.182 * [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))))) 1547111151.182 * * * * [misc]progress: [ 51 / 77 ] simplifiying candidate # 1547111151.182 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1547111151.182 * * [misc]simplify: iters left: 6 (14 enodes) 1547111151.184 * * [misc]simplify: iters left: 5 (20 enodes) 1547111151.187 * * [misc]simplify: iters left: 4 (29 enodes) 1547111151.191 * * [misc]simplify: iters left: 3 (30 enodes) 1547111151.194 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1547111151.194 * [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))))) 1547111151.194 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1547111151.195 * * [misc]simplify: iters left: 6 (14 enodes) 1547111151.197 * * [misc]simplify: iters left: 5 (20 enodes) 1547111151.199 * * [misc]simplify: iters left: 4 (29 enodes) 1547111151.203 * * [misc]simplify: iters left: 3 (30 enodes) 1547111151.207 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1547111151.207 * [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))))) 1547111151.207 * * * * [misc]progress: [ 52 / 77 ] simplifiying candidate # 1547111151.207 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1) 1547111151.207 * * [misc]simplify: iters left: 6 (13 enodes) 1547111151.209 * * [misc]simplify: iters left: 5 (21 enodes) 1547111151.212 * * [misc]simplify: iters left: 4 (32 enodes) 1547111151.217 * * [misc]simplify: iters left: 3 (33 enodes) 1547111151.224 * [exit]simplify: Simplified to (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) 1547111151.224 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt k)))) 1547111151.224 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt k)) 1547111151.224 * * [misc]simplify: iters left: 6 (13 enodes) 1547111151.229 * * [misc]simplify: iters left: 5 (19 enodes) 1547111151.234 * * [misc]simplify: iters left: 4 (28 enodes) 1547111151.241 * * [misc]simplify: iters left: 3 (30 enodes) 1547111151.249 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt k)) 1547111151.249 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt k)))) 1547111151.249 * * * * [misc]progress: [ 53 / 77 ] simplifiying candidate # 1547111151.249 * [enter]simplify: Simplifying (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1547111151.249 * * [misc]simplify: iters left: 6 (6 enodes) 1547111151.251 * * [misc]simplify: iters left: 5 (10 enodes) 1547111151.254 * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) 1547111151.254 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (cbrt (sqrt k))))) 1547111151.254 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1547111151.254 * * [misc]simplify: iters left: 6 (13 enodes) 1547111151.258 * * [misc]simplify: iters left: 5 (19 enodes) 1547111151.263 * * [misc]simplify: iters left: 4 (28 enodes) 1547111151.271 * * [misc]simplify: iters left: 3 (30 enodes) 1547111151.278 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1547111151.278 * [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))))) 1547111151.278 * * * * [misc]progress: [ 54 / 77 ] simplifiying candidate # 1547111151.279 * [enter]simplify: Simplifying (/ 1 (sqrt (sqrt k))) 1547111151.279 * * [misc]simplify: iters left: 4 (5 enodes) 1547111151.280 * * [misc]simplify: iters left: 3 (7 enodes) 1547111151.282 * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt k))) 1547111151.282 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) 1547111151.282 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1547111151.282 * * [misc]simplify: iters left: 6 (13 enodes) 1547111151.287 * * [misc]simplify: iters left: 5 (19 enodes) 1547111151.293 * * [misc]simplify: iters left: 4 (28 enodes) 1547111151.300 * * [misc]simplify: iters left: 3 (30 enodes) 1547111151.309 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1547111151.309 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) 1547111151.309 * * * * [misc]progress: [ 55 / 77 ] simplifiying candidate # 1547111151.309 * [enter]simplify: Simplifying (/ 1 1) 1547111151.309 * * [misc]simplify: iters left: 2 (2 enodes) 1547111151.310 * * [misc]simplify: iters left: 1 (4 enodes) 1547111151.311 * [exit]simplify: Simplified to 1 1547111151.311 * [misc]simplify: Simplified (2 1) to (λ (k n) (* 1 (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))) 1547111151.311 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)) 1547111151.311 * * [misc]simplify: iters left: 6 (12 enodes) 1547111151.315 * * [misc]simplify: iters left: 5 (18 enodes) 1547111151.321 * * [misc]simplify: iters left: 4 (27 enodes) 1547111151.328 * * [misc]simplify: iters left: 3 (29 enodes) 1547111151.335 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k)) 1547111151.335 * [misc]simplify: Simplified (2 2) to (λ (k n) (* 1 (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k)))) 1547111151.335 * * * * [misc]progress: [ 56 / 77 ] simplifiying candidate # 1547111151.336 * * * * [misc]progress: [ 57 / 77 ] simplifiying candidate # 1547111151.336 * * * * [misc]progress: [ 58 / 77 ] simplifiying candidate # 1547111151.336 * * * * [misc]progress: [ 59 / 77 ] simplifiying candidate # 1547111151.336 * [enter]simplify: Simplifying (cbrt (sqrt k)) 1547111151.336 * * [misc]simplify: iters left: 2 (3 enodes) 1547111151.337 * [exit]simplify: Simplified to (cbrt (sqrt k)) 1547111151.337 * [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)))) 1547111151.337 * * * * [misc]progress: [ 60 / 77 ] simplifiying candidate # 1547111151.337 * [enter]simplify: Simplifying (sqrt (sqrt k)) 1547111151.337 * * [misc]simplify: iters left: 2 (3 enodes) 1547111151.338 * [exit]simplify: Simplified to (sqrt (sqrt k)) 1547111151.338 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k)))) 1547111151.338 * * * * [misc]progress: [ 61 / 77 ] simplifiying candidate # 1547111151.338 * [enter]simplify: Simplifying (sqrt k) 1547111151.338 * * [misc]simplify: iters left: 1 (2 enodes) 1547111151.339 * [exit]simplify: Simplified to (sqrt k) 1547111151.339 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) 1) (sqrt k))) 1547111151.339 * * * * [misc]progress: [ 62 / 77 ] simplifiying candidate # 1547111151.339 * [enter]simplify: Simplifying (pow (* PI (* n 2)) 1/2) 1547111151.339 * * [misc]simplify: iters left: 5 (7 enodes) 1547111151.342 * * [misc]simplify: iters left: 4 (12 enodes) 1547111151.345 * * [misc]simplify: iters left: 3 (18 enodes) 1547111151.350 * * [misc]simplify: iters left: 2 (20 enodes) 1547111151.355 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1547111151.355 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2)))))) 1547111151.355 * * * * [misc]progress: [ 63 / 77 ] simplifiying candidate # 1547111151.355 * [enter]simplify: Simplifying (pow (* PI (* n 2)) 1/2) 1547111151.355 * * [misc]simplify: iters left: 5 (7 enodes) 1547111151.358 * * [misc]simplify: iters left: 4 (12 enodes) 1547111151.361 * * [misc]simplify: iters left: 3 (18 enodes) 1547111151.366 * * [misc]simplify: iters left: 2 (20 enodes) 1547111151.370 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1547111151.370 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2)))))) 1547111151.370 * * * * [misc]progress: [ 64 / 77 ] simplifiying candidate # 1547111151.371 * [enter]simplify: Simplifying (pow PI (- 1/2 (/ k 2))) 1547111151.371 * * [misc]simplify: iters left: 5 (7 enodes) 1547111151.373 * * [misc]simplify: iters left: 4 (9 enodes) 1547111151.375 * * [misc]simplify: iters left: 3 (12 enodes) 1547111151.379 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1547111151.379 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (pow PI (- 1/2 (/ k 2))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2)))))) 1547111151.379 * * * * [misc]progress: [ 65 / 77 ] simplifiying candidate # 1547111151.379 * [enter]simplify: Simplifying (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1547111151.379 * * [misc]simplify: iters left: 6 (12 enodes) 1547111151.383 * * [misc]simplify: iters left: 5 (18 enodes) 1547111151.388 * * [misc]simplify: iters left: 4 (27 enodes) 1547111151.395 * * [misc]simplify: iters left: 3 (29 enodes) 1547111151.403 * [exit]simplify: Simplified to (* (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) 1547111151.403 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (* (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) (/ (sqrt k) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))) 1547111151.403 * * * * [misc]progress: [ 66 / 77 ] simplifiying candidate # 1547111151.404 * [enter]simplify: Simplifying (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1547111151.404 * * [misc]simplify: iters left: 6 (11 enodes) 1547111151.407 * * [misc]simplify: iters left: 5 (17 enodes) 1547111151.412 * * [misc]simplify: iters left: 4 (26 enodes) 1547111151.419 * * [misc]simplify: iters left: 3 (27 enodes) 1547111151.425 * [exit]simplify: Simplified to (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) 1547111151.425 * [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))))))) 1547111151.425 * * * * [misc]progress: [ 67 / 77 ] simplifiying candidate # 1547111151.425 * * * * [misc]progress: [ 68 / 77 ] simplifiying candidate # 1547111151.426 * [enter]simplify: Simplifying (pow (* PI (* n 2)) 1/2) 1547111151.426 * * [misc]simplify: iters left: 5 (7 enodes) 1547111151.428 * * [misc]simplify: iters left: 4 (12 enodes) 1547111151.431 * * [misc]simplify: iters left: 3 (18 enodes) 1547111151.433 * * [misc]simplify: iters left: 2 (20 enodes) 1547111151.436 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1547111151.436 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2))))) 1547111151.436 * * * * [misc]progress: [ 69 / 77 ] simplifiying candidate # 1547111151.437 * [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))))) 1547111151.437 * * [misc]simplify: iters left: 6 (37 enodes) 1547111151.444 * * [misc]simplify: iters left: 5 (105 enodes) 1547111151.472 * * [misc]simplify: iters left: 4 (339 enodes) 1547111151.693 * [exit]simplify: Simplified to (+ (+ (* (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) -1/2) (+ (* (* (* k (log n)) (* k (log n))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (pow (* PI 2) 1/2) (pow n 1/2)))) (* (* k k) (+ (* (* (log (* PI 2)) (log (* PI 2))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (* (* (log n) (pow n 1/2)) (pow (* PI 2) 1/2)) (* (log (* PI 2)) 1/4))))) 1547111151.693 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (+ (+ (* (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) -1/2) (+ (* (* (* k (log n)) (* k (log n))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (pow (* PI 2) 1/2) (pow n 1/2)))) (* (* k k) (+ (* (* (log (* PI 2)) (log (* PI 2))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (* (* (log n) (pow n 1/2)) (pow (* PI 2) 1/2)) (* (log (* PI 2)) 1/4))))) (sqrt k))) 1547111151.693 * * * * [misc]progress: [ 70 / 77 ] simplifiying candidate # 1547111151.693 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 1547111151.693 * * [misc]simplify: iters left: 6 (15 enodes) 1547111151.696 * * [misc]simplify: iters left: 5 (33 enodes) 1547111151.702 * * [misc]simplify: iters left: 4 (64 enodes) 1547111151.714 * * [misc]simplify: iters left: 3 (171 enodes) 1547111151.834 * [exit]simplify: Simplified to (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow n (- 1/2 (* 1/2 k)))) 1547111151.834 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow n (- 1/2 (* 1/2 k)))) (sqrt k))) 1547111151.835 * * * * [misc]progress: [ 71 / 77 ] simplifiying candidate # 1547111151.835 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 1547111151.835 * * [misc]simplify: iters left: 6 (15 enodes) 1547111151.841 * * [misc]simplify: iters left: 5 (30 enodes) 1547111151.852 * * [misc]simplify: iters left: 4 (65 enodes) 1547111151.877 * * [misc]simplify: iters left: 3 (200 enodes) 1547111152.006 * [exit]simplify: Simplified to (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))) 1547111152.006 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))) (sqrt k))) 1547111152.006 * * * * [misc]progress: [ 72 / 77 ] simplifiying candidate # 1547111152.006 * [enter]simplify: Simplifying (* 2 (* n PI)) 1547111152.006 * * [misc]simplify: iters left: 4 (5 enodes) 1547111152.007 * * [misc]simplify: iters left: 3 (9 enodes) 1547111152.008 * * [misc]simplify: iters left: 2 (15 enodes) 1547111152.010 * * [misc]simplify: iters left: 1 (17 enodes) 1547111152.012 * [exit]simplify: Simplified to (* (* PI n) 2) 1547111152.012 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt k))) 1547111152.012 * * * * [misc]progress: [ 73 / 77 ] simplifiying candidate # 1547111152.013 * [enter]simplify: Simplifying (* 2 (* n PI)) 1547111152.013 * * [misc]simplify: iters left: 4 (5 enodes) 1547111152.013 * * [misc]simplify: iters left: 3 (9 enodes) 1547111152.015 * * [misc]simplify: iters left: 2 (15 enodes) 1547111152.017 * * [misc]simplify: iters left: 1 (17 enodes) 1547111152.018 * [exit]simplify: Simplified to (* (* PI n) 2) 1547111152.018 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt k))) 1547111152.019 * * * * [misc]progress: [ 74 / 77 ] simplifiying candidate # 1547111152.019 * [enter]simplify: Simplifying (* 2 (* n PI)) 1547111152.019 * * [misc]simplify: iters left: 4 (5 enodes) 1547111152.020 * * [misc]simplify: iters left: 3 (9 enodes) 1547111152.021 * * [misc]simplify: iters left: 2 (15 enodes) 1547111152.023 * * [misc]simplify: iters left: 1 (17 enodes) 1547111152.025 * [exit]simplify: Simplified to (* (* PI n) 2) 1547111152.025 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt k))) 1547111152.025 * * * * [misc]progress: [ 75 / 77 ] simplifiying candidate # 1547111152.025 * [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)))))))))))))))))))))) 1547111152.025 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1547111152.025 * * * * [misc]progress: [ 76 / 77 ] simplifiying candidate # 1547111152.025 * [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)))))))) 1547111152.025 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1547111152.025 * * * * [misc]progress: [ 77 / 77 ] simplifiying candidate # 1547111152.026 * [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))))))))))) 1547111152.026 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1547111152.026 * * * [misc]progress: adding candidates to table 1547111152.817 * * [misc]progress: iteration 2 / 4 1547111152.817 * * * [misc]progress: picking best candidate 1547111152.877 * * * * [misc]pick: Picked # 1547111152.877 * * * [misc]progress: localizing error 1547111152.922 * * * [misc]progress: generating rewritten candidates 1547111152.922 * * * * [misc]progress: [ 1 / 4 ] rewriting at (2 2) 1547111152.927 * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 1) 1547111152.928 * * * * [misc]progress: [ 3 / 4 ] rewriting at (2 2 1) 1547111152.932 * * * * [misc]progress: [ 4 / 4 ] rewriting at (2) 1547111152.950 * * * [misc]progress: generating series expansions 1547111152.950 * * * * [misc]progress: [ 1 / 4 ] generating series at (2 2) 1547111152.951 * [misc]backup-simplify: Simplify (pow (* (* 2 PI) n) (/ (- 1 k) 2)) into (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) 1547111152.951 * [misc]approximate: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in (n k) around 0 1547111152.951 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k 1547111152.951 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k 1547111152.951 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k 1547111152.951 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 k)) in k 1547111152.951 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111152.951 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111152.951 * [misc]taylor: Taking taylor expansion of (- 1 k) in k 1547111152.951 * [misc]taylor: Taking taylor expansion of 1 in k 1547111152.951 * [misc]backup-simplify: Simplify 1 into 1 1547111152.951 * [misc]taylor: Taking taylor expansion of k in k 1547111152.951 * [misc]backup-simplify: Simplify 0 into 0 1547111152.951 * [misc]backup-simplify: Simplify 1 into 1 1547111152.951 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1547111152.951 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1547111152.951 * [misc]taylor: Taking taylor expansion of 2 in k 1547111152.951 * [misc]backup-simplify: Simplify 2 into 2 1547111152.951 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1547111152.951 * [misc]taylor: Taking taylor expansion of n in k 1547111152.951 * [misc]backup-simplify: Simplify n into n 1547111152.951 * [misc]taylor: Taking taylor expansion of PI in k 1547111152.951 * [misc]backup-simplify: Simplify PI into PI 1547111152.951 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1547111152.951 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1547111152.951 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1547111152.952 * [misc]backup-simplify: Simplify (- 0) into 0 1547111152.952 * [misc]backup-simplify: Simplify (+ 1 0) into 1 1547111152.952 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1547111152.952 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1547111152.952 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1547111152.952 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n 1547111152.952 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n 1547111152.952 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n 1547111152.952 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 k)) in n 1547111152.952 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111152.952 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111152.952 * [misc]taylor: Taking taylor expansion of (- 1 k) in n 1547111152.952 * [misc]taylor: Taking taylor expansion of 1 in n 1547111152.952 * [misc]backup-simplify: Simplify 1 into 1 1547111152.953 * [misc]taylor: Taking taylor expansion of k in n 1547111152.953 * [misc]backup-simplify: Simplify k into k 1547111152.953 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1547111152.953 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1547111152.953 * [misc]taylor: Taking taylor expansion of 2 in n 1547111152.953 * [misc]backup-simplify: Simplify 2 into 2 1547111152.953 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547111152.953 * [misc]taylor: Taking taylor expansion of n in n 1547111152.953 * [misc]backup-simplify: Simplify 0 into 0 1547111152.953 * [misc]backup-simplify: Simplify 1 into 1 1547111152.953 * [misc]taylor: Taking taylor expansion of PI in n 1547111152.953 * [misc]backup-simplify: Simplify PI into PI 1547111152.953 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547111152.953 * [misc]backup-simplify: Simplify (* 2 0) into 0 1547111152.954 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547111152.954 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1547111152.955 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547111152.955 * [misc]backup-simplify: Simplify (- k) into (- k) 1547111152.955 * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) 1547111152.955 * [misc]backup-simplify: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k)) 1547111152.956 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547111152.956 * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) 1547111152.957 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 1547111152.957 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n 1547111152.957 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n 1547111152.957 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n 1547111152.957 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 k)) in n 1547111152.957 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111152.957 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111152.957 * [misc]taylor: Taking taylor expansion of (- 1 k) in n 1547111152.957 * [misc]taylor: Taking taylor expansion of 1 in n 1547111152.957 * [misc]backup-simplify: Simplify 1 into 1 1547111152.957 * [misc]taylor: Taking taylor expansion of k in n 1547111152.957 * [misc]backup-simplify: Simplify k into k 1547111152.957 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1547111152.957 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1547111152.957 * [misc]taylor: Taking taylor expansion of 2 in n 1547111152.957 * [misc]backup-simplify: Simplify 2 into 2 1547111152.957 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547111152.957 * [misc]taylor: Taking taylor expansion of n in n 1547111152.958 * [misc]backup-simplify: Simplify 0 into 0 1547111152.958 * [misc]backup-simplify: Simplify 1 into 1 1547111152.958 * [misc]taylor: Taking taylor expansion of PI in n 1547111152.958 * [misc]backup-simplify: Simplify PI into PI 1547111152.958 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547111152.958 * [misc]backup-simplify: Simplify (* 2 0) into 0 1547111152.959 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547111152.960 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1547111152.960 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547111152.960 * [misc]backup-simplify: Simplify (- k) into (- k) 1547111152.960 * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) 1547111152.960 * [misc]backup-simplify: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k)) 1547111152.961 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547111152.962 * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) 1547111152.962 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 1547111152.962 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) in k 1547111152.962 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) in k 1547111152.962 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111152.962 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111152.962 * [misc]taylor: Taking taylor expansion of (* (- 1 k) (+ (log n) (log (* 2 PI)))) in k 1547111152.962 * [misc]taylor: Taking taylor expansion of (- 1 k) in k 1547111152.962 * [misc]taylor: Taking taylor expansion of 1 in k 1547111152.962 * [misc]backup-simplify: Simplify 1 into 1 1547111152.963 * [misc]taylor: Taking taylor expansion of k in k 1547111152.963 * [misc]backup-simplify: Simplify 0 into 0 1547111152.963 * [misc]backup-simplify: Simplify 1 into 1 1547111152.963 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1547111152.963 * [misc]taylor: Taking taylor expansion of (log n) in k 1547111152.963 * [misc]taylor: Taking taylor expansion of n in k 1547111152.963 * [misc]backup-simplify: Simplify n into n 1547111152.963 * [misc]backup-simplify: Simplify (log n) into (log n) 1547111152.963 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1547111152.963 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1547111152.963 * [misc]taylor: Taking taylor expansion of 2 in k 1547111152.963 * [misc]backup-simplify: Simplify 2 into 2 1547111152.963 * [misc]taylor: Taking taylor expansion of PI in k 1547111152.963 * [misc]backup-simplify: Simplify PI into PI 1547111152.963 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547111152.964 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547111152.964 * [misc]backup-simplify: Simplify (- 0) into 0 1547111152.964 * [misc]backup-simplify: Simplify (+ 1 0) into 1 1547111152.964 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547111152.964 * [misc]backup-simplify: Simplify (* 1 (+ (log n) (log (* 2 PI)))) into (+ (log n) (log (* 2 PI))) 1547111152.965 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1547111152.965 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1547111152.965 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1547111152.966 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1547111152.967 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1547111152.968 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1547111152.968 * [misc]backup-simplify: Simplify (- 0) into 0 1547111152.968 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111152.969 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- 1 k))) into 0 1547111152.969 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547111152.969 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1547111152.970 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0 1547111152.970 * [misc]taylor: Taking taylor expansion of 0 in k 1547111152.970 * [misc]backup-simplify: Simplify 0 into 0 1547111152.970 * [misc]backup-simplify: Simplify 0 into 0 1547111152.971 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1547111152.971 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1547111152.973 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1547111152.973 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111152.973 * [misc]backup-simplify: Simplify (- 1) into -1 1547111152.973 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 1547111152.974 * [misc]backup-simplify: Simplify (+ (* 1 0) (* -1 (+ (log n) (log (* 2 PI))))) into (- (+ (log (* 2 PI)) (log n))) 1547111152.975 * [misc]backup-simplify: Simplify (+ (* 1/2 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1547111152.976 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 1547111152.976 * [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))))))) 1547111152.977 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1547111152.978 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1547111152.981 * [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 1547111152.981 * [misc]backup-simplify: Simplify (- 0) into 0 1547111152.981 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111152.981 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0 1547111152.982 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547111152.982 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1547111152.984 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1547111152.984 * [misc]taylor: Taking taylor expansion of 0 in k 1547111152.984 * [misc]backup-simplify: Simplify 0 into 0 1547111152.984 * [misc]backup-simplify: Simplify 0 into 0 1547111152.984 * [misc]backup-simplify: Simplify 0 into 0 1547111152.985 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1547111152.985 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1547111152.988 * [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 1547111152.988 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111152.988 * [misc]backup-simplify: Simplify (- 0) into 0 1547111152.988 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111152.989 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1547111152.990 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1547111152.991 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 1547111152.993 * [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))))) 1547111152.995 * [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))))) 1547111152.996 * [misc]backup-simplify: Simplify (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) into (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) 1547111152.996 * [misc]approximate: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in (n k) around 0 1547111152.996 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k 1547111152.996 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1547111152.996 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1547111152.996 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k 1547111152.996 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111152.996 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111152.996 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k 1547111152.996 * [misc]taylor: Taking taylor expansion of 1 in k 1547111152.996 * [misc]backup-simplify: Simplify 1 into 1 1547111152.996 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547111152.996 * [misc]taylor: Taking taylor expansion of k in k 1547111152.996 * [misc]backup-simplify: Simplify 0 into 0 1547111152.996 * [misc]backup-simplify: Simplify 1 into 1 1547111152.996 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547111152.996 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1547111152.996 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1547111152.996 * [misc]taylor: Taking taylor expansion of 2 in k 1547111152.996 * [misc]backup-simplify: Simplify 2 into 2 1547111152.996 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1547111152.996 * [misc]taylor: Taking taylor expansion of PI in k 1547111152.996 * [misc]backup-simplify: Simplify PI into PI 1547111152.996 * [misc]taylor: Taking taylor expansion of n in k 1547111152.996 * [misc]backup-simplify: Simplify n into n 1547111152.996 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1547111152.997 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1547111152.997 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1547111152.997 * [misc]backup-simplify: Simplify (- 1) into -1 1547111152.997 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 1547111152.997 * [misc]backup-simplify: Simplify (* 1/2 -1) into -1/2 1547111152.997 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1547111152.997 * [misc]backup-simplify: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 1547111152.997 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n 1547111152.997 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1547111152.997 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1547111152.997 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n 1547111152.997 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111152.997 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111152.997 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n 1547111152.997 * [misc]taylor: Taking taylor expansion of 1 in n 1547111152.997 * [misc]backup-simplify: Simplify 1 into 1 1547111152.997 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547111152.997 * [misc]taylor: Taking taylor expansion of k in n 1547111152.997 * [misc]backup-simplify: Simplify k into k 1547111152.997 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547111152.997 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1547111152.997 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1547111152.997 * [misc]taylor: Taking taylor expansion of 2 in n 1547111152.997 * [misc]backup-simplify: Simplify 2 into 2 1547111152.997 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547111152.997 * [misc]taylor: Taking taylor expansion of PI in n 1547111152.997 * [misc]backup-simplify: Simplify PI into PI 1547111152.997 * [misc]taylor: Taking taylor expansion of n in n 1547111152.997 * [misc]backup-simplify: Simplify 0 into 0 1547111152.997 * [misc]backup-simplify: Simplify 1 into 1 1547111152.998 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547111152.998 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547111152.998 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547111152.998 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1547111152.998 * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 1547111152.998 * [misc]backup-simplify: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k))) 1547111152.999 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547111152.999 * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 1547111153.000 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 1547111153.000 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n 1547111153.000 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1547111153.000 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1547111153.000 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n 1547111153.000 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111153.000 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111153.000 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n 1547111153.000 * [misc]taylor: Taking taylor expansion of 1 in n 1547111153.000 * [misc]backup-simplify: Simplify 1 into 1 1547111153.000 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547111153.000 * [misc]taylor: Taking taylor expansion of k in n 1547111153.000 * [misc]backup-simplify: Simplify k into k 1547111153.000 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547111153.000 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1547111153.000 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1547111153.000 * [misc]taylor: Taking taylor expansion of 2 in n 1547111153.000 * [misc]backup-simplify: Simplify 2 into 2 1547111153.000 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547111153.000 * [misc]taylor: Taking taylor expansion of PI in n 1547111153.000 * [misc]backup-simplify: Simplify PI into PI 1547111153.000 * [misc]taylor: Taking taylor expansion of n in n 1547111153.000 * [misc]backup-simplify: Simplify 0 into 0 1547111153.000 * [misc]backup-simplify: Simplify 1 into 1 1547111153.000 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547111153.000 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547111153.001 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547111153.001 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1547111153.001 * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 1547111153.001 * [misc]backup-simplify: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k))) 1547111153.001 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547111153.002 * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 1547111153.002 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 1547111153.002 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k 1547111153.002 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k 1547111153.002 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111153.002 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111153.002 * [misc]taylor: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k 1547111153.002 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k 1547111153.002 * [misc]taylor: Taking taylor expansion of 1 in k 1547111153.002 * [misc]backup-simplify: Simplify 1 into 1 1547111153.002 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547111153.002 * [misc]taylor: Taking taylor expansion of k in k 1547111153.002 * [misc]backup-simplify: Simplify 0 into 0 1547111153.002 * [misc]backup-simplify: Simplify 1 into 1 1547111153.002 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547111153.002 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1547111153.002 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1547111153.002 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1547111153.002 * [misc]taylor: Taking taylor expansion of 2 in k 1547111153.002 * [misc]backup-simplify: Simplify 2 into 2 1547111153.003 * [misc]taylor: Taking taylor expansion of PI in k 1547111153.003 * [misc]backup-simplify: Simplify PI into PI 1547111153.003 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547111153.003 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547111153.003 * [misc]taylor: Taking taylor expansion of (log n) in k 1547111153.003 * [misc]taylor: Taking taylor expansion of n in k 1547111153.003 * [misc]backup-simplify: Simplify n into n 1547111153.003 * [misc]backup-simplify: Simplify (log n) into (log n) 1547111153.003 * [misc]backup-simplify: Simplify (- 1) into -1 1547111153.003 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 1547111153.003 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1547111153.004 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1547111153.004 * [misc]backup-simplify: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n))) 1547111153.005 * [misc]backup-simplify: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1547111153.006 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 1547111153.006 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 1547111153.007 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1547111153.008 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1547111153.015 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1547111153.016 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1547111153.016 * [misc]backup-simplify: Simplify (- 0) into 0 1547111153.016 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111153.016 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- 1 (/ 1 k)))) into 0 1547111153.017 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547111153.018 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1547111153.019 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1547111153.019 * [misc]taylor: Taking taylor expansion of 0 in k 1547111153.019 * [misc]backup-simplify: Simplify 0 into 0 1547111153.019 * [misc]backup-simplify: Simplify 0 into 0 1547111153.019 * [misc]backup-simplify: Simplify 0 into 0 1547111153.021 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111153.022 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1547111153.027 * [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 1547111153.027 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1547111153.027 * [misc]backup-simplify: Simplify (- 0) into 0 1547111153.028 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111153.028 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0 1547111153.029 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547111153.029 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1547111153.032 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1547111153.032 * [misc]taylor: Taking taylor expansion of 0 in k 1547111153.032 * [misc]backup-simplify: Simplify 0 into 0 1547111153.032 * [misc]backup-simplify: Simplify 0 into 0 1547111153.032 * [misc]backup-simplify: Simplify 0 into 0 1547111153.032 * [misc]backup-simplify: Simplify 0 into 0 1547111153.033 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111153.034 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1547111153.038 * [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 1547111153.038 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1547111153.038 * [misc]backup-simplify: Simplify (- 0) into 0 1547111153.038 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111153.039 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0 1547111153.039 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547111153.040 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1547111153.042 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1547111153.042 * [misc]taylor: Taking taylor expansion of 0 in k 1547111153.042 * [misc]backup-simplify: Simplify 0 into 0 1547111153.042 * [misc]backup-simplify: Simplify 0 into 0 1547111153.042 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) 1547111153.043 * [misc]backup-simplify: Simplify (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) into (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) 1547111153.043 * [misc]approximate: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in (n k) around 0 1547111153.043 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k 1547111153.043 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k 1547111153.043 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k 1547111153.043 * [misc]taylor: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k 1547111153.043 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111153.043 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111153.043 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in k 1547111153.043 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547111153.043 * [misc]taylor: Taking taylor expansion of k in k 1547111153.043 * [misc]backup-simplify: Simplify 0 into 0 1547111153.043 * [misc]backup-simplify: Simplify 1 into 1 1547111153.043 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547111153.043 * [misc]taylor: Taking taylor expansion of 1 in k 1547111153.043 * [misc]backup-simplify: Simplify 1 into 1 1547111153.043 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1547111153.043 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1547111153.043 * [misc]taylor: Taking taylor expansion of -2 in k 1547111153.043 * [misc]backup-simplify: Simplify -2 into -2 1547111153.043 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1547111153.043 * [misc]taylor: Taking taylor expansion of PI in k 1547111153.043 * [misc]backup-simplify: Simplify PI into PI 1547111153.043 * [misc]taylor: Taking taylor expansion of n in k 1547111153.043 * [misc]backup-simplify: Simplify n into n 1547111153.043 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1547111153.043 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1547111153.043 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1547111153.044 * [misc]backup-simplify: Simplify (+ 1 0) into 1 1547111153.044 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1547111153.044 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1547111153.044 * [misc]backup-simplify: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) 1547111153.044 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n 1547111153.044 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n 1547111153.044 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n 1547111153.044 * [misc]taylor: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n 1547111153.044 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111153.044 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111153.044 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in n 1547111153.044 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547111153.044 * [misc]taylor: Taking taylor expansion of k in n 1547111153.044 * [misc]backup-simplify: Simplify k into k 1547111153.044 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547111153.044 * [misc]taylor: Taking taylor expansion of 1 in n 1547111153.044 * [misc]backup-simplify: Simplify 1 into 1 1547111153.044 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1547111153.044 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1547111153.044 * [misc]taylor: Taking taylor expansion of -2 in n 1547111153.044 * [misc]backup-simplify: Simplify -2 into -2 1547111153.044 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547111153.044 * [misc]taylor: Taking taylor expansion of PI in n 1547111153.044 * [misc]backup-simplify: Simplify PI into PI 1547111153.044 * [misc]taylor: Taking taylor expansion of n in n 1547111153.044 * [misc]backup-simplify: Simplify 0 into 0 1547111153.044 * [misc]backup-simplify: Simplify 1 into 1 1547111153.044 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547111153.045 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547111153.045 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1547111153.045 * [misc]backup-simplify: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 1547111153.045 * [misc]backup-simplify: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1)) 1547111153.045 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547111153.046 * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 1547111153.046 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 1547111153.046 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n 1547111153.046 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n 1547111153.046 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n 1547111153.046 * [misc]taylor: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n 1547111153.046 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111153.046 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111153.046 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in n 1547111153.046 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547111153.046 * [misc]taylor: Taking taylor expansion of k in n 1547111153.046 * [misc]backup-simplify: Simplify k into k 1547111153.046 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547111153.046 * [misc]taylor: Taking taylor expansion of 1 in n 1547111153.046 * [misc]backup-simplify: Simplify 1 into 1 1547111153.046 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1547111153.046 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1547111153.046 * [misc]taylor: Taking taylor expansion of -2 in n 1547111153.046 * [misc]backup-simplify: Simplify -2 into -2 1547111153.046 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547111153.046 * [misc]taylor: Taking taylor expansion of PI in n 1547111153.046 * [misc]backup-simplify: Simplify PI into PI 1547111153.046 * [misc]taylor: Taking taylor expansion of n in n 1547111153.046 * [misc]backup-simplify: Simplify 0 into 0 1547111153.046 * [misc]backup-simplify: Simplify 1 into 1 1547111153.047 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547111153.047 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547111153.047 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1547111153.047 * [misc]backup-simplify: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 1547111153.047 * [misc]backup-simplify: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1)) 1547111153.048 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547111153.048 * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 1547111153.048 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 1547111153.048 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k 1547111153.049 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) in k 1547111153.049 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111153.049 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111153.049 * [misc]taylor: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) in k 1547111153.049 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in k 1547111153.049 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547111153.049 * [misc]taylor: Taking taylor expansion of k in k 1547111153.049 * [misc]backup-simplify: Simplify 0 into 0 1547111153.049 * [misc]backup-simplify: Simplify 1 into 1 1547111153.049 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547111153.049 * [misc]taylor: Taking taylor expansion of 1 in k 1547111153.049 * [misc]backup-simplify: Simplify 1 into 1 1547111153.049 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1547111153.049 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1547111153.049 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1547111153.049 * [misc]taylor: Taking taylor expansion of -2 in k 1547111153.049 * [misc]backup-simplify: Simplify -2 into -2 1547111153.049 * [misc]taylor: Taking taylor expansion of PI in k 1547111153.049 * [misc]backup-simplify: Simplify PI into PI 1547111153.049 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547111153.049 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1547111153.050 * [misc]taylor: Taking taylor expansion of (log n) in k 1547111153.050 * [misc]taylor: Taking taylor expansion of n in k 1547111153.050 * [misc]backup-simplify: Simplify n into n 1547111153.050 * [misc]backup-simplify: Simplify (log n) into (log n) 1547111153.050 * [misc]backup-simplify: Simplify (+ 1 0) into 1 1547111153.050 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1547111153.050 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1547111153.050 * [misc]backup-simplify: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n)) 1547111153.051 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1547111153.051 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 1547111153.051 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 1547111153.052 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1547111153.053 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1547111153.054 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1547111153.054 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1547111153.054 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111153.054 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (+ (/ 1 k) 1))) into 0 1547111153.055 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547111153.055 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1547111153.056 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1547111153.056 * [misc]taylor: Taking taylor expansion of 0 in k 1547111153.056 * [misc]backup-simplify: Simplify 0 into 0 1547111153.056 * [misc]backup-simplify: Simplify 0 into 0 1547111153.056 * [misc]backup-simplify: Simplify 0 into 0 1547111153.057 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111153.058 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1547111153.061 * [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 1547111153.061 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1547111153.061 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111153.061 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0 1547111153.061 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547111153.062 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1547111153.063 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1547111153.063 * [misc]taylor: Taking taylor expansion of 0 in k 1547111153.063 * [misc]backup-simplify: Simplify 0 into 0 1547111153.063 * [misc]backup-simplify: Simplify 0 into 0 1547111153.063 * [misc]backup-simplify: Simplify 0 into 0 1547111153.063 * [misc]backup-simplify: Simplify 0 into 0 1547111153.064 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111153.065 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1547111153.070 * [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 1547111153.070 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1547111153.070 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111153.071 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1))))) into 0 1547111153.071 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547111153.072 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 1547111153.074 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1547111153.074 * [misc]taylor: Taking taylor expansion of 0 in k 1547111153.074 * [misc]backup-simplify: Simplify 0 into 0 1547111153.074 * [misc]backup-simplify: Simplify 0 into 0 1547111153.074 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) 1547111153.074 * * * * [misc]progress: [ 2 / 4 ] generating series at (2 1) 1547111153.075 * [misc]backup-simplify: Simplify (/ 1 (sqrt k)) into (sqrt (/ 1 k)) 1547111153.075 * [misc]approximate: Taking taylor expansion of (sqrt (/ 1 k)) in (k) around 0 1547111153.075 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1547111153.075 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547111153.075 * [misc]taylor: Taking taylor expansion of k in k 1547111153.075 * [misc]backup-simplify: Simplify 0 into 0 1547111153.075 * [misc]backup-simplify: Simplify 1 into 1 1547111153.075 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547111153.075 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547111153.075 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1547111153.075 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1547111153.075 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547111153.075 * [misc]taylor: Taking taylor expansion of k in k 1547111153.075 * [misc]backup-simplify: Simplify 0 into 0 1547111153.075 * [misc]backup-simplify: Simplify 1 into 1 1547111153.075 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547111153.075 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547111153.076 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1547111153.076 * [misc]backup-simplify: Simplify 0 into 0 1547111153.076 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547111153.076 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1547111153.077 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1547111153.077 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547111153.077 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111153.078 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1547111153.078 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547111153.078 * [misc]backup-simplify: Simplify (+ (* +nan.0 (pow k 2)) (+ (* +nan.0 k) +nan.0)) into (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) 1547111153.078 * [misc]backup-simplify: Simplify (/ 1 (sqrt (/ 1 k))) into (sqrt k) 1547111153.078 * [misc]approximate: Taking taylor expansion of (sqrt k) in (k) around 0 1547111153.078 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1547111153.078 * [misc]taylor: Taking taylor expansion of k in k 1547111153.078 * [misc]backup-simplify: Simplify 0 into 0 1547111153.078 * [misc]backup-simplify: Simplify 1 into 1 1547111153.078 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547111153.078 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1547111153.078 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1547111153.078 * [misc]taylor: Taking taylor expansion of k in k 1547111153.078 * [misc]backup-simplify: Simplify 0 into 0 1547111153.078 * [misc]backup-simplify: Simplify 1 into 1 1547111153.079 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547111153.079 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1547111153.079 * [misc]backup-simplify: Simplify 0 into 0 1547111153.079 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547111153.080 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1547111153.080 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547111153.080 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1547111153.080 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547111153.081 * [misc]backup-simplify: Simplify (+ (* +nan.0 (pow (/ 1 k) 3)) (+ (* +nan.0 (pow (/ 1 k) 2)) (* +nan.0 (/ 1 k)))) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) 1547111153.081 * [misc]backup-simplify: Simplify (/ 1 (sqrt (/ 1 (- k)))) into (/ 1 (sqrt (/ -1 k))) 1547111153.081 * [misc]approximate: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in (k) around 0 1547111153.081 * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 1547111153.081 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1547111153.081 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1547111153.081 * [misc]taylor: Taking taylor expansion of -1 in k 1547111153.081 * [misc]backup-simplify: Simplify -1 into -1 1547111153.081 * [misc]taylor: Taking taylor expansion of k in k 1547111153.081 * [misc]backup-simplify: Simplify 0 into 0 1547111153.081 * [misc]backup-simplify: Simplify 1 into 1 1547111153.081 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1547111153.081 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547111153.081 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1547111153.081 * [misc]backup-simplify: Simplify (/ 1 +nan.0) into +nan.0 1547111153.081 * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 1547111153.081 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1547111153.081 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1547111153.082 * [misc]taylor: Taking taylor expansion of -1 in k 1547111153.082 * [misc]backup-simplify: Simplify -1 into -1 1547111153.082 * [misc]taylor: Taking taylor expansion of k in k 1547111153.082 * [misc]backup-simplify: Simplify 0 into 0 1547111153.082 * [misc]backup-simplify: Simplify 1 into 1 1547111153.082 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1547111153.082 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547111153.082 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1547111153.082 * [misc]backup-simplify: Simplify (/ 1 +nan.0) into +nan.0 1547111153.082 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547111153.082 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1547111153.083 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1547111153.083 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 1547111153.084 * [misc]backup-simplify: Simplify (- +nan.0) into (- +nan.0) 1547111153.084 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111153.084 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1547111153.085 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 1547111153.085 * [misc]backup-simplify: Simplify (- +nan.0) into (- +nan.0) 1547111153.086 * [misc]backup-simplify: Simplify (+ (* (- +nan.0) (pow (/ 1 (- k)) 2)) (+ (* (- +nan.0) (/ 1 (- k))) +nan.0)) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) 1547111153.086 * * * * [misc]progress: [ 3 / 4 ] generating series at (2 2 1) 1547111153.086 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1547111153.086 * [misc]approximate: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1547111153.086 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1547111153.086 * [misc]taylor: Taking taylor expansion of 2 in n 1547111153.086 * [misc]backup-simplify: Simplify 2 into 2 1547111153.086 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547111153.086 * [misc]taylor: Taking taylor expansion of n in n 1547111153.086 * [misc]backup-simplify: Simplify 0 into 0 1547111153.086 * [misc]backup-simplify: Simplify 1 into 1 1547111153.086 * [misc]taylor: Taking taylor expansion of PI in n 1547111153.086 * [misc]backup-simplify: Simplify PI into PI 1547111153.086 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1547111153.086 * [misc]taylor: Taking taylor expansion of 2 in n 1547111153.086 * [misc]backup-simplify: Simplify 2 into 2 1547111153.086 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547111153.086 * [misc]taylor: Taking taylor expansion of n in n 1547111153.086 * [misc]backup-simplify: Simplify 0 into 0 1547111153.086 * [misc]backup-simplify: Simplify 1 into 1 1547111153.086 * [misc]taylor: Taking taylor expansion of PI in n 1547111153.086 * [misc]backup-simplify: Simplify PI into PI 1547111153.086 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547111153.087 * [misc]backup-simplify: Simplify (* 2 0) into 0 1547111153.087 * [misc]backup-simplify: Simplify 0 into 0 1547111153.087 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547111153.087 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1547111153.088 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547111153.088 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1547111153.089 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1547111153.089 * [misc]backup-simplify: Simplify 0 into 0 1547111153.090 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1547111153.091 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1547111153.091 * [misc]backup-simplify: Simplify 0 into 0 1547111153.092 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1547111153.093 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1547111153.093 * [misc]backup-simplify: Simplify 0 into 0 1547111153.094 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1547111153.096 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1547111153.096 * [misc]backup-simplify: Simplify 0 into 0 1547111153.098 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1547111153.100 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1547111153.100 * [misc]backup-simplify: Simplify 0 into 0 1547111153.102 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1547111153.104 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1547111153.104 * [misc]backup-simplify: Simplify 0 into 0 1547111153.105 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1547111153.105 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 n)) into (* 2 (/ PI n)) 1547111153.105 * [misc]approximate: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1547111153.105 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1547111153.105 * [misc]taylor: Taking taylor expansion of 2 in n 1547111153.105 * [misc]backup-simplify: Simplify 2 into 2 1547111153.105 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547111153.105 * [misc]taylor: Taking taylor expansion of PI in n 1547111153.105 * [misc]backup-simplify: Simplify PI into PI 1547111153.105 * [misc]taylor: Taking taylor expansion of n in n 1547111153.105 * [misc]backup-simplify: Simplify 0 into 0 1547111153.105 * [misc]backup-simplify: Simplify 1 into 1 1547111153.105 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547111153.105 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1547111153.105 * [misc]taylor: Taking taylor expansion of 2 in n 1547111153.105 * [misc]backup-simplify: Simplify 2 into 2 1547111153.105 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547111153.105 * [misc]taylor: Taking taylor expansion of PI in n 1547111153.105 * [misc]backup-simplify: Simplify PI into PI 1547111153.105 * [misc]taylor: Taking taylor expansion of n in n 1547111153.105 * [misc]backup-simplify: Simplify 0 into 0 1547111153.105 * [misc]backup-simplify: Simplify 1 into 1 1547111153.105 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547111153.106 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547111153.106 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547111153.107 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1547111153.107 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1547111153.107 * [misc]backup-simplify: Simplify 0 into 0 1547111153.108 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111153.108 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1547111153.108 * [misc]backup-simplify: Simplify 0 into 0 1547111153.109 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111153.110 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1547111153.110 * [misc]backup-simplify: Simplify 0 into 0 1547111153.111 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111153.112 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1547111153.112 * [misc]backup-simplify: Simplify 0 into 0 1547111153.114 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111153.116 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1547111153.116 * [misc]backup-simplify: Simplify 0 into 0 1547111153.117 * [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 1547111153.119 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1547111153.119 * [misc]backup-simplify: Simplify 0 into 0 1547111153.120 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 1547111153.120 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (- n))) into (* -2 (/ PI n)) 1547111153.120 * [misc]approximate: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1547111153.120 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1547111153.120 * [misc]taylor: Taking taylor expansion of -2 in n 1547111153.120 * [misc]backup-simplify: Simplify -2 into -2 1547111153.120 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547111153.120 * [misc]taylor: Taking taylor expansion of PI in n 1547111153.120 * [misc]backup-simplify: Simplify PI into PI 1547111153.120 * [misc]taylor: Taking taylor expansion of n in n 1547111153.120 * [misc]backup-simplify: Simplify 0 into 0 1547111153.120 * [misc]backup-simplify: Simplify 1 into 1 1547111153.120 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547111153.121 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1547111153.121 * [misc]taylor: Taking taylor expansion of -2 in n 1547111153.121 * [misc]backup-simplify: Simplify -2 into -2 1547111153.121 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547111153.121 * [misc]taylor: Taking taylor expansion of PI in n 1547111153.121 * [misc]backup-simplify: Simplify PI into PI 1547111153.121 * [misc]taylor: Taking taylor expansion of n in n 1547111153.121 * [misc]backup-simplify: Simplify 0 into 0 1547111153.121 * [misc]backup-simplify: Simplify 1 into 1 1547111153.121 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547111153.121 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547111153.121 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547111153.122 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1547111153.122 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1547111153.122 * [misc]backup-simplify: Simplify 0 into 0 1547111153.123 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111153.124 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1547111153.124 * [misc]backup-simplify: Simplify 0 into 0 1547111153.125 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111153.126 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1547111153.126 * [misc]backup-simplify: Simplify 0 into 0 1547111153.127 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111153.129 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1547111153.129 * [misc]backup-simplify: Simplify 0 into 0 1547111153.131 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111153.134 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1547111153.134 * [misc]backup-simplify: Simplify 0 into 0 1547111153.137 * [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 1547111153.140 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1547111153.140 * [misc]backup-simplify: Simplify 0 into 0 1547111153.141 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 1547111153.141 * * * * [misc]progress: [ 4 / 4 ] generating series at (2) 1547111153.141 * [misc]backup-simplify: Simplify (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) into (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) 1547111153.141 * [misc]approximate: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in (k n) around 0 1547111153.141 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in n 1547111153.141 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n 1547111153.142 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n 1547111153.142 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n 1547111153.142 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 k)) in n 1547111153.142 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111153.142 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111153.142 * [misc]taylor: Taking taylor expansion of (- 1 k) in n 1547111153.142 * [misc]taylor: Taking taylor expansion of 1 in n 1547111153.142 * [misc]backup-simplify: Simplify 1 into 1 1547111153.142 * [misc]taylor: Taking taylor expansion of k in n 1547111153.142 * [misc]backup-simplify: Simplify k into k 1547111153.142 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1547111153.142 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1547111153.142 * [misc]taylor: Taking taylor expansion of 2 in n 1547111153.142 * [misc]backup-simplify: Simplify 2 into 2 1547111153.142 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547111153.142 * [misc]taylor: Taking taylor expansion of n in n 1547111153.142 * [misc]backup-simplify: Simplify 0 into 0 1547111153.142 * [misc]backup-simplify: Simplify 1 into 1 1547111153.142 * [misc]taylor: Taking taylor expansion of PI in n 1547111153.142 * [misc]backup-simplify: Simplify PI into PI 1547111153.142 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547111153.143 * [misc]backup-simplify: Simplify (* 2 0) into 0 1547111153.143 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547111153.144 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1547111153.144 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547111153.144 * [misc]backup-simplify: Simplify (- k) into (- k) 1547111153.144 * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) 1547111153.144 * [misc]backup-simplify: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k)) 1547111153.145 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547111153.146 * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) 1547111153.146 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 1547111153.146 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1547111153.146 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547111153.146 * [misc]taylor: Taking taylor expansion of k in n 1547111153.146 * [misc]backup-simplify: Simplify k into k 1547111153.147 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547111153.147 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1547111153.147 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1547111153.147 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1547111153.147 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k 1547111153.147 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k 1547111153.147 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k 1547111153.147 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k 1547111153.147 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 k)) in k 1547111153.147 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111153.147 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111153.147 * [misc]taylor: Taking taylor expansion of (- 1 k) in k 1547111153.147 * [misc]taylor: Taking taylor expansion of 1 in k 1547111153.147 * [misc]backup-simplify: Simplify 1 into 1 1547111153.147 * [misc]taylor: Taking taylor expansion of k in k 1547111153.147 * [misc]backup-simplify: Simplify 0 into 0 1547111153.147 * [misc]backup-simplify: Simplify 1 into 1 1547111153.147 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1547111153.147 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1547111153.147 * [misc]taylor: Taking taylor expansion of 2 in k 1547111153.147 * [misc]backup-simplify: Simplify 2 into 2 1547111153.147 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1547111153.147 * [misc]taylor: Taking taylor expansion of n in k 1547111153.147 * [misc]backup-simplify: Simplify n into n 1547111153.148 * [misc]taylor: Taking taylor expansion of PI in k 1547111153.148 * [misc]backup-simplify: Simplify PI into PI 1547111153.148 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1547111153.148 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1547111153.148 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1547111153.148 * [misc]backup-simplify: Simplify (- 0) into 0 1547111153.148 * [misc]backup-simplify: Simplify (+ 1 0) into 1 1547111153.148 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1547111153.148 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1547111153.149 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1547111153.149 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1547111153.149 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547111153.149 * [misc]taylor: Taking taylor expansion of k in k 1547111153.149 * [misc]backup-simplify: Simplify 0 into 0 1547111153.149 * [misc]backup-simplify: Simplify 1 into 1 1547111153.149 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547111153.149 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547111153.149 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1547111153.150 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k 1547111153.150 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k 1547111153.150 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k 1547111153.150 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k 1547111153.150 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 k)) in k 1547111153.150 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111153.150 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111153.150 * [misc]taylor: Taking taylor expansion of (- 1 k) in k 1547111153.150 * [misc]taylor: Taking taylor expansion of 1 in k 1547111153.150 * [misc]backup-simplify: Simplify 1 into 1 1547111153.150 * [misc]taylor: Taking taylor expansion of k in k 1547111153.150 * [misc]backup-simplify: Simplify 0 into 0 1547111153.150 * [misc]backup-simplify: Simplify 1 into 1 1547111153.150 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1547111153.150 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1547111153.150 * [misc]taylor: Taking taylor expansion of 2 in k 1547111153.150 * [misc]backup-simplify: Simplify 2 into 2 1547111153.150 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1547111153.150 * [misc]taylor: Taking taylor expansion of n in k 1547111153.150 * [misc]backup-simplify: Simplify n into n 1547111153.150 * [misc]taylor: Taking taylor expansion of PI in k 1547111153.150 * [misc]backup-simplify: Simplify PI into PI 1547111153.150 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1547111153.150 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1547111153.150 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1547111153.151 * [misc]backup-simplify: Simplify (- 0) into 0 1547111153.151 * [misc]backup-simplify: Simplify (+ 1 0) into 1 1547111153.151 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1547111153.151 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1547111153.151 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1547111153.151 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1547111153.151 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547111153.151 * [misc]taylor: Taking taylor expansion of k in k 1547111153.151 * [misc]backup-simplify: Simplify 0 into 0 1547111153.151 * [misc]backup-simplify: Simplify 1 into 1 1547111153.152 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547111153.152 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547111153.152 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1547111153.152 * [misc]backup-simplify: Simplify (* (pow (* 2 (* n PI)) 1/2) 0) into 0 1547111153.152 * [misc]taylor: Taking taylor expansion of 0 in n 1547111153.152 * [misc]backup-simplify: Simplify 0 into 0 1547111153.152 * [misc]backup-simplify: Simplify 0 into 0 1547111153.153 * [misc]backup-simplify: Simplify (+ (* n 0) (* 0 PI)) into 0 1547111153.153 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0 1547111153.154 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 1547111153.154 * [misc]backup-simplify: Simplify (- 1) into -1 1547111153.154 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 1547111153.154 * [misc]backup-simplify: Simplify (+ (* 1/2 -1) (* 0 1)) into -1/2 1547111153.155 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI))))) 1547111153.155 * [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))))) 1547111153.156 * [misc]backup-simplify: Simplify (+ (* (pow (* 2 (* n PI)) 1/2) +nan.0) (* (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) 0)) into (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) 1547111153.156 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 1547111153.156 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 1547111153.156 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1547111153.156 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547111153.156 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1547111153.156 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1547111153.156 * [misc]taylor: Taking taylor expansion of 2 in n 1547111153.156 * [misc]backup-simplify: Simplify 2 into 2 1547111153.156 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1547111153.156 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1547111153.156 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1547111153.156 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547111153.156 * [misc]taylor: Taking taylor expansion of n in n 1547111153.156 * [misc]backup-simplify: Simplify 0 into 0 1547111153.156 * [misc]backup-simplify: Simplify 1 into 1 1547111153.156 * [misc]taylor: Taking taylor expansion of PI in n 1547111153.157 * [misc]backup-simplify: Simplify PI into PI 1547111153.157 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547111153.157 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547111153.158 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547111153.158 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1547111153.158 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1547111153.159 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1547111153.159 * [misc]backup-simplify: Simplify (- 0) into 0 1547111153.159 * [misc]backup-simplify: Simplify 0 into 0 1547111153.159 * [misc]backup-simplify: Simplify 0 into 0 1547111153.159 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1547111153.160 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1547111153.161 * [misc]backup-simplify: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 1547111153.161 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 1547111153.163 * [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 1547111153.163 * [misc]backup-simplify: Simplify (- 0) into 0 1547111153.163 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111153.163 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 -1) (* 0 1))) into 0 1547111153.164 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0 1547111153.165 * [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))) 1547111153.166 * [misc]backup-simplify: Simplify (+ (* (pow (* 2 (* n PI)) 1/2) +nan.0) (+ (* (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) +nan.0) (* (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) 0))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) 1547111153.166 * [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 1547111153.166 * [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 1547111153.166 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n 1547111153.166 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1547111153.166 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547111153.166 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n 1547111153.166 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n 1547111153.166 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1547111153.166 * [misc]taylor: Taking taylor expansion of 2 in n 1547111153.166 * [misc]backup-simplify: Simplify 2 into 2 1547111153.166 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1547111153.166 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1547111153.166 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1547111153.167 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1547111153.167 * [misc]taylor: Taking taylor expansion of 2 in n 1547111153.167 * [misc]backup-simplify: Simplify 2 into 2 1547111153.167 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547111153.167 * [misc]taylor: Taking taylor expansion of n in n 1547111153.167 * [misc]backup-simplify: Simplify 0 into 0 1547111153.167 * [misc]backup-simplify: Simplify 1 into 1 1547111153.167 * [misc]taylor: Taking taylor expansion of PI in n 1547111153.167 * [misc]backup-simplify: Simplify PI into PI 1547111153.167 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547111153.167 * [misc]backup-simplify: Simplify (* 2 0) into 0 1547111153.168 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547111153.168 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1547111153.169 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547111153.169 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1547111153.169 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547111153.169 * [misc]taylor: Taking taylor expansion of n in n 1547111153.169 * [misc]backup-simplify: Simplify 0 into 0 1547111153.169 * [misc]backup-simplify: Simplify 1 into 1 1547111153.169 * [misc]taylor: Taking taylor expansion of PI in n 1547111153.169 * [misc]backup-simplify: Simplify PI into PI 1547111153.169 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547111153.170 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547111153.171 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547111153.171 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1547111153.171 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 1547111153.171 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 1547111153.171 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1547111153.171 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547111153.171 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1547111153.171 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1547111153.171 * [misc]taylor: Taking taylor expansion of 2 in n 1547111153.171 * [misc]backup-simplify: Simplify 2 into 2 1547111153.172 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1547111153.172 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1547111153.172 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1547111153.172 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547111153.172 * [misc]taylor: Taking taylor expansion of n in n 1547111153.172 * [misc]backup-simplify: Simplify 0 into 0 1547111153.172 * [misc]backup-simplify: Simplify 1 into 1 1547111153.172 * [misc]taylor: Taking taylor expansion of PI in n 1547111153.172 * [misc]backup-simplify: Simplify PI into PI 1547111153.172 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547111153.173 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547111153.173 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547111153.173 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1547111153.174 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547111153.175 * [misc]backup-simplify: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 1547111153.175 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0 1547111153.176 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1547111153.176 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1547111153.176 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1547111153.176 * [misc]backup-simplify: Simplify (- 0) into 0 1547111153.176 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111153.176 * [misc]backup-simplify: Simplify (- 0) into 0 1547111153.176 * [misc]backup-simplify: Simplify 0 into 0 1547111153.178 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1547111153.179 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1547111153.181 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 1547111153.182 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI))) 1547111153.182 * [misc]backup-simplify: Simplify 0 into 0 1547111153.182 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111153.183 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1547111153.184 * [misc]backup-simplify: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1547111153.185 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 1547111153.187 * [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 1547111153.188 * [misc]backup-simplify: Simplify (- 0) into 0 1547111153.188 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111153.188 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1)))) into 0 1547111153.189 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log (* 2 (* n PI))))))) into 0 1547111153.190 * [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))) 1547111153.192 * [misc]backup-simplify: Simplify (+ (* (pow (* 2 (* n PI)) 1/2) +nan.0) (+ (* (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) +nan.0) (+ (* (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) +nan.0) (* (* -1/48 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 3))) 0)))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))))))) 1547111153.192 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))))))) in n 1547111153.192 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))))))) in n 1547111153.192 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n 1547111153.192 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1547111153.192 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547111153.192 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n 1547111153.192 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n 1547111153.192 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1547111153.192 * [misc]taylor: Taking taylor expansion of 2 in n 1547111153.192 * [misc]backup-simplify: Simplify 2 into 2 1547111153.193 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1547111153.193 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1547111153.193 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1547111153.193 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1547111153.193 * [misc]taylor: Taking taylor expansion of 2 in n 1547111153.193 * [misc]backup-simplify: Simplify 2 into 2 1547111153.193 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547111153.193 * [misc]taylor: Taking taylor expansion of n in n 1547111153.193 * [misc]backup-simplify: Simplify 0 into 0 1547111153.193 * [misc]backup-simplify: Simplify 1 into 1 1547111153.193 * [misc]taylor: Taking taylor expansion of PI in n 1547111153.193 * [misc]backup-simplify: Simplify PI into PI 1547111153.193 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547111153.193 * [misc]backup-simplify: Simplify (* 2 0) into 0 1547111153.194 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547111153.195 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1547111153.195 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547111153.195 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1547111153.195 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547111153.195 * [misc]taylor: Taking taylor expansion of n in n 1547111153.195 * [misc]backup-simplify: Simplify 0 into 0 1547111153.195 * [misc]backup-simplify: Simplify 1 into 1 1547111153.195 * [misc]taylor: Taking taylor expansion of PI in n 1547111153.195 * [misc]backup-simplify: Simplify PI into PI 1547111153.196 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547111153.196 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547111153.196 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547111153.197 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1547111153.197 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))))) in n 1547111153.197 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))))) in n 1547111153.197 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 1547111153.197 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1547111153.197 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547111153.197 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1547111153.197 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1547111153.197 * [misc]taylor: Taking taylor expansion of 2 in n 1547111153.197 * [misc]backup-simplify: Simplify 2 into 2 1547111153.197 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1547111153.198 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1547111153.198 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1547111153.198 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547111153.198 * [misc]taylor: Taking taylor expansion of n in n 1547111153.198 * [misc]backup-simplify: Simplify 0 into 0 1547111153.198 * [misc]backup-simplify: Simplify 1 into 1 1547111153.198 * [misc]taylor: Taking taylor expansion of PI in n 1547111153.198 * [misc]backup-simplify: Simplify PI into PI 1547111153.198 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547111153.199 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547111153.199 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547111153.199 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1547111153.199 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))) in n 1547111153.199 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) in n 1547111153.199 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1547111153.199 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547111153.199 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))) in n 1547111153.200 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) in n 1547111153.200 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1547111153.200 * [misc]taylor: Taking taylor expansion of 2 in n 1547111153.200 * [misc]backup-simplify: Simplify 2 into 2 1547111153.200 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1547111153.200 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1547111153.200 * [misc]taylor: Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n 1547111153.200 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1547111153.200 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1547111153.200 * [misc]taylor: Taking taylor expansion of 2 in n 1547111153.200 * [misc]backup-simplify: Simplify 2 into 2 1547111153.200 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547111153.200 * [misc]taylor: Taking taylor expansion of n in n 1547111153.200 * [misc]backup-simplify: Simplify 0 into 0 1547111153.200 * [misc]backup-simplify: Simplify 1 into 1 1547111153.200 * [misc]taylor: Taking taylor expansion of PI in n 1547111153.200 * [misc]backup-simplify: Simplify PI into PI 1547111153.201 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547111153.201 * [misc]backup-simplify: Simplify (* 2 0) into 0 1547111153.201 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547111153.202 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1547111153.202 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547111153.203 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547111153.203 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1547111153.203 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547111153.203 * [misc]taylor: Taking taylor expansion of n in n 1547111153.203 * [misc]backup-simplify: Simplify 0 into 0 1547111153.203 * [misc]backup-simplify: Simplify 1 into 1 1547111153.203 * [misc]taylor: Taking taylor expansion of PI in n 1547111153.203 * [misc]backup-simplify: Simplify PI into PI 1547111153.204 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547111153.204 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547111153.204 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547111153.205 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1547111153.205 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547111153.206 * [misc]backup-simplify: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 1547111153.207 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0 1547111153.207 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1547111153.207 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1547111153.207 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1547111153.208 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547111153.208 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547111153.209 * [misc]backup-simplify: Simplify (* (+ (log n) (log (* 2 PI))) (+ (log n) (log (* 2 PI)))) into (pow (+ (log n) (log (* 2 PI))) 2) 1547111153.209 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) into (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 1547111153.209 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 0) into 0 1547111153.210 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1547111153.210 * [misc]backup-simplify: Simplify (- 0) into 0 1547111153.210 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111153.210 * [misc]backup-simplify: Simplify (- 0) into 0 1547111153.210 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111153.210 * [misc]backup-simplify: Simplify (- 0) into 0 1547111153.210 * [misc]backup-simplify: Simplify 0 into 0 1547111153.211 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1547111153.211 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1547111153.213 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1547111153.213 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547111153.214 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1547111153.214 * [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)))))))) 1547111153.216 * [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)))))))) 1547111153.217 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1547111153.218 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1547111153.218 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 1547111153.220 * [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)))))))))) 1547111153.222 * [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))))))) 1547111153.224 * [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))))))) 1547111153.225 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1547111153.226 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 1547111153.227 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1547111153.228 * [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)))) 1547111153.230 * [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)))) 1547111153.232 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 1547111153.233 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 1547111153.236 * [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))))))))))))) 1547111153.237 * [misc]backup-simplify: Simplify (* (/ 1 (sqrt (/ 1 k))) (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2))) into (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) 1547111153.237 * [misc]approximate: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in (k n) around 0 1547111153.237 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in n 1547111153.237 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n 1547111153.237 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1547111153.237 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1547111153.237 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n 1547111153.237 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111153.237 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111153.237 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n 1547111153.237 * [misc]taylor: Taking taylor expansion of 1 in n 1547111153.237 * [misc]backup-simplify: Simplify 1 into 1 1547111153.237 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547111153.237 * [misc]taylor: Taking taylor expansion of k in n 1547111153.237 * [misc]backup-simplify: Simplify k into k 1547111153.237 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547111153.237 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1547111153.237 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1547111153.237 * [misc]taylor: Taking taylor expansion of 2 in n 1547111153.237 * [misc]backup-simplify: Simplify 2 into 2 1547111153.237 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547111153.237 * [misc]taylor: Taking taylor expansion of PI in n 1547111153.237 * [misc]backup-simplify: Simplify PI into PI 1547111153.237 * [misc]taylor: Taking taylor expansion of n in n 1547111153.237 * [misc]backup-simplify: Simplify 0 into 0 1547111153.237 * [misc]backup-simplify: Simplify 1 into 1 1547111153.237 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547111153.237 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547111153.238 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547111153.238 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1547111153.238 * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 1547111153.238 * [misc]backup-simplify: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k))) 1547111153.238 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547111153.239 * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 1547111153.239 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 1547111153.239 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1547111153.239 * [misc]taylor: Taking taylor expansion of k in n 1547111153.239 * [misc]backup-simplify: Simplify k into k 1547111153.239 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1547111153.239 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1547111153.239 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k 1547111153.240 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k 1547111153.240 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1547111153.240 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1547111153.240 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k 1547111153.240 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111153.240 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111153.240 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k 1547111153.240 * [misc]taylor: Taking taylor expansion of 1 in k 1547111153.240 * [misc]backup-simplify: Simplify 1 into 1 1547111153.240 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547111153.240 * [misc]taylor: Taking taylor expansion of k in k 1547111153.240 * [misc]backup-simplify: Simplify 0 into 0 1547111153.240 * [misc]backup-simplify: Simplify 1 into 1 1547111153.240 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547111153.240 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1547111153.240 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1547111153.240 * [misc]taylor: Taking taylor expansion of 2 in k 1547111153.240 * [misc]backup-simplify: Simplify 2 into 2 1547111153.240 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1547111153.240 * [misc]taylor: Taking taylor expansion of PI in k 1547111153.240 * [misc]backup-simplify: Simplify PI into PI 1547111153.240 * [misc]taylor: Taking taylor expansion of n in k 1547111153.240 * [misc]backup-simplify: Simplify n into n 1547111153.240 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1547111153.240 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1547111153.240 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1547111153.241 * [misc]backup-simplify: Simplify (- 1) into -1 1547111153.241 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 1547111153.241 * [misc]backup-simplify: Simplify (* 1/2 -1) into -1/2 1547111153.241 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1547111153.241 * [misc]backup-simplify: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 1547111153.241 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1547111153.241 * [misc]taylor: Taking taylor expansion of k in k 1547111153.241 * [misc]backup-simplify: Simplify 0 into 0 1547111153.241 * [misc]backup-simplify: Simplify 1 into 1 1547111153.242 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547111153.242 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1547111153.242 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k 1547111153.242 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k 1547111153.242 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1547111153.242 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1547111153.242 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k 1547111153.242 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111153.242 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111153.242 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k 1547111153.242 * [misc]taylor: Taking taylor expansion of 1 in k 1547111153.242 * [misc]backup-simplify: Simplify 1 into 1 1547111153.242 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547111153.242 * [misc]taylor: Taking taylor expansion of k in k 1547111153.242 * [misc]backup-simplify: Simplify 0 into 0 1547111153.242 * [misc]backup-simplify: Simplify 1 into 1 1547111153.243 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547111153.243 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1547111153.243 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1547111153.243 * [misc]taylor: Taking taylor expansion of 2 in k 1547111153.243 * [misc]backup-simplify: Simplify 2 into 2 1547111153.243 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1547111153.243 * [misc]taylor: Taking taylor expansion of PI in k 1547111153.243 * [misc]backup-simplify: Simplify PI into PI 1547111153.243 * [misc]taylor: Taking taylor expansion of n in k 1547111153.243 * [misc]backup-simplify: Simplify n into n 1547111153.243 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1547111153.243 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1547111153.243 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1547111153.243 * [misc]backup-simplify: Simplify (- 1) into -1 1547111153.243 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 1547111153.244 * [misc]backup-simplify: Simplify (* 1/2 -1) into -1/2 1547111153.244 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1547111153.244 * [misc]backup-simplify: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 1547111153.244 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1547111153.244 * [misc]taylor: Taking taylor expansion of k in k 1547111153.244 * [misc]backup-simplify: Simplify 0 into 0 1547111153.244 * [misc]backup-simplify: Simplify 1 into 1 1547111153.244 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547111153.245 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1547111153.245 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 0) into 0 1547111153.245 * [misc]taylor: Taking taylor expansion of 0 in n 1547111153.245 * [misc]backup-simplify: Simplify 0 into 0 1547111153.245 * [misc]backup-simplify: Simplify 0 into 0 1547111153.246 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) 1547111153.246 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n 1547111153.247 * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n 1547111153.247 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1547111153.247 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547111153.247 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n 1547111153.247 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n 1547111153.247 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111153.247 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111153.247 * [misc]taylor: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n 1547111153.247 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n 1547111153.247 * [misc]taylor: Taking taylor expansion of 1 in n 1547111153.247 * [misc]backup-simplify: Simplify 1 into 1 1547111153.247 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547111153.247 * [misc]taylor: Taking taylor expansion of k in n 1547111153.247 * [misc]backup-simplify: Simplify k into k 1547111153.247 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547111153.247 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1547111153.247 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1547111153.247 * [misc]taylor: Taking taylor expansion of 2 in n 1547111153.247 * [misc]backup-simplify: Simplify 2 into 2 1547111153.247 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547111153.247 * [misc]taylor: Taking taylor expansion of PI in n 1547111153.247 * [misc]backup-simplify: Simplify PI into PI 1547111153.247 * [misc]taylor: Taking taylor expansion of n in n 1547111153.247 * [misc]backup-simplify: Simplify 0 into 0 1547111153.247 * [misc]backup-simplify: Simplify 1 into 1 1547111153.248 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547111153.248 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547111153.248 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547111153.249 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1547111153.249 * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 1547111153.249 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547111153.250 * [misc]backup-simplify: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) 1547111153.251 * [misc]backup-simplify: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 1547111153.251 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 1547111153.252 * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) 1547111153.253 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 1547111153.253 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 1547111153.253 * [misc]backup-simplify: Simplify 0 into 0 1547111153.255 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1547111153.255 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) 1547111153.255 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n 1547111153.255 * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n 1547111153.255 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1547111153.255 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547111153.255 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n 1547111153.255 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n 1547111153.255 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111153.255 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111153.255 * [misc]taylor: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n 1547111153.255 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n 1547111153.255 * [misc]taylor: Taking taylor expansion of 1 in n 1547111153.256 * [misc]backup-simplify: Simplify 1 into 1 1547111153.256 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547111153.256 * [misc]taylor: Taking taylor expansion of k in n 1547111153.256 * [misc]backup-simplify: Simplify k into k 1547111153.256 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547111153.256 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1547111153.256 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1547111153.256 * [misc]taylor: Taking taylor expansion of 2 in n 1547111153.256 * [misc]backup-simplify: Simplify 2 into 2 1547111153.256 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547111153.256 * [misc]taylor: Taking taylor expansion of PI in n 1547111153.256 * [misc]backup-simplify: Simplify PI into PI 1547111153.256 * [misc]taylor: Taking taylor expansion of n in n 1547111153.256 * [misc]backup-simplify: Simplify 0 into 0 1547111153.256 * [misc]backup-simplify: Simplify 1 into 1 1547111153.256 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547111153.256 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547111153.257 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547111153.257 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1547111153.257 * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 1547111153.258 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547111153.258 * [misc]backup-simplify: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) 1547111153.259 * [misc]backup-simplify: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 1547111153.260 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 1547111153.260 * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) 1547111153.261 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 1547111153.262 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 1547111153.263 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1547111153.264 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1547111153.266 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1547111153.267 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1547111153.267 * [misc]backup-simplify: Simplify (- 0) into 0 1547111153.267 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111153.267 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547111153.268 * [misc]backup-simplify: Simplify (+ (* (- 1 (/ 1 k)) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1547111153.268 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into 0 1547111153.269 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1547111153.270 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into 0 1547111153.270 * [misc]backup-simplify: Simplify (- 0) into 0 1547111153.270 * [misc]backup-simplify: Simplify 0 into 0 1547111153.270 * [misc]backup-simplify: Simplify 0 into 0 1547111153.271 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1547111153.271 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) 1547111153.271 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n 1547111153.271 * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n 1547111153.271 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1547111153.271 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547111153.271 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n 1547111153.271 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n 1547111153.271 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111153.271 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111153.271 * [misc]taylor: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n 1547111153.271 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n 1547111153.271 * [misc]taylor: Taking taylor expansion of 1 in n 1547111153.271 * [misc]backup-simplify: Simplify 1 into 1 1547111153.271 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547111153.271 * [misc]taylor: Taking taylor expansion of k in n 1547111153.271 * [misc]backup-simplify: Simplify k into k 1547111153.271 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547111153.271 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1547111153.271 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1547111153.271 * [misc]taylor: Taking taylor expansion of 2 in n 1547111153.271 * [misc]backup-simplify: Simplify 2 into 2 1547111153.271 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547111153.271 * [misc]taylor: Taking taylor expansion of PI in n 1547111153.271 * [misc]backup-simplify: Simplify PI into PI 1547111153.271 * [misc]taylor: Taking taylor expansion of n in n 1547111153.271 * [misc]backup-simplify: Simplify 0 into 0 1547111153.271 * [misc]backup-simplify: Simplify 1 into 1 1547111153.272 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547111153.272 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547111153.272 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547111153.272 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1547111153.272 * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 1547111153.273 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547111153.273 * [misc]backup-simplify: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) 1547111153.273 * [misc]backup-simplify: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 1547111153.274 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 1547111153.274 * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) 1547111153.275 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 1547111153.275 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 1547111153.277 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3)))))))) 1547111153.277 * [misc]backup-simplify: Simplify (* (/ 1 (sqrt (/ 1 (- k)))) (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2))) into (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) 1547111153.277 * [misc]approximate: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in (k n) around 0 1547111153.277 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in n 1547111153.277 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n 1547111153.277 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n 1547111153.277 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n 1547111153.277 * [misc]taylor: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n 1547111153.277 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111153.277 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111153.277 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in n 1547111153.277 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547111153.277 * [misc]taylor: Taking taylor expansion of k in n 1547111153.277 * [misc]backup-simplify: Simplify k into k 1547111153.277 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547111153.277 * [misc]taylor: Taking taylor expansion of 1 in n 1547111153.277 * [misc]backup-simplify: Simplify 1 into 1 1547111153.277 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1547111153.277 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1547111153.277 * [misc]taylor: Taking taylor expansion of -2 in n 1547111153.277 * [misc]backup-simplify: Simplify -2 into -2 1547111153.277 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547111153.277 * [misc]taylor: Taking taylor expansion of PI in n 1547111153.277 * [misc]backup-simplify: Simplify PI into PI 1547111153.277 * [misc]taylor: Taking taylor expansion of n in n 1547111153.277 * [misc]backup-simplify: Simplify 0 into 0 1547111153.277 * [misc]backup-simplify: Simplify 1 into 1 1547111153.278 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547111153.278 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547111153.278 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1547111153.278 * [misc]backup-simplify: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 1547111153.278 * [misc]backup-simplify: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1)) 1547111153.279 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547111153.279 * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 1547111153.279 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 1547111153.279 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1547111153.279 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1547111153.279 * [misc]taylor: Taking taylor expansion of -1 in n 1547111153.279 * [misc]backup-simplify: Simplify -1 into -1 1547111153.279 * [misc]taylor: Taking taylor expansion of k in n 1547111153.279 * [misc]backup-simplify: Simplify k into k 1547111153.279 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1547111153.279 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1547111153.280 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1547111153.280 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1547111153.280 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) 1547111153.280 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in k 1547111153.280 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k 1547111153.280 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k 1547111153.280 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k 1547111153.280 * [misc]taylor: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k 1547111153.280 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111153.280 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111153.280 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in k 1547111153.280 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547111153.280 * [misc]taylor: Taking taylor expansion of k in k 1547111153.280 * [misc]backup-simplify: Simplify 0 into 0 1547111153.280 * [misc]backup-simplify: Simplify 1 into 1 1547111153.280 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547111153.280 * [misc]taylor: Taking taylor expansion of 1 in k 1547111153.280 * [misc]backup-simplify: Simplify 1 into 1 1547111153.280 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1547111153.280 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1547111153.280 * [misc]taylor: Taking taylor expansion of -2 in k 1547111153.280 * [misc]backup-simplify: Simplify -2 into -2 1547111153.280 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1547111153.281 * [misc]taylor: Taking taylor expansion of PI in k 1547111153.281 * [misc]backup-simplify: Simplify PI into PI 1547111153.281 * [misc]taylor: Taking taylor expansion of n in k 1547111153.281 * [misc]backup-simplify: Simplify n into n 1547111153.281 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1547111153.281 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1547111153.281 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1547111153.281 * [misc]backup-simplify: Simplify (+ 1 0) into 1 1547111153.281 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1547111153.281 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1547111153.281 * [misc]backup-simplify: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) 1547111153.281 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1547111153.281 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1547111153.281 * [misc]taylor: Taking taylor expansion of -1 in k 1547111153.281 * [misc]backup-simplify: Simplify -1 into -1 1547111153.281 * [misc]taylor: Taking taylor expansion of k in k 1547111153.281 * [misc]backup-simplify: Simplify 0 into 0 1547111153.281 * [misc]backup-simplify: Simplify 1 into 1 1547111153.282 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1547111153.282 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547111153.282 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1547111153.282 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) 1547111153.282 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in k 1547111153.282 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k 1547111153.282 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k 1547111153.282 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k 1547111153.282 * [misc]taylor: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k 1547111153.282 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111153.282 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111153.282 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in k 1547111153.282 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547111153.282 * [misc]taylor: Taking taylor expansion of k in k 1547111153.282 * [misc]backup-simplify: Simplify 0 into 0 1547111153.282 * [misc]backup-simplify: Simplify 1 into 1 1547111153.282 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547111153.282 * [misc]taylor: Taking taylor expansion of 1 in k 1547111153.282 * [misc]backup-simplify: Simplify 1 into 1 1547111153.283 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1547111153.283 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1547111153.283 * [misc]taylor: Taking taylor expansion of -2 in k 1547111153.283 * [misc]backup-simplify: Simplify -2 into -2 1547111153.283 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1547111153.283 * [misc]taylor: Taking taylor expansion of PI in k 1547111153.283 * [misc]backup-simplify: Simplify PI into PI 1547111153.283 * [misc]taylor: Taking taylor expansion of n in k 1547111153.283 * [misc]backup-simplify: Simplify n into n 1547111153.283 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1547111153.283 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1547111153.283 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1547111153.283 * [misc]backup-simplify: Simplify (+ 1 0) into 1 1547111153.283 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1547111153.283 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1547111153.283 * [misc]backup-simplify: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) 1547111153.283 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1547111153.283 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1547111153.283 * [misc]taylor: Taking taylor expansion of -1 in k 1547111153.283 * [misc]backup-simplify: Simplify -1 into -1 1547111153.283 * [misc]taylor: Taking taylor expansion of k in k 1547111153.283 * [misc]backup-simplify: Simplify 0 into 0 1547111153.283 * [misc]backup-simplify: Simplify 1 into 1 1547111153.283 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1547111153.284 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547111153.284 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1547111153.284 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) 1547111153.284 * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n 1547111153.284 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1547111153.284 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547111153.284 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n 1547111153.284 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n 1547111153.284 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111153.284 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111153.284 * [misc]taylor: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n 1547111153.284 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1547111153.284 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1547111153.284 * [misc]taylor: Taking taylor expansion of -2 in n 1547111153.284 * [misc]backup-simplify: Simplify -2 into -2 1547111153.284 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547111153.284 * [misc]taylor: Taking taylor expansion of PI in n 1547111153.284 * [misc]backup-simplify: Simplify PI into PI 1547111153.284 * [misc]taylor: Taking taylor expansion of n in n 1547111153.284 * [misc]backup-simplify: Simplify 0 into 0 1547111153.284 * [misc]backup-simplify: Simplify 1 into 1 1547111153.284 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547111153.285 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547111153.285 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1547111153.285 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in n 1547111153.285 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547111153.285 * [misc]taylor: Taking taylor expansion of k in n 1547111153.285 * [misc]backup-simplify: Simplify k into k 1547111153.285 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547111153.285 * [misc]taylor: Taking taylor expansion of 1 in n 1547111153.285 * [misc]backup-simplify: Simplify 1 into 1 1547111153.286 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547111153.286 * [misc]backup-simplify: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 1547111153.286 * [misc]backup-simplify: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) 1547111153.287 * [misc]backup-simplify: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 1547111153.287 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 1547111153.287 * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) 1547111153.288 * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) 1547111153.288 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1547111153.289 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1547111153.289 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) 1547111153.289 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n 1547111153.289 * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n 1547111153.289 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1547111153.289 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547111153.289 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n 1547111153.289 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n 1547111153.289 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111153.289 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111153.289 * [misc]taylor: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n 1547111153.289 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1547111153.289 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1547111153.289 * [misc]taylor: Taking taylor expansion of -2 in n 1547111153.289 * [misc]backup-simplify: Simplify -2 into -2 1547111153.289 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547111153.289 * [misc]taylor: Taking taylor expansion of PI in n 1547111153.289 * [misc]backup-simplify: Simplify PI into PI 1547111153.289 * [misc]taylor: Taking taylor expansion of n in n 1547111153.289 * [misc]backup-simplify: Simplify 0 into 0 1547111153.289 * [misc]backup-simplify: Simplify 1 into 1 1547111153.289 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547111153.290 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547111153.290 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1547111153.290 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in n 1547111153.290 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547111153.290 * [misc]taylor: Taking taylor expansion of k in n 1547111153.290 * [misc]backup-simplify: Simplify k into k 1547111153.290 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547111153.290 * [misc]taylor: Taking taylor expansion of 1 in n 1547111153.290 * [misc]backup-simplify: Simplify 1 into 1 1547111153.290 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547111153.291 * [misc]backup-simplify: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 1547111153.291 * [misc]backup-simplify: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) 1547111153.291 * [misc]backup-simplify: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 1547111153.292 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 1547111153.292 * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) 1547111153.293 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) 1547111153.293 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) 1547111153.294 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547111153.294 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1547111153.294 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111153.294 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1547111153.295 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1547111153.296 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1547111153.297 * [misc]backup-simplify: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (/ 1 k) 1))) into 0 1547111153.297 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into 0 1547111153.298 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1547111153.299 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into 0 1547111153.299 * [misc]backup-simplify: Simplify 0 into 0 1547111153.299 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111153.300 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1547111153.300 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) 1547111153.301 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n 1547111153.301 * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n 1547111153.301 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1547111153.301 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547111153.301 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n 1547111153.301 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n 1547111153.301 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111153.301 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111153.301 * [misc]taylor: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n 1547111153.301 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1547111153.301 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1547111153.301 * [misc]taylor: Taking taylor expansion of -2 in n 1547111153.301 * [misc]backup-simplify: Simplify -2 into -2 1547111153.301 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547111153.301 * [misc]taylor: Taking taylor expansion of PI in n 1547111153.301 * [misc]backup-simplify: Simplify PI into PI 1547111153.301 * [misc]taylor: Taking taylor expansion of n in n 1547111153.301 * [misc]backup-simplify: Simplify 0 into 0 1547111153.301 * [misc]backup-simplify: Simplify 1 into 1 1547111153.301 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547111153.301 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547111153.302 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1547111153.302 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in n 1547111153.302 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547111153.302 * [misc]taylor: Taking taylor expansion of k in n 1547111153.302 * [misc]backup-simplify: Simplify k into k 1547111153.302 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547111153.302 * [misc]taylor: Taking taylor expansion of 1 in n 1547111153.302 * [misc]backup-simplify: Simplify 1 into 1 1547111153.302 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547111153.302 * [misc]backup-simplify: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 1547111153.302 * [misc]backup-simplify: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) 1547111153.303 * [misc]backup-simplify: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 1547111153.303 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 1547111153.304 * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) 1547111153.304 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) 1547111153.305 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) 1547111153.306 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (* 1 (/ 1 (- k)))) (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))))))))) 1547111153.306 * * * [misc]progress: simplifying candidates 1547111153.306 * * * * [misc]progress: [ 1 / 80 ] simplifiying candidate # 1547111153.306 * [enter]simplify: Simplifying (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)) 1547111153.307 * * [misc]simplify: iters left: 6 (11 enodes) 1547111153.311 * * [misc]simplify: iters left: 5 (29 enodes) 1547111153.319 * * [misc]simplify: iters left: 4 (59 enodes) 1547111153.340 * * [misc]simplify: iters left: 3 (142 enodes) 1547111153.390 * * [misc]simplify: iters left: 2 (497 enodes) 1547111153.813 * [exit]simplify: Simplified to (* (- 1/2 (/ k 2)) (log (* (* 2 PI) n))) 1547111153.813 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ 1 (sqrt k)) (exp (* (- 1/2 (/ k 2)) (log (* (* 2 PI) n)))))) 1547111153.813 * * * * [misc]progress: [ 2 / 80 ] simplifiying candidate # 1547111153.814 * * * * [misc]progress: [ 3 / 80 ] simplifiying candidate # 1547111153.814 * [enter]simplify: Simplifying (* (* 2 PI) n) 1547111153.814 * * [misc]simplify: iters left: 4 (5 enodes) 1547111153.815 * * [misc]simplify: iters left: 3 (9 enodes) 1547111153.819 * * [misc]simplify: iters left: 2 (15 enodes) 1547111153.821 * * [misc]simplify: iters left: 1 (17 enodes) 1547111153.823 * [exit]simplify: Simplified to (* (* 2 PI) n) 1547111153.823 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (* 1 (/ (- 1 k) 2))))) 1547111153.823 * * * * [misc]progress: [ 4 / 80 ] simplifiying candidate # 1547111153.824 * [enter]simplify: Simplifying (pow (* (* 2 PI) n) (/ k 2)) 1547111153.824 * * [misc]simplify: iters left: 5 (8 enodes) 1547111153.825 * * [misc]simplify: iters left: 4 (12 enodes) 1547111153.827 * * [misc]simplify: iters left: 3 (18 enodes) 1547111153.829 * * [misc]simplify: iters left: 2 (20 enodes) 1547111153.832 * [exit]simplify: Simplified to (pow (* 2 (* n PI)) (/ k 2)) 1547111153.832 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ 1 (sqrt k)) (/ (pow (* (* 2 PI) n) (/ 1 2)) (pow (* 2 (* n PI)) (/ k 2))))) 1547111153.832 * * * * [misc]progress: [ 5 / 80 ] simplifiying candidate # 1547111153.832 * [enter]simplify: Simplifying (cbrt (/ (- 1 k) 2)) 1547111153.832 * * [misc]simplify: iters left: 5 (6 enodes) 1547111153.835 * * [misc]simplify: iters left: 4 (14 enodes) 1547111153.839 * * [misc]simplify: iters left: 3 (17 enodes) 1547111153.843 * * [misc]simplify: iters left: 2 (19 enodes) 1547111153.847 * [exit]simplify: Simplified to (cbrt (/ (- 1 k) 2)) 1547111153.848 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) (cbrt (/ (- 1 k) 2))))) 1547111153.848 * * * * [misc]progress: [ 6 / 80 ] simplifiying candidate # 1547111153.848 * [enter]simplify: Simplifying (sqrt (/ (- 1 k) 2)) 1547111153.848 * * [misc]simplify: iters left: 5 (6 enodes) 1547111153.851 * * [misc]simplify: iters left: 4 (14 enodes) 1547111153.854 * * [misc]simplify: iters left: 3 (17 enodes) 1547111153.859 * * [misc]simplify: iters left: 2 (19 enodes) 1547111153.863 * [exit]simplify: Simplified to (sqrt (/ (- 1 k) 2)) 1547111153.863 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (sqrt (/ (- 1 k) 2))) (sqrt (/ (- 1 k) 2))))) 1547111153.863 * * * * [misc]progress: [ 7 / 80 ] simplifiying candidate # 1547111153.864 * [enter]simplify: Simplifying (/ (- 1 k) 2) 1547111153.864 * * [misc]simplify: iters left: 4 (5 enodes) 1547111153.866 * * [misc]simplify: iters left: 3 (13 enodes) 1547111153.869 * * [misc]simplify: iters left: 2 (16 enodes) 1547111153.873 * * [misc]simplify: iters left: 1 (18 enodes) 1547111153.877 * [exit]simplify: Simplified to (/ (- 1 k) 2) 1547111153.877 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) 1) (/ (- 1 k) 2)))) 1547111153.877 * * * * [misc]progress: [ 8 / 80 ] simplifiying candidate # 1547111153.878 * [enter]simplify: Simplifying (/ 1 2) 1547111153.878 * * [misc]simplify: iters left: 2 (3 enodes) 1547111153.879 * * [misc]simplify: iters left: 1 (6 enodes) 1547111153.881 * [exit]simplify: Simplified to 1/2 1547111153.881 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (- 1 k)) 1/2))) 1547111153.881 * * * * [misc]progress: [ 9 / 80 ] simplifiying candidate # 1547111153.881 * [enter]simplify: Simplifying (pow (* 2 PI) (/ (- 1 k) 2)) 1547111153.881 * * [misc]simplify: iters left: 5 (8 enodes) 1547111153.884 * * [misc]simplify: iters left: 4 (17 enodes) 1547111153.889 * * [misc]simplify: iters left: 3 (20 enodes) 1547111153.894 * * [misc]simplify: iters left: 2 (22 enodes) 1547111153.899 * [exit]simplify: Simplified to (pow (* 2 PI) (- 1/2 (/ k 2))) 1547111153.899 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* 2 PI) (- 1/2 (/ k 2))) (pow n (/ (- 1 k) 2))))) 1547111153.899 * * * * [misc]progress: [ 10 / 80 ] simplifiying candidate # 1547111153.899 * * * * [misc]progress: [ 11 / 80 ] simplifiying candidate # 1547111153.899 * * * * [misc]progress: [ 12 / 80 ] simplifiying candidate # 1547111153.899 * * * * [misc]progress: [ 13 / 80 ] simplifiying candidate # 1547111153.900 * * * * [misc]progress: [ 14 / 80 ] simplifiying candidate # 1547111153.900 * * * * [misc]progress: [ 15 / 80 ] simplifiying candidate # 1547111153.900 * * * * [misc]progress: [ 16 / 80 ] simplifiying candidate # 1547111153.900 * * * * [misc]progress: [ 17 / 80 ] simplifiying candidate # 1547111153.900 * * * * [misc]progress: [ 18 / 80 ] simplifiying candidate # 1547111153.900 * [enter]simplify: Simplifying (- 1/2) 1547111153.900 * * [misc]simplify: iters left: 2 (2 enodes) 1547111153.901 * * [misc]simplify: iters left: 1 (3 enodes) 1547111153.902 * [exit]simplify: Simplified to -1/2 1547111153.902 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) 1547111153.902 * * * * [misc]progress: [ 19 / 80 ] simplifiying candidate # 1547111153.902 * [enter]simplify: Simplifying (- 1) 1547111153.902 * * [misc]simplify: iters left: 2 (2 enodes) 1547111153.903 * * [misc]simplify: iters left: 1 (5 enodes) 1547111153.904 * [exit]simplify: Simplified to -1 1547111153.904 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (pow (sqrt k) -1) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) 1547111153.904 * * * * [misc]progress: [ 20 / 80 ] simplifiying candidate # 1547111153.904 * * * * [misc]progress: [ 21 / 80 ] simplifiying candidate # 1547111153.904 * * * * [misc]progress: [ 22 / 80 ] simplifiying candidate # 1547111153.905 * * * * [misc]progress: [ 23 / 80 ] simplifiying candidate # 1547111153.905 * * * * [misc]progress: [ 24 / 80 ] simplifiying candidate # 1547111153.905 * * * * [misc]progress: [ 25 / 80 ] simplifiying candidate # 1547111153.905 * * * * [misc]progress: [ 26 / 80 ] simplifiying candidate # 1547111153.905 * * * * [misc]progress: [ 27 / 80 ] simplifiying candidate # 1547111153.905 * * * * [misc]progress: [ 28 / 80 ] simplifiying candidate # 1547111153.905 * * * * [misc]progress: [ 29 / 80 ] simplifiying candidate # 1547111153.905 * * * * [misc]progress: [ 30 / 80 ] simplifiying candidate # 1547111153.905 * * * * [misc]progress: [ 31 / 80 ] simplifiying candidate # 1547111153.905 * [enter]simplify: Simplifying (cbrt (sqrt k)) 1547111153.905 * * [misc]simplify: iters left: 2 (3 enodes) 1547111153.906 * [exit]simplify: Simplified to (cbrt (sqrt k)) 1547111153.906 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (/ (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) 1547111153.906 * * * * [misc]progress: [ 32 / 80 ] simplifiying candidate # 1547111153.907 * [enter]simplify: Simplifying (sqrt (sqrt k)) 1547111153.907 * * [misc]simplify: iters left: 2 (3 enodes) 1547111153.907 * [exit]simplify: Simplified to (sqrt (sqrt k)) 1547111153.907 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) 1547111153.908 * * * * [misc]progress: [ 33 / 80 ] simplifiying candidate # 1547111153.908 * [enter]simplify: Simplifying (sqrt k) 1547111153.908 * * [misc]simplify: iters left: 1 (2 enodes) 1547111153.908 * [exit]simplify: Simplified to (sqrt k) 1547111153.908 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (/ (/ 1 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) 1547111153.909 * * * * [misc]progress: [ 34 / 80 ] simplifiying candidate # 1547111153.909 * * * * [misc]progress: [ 35 / 80 ] simplifiying candidate # 1547111153.909 * * * * [misc]progress: [ 36 / 80 ] simplifiying candidate # 1547111153.909 * * * * [misc]progress: [ 37 / 80 ] simplifiying candidate # 1547111153.909 * * * * [misc]progress: [ 38 / 80 ] simplifiying candidate # 1547111153.909 * * * * [misc]progress: [ 39 / 80 ] simplifiying candidate # 1547111153.909 * * * * [misc]progress: [ 40 / 80 ] simplifiying candidate # 1547111153.909 * * * * [misc]progress: [ 41 / 80 ] simplifiying candidate # 1547111153.909 * * * * [misc]progress: [ 42 / 80 ] simplifiying candidate # 1547111153.909 * * * * [misc]progress: [ 43 / 80 ] simplifiying candidate # 1547111153.909 * * * * [misc]progress: [ 44 / 80 ] simplifiying candidate # 1547111153.909 * [enter]simplify: Simplifying (+ (- (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))) 1547111153.910 * * [misc]simplify: iters left: 6 (15 enodes) 1547111153.915 * * [misc]simplify: iters left: 5 (34 enodes) 1547111153.926 * * [misc]simplify: iters left: 4 (65 enodes) 1547111153.947 * * [misc]simplify: iters left: 3 (160 enodes) 1547111154.053 * [exit]simplify: Simplified to (- (* (log (* (* n 2) PI)) (- 1/2 (/ k 2))) (log (sqrt k))) 1547111154.053 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (log (* (* n 2) PI)) (- 1/2 (/ k 2))) (log (sqrt k))))) 1547111154.053 * * * * [misc]progress: [ 45 / 80 ] simplifiying candidate # 1547111154.054 * [enter]simplify: Simplifying (+ (- (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))) 1547111154.054 * * [misc]simplify: iters left: 6 (15 enodes) 1547111154.059 * * [misc]simplify: iters left: 5 (34 enodes) 1547111154.070 * * [misc]simplify: iters left: 4 (65 enodes) 1547111154.083 * * [misc]simplify: iters left: 3 (160 enodes) 1547111154.142 * [exit]simplify: Simplified to (- (* (log (* (* n 2) PI)) (- 1/2 (/ k 2))) (log (sqrt k))) 1547111154.142 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (log (* (* n 2) PI)) (- 1/2 (/ k 2))) (log (sqrt k))))) 1547111154.142 * * * * [misc]progress: [ 46 / 80 ] simplifiying candidate # 1547111154.143 * [enter]simplify: Simplifying (+ (- (log (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) 1547111154.143 * * [misc]simplify: iters left: 6 (15 enodes) 1547111154.148 * * [misc]simplify: iters left: 5 (30 enodes) 1547111154.157 * * [misc]simplify: iters left: 4 (50 enodes) 1547111154.171 * * [misc]simplify: iters left: 3 (97 enodes) 1547111154.216 * * [misc]simplify: iters left: 2 (285 enodes) 1547111154.392 * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (log (* 2 (* n PI)))) (log (sqrt k))) 1547111154.392 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (/ (- 1 k) 2) (log (* 2 (* n PI)))) (log (sqrt k))))) 1547111154.392 * * * * [misc]progress: [ 47 / 80 ] simplifiying candidate # 1547111154.392 * [enter]simplify: Simplifying (+ (log (/ 1 (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))) 1547111154.393 * * [misc]simplify: iters left: 6 (15 enodes) 1547111154.396 * * [misc]simplify: iters left: 5 (38 enodes) 1547111154.401 * * [misc]simplify: iters left: 4 (69 enodes) 1547111154.414 * * [misc]simplify: iters left: 3 (167 enodes) 1547111154.493 * [exit]simplify: Simplified to (- (/ (log (* PI (* n 2))) (/ 2 (- 1 k))) (log (sqrt k))) 1547111154.493 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (/ (log (* PI (* n 2))) (/ 2 (- 1 k))) (log (sqrt k))))) 1547111154.493 * * * * [misc]progress: [ 48 / 80 ] simplifiying candidate # 1547111154.493 * [enter]simplify: Simplifying (+ (log (/ 1 (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))) 1547111154.493 * * [misc]simplify: iters left: 6 (15 enodes) 1547111154.496 * * [misc]simplify: iters left: 5 (38 enodes) 1547111154.502 * * [misc]simplify: iters left: 4 (69 enodes) 1547111154.526 * * [misc]simplify: iters left: 3 (167 enodes) 1547111154.608 * [exit]simplify: Simplified to (- (/ (log (* PI (* n 2))) (/ 2 (- 1 k))) (log (sqrt k))) 1547111154.608 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (/ (log (* PI (* n 2))) (/ 2 (- 1 k))) (log (sqrt k))))) 1547111154.608 * * * * [misc]progress: [ 49 / 80 ] simplifiying candidate # 1547111154.609 * [enter]simplify: Simplifying (+ (log (/ 1 (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) 1547111154.609 * * [misc]simplify: iters left: 6 (15 enodes) 1547111154.612 * * [misc]simplify: iters left: 5 (34 enodes) 1547111154.616 * * [misc]simplify: iters left: 4 (54 enodes) 1547111154.624 * * [misc]simplify: iters left: 3 (105 enodes) 1547111154.662 * * [misc]simplify: iters left: 2 (329 enodes) 1547111154.927 * [exit]simplify: Simplified to (- (* (log (* (* n 2) PI)) (- 1/2 (/ k 2))) (log (sqrt k))) 1547111154.927 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (log (* (* n 2) PI)) (- 1/2 (/ k 2))) (log (sqrt k))))) 1547111154.928 * * * * [misc]progress: [ 50 / 80 ] simplifiying candidate # 1547111154.928 * * * * [misc]progress: [ 51 / 80 ] simplifiying candidate # 1547111154.928 * * * * [misc]progress: [ 52 / 80 ] simplifiying candidate # 1547111154.928 * [enter]simplify: Simplifying (* (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k))) (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) 1547111154.928 * * [misc]simplify: iters left: 6 (17 enodes) 1547111154.935 * * [misc]simplify: iters left: 5 (42 enodes) 1547111154.951 * * [misc]simplify: iters left: 4 (98 enodes) 1547111154.994 * * [misc]simplify: iters left: 3 (175 enodes) 1547111155.035 * * [misc]simplify: iters left: 2 (325 enodes) 1547111155.211 * * [misc]simplify: iters left: 1 (454 enodes) 1547111155.418 * [exit]simplify: Simplified to (* (* (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (* (sqrt k) k))) 1547111155.418 * [misc]simplify: Simplified (2 1) to (λ (k n) (cbrt (* (* (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (* (sqrt k) k))))) 1547111155.418 * * * * [misc]progress: [ 53 / 80 ] simplifiying candidate # 1547111155.419 * * * * [misc]progress: [ 54 / 80 ] simplifiying candidate # 1547111155.419 * * * * [misc]progress: [ 55 / 80 ] simplifiying candidate # 1547111155.419 * * * * [misc]progress: [ 56 / 80 ] simplifiying candidate # 1547111155.419 * [enter]simplify: Simplifying (* 1 (pow (* (* 2 PI) n) (/ 1 2))) 1547111155.419 * * [misc]simplify: iters left: 6 (9 enodes) 1547111155.423 * * [misc]simplify: iters left: 5 (17 enodes) 1547111155.428 * * [misc]simplify: iters left: 4 (26 enodes) 1547111155.440 * * [misc]simplify: iters left: 3 (27 enodes) 1547111155.443 * [exit]simplify: Simplified to (sqrt (* PI (* 2 n))) 1547111155.443 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* PI (* 2 n))) (* (sqrt k) (pow (* (* 2 PI) n) (/ k 2))))) 1547111155.443 * [enter]simplify: Simplifying (* (sqrt k) (pow (* (* 2 PI) n) (/ k 2))) 1547111155.443 * * [misc]simplify: iters left: 6 (10 enodes) 1547111155.444 * * [misc]simplify: iters left: 5 (15 enodes) 1547111155.447 * * [misc]simplify: iters left: 4 (21 enodes) 1547111155.449 * * [misc]simplify: iters left: 3 (22 enodes) 1547111155.453 * [exit]simplify: Simplified to (* (pow (* (* 2 PI) n) (/ k 2)) (sqrt k)) 1547111155.453 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (sqrt (* PI (* 2 n))) (* (pow (* (* 2 PI) n) (/ k 2)) (sqrt k)))) 1547111155.453 * * * * [misc]progress: [ 57 / 80 ] simplifiying candidate # 1547111155.453 * * * * [misc]progress: [ 58 / 80 ] simplifiying candidate # 1547111155.453 * [enter]simplify: Simplifying (pow n (/ (- 1 k) 2)) 1547111155.453 * * [misc]simplify: iters left: 5 (7 enodes) 1547111155.455 * * [misc]simplify: iters left: 4 (15 enodes) 1547111155.456 * * [misc]simplify: iters left: 3 (18 enodes) 1547111155.458 * * [misc]simplify: iters left: 2 (20 enodes) 1547111155.461 * [exit]simplify: Simplified to (pow n (- 1/2 (/ k 2))) 1547111155.461 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ 1 (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2))) (pow n (- 1/2 (/ k 2))))) 1547111155.461 * * * * [misc]progress: [ 59 / 80 ] simplifiying candidate # 1547111155.461 * [enter]simplify: Simplifying (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) 1547111155.461 * * [misc]simplify: iters left: 6 (11 enodes) 1547111155.463 * * [misc]simplify: iters left: 5 (23 enodes) 1547111155.466 * * [misc]simplify: iters left: 4 (32 enodes) 1547111155.470 * * [misc]simplify: iters left: 3 (35 enodes) 1547111155.825 * [exit]simplify: Simplified to (cbrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) 1547111155.825 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ 1 (sqrt k)) (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) (cbrt (pow (* PI (* n 2)) (/ (- 1 k) 2))))) 1547111155.825 * * * * [misc]progress: [ 60 / 80 ] simplifiying candidate # 1547111155.825 * [enter]simplify: Simplifying (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) 1547111155.825 * * [misc]simplify: iters left: 6 (11 enodes) 1547111155.828 * * [misc]simplify: iters left: 5 (23 enodes) 1547111155.831 * * [misc]simplify: iters left: 4 (32 enodes) 1547111155.838 * * [misc]simplify: iters left: 3 (35 enodes) 1547111155.842 * [exit]simplify: Simplified to (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) 1547111155.842 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ 1 (sqrt k)) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))))) 1547111155.842 * * * * [misc]progress: [ 61 / 80 ] simplifiying candidate # 1547111155.842 * [enter]simplify: Simplifying (pow (* (* 2 PI) n) (/ (- 1 k) 2)) 1547111155.842 * * [misc]simplify: iters left: 5 (10 enodes) 1547111155.845 * * [misc]simplify: iters left: 4 (22 enodes) 1547111155.851 * * [misc]simplify: iters left: 3 (31 enodes) 1547111155.858 * * [misc]simplify: iters left: 2 (34 enodes) 1547111155.866 * [exit]simplify: Simplified to (pow (* (* n 2) PI) (/ (- 1 k) 2)) 1547111155.866 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ 1 (sqrt k)) 1) (pow (* (* n 2) PI) (/ (- 1 k) 2)))) 1547111155.866 * * * * [misc]progress: [ 62 / 80 ] simplifiying candidate # 1547111155.867 * [enter]simplify: Simplifying (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k)))) 1547111155.867 * * [misc]simplify: iters left: 6 (6 enodes) 1547111155.868 * * [misc]simplify: iters left: 5 (8 enodes) 1547111155.871 * [exit]simplify: Simplified to (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k)))) 1547111155.871 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k)))) (* (cbrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) 1547111155.871 * * * * [misc]progress: [ 63 / 80 ] simplifiying candidate # 1547111155.871 * [enter]simplify: Simplifying (sqrt (/ 1 (sqrt k))) 1547111155.871 * * [misc]simplify: iters left: 4 (5 enodes) 1547111155.873 * * [misc]simplify: iters left: 3 (7 enodes) 1547111155.874 * [exit]simplify: Simplified to (sqrt (/ 1 (sqrt k))) 1547111155.874 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (/ 1 (sqrt k))) (* (sqrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) 1547111155.874 * * * * [misc]progress: [ 64 / 80 ] simplifiying candidate # 1547111155.874 * * * * [misc]progress: [ 65 / 80 ] simplifiying candidate # 1547111155.874 * * * * [misc]progress: [ 66 / 80 ] simplifiying candidate # 1547111155.875 * [enter]simplify: Simplifying (pow (* (* 2 PI) n) (/ k 2)) 1547111155.875 * * [misc]simplify: iters left: 5 (8 enodes) 1547111155.878 * * [misc]simplify: iters left: 4 (12 enodes) 1547111155.881 * * [misc]simplify: iters left: 3 (18 enodes) 1547111155.886 * * [misc]simplify: iters left: 2 (20 enodes) 1547111155.891 * [exit]simplify: Simplified to (pow (* 2 (* n PI)) (/ k 2)) 1547111155.891 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ 1 2))) (pow (* 2 (* n PI)) (/ k 2)))) 1547111155.891 * * * * [misc]progress: [ 67 / 80 ] simplifiying candidate # 1547111155.891 * [enter]simplify: Simplifying (* 1 (pow (* (* 2 PI) n) (/ (- 1 k) 2))) 1547111155.892 * * [misc]simplify: iters left: 6 (11 enodes) 1547111155.896 * * [misc]simplify: iters left: 5 (24 enodes) 1547111155.903 * * [misc]simplify: iters left: 4 (35 enodes) 1547111155.911 * * [misc]simplify: iters left: 3 (38 enodes) 1547111155.919 * [exit]simplify: Simplified to (pow (* (* n PI) 2) (- 1/2 (/ k 2))) 1547111155.919 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (pow (* (* n PI) 2) (- 1/2 (/ k 2))) (sqrt k))) 1547111155.919 * * * * [misc]progress: [ 68 / 80 ] simplifiying candidate # 1547111155.919 * * * * [misc]progress: [ 69 / 80 ] simplifiying candidate # 1547111155.920 * [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))))) 1547111155.920 * * [misc]simplify: iters left: 6 (37 enodes) 1547111155.928 * * [misc]simplify: iters left: 5 (105 enodes) 1547111155.953 * * [misc]simplify: iters left: 4 (339 enodes) 1547111156.162 * [exit]simplify: Simplified to (+ (+ (* (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) -1/2) (+ (* (* (* k (log n)) (* k (log n))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (pow (* PI 2) 1/2) (pow n 1/2)))) (* (* k k) (+ (* (* (log (* PI 2)) (log (* PI 2))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (* (* (log n) (pow n 1/2)) (pow (* PI 2) 1/2)) (* (log (* PI 2)) 1/4))))) 1547111156.162 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ 1 (sqrt k)) (+ (+ (* (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) -1/2) (+ (* (* (* k (log n)) (* k (log n))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (pow (* PI 2) 1/2) (pow n 1/2)))) (* (* k k) (+ (* (* (log (* PI 2)) (log (* PI 2))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (* (* (log n) (pow n 1/2)) (pow (* PI 2) 1/2)) (* (log (* PI 2)) 1/4))))))) 1547111156.162 * * * * [misc]progress: [ 70 / 80 ] simplifiying candidate # 1547111156.162 * [enter]simplify: Simplifying (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) 1547111156.162 * * [misc]simplify: iters left: 6 (15 enodes) 1547111156.166 * * [misc]simplify: iters left: 5 (35 enodes) 1547111156.173 * * [misc]simplify: iters left: 4 (72 enodes) 1547111156.188 * * [misc]simplify: iters left: 3 (234 enodes) 1547111156.280 * [exit]simplify: Simplified to (* (pow n (- 1/2 (* 1/2 k))) (pow (* 2 PI) (- 1/2 (* 1/2 k)))) 1547111156.280 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ 1 (sqrt k)) (* (pow n (- 1/2 (* 1/2 k))) (pow (* 2 PI) (- 1/2 (* 1/2 k)))))) 1547111156.280 * * * * [misc]progress: [ 71 / 80 ] simplifiying candidate # 1547111156.281 * [enter]simplify: Simplifying (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) 1547111156.281 * * [misc]simplify: iters left: 6 (16 enodes) 1547111156.284 * * [misc]simplify: iters left: 5 (35 enodes) 1547111156.295 * * [misc]simplify: iters left: 4 (76 enodes) 1547111156.335 * * [misc]simplify: iters left: 3 (272 enodes) 1547111156.481 * [exit]simplify: Simplified to (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))) 1547111156.481 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ 1 (sqrt k)) (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))))) 1547111156.481 * * * * [misc]progress: [ 72 / 80 ] simplifiying candidate # 1547111156.482 * [enter]simplify: Simplifying (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) 1547111156.482 * [misc]simplify: Simplified (2 1) to (λ (k n) (* +nan.0 (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) 1547111156.482 * * * * [misc]progress: [ 73 / 80 ] simplifiying candidate # 1547111156.482 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) 1547111156.482 * [misc]simplify: Simplified (2 1) to (λ (k n) (* +nan.0 (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) 1547111156.482 * * * * [misc]progress: [ 74 / 80 ] simplifiying candidate # 1547111156.482 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) 1547111156.482 * [misc]simplify: Simplified (2 1) to (λ (k n) (* +nan.0 (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) 1547111156.482 * * * * [misc]progress: [ 75 / 80 ] simplifiying candidate # 1547111156.483 * [enter]simplify: Simplifying (* 2 (* n PI)) 1547111156.483 * * [misc]simplify: iters left: 4 (5 enodes) 1547111156.484 * * [misc]simplify: iters left: 3 (9 enodes) 1547111156.487 * * [misc]simplify: iters left: 2 (15 enodes) 1547111156.491 * * [misc]simplify: iters left: 1 (17 enodes) 1547111156.495 * [exit]simplify: Simplified to (* (* PI n) 2) 1547111156.495 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* PI n) 2) (/ (- 1 k) 2)))) 1547111156.495 * * * * [misc]progress: [ 76 / 80 ] simplifiying candidate # 1547111156.496 * [enter]simplify: Simplifying (* 2 (* n PI)) 1547111156.496 * * [misc]simplify: iters left: 4 (5 enodes) 1547111156.497 * * [misc]simplify: iters left: 3 (9 enodes) 1547111156.500 * * [misc]simplify: iters left: 2 (15 enodes) 1547111156.504 * * [misc]simplify: iters left: 1 (17 enodes) 1547111156.508 * [exit]simplify: Simplified to (* (* PI n) 2) 1547111156.508 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* PI n) 2) (/ (- 1 k) 2)))) 1547111156.508 * * * * [misc]progress: [ 77 / 80 ] simplifiying candidate # 1547111156.509 * [enter]simplify: Simplifying (* 2 (* n PI)) 1547111156.509 * * [misc]simplify: iters left: 4 (5 enodes) 1547111156.510 * * [misc]simplify: iters left: 3 (9 enodes) 1547111156.513 * * [misc]simplify: iters left: 2 (15 enodes) 1547111156.517 * * [misc]simplify: iters left: 1 (17 enodes) 1547111156.522 * [exit]simplify: Simplified to (* (* PI n) 2) 1547111156.522 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* PI n) 2) (/ (- 1 k) 2)))) 1547111156.522 * * * * [misc]progress: [ 78 / 80 ] simplifiying candidate # 1547111156.522 * [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))))))))))))) 1547111156.522 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1547111156.522 * * * * [misc]progress: [ 79 / 80 ] simplifiying candidate # 1547111156.522 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3)))))))) 1547111156.523 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1547111156.523 * * * * [misc]progress: [ 80 / 80 ] simplifiying candidate # 1547111156.523 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))))))))) 1547111156.523 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1547111156.523 * * * [misc]progress: adding candidates to table 1547111157.315 * * [misc]progress: iteration 3 / 4 1547111157.315 * * * [misc]progress: picking best candidate 1547111157.334 * * * * [misc]pick: Picked # 1547111157.335 * * * [misc]progress: localizing error 1547111157.348 * * * [misc]progress: generating rewritten candidates 1547111157.348 * * * * [misc]progress: [ 1 / 3 ] rewriting at (2 2) 1547111157.351 * * * * [misc]progress: [ 2 / 3 ] rewriting at (2 2 1) 1547111157.353 * * * * [misc]progress: [ 3 / 3 ] rewriting at (2) 1547111157.360 * * * [misc]progress: generating series expansions 1547111157.360 * * * * [misc]progress: [ 1 / 3 ] generating series at (2 2) 1547111157.361 * [misc]backup-simplify: Simplify (pow (* (* 2 PI) n) (/ (- 1 k) 2)) into (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) 1547111157.361 * [misc]approximate: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in (n k) around 0 1547111157.361 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k 1547111157.361 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k 1547111157.361 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k 1547111157.361 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 k)) in k 1547111157.361 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111157.361 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111157.361 * [misc]taylor: Taking taylor expansion of (- 1 k) in k 1547111157.361 * [misc]taylor: Taking taylor expansion of 1 in k 1547111157.361 * [misc]backup-simplify: Simplify 1 into 1 1547111157.361 * [misc]taylor: Taking taylor expansion of k in k 1547111157.361 * [misc]backup-simplify: Simplify 0 into 0 1547111157.361 * [misc]backup-simplify: Simplify 1 into 1 1547111157.361 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1547111157.361 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1547111157.361 * [misc]taylor: Taking taylor expansion of 2 in k 1547111157.361 * [misc]backup-simplify: Simplify 2 into 2 1547111157.361 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1547111157.361 * [misc]taylor: Taking taylor expansion of n in k 1547111157.361 * [misc]backup-simplify: Simplify n into n 1547111157.361 * [misc]taylor: Taking taylor expansion of PI in k 1547111157.361 * [misc]backup-simplify: Simplify PI into PI 1547111157.361 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1547111157.361 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1547111157.361 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1547111157.362 * [misc]backup-simplify: Simplify (- 0) into 0 1547111157.362 * [misc]backup-simplify: Simplify (+ 1 0) into 1 1547111157.362 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1547111157.362 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1547111157.362 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1547111157.362 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n 1547111157.362 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n 1547111157.362 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n 1547111157.362 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 k)) in n 1547111157.362 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111157.362 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111157.362 * [misc]taylor: Taking taylor expansion of (- 1 k) in n 1547111157.362 * [misc]taylor: Taking taylor expansion of 1 in n 1547111157.362 * [misc]backup-simplify: Simplify 1 into 1 1547111157.362 * [misc]taylor: Taking taylor expansion of k in n 1547111157.362 * [misc]backup-simplify: Simplify k into k 1547111157.362 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1547111157.362 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1547111157.362 * [misc]taylor: Taking taylor expansion of 2 in n 1547111157.362 * [misc]backup-simplify: Simplify 2 into 2 1547111157.362 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547111157.362 * [misc]taylor: Taking taylor expansion of n in n 1547111157.362 * [misc]backup-simplify: Simplify 0 into 0 1547111157.362 * [misc]backup-simplify: Simplify 1 into 1 1547111157.362 * [misc]taylor: Taking taylor expansion of PI in n 1547111157.362 * [misc]backup-simplify: Simplify PI into PI 1547111157.362 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547111157.363 * [misc]backup-simplify: Simplify (* 2 0) into 0 1547111157.363 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547111157.363 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1547111157.364 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547111157.364 * [misc]backup-simplify: Simplify (- k) into (- k) 1547111157.364 * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) 1547111157.364 * [misc]backup-simplify: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k)) 1547111157.364 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547111157.365 * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) 1547111157.365 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 1547111157.365 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n 1547111157.365 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n 1547111157.365 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n 1547111157.365 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 k)) in n 1547111157.365 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111157.365 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111157.365 * [misc]taylor: Taking taylor expansion of (- 1 k) in n 1547111157.365 * [misc]taylor: Taking taylor expansion of 1 in n 1547111157.365 * [misc]backup-simplify: Simplify 1 into 1 1547111157.365 * [misc]taylor: Taking taylor expansion of k in n 1547111157.365 * [misc]backup-simplify: Simplify k into k 1547111157.365 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1547111157.365 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1547111157.365 * [misc]taylor: Taking taylor expansion of 2 in n 1547111157.365 * [misc]backup-simplify: Simplify 2 into 2 1547111157.365 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547111157.365 * [misc]taylor: Taking taylor expansion of n in n 1547111157.365 * [misc]backup-simplify: Simplify 0 into 0 1547111157.365 * [misc]backup-simplify: Simplify 1 into 1 1547111157.365 * [misc]taylor: Taking taylor expansion of PI in n 1547111157.365 * [misc]backup-simplify: Simplify PI into PI 1547111157.366 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547111157.366 * [misc]backup-simplify: Simplify (* 2 0) into 0 1547111157.366 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547111157.367 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1547111157.367 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547111157.367 * [misc]backup-simplify: Simplify (- k) into (- k) 1547111157.367 * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) 1547111157.367 * [misc]backup-simplify: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k)) 1547111157.367 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547111157.368 * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) 1547111157.368 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 1547111157.368 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) in k 1547111157.368 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) in k 1547111157.368 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111157.368 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111157.368 * [misc]taylor: Taking taylor expansion of (* (- 1 k) (+ (log n) (log (* 2 PI)))) in k 1547111157.368 * [misc]taylor: Taking taylor expansion of (- 1 k) in k 1547111157.369 * [misc]taylor: Taking taylor expansion of 1 in k 1547111157.369 * [misc]backup-simplify: Simplify 1 into 1 1547111157.369 * [misc]taylor: Taking taylor expansion of k in k 1547111157.369 * [misc]backup-simplify: Simplify 0 into 0 1547111157.369 * [misc]backup-simplify: Simplify 1 into 1 1547111157.369 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1547111157.369 * [misc]taylor: Taking taylor expansion of (log n) in k 1547111157.369 * [misc]taylor: Taking taylor expansion of n in k 1547111157.369 * [misc]backup-simplify: Simplify n into n 1547111157.369 * [misc]backup-simplify: Simplify (log n) into (log n) 1547111157.369 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1547111157.369 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1547111157.369 * [misc]taylor: Taking taylor expansion of 2 in k 1547111157.369 * [misc]backup-simplify: Simplify 2 into 2 1547111157.369 * [misc]taylor: Taking taylor expansion of PI in k 1547111157.369 * [misc]backup-simplify: Simplify PI into PI 1547111157.369 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547111157.369 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547111157.369 * [misc]backup-simplify: Simplify (- 0) into 0 1547111157.369 * [misc]backup-simplify: Simplify (+ 1 0) into 1 1547111157.370 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547111157.370 * [misc]backup-simplify: Simplify (* 1 (+ (log n) (log (* 2 PI)))) into (+ (log n) (log (* 2 PI))) 1547111157.370 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1547111157.371 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1547111157.371 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1547111157.372 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1547111157.372 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1547111157.374 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1547111157.374 * [misc]backup-simplify: Simplify (- 0) into 0 1547111157.374 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111157.374 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- 1 k))) into 0 1547111157.375 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547111157.375 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1547111157.376 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0 1547111157.376 * [misc]taylor: Taking taylor expansion of 0 in k 1547111157.376 * [misc]backup-simplify: Simplify 0 into 0 1547111157.376 * [misc]backup-simplify: Simplify 0 into 0 1547111157.377 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1547111157.377 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1547111157.379 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1547111157.379 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111157.379 * [misc]backup-simplify: Simplify (- 1) into -1 1547111157.379 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 1547111157.380 * [misc]backup-simplify: Simplify (+ (* 1 0) (* -1 (+ (log n) (log (* 2 PI))))) into (- (+ (log (* 2 PI)) (log n))) 1547111157.380 * [misc]backup-simplify: Simplify (+ (* 1/2 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1547111157.381 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 1547111157.382 * [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))))))) 1547111157.383 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1547111157.384 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1547111157.387 * [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 1547111157.387 * [misc]backup-simplify: Simplify (- 0) into 0 1547111157.387 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111157.387 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0 1547111157.388 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547111157.388 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1547111157.390 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1547111157.390 * [misc]taylor: Taking taylor expansion of 0 in k 1547111157.390 * [misc]backup-simplify: Simplify 0 into 0 1547111157.390 * [misc]backup-simplify: Simplify 0 into 0 1547111157.390 * [misc]backup-simplify: Simplify 0 into 0 1547111157.391 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1547111157.392 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1547111157.396 * [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 1547111157.397 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111157.397 * [misc]backup-simplify: Simplify (- 0) into 0 1547111157.397 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111157.397 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1547111157.398 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1547111157.400 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 1547111157.401 * [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))))) 1547111157.404 * [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))))) 1547111157.404 * [misc]backup-simplify: Simplify (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) into (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) 1547111157.404 * [misc]approximate: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in (n k) around 0 1547111157.404 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k 1547111157.404 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1547111157.404 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1547111157.405 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k 1547111157.405 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111157.405 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111157.405 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k 1547111157.405 * [misc]taylor: Taking taylor expansion of 1 in k 1547111157.405 * [misc]backup-simplify: Simplify 1 into 1 1547111157.405 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547111157.405 * [misc]taylor: Taking taylor expansion of k in k 1547111157.405 * [misc]backup-simplify: Simplify 0 into 0 1547111157.405 * [misc]backup-simplify: Simplify 1 into 1 1547111157.405 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547111157.405 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1547111157.405 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1547111157.405 * [misc]taylor: Taking taylor expansion of 2 in k 1547111157.405 * [misc]backup-simplify: Simplify 2 into 2 1547111157.405 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1547111157.405 * [misc]taylor: Taking taylor expansion of PI in k 1547111157.405 * [misc]backup-simplify: Simplify PI into PI 1547111157.405 * [misc]taylor: Taking taylor expansion of n in k 1547111157.405 * [misc]backup-simplify: Simplify n into n 1547111157.405 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1547111157.405 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1547111157.405 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1547111157.405 * [misc]backup-simplify: Simplify (- 1) into -1 1547111157.405 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 1547111157.405 * [misc]backup-simplify: Simplify (* 1/2 -1) into -1/2 1547111157.405 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1547111157.406 * [misc]backup-simplify: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 1547111157.406 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n 1547111157.406 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1547111157.406 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1547111157.406 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n 1547111157.406 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111157.406 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111157.406 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n 1547111157.406 * [misc]taylor: Taking taylor expansion of 1 in n 1547111157.406 * [misc]backup-simplify: Simplify 1 into 1 1547111157.406 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547111157.406 * [misc]taylor: Taking taylor expansion of k in n 1547111157.406 * [misc]backup-simplify: Simplify k into k 1547111157.406 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547111157.406 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1547111157.406 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1547111157.406 * [misc]taylor: Taking taylor expansion of 2 in n 1547111157.406 * [misc]backup-simplify: Simplify 2 into 2 1547111157.406 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547111157.406 * [misc]taylor: Taking taylor expansion of PI in n 1547111157.406 * [misc]backup-simplify: Simplify PI into PI 1547111157.406 * [misc]taylor: Taking taylor expansion of n in n 1547111157.406 * [misc]backup-simplify: Simplify 0 into 0 1547111157.406 * [misc]backup-simplify: Simplify 1 into 1 1547111157.406 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547111157.406 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547111157.407 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547111157.407 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1547111157.407 * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 1547111157.407 * [misc]backup-simplify: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k))) 1547111157.407 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547111157.408 * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 1547111157.408 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 1547111157.408 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n 1547111157.408 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1547111157.408 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1547111157.408 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n 1547111157.408 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111157.408 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111157.408 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n 1547111157.408 * [misc]taylor: Taking taylor expansion of 1 in n 1547111157.408 * [misc]backup-simplify: Simplify 1 into 1 1547111157.408 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547111157.408 * [misc]taylor: Taking taylor expansion of k in n 1547111157.408 * [misc]backup-simplify: Simplify k into k 1547111157.409 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547111157.409 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1547111157.409 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1547111157.409 * [misc]taylor: Taking taylor expansion of 2 in n 1547111157.409 * [misc]backup-simplify: Simplify 2 into 2 1547111157.409 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547111157.409 * [misc]taylor: Taking taylor expansion of PI in n 1547111157.409 * [misc]backup-simplify: Simplify PI into PI 1547111157.409 * [misc]taylor: Taking taylor expansion of n in n 1547111157.409 * [misc]backup-simplify: Simplify 0 into 0 1547111157.409 * [misc]backup-simplify: Simplify 1 into 1 1547111157.409 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547111157.409 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547111157.409 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547111157.410 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1547111157.410 * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 1547111157.410 * [misc]backup-simplify: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k))) 1547111157.410 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547111157.411 * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 1547111157.411 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 1547111157.411 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k 1547111157.411 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k 1547111157.411 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111157.411 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111157.411 * [misc]taylor: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k 1547111157.411 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k 1547111157.411 * [misc]taylor: Taking taylor expansion of 1 in k 1547111157.411 * [misc]backup-simplify: Simplify 1 into 1 1547111157.411 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547111157.411 * [misc]taylor: Taking taylor expansion of k in k 1547111157.411 * [misc]backup-simplify: Simplify 0 into 0 1547111157.411 * [misc]backup-simplify: Simplify 1 into 1 1547111157.411 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547111157.411 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1547111157.411 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1547111157.411 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1547111157.411 * [misc]taylor: Taking taylor expansion of 2 in k 1547111157.411 * [misc]backup-simplify: Simplify 2 into 2 1547111157.411 * [misc]taylor: Taking taylor expansion of PI in k 1547111157.411 * [misc]backup-simplify: Simplify PI into PI 1547111157.412 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547111157.412 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547111157.412 * [misc]taylor: Taking taylor expansion of (log n) in k 1547111157.412 * [misc]taylor: Taking taylor expansion of n in k 1547111157.412 * [misc]backup-simplify: Simplify n into n 1547111157.412 * [misc]backup-simplify: Simplify (log n) into (log n) 1547111157.412 * [misc]backup-simplify: Simplify (- 1) into -1 1547111157.412 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 1547111157.412 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1547111157.413 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1547111157.413 * [misc]backup-simplify: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n))) 1547111157.413 * [misc]backup-simplify: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1547111157.414 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 1547111157.414 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 1547111157.415 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1547111157.415 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1547111157.417 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1547111157.417 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1547111157.417 * [misc]backup-simplify: Simplify (- 0) into 0 1547111157.417 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111157.417 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- 1 (/ 1 k)))) into 0 1547111157.418 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547111157.418 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1547111157.420 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1547111157.420 * [misc]taylor: Taking taylor expansion of 0 in k 1547111157.420 * [misc]backup-simplify: Simplify 0 into 0 1547111157.420 * [misc]backup-simplify: Simplify 0 into 0 1547111157.420 * [misc]backup-simplify: Simplify 0 into 0 1547111157.421 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111157.421 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1547111157.424 * [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 1547111157.424 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1547111157.424 * [misc]backup-simplify: Simplify (- 0) into 0 1547111157.425 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111157.425 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0 1547111157.425 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547111157.426 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1547111157.427 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1547111157.427 * [misc]taylor: Taking taylor expansion of 0 in k 1547111157.427 * [misc]backup-simplify: Simplify 0 into 0 1547111157.427 * [misc]backup-simplify: Simplify 0 into 0 1547111157.427 * [misc]backup-simplify: Simplify 0 into 0 1547111157.427 * [misc]backup-simplify: Simplify 0 into 0 1547111157.428 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111157.429 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1547111157.434 * [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 1547111157.434 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1547111157.434 * [misc]backup-simplify: Simplify (- 0) into 0 1547111157.434 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111157.434 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0 1547111157.435 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547111157.435 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1547111157.438 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1547111157.438 * [misc]taylor: Taking taylor expansion of 0 in k 1547111157.438 * [misc]backup-simplify: Simplify 0 into 0 1547111157.438 * [misc]backup-simplify: Simplify 0 into 0 1547111157.438 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) 1547111157.439 * [misc]backup-simplify: Simplify (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) into (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) 1547111157.439 * [misc]approximate: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in (n k) around 0 1547111157.439 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k 1547111157.439 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k 1547111157.439 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k 1547111157.439 * [misc]taylor: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k 1547111157.439 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111157.439 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111157.439 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in k 1547111157.439 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547111157.439 * [misc]taylor: Taking taylor expansion of k in k 1547111157.439 * [misc]backup-simplify: Simplify 0 into 0 1547111157.439 * [misc]backup-simplify: Simplify 1 into 1 1547111157.439 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547111157.439 * [misc]taylor: Taking taylor expansion of 1 in k 1547111157.439 * [misc]backup-simplify: Simplify 1 into 1 1547111157.439 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1547111157.439 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1547111157.439 * [misc]taylor: Taking taylor expansion of -2 in k 1547111157.439 * [misc]backup-simplify: Simplify -2 into -2 1547111157.439 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1547111157.439 * [misc]taylor: Taking taylor expansion of PI in k 1547111157.439 * [misc]backup-simplify: Simplify PI into PI 1547111157.439 * [misc]taylor: Taking taylor expansion of n in k 1547111157.439 * [misc]backup-simplify: Simplify n into n 1547111157.439 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1547111157.439 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1547111157.439 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1547111157.439 * [misc]backup-simplify: Simplify (+ 1 0) into 1 1547111157.439 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1547111157.440 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1547111157.440 * [misc]backup-simplify: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) 1547111157.440 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n 1547111157.440 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n 1547111157.440 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n 1547111157.440 * [misc]taylor: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n 1547111157.440 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111157.440 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111157.440 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in n 1547111157.440 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547111157.440 * [misc]taylor: Taking taylor expansion of k in n 1547111157.440 * [misc]backup-simplify: Simplify k into k 1547111157.440 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547111157.440 * [misc]taylor: Taking taylor expansion of 1 in n 1547111157.440 * [misc]backup-simplify: Simplify 1 into 1 1547111157.440 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1547111157.440 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1547111157.440 * [misc]taylor: Taking taylor expansion of -2 in n 1547111157.440 * [misc]backup-simplify: Simplify -2 into -2 1547111157.440 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547111157.440 * [misc]taylor: Taking taylor expansion of PI in n 1547111157.440 * [misc]backup-simplify: Simplify PI into PI 1547111157.440 * [misc]taylor: Taking taylor expansion of n in n 1547111157.440 * [misc]backup-simplify: Simplify 0 into 0 1547111157.440 * [misc]backup-simplify: Simplify 1 into 1 1547111157.440 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547111157.440 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547111157.441 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1547111157.441 * [misc]backup-simplify: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 1547111157.441 * [misc]backup-simplify: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1)) 1547111157.441 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547111157.442 * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 1547111157.442 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 1547111157.442 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n 1547111157.442 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n 1547111157.442 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n 1547111157.442 * [misc]taylor: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n 1547111157.442 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111157.442 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111157.442 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in n 1547111157.442 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547111157.442 * [misc]taylor: Taking taylor expansion of k in n 1547111157.442 * [misc]backup-simplify: Simplify k into k 1547111157.442 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547111157.442 * [misc]taylor: Taking taylor expansion of 1 in n 1547111157.442 * [misc]backup-simplify: Simplify 1 into 1 1547111157.442 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1547111157.442 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1547111157.442 * [misc]taylor: Taking taylor expansion of -2 in n 1547111157.442 * [misc]backup-simplify: Simplify -2 into -2 1547111157.442 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547111157.442 * [misc]taylor: Taking taylor expansion of PI in n 1547111157.442 * [misc]backup-simplify: Simplify PI into PI 1547111157.442 * [misc]taylor: Taking taylor expansion of n in n 1547111157.442 * [misc]backup-simplify: Simplify 0 into 0 1547111157.442 * [misc]backup-simplify: Simplify 1 into 1 1547111157.443 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547111157.443 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547111157.443 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1547111157.443 * [misc]backup-simplify: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 1547111157.443 * [misc]backup-simplify: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1)) 1547111157.444 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547111157.444 * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 1547111157.444 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 1547111157.444 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k 1547111157.444 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) in k 1547111157.444 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111157.445 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111157.445 * [misc]taylor: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) in k 1547111157.445 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in k 1547111157.445 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547111157.445 * [misc]taylor: Taking taylor expansion of k in k 1547111157.445 * [misc]backup-simplify: Simplify 0 into 0 1547111157.445 * [misc]backup-simplify: Simplify 1 into 1 1547111157.445 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547111157.445 * [misc]taylor: Taking taylor expansion of 1 in k 1547111157.445 * [misc]backup-simplify: Simplify 1 into 1 1547111157.445 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1547111157.445 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1547111157.445 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1547111157.445 * [misc]taylor: Taking taylor expansion of -2 in k 1547111157.445 * [misc]backup-simplify: Simplify -2 into -2 1547111157.445 * [misc]taylor: Taking taylor expansion of PI in k 1547111157.445 * [misc]backup-simplify: Simplify PI into PI 1547111157.445 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547111157.445 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1547111157.445 * [misc]taylor: Taking taylor expansion of (log n) in k 1547111157.445 * [misc]taylor: Taking taylor expansion of n in k 1547111157.445 * [misc]backup-simplify: Simplify n into n 1547111157.445 * [misc]backup-simplify: Simplify (log n) into (log n) 1547111157.446 * [misc]backup-simplify: Simplify (+ 1 0) into 1 1547111157.446 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1547111157.446 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1547111157.446 * [misc]backup-simplify: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n)) 1547111157.447 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1547111157.447 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 1547111157.447 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 1547111157.448 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1547111157.448 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1547111157.450 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1547111157.450 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1547111157.450 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111157.450 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (+ (/ 1 k) 1))) into 0 1547111157.451 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547111157.451 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1547111157.452 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1547111157.452 * [misc]taylor: Taking taylor expansion of 0 in k 1547111157.452 * [misc]backup-simplify: Simplify 0 into 0 1547111157.452 * [misc]backup-simplify: Simplify 0 into 0 1547111157.452 * [misc]backup-simplify: Simplify 0 into 0 1547111157.453 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111157.454 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1547111157.457 * [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 1547111157.457 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1547111157.457 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111157.457 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0 1547111157.458 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547111157.458 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1547111157.460 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1547111157.460 * [misc]taylor: Taking taylor expansion of 0 in k 1547111157.460 * [misc]backup-simplify: Simplify 0 into 0 1547111157.460 * [misc]backup-simplify: Simplify 0 into 0 1547111157.460 * [misc]backup-simplify: Simplify 0 into 0 1547111157.460 * [misc]backup-simplify: Simplify 0 into 0 1547111157.461 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111157.462 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1547111157.468 * [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 1547111157.468 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1547111157.469 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111157.469 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1))))) into 0 1547111157.470 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547111157.471 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 1547111157.474 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1547111157.474 * [misc]taylor: Taking taylor expansion of 0 in k 1547111157.474 * [misc]backup-simplify: Simplify 0 into 0 1547111157.474 * [misc]backup-simplify: Simplify 0 into 0 1547111157.475 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) 1547111157.475 * * * * [misc]progress: [ 2 / 3 ] generating series at (2 2 1) 1547111157.476 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1547111157.476 * [misc]approximate: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1547111157.476 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1547111157.476 * [misc]taylor: Taking taylor expansion of 2 in n 1547111157.476 * [misc]backup-simplify: Simplify 2 into 2 1547111157.476 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547111157.476 * [misc]taylor: Taking taylor expansion of n in n 1547111157.476 * [misc]backup-simplify: Simplify 0 into 0 1547111157.476 * [misc]backup-simplify: Simplify 1 into 1 1547111157.476 * [misc]taylor: Taking taylor expansion of PI in n 1547111157.476 * [misc]backup-simplify: Simplify PI into PI 1547111157.476 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1547111157.476 * [misc]taylor: Taking taylor expansion of 2 in n 1547111157.476 * [misc]backup-simplify: Simplify 2 into 2 1547111157.476 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547111157.476 * [misc]taylor: Taking taylor expansion of n in n 1547111157.476 * [misc]backup-simplify: Simplify 0 into 0 1547111157.476 * [misc]backup-simplify: Simplify 1 into 1 1547111157.476 * [misc]taylor: Taking taylor expansion of PI in n 1547111157.476 * [misc]backup-simplify: Simplify PI into PI 1547111157.477 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547111157.477 * [misc]backup-simplify: Simplify (* 2 0) into 0 1547111157.477 * [misc]backup-simplify: Simplify 0 into 0 1547111157.477 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547111157.478 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1547111157.478 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547111157.480 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1547111157.481 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1547111157.481 * [misc]backup-simplify: Simplify 0 into 0 1547111157.483 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1547111157.484 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1547111157.484 * [misc]backup-simplify: Simplify 0 into 0 1547111157.486 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1547111157.488 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1547111157.488 * [misc]backup-simplify: Simplify 0 into 0 1547111157.491 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1547111157.494 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1547111157.494 * [misc]backup-simplify: Simplify 0 into 0 1547111157.497 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1547111157.500 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1547111157.500 * [misc]backup-simplify: Simplify 0 into 0 1547111157.505 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1547111157.509 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1547111157.509 * [misc]backup-simplify: Simplify 0 into 0 1547111157.509 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1547111157.509 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 n)) into (* 2 (/ PI n)) 1547111157.509 * [misc]approximate: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1547111157.509 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1547111157.510 * [misc]taylor: Taking taylor expansion of 2 in n 1547111157.510 * [misc]backup-simplify: Simplify 2 into 2 1547111157.510 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547111157.510 * [misc]taylor: Taking taylor expansion of PI in n 1547111157.510 * [misc]backup-simplify: Simplify PI into PI 1547111157.510 * [misc]taylor: Taking taylor expansion of n in n 1547111157.510 * [misc]backup-simplify: Simplify 0 into 0 1547111157.510 * [misc]backup-simplify: Simplify 1 into 1 1547111157.510 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547111157.510 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1547111157.510 * [misc]taylor: Taking taylor expansion of 2 in n 1547111157.510 * [misc]backup-simplify: Simplify 2 into 2 1547111157.510 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547111157.510 * [misc]taylor: Taking taylor expansion of PI in n 1547111157.510 * [misc]backup-simplify: Simplify PI into PI 1547111157.510 * [misc]taylor: Taking taylor expansion of n in n 1547111157.510 * [misc]backup-simplify: Simplify 0 into 0 1547111157.510 * [misc]backup-simplify: Simplify 1 into 1 1547111157.510 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547111157.511 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547111157.511 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547111157.512 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1547111157.513 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1547111157.513 * [misc]backup-simplify: Simplify 0 into 0 1547111157.514 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111157.516 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1547111157.517 * [misc]backup-simplify: Simplify 0 into 0 1547111157.518 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111157.520 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1547111157.520 * [misc]backup-simplify: Simplify 0 into 0 1547111157.522 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111157.524 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1547111157.524 * [misc]backup-simplify: Simplify 0 into 0 1547111157.526 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111157.528 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1547111157.529 * [misc]backup-simplify: Simplify 0 into 0 1547111157.531 * [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 1547111157.534 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1547111157.535 * [misc]backup-simplify: Simplify 0 into 0 1547111157.535 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 1547111157.535 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (- n))) into (* -2 (/ PI n)) 1547111157.535 * [misc]approximate: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1547111157.535 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1547111157.535 * [misc]taylor: Taking taylor expansion of -2 in n 1547111157.535 * [misc]backup-simplify: Simplify -2 into -2 1547111157.535 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547111157.535 * [misc]taylor: Taking taylor expansion of PI in n 1547111157.535 * [misc]backup-simplify: Simplify PI into PI 1547111157.535 * [misc]taylor: Taking taylor expansion of n in n 1547111157.535 * [misc]backup-simplify: Simplify 0 into 0 1547111157.535 * [misc]backup-simplify: Simplify 1 into 1 1547111157.536 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547111157.536 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1547111157.536 * [misc]taylor: Taking taylor expansion of -2 in n 1547111157.536 * [misc]backup-simplify: Simplify -2 into -2 1547111157.536 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547111157.536 * [misc]taylor: Taking taylor expansion of PI in n 1547111157.536 * [misc]backup-simplify: Simplify PI into PI 1547111157.536 * [misc]taylor: Taking taylor expansion of n in n 1547111157.536 * [misc]backup-simplify: Simplify 0 into 0 1547111157.536 * [misc]backup-simplify: Simplify 1 into 1 1547111157.536 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547111157.537 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547111157.537 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547111157.538 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1547111157.539 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1547111157.539 * [misc]backup-simplify: Simplify 0 into 0 1547111157.540 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111157.541 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1547111157.542 * [misc]backup-simplify: Simplify 0 into 0 1547111157.543 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111157.545 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1547111157.545 * [misc]backup-simplify: Simplify 0 into 0 1547111157.546 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111157.548 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1547111157.549 * [misc]backup-simplify: Simplify 0 into 0 1547111157.551 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111157.553 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1547111157.553 * [misc]backup-simplify: Simplify 0 into 0 1547111157.556 * [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 1547111157.559 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1547111157.559 * [misc]backup-simplify: Simplify 0 into 0 1547111157.559 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 1547111157.559 * * * * [misc]progress: [ 3 / 3 ] generating series at (2) 1547111157.560 * [misc]backup-simplify: Simplify (* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) into (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) 1547111157.560 * [misc]approximate: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in (k n) around 0 1547111157.560 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in n 1547111157.560 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n 1547111157.560 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n 1547111157.560 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n 1547111157.560 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 k)) in n 1547111157.560 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111157.560 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111157.560 * [misc]taylor: Taking taylor expansion of (- 1 k) in n 1547111157.560 * [misc]taylor: Taking taylor expansion of 1 in n 1547111157.560 * [misc]backup-simplify: Simplify 1 into 1 1547111157.560 * [misc]taylor: Taking taylor expansion of k in n 1547111157.560 * [misc]backup-simplify: Simplify k into k 1547111157.560 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1547111157.560 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1547111157.560 * [misc]taylor: Taking taylor expansion of 2 in n 1547111157.560 * [misc]backup-simplify: Simplify 2 into 2 1547111157.560 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547111157.560 * [misc]taylor: Taking taylor expansion of n in n 1547111157.560 * [misc]backup-simplify: Simplify 0 into 0 1547111157.560 * [misc]backup-simplify: Simplify 1 into 1 1547111157.560 * [misc]taylor: Taking taylor expansion of PI in n 1547111157.560 * [misc]backup-simplify: Simplify PI into PI 1547111157.560 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547111157.560 * [misc]backup-simplify: Simplify (* 2 0) into 0 1547111157.561 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547111157.561 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1547111157.562 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547111157.562 * [misc]backup-simplify: Simplify (- k) into (- k) 1547111157.562 * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) 1547111157.562 * [misc]backup-simplify: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k)) 1547111157.562 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547111157.562 * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) 1547111157.563 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 1547111157.563 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1547111157.563 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547111157.563 * [misc]taylor: Taking taylor expansion of k in n 1547111157.563 * [misc]backup-simplify: Simplify k into k 1547111157.563 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547111157.563 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1547111157.563 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1547111157.563 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1547111157.563 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k 1547111157.563 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k 1547111157.563 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k 1547111157.563 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k 1547111157.563 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 k)) in k 1547111157.563 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111157.563 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111157.563 * [misc]taylor: Taking taylor expansion of (- 1 k) in k 1547111157.563 * [misc]taylor: Taking taylor expansion of 1 in k 1547111157.563 * [misc]backup-simplify: Simplify 1 into 1 1547111157.563 * [misc]taylor: Taking taylor expansion of k in k 1547111157.563 * [misc]backup-simplify: Simplify 0 into 0 1547111157.563 * [misc]backup-simplify: Simplify 1 into 1 1547111157.563 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1547111157.563 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1547111157.563 * [misc]taylor: Taking taylor expansion of 2 in k 1547111157.563 * [misc]backup-simplify: Simplify 2 into 2 1547111157.563 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1547111157.563 * [misc]taylor: Taking taylor expansion of n in k 1547111157.563 * [misc]backup-simplify: Simplify n into n 1547111157.563 * [misc]taylor: Taking taylor expansion of PI in k 1547111157.563 * [misc]backup-simplify: Simplify PI into PI 1547111157.563 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1547111157.564 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1547111157.564 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1547111157.564 * [misc]backup-simplify: Simplify (- 0) into 0 1547111157.564 * [misc]backup-simplify: Simplify (+ 1 0) into 1 1547111157.564 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1547111157.564 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1547111157.564 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1547111157.564 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1547111157.564 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547111157.564 * [misc]taylor: Taking taylor expansion of k in k 1547111157.564 * [misc]backup-simplify: Simplify 0 into 0 1547111157.564 * [misc]backup-simplify: Simplify 1 into 1 1547111157.564 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547111157.564 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547111157.565 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1547111157.565 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k 1547111157.565 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k 1547111157.565 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k 1547111157.565 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k 1547111157.565 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 k)) in k 1547111157.565 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111157.565 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111157.565 * [misc]taylor: Taking taylor expansion of (- 1 k) in k 1547111157.565 * [misc]taylor: Taking taylor expansion of 1 in k 1547111157.565 * [misc]backup-simplify: Simplify 1 into 1 1547111157.565 * [misc]taylor: Taking taylor expansion of k in k 1547111157.565 * [misc]backup-simplify: Simplify 0 into 0 1547111157.565 * [misc]backup-simplify: Simplify 1 into 1 1547111157.565 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1547111157.565 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1547111157.565 * [misc]taylor: Taking taylor expansion of 2 in k 1547111157.565 * [misc]backup-simplify: Simplify 2 into 2 1547111157.565 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1547111157.565 * [misc]taylor: Taking taylor expansion of n in k 1547111157.565 * [misc]backup-simplify: Simplify n into n 1547111157.565 * [misc]taylor: Taking taylor expansion of PI in k 1547111157.565 * [misc]backup-simplify: Simplify PI into PI 1547111157.565 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1547111157.565 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1547111157.565 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1547111157.565 * [misc]backup-simplify: Simplify (- 0) into 0 1547111157.565 * [misc]backup-simplify: Simplify (+ 1 0) into 1 1547111157.565 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1547111157.565 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1547111157.566 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1547111157.566 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1547111157.566 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547111157.566 * [misc]taylor: Taking taylor expansion of k in k 1547111157.566 * [misc]backup-simplify: Simplify 0 into 0 1547111157.566 * [misc]backup-simplify: Simplify 1 into 1 1547111157.566 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547111157.566 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547111157.566 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1547111157.566 * [misc]backup-simplify: Simplify (* (pow (* 2 (* n PI)) 1/2) 0) into 0 1547111157.566 * [misc]taylor: Taking taylor expansion of 0 in n 1547111157.566 * [misc]backup-simplify: Simplify 0 into 0 1547111157.566 * [misc]backup-simplify: Simplify 0 into 0 1547111157.567 * [misc]backup-simplify: Simplify (+ (* n 0) (* 0 PI)) into 0 1547111157.567 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0 1547111157.567 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 1547111157.567 * [misc]backup-simplify: Simplify (- 1) into -1 1547111157.567 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 1547111157.568 * [misc]backup-simplify: Simplify (+ (* 1/2 -1) (* 0 1)) into -1/2 1547111157.568 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI))))) 1547111157.568 * [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))))) 1547111157.568 * [misc]backup-simplify: Simplify (+ (* (pow (* 2 (* n PI)) 1/2) +nan.0) (* (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) 0)) into (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) 1547111157.568 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 1547111157.568 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 1547111157.568 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1547111157.568 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547111157.568 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1547111157.568 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1547111157.568 * [misc]taylor: Taking taylor expansion of 2 in n 1547111157.568 * [misc]backup-simplify: Simplify 2 into 2 1547111157.568 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1547111157.569 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1547111157.569 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1547111157.569 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547111157.569 * [misc]taylor: Taking taylor expansion of n in n 1547111157.569 * [misc]backup-simplify: Simplify 0 into 0 1547111157.569 * [misc]backup-simplify: Simplify 1 into 1 1547111157.569 * [misc]taylor: Taking taylor expansion of PI in n 1547111157.569 * [misc]backup-simplify: Simplify PI into PI 1547111157.569 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547111157.569 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547111157.569 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547111157.570 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1547111157.570 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1547111157.570 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1547111157.570 * [misc]backup-simplify: Simplify (- 0) into 0 1547111157.570 * [misc]backup-simplify: Simplify 0 into 0 1547111157.570 * [misc]backup-simplify: Simplify 0 into 0 1547111157.570 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1547111157.571 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1547111157.571 * [misc]backup-simplify: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 1547111157.572 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 1547111157.572 * [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 1547111157.573 * [misc]backup-simplify: Simplify (- 0) into 0 1547111157.573 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111157.573 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 -1) (* 0 1))) into 0 1547111157.573 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0 1547111157.574 * [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))) 1547111157.574 * [misc]backup-simplify: Simplify (+ (* (pow (* 2 (* n PI)) 1/2) +nan.0) (+ (* (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) +nan.0) (* (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) 0))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) 1547111157.574 * [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 1547111157.574 * [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 1547111157.574 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n 1547111157.574 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1547111157.574 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547111157.574 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n 1547111157.574 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n 1547111157.574 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1547111157.574 * [misc]taylor: Taking taylor expansion of 2 in n 1547111157.574 * [misc]backup-simplify: Simplify 2 into 2 1547111157.574 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1547111157.575 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1547111157.575 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1547111157.575 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1547111157.575 * [misc]taylor: Taking taylor expansion of 2 in n 1547111157.575 * [misc]backup-simplify: Simplify 2 into 2 1547111157.575 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547111157.575 * [misc]taylor: Taking taylor expansion of n in n 1547111157.575 * [misc]backup-simplify: Simplify 0 into 0 1547111157.575 * [misc]backup-simplify: Simplify 1 into 1 1547111157.575 * [misc]taylor: Taking taylor expansion of PI in n 1547111157.575 * [misc]backup-simplify: Simplify PI into PI 1547111157.575 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547111157.575 * [misc]backup-simplify: Simplify (* 2 0) into 0 1547111157.575 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547111157.576 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1547111157.576 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547111157.576 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1547111157.576 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547111157.576 * [misc]taylor: Taking taylor expansion of n in n 1547111157.576 * [misc]backup-simplify: Simplify 0 into 0 1547111157.576 * [misc]backup-simplify: Simplify 1 into 1 1547111157.576 * [misc]taylor: Taking taylor expansion of PI in n 1547111157.576 * [misc]backup-simplify: Simplify PI into PI 1547111157.576 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547111157.577 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547111157.577 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547111157.577 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1547111157.577 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 1547111157.577 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 1547111157.577 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1547111157.577 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547111157.577 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1547111157.577 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1547111157.577 * [misc]taylor: Taking taylor expansion of 2 in n 1547111157.577 * [misc]backup-simplify: Simplify 2 into 2 1547111157.577 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1547111157.577 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1547111157.577 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1547111157.577 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547111157.578 * [misc]taylor: Taking taylor expansion of n in n 1547111157.578 * [misc]backup-simplify: Simplify 0 into 0 1547111157.578 * [misc]backup-simplify: Simplify 1 into 1 1547111157.578 * [misc]taylor: Taking taylor expansion of PI in n 1547111157.578 * [misc]backup-simplify: Simplify PI into PI 1547111157.578 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547111157.578 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547111157.578 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547111157.578 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1547111157.579 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547111157.579 * [misc]backup-simplify: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 1547111157.580 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0 1547111157.580 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1547111157.580 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1547111157.580 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1547111157.580 * [misc]backup-simplify: Simplify (- 0) into 0 1547111157.580 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111157.580 * [misc]backup-simplify: Simplify (- 0) into 0 1547111157.580 * [misc]backup-simplify: Simplify 0 into 0 1547111157.581 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1547111157.582 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1547111157.583 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 1547111157.584 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI))) 1547111157.584 * [misc]backup-simplify: Simplify 0 into 0 1547111157.584 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111157.584 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1547111157.585 * [misc]backup-simplify: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1547111157.585 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 1547111157.587 * [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 1547111157.587 * [misc]backup-simplify: Simplify (- 0) into 0 1547111157.587 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111157.587 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1)))) into 0 1547111157.588 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log (* 2 (* n PI))))))) into 0 1547111157.589 * [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))) 1547111157.590 * [misc]backup-simplify: Simplify (+ (* (pow (* 2 (* n PI)) 1/2) +nan.0) (+ (* (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) +nan.0) (+ (* (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) +nan.0) (* (* -1/48 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 3))) 0)))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))))))) 1547111157.590 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))))))) in n 1547111157.590 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))))))) in n 1547111157.590 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n 1547111157.590 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1547111157.590 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547111157.590 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n 1547111157.590 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n 1547111157.590 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1547111157.590 * [misc]taylor: Taking taylor expansion of 2 in n 1547111157.590 * [misc]backup-simplify: Simplify 2 into 2 1547111157.590 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1547111157.590 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1547111157.590 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1547111157.590 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1547111157.590 * [misc]taylor: Taking taylor expansion of 2 in n 1547111157.590 * [misc]backup-simplify: Simplify 2 into 2 1547111157.590 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547111157.590 * [misc]taylor: Taking taylor expansion of n in n 1547111157.590 * [misc]backup-simplify: Simplify 0 into 0 1547111157.590 * [misc]backup-simplify: Simplify 1 into 1 1547111157.590 * [misc]taylor: Taking taylor expansion of PI in n 1547111157.590 * [misc]backup-simplify: Simplify PI into PI 1547111157.590 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547111157.590 * [misc]backup-simplify: Simplify (* 2 0) into 0 1547111157.591 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547111157.591 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1547111157.592 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547111157.592 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1547111157.592 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547111157.592 * [misc]taylor: Taking taylor expansion of n in n 1547111157.592 * [misc]backup-simplify: Simplify 0 into 0 1547111157.592 * [misc]backup-simplify: Simplify 1 into 1 1547111157.592 * [misc]taylor: Taking taylor expansion of PI in n 1547111157.592 * [misc]backup-simplify: Simplify PI into PI 1547111157.592 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547111157.593 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547111157.593 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547111157.593 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1547111157.593 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))))) in n 1547111157.594 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))))) in n 1547111157.594 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 1547111157.594 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1547111157.594 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547111157.594 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1547111157.594 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1547111157.594 * [misc]taylor: Taking taylor expansion of 2 in n 1547111157.594 * [misc]backup-simplify: Simplify 2 into 2 1547111157.594 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1547111157.594 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1547111157.594 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1547111157.594 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547111157.594 * [misc]taylor: Taking taylor expansion of n in n 1547111157.594 * [misc]backup-simplify: Simplify 0 into 0 1547111157.594 * [misc]backup-simplify: Simplify 1 into 1 1547111157.594 * [misc]taylor: Taking taylor expansion of PI in n 1547111157.594 * [misc]backup-simplify: Simplify PI into PI 1547111157.595 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547111157.596 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547111157.596 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547111157.596 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1547111157.596 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))) in n 1547111157.596 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) in n 1547111157.597 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1547111157.597 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547111157.597 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))) in n 1547111157.597 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) in n 1547111157.597 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1547111157.597 * [misc]taylor: Taking taylor expansion of 2 in n 1547111157.597 * [misc]backup-simplify: Simplify 2 into 2 1547111157.597 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1547111157.597 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1547111157.597 * [misc]taylor: Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n 1547111157.597 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1547111157.597 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1547111157.597 * [misc]taylor: Taking taylor expansion of 2 in n 1547111157.597 * [misc]backup-simplify: Simplify 2 into 2 1547111157.597 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547111157.597 * [misc]taylor: Taking taylor expansion of n in n 1547111157.597 * [misc]backup-simplify: Simplify 0 into 0 1547111157.597 * [misc]backup-simplify: Simplify 1 into 1 1547111157.597 * [misc]taylor: Taking taylor expansion of PI in n 1547111157.597 * [misc]backup-simplify: Simplify PI into PI 1547111157.598 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547111157.598 * [misc]backup-simplify: Simplify (* 2 0) into 0 1547111157.598 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547111157.599 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1547111157.600 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547111157.600 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547111157.600 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1547111157.600 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547111157.600 * [misc]taylor: Taking taylor expansion of n in n 1547111157.600 * [misc]backup-simplify: Simplify 0 into 0 1547111157.600 * [misc]backup-simplify: Simplify 1 into 1 1547111157.600 * [misc]taylor: Taking taylor expansion of PI in n 1547111157.600 * [misc]backup-simplify: Simplify PI into PI 1547111157.601 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547111157.601 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547111157.601 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547111157.602 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1547111157.603 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547111157.603 * [misc]backup-simplify: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 1547111157.604 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0 1547111157.604 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1547111157.604 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1547111157.604 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1547111157.605 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547111157.606 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547111157.607 * [misc]backup-simplify: Simplify (* (+ (log n) (log (* 2 PI))) (+ (log n) (log (* 2 PI)))) into (pow (+ (log n) (log (* 2 PI))) 2) 1547111157.607 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) into (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 1547111157.608 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 0) into 0 1547111157.608 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1547111157.609 * [misc]backup-simplify: Simplify (- 0) into 0 1547111157.609 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111157.609 * [misc]backup-simplify: Simplify (- 0) into 0 1547111157.609 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111157.609 * [misc]backup-simplify: Simplify (- 0) into 0 1547111157.609 * [misc]backup-simplify: Simplify 0 into 0 1547111157.610 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1547111157.612 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1547111157.614 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1547111157.615 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547111157.616 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1547111157.617 * [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)))))))) 1547111157.620 * [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)))))))) 1547111157.621 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1547111157.623 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1547111157.624 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 1547111157.627 * [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)))))))))) 1547111157.631 * [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))))))) 1547111157.634 * [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))))))) 1547111157.635 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1547111157.637 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 1547111157.638 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1547111157.640 * [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)))) 1547111157.645 * [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)))) 1547111157.646 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 1547111157.648 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 1547111157.655 * [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))))))))))))) 1547111157.656 * [misc]backup-simplify: Simplify (* (pow (/ 1 k) -1/2) (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2))) into (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) 1547111157.656 * [misc]approximate: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in (k n) around 0 1547111157.656 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in n 1547111157.656 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n 1547111157.656 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1547111157.656 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1547111157.656 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n 1547111157.657 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111157.657 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111157.657 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n 1547111157.657 * [misc]taylor: Taking taylor expansion of 1 in n 1547111157.657 * [misc]backup-simplify: Simplify 1 into 1 1547111157.657 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547111157.657 * [misc]taylor: Taking taylor expansion of k in n 1547111157.657 * [misc]backup-simplify: Simplify k into k 1547111157.657 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547111157.657 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1547111157.657 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1547111157.657 * [misc]taylor: Taking taylor expansion of 2 in n 1547111157.657 * [misc]backup-simplify: Simplify 2 into 2 1547111157.657 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547111157.657 * [misc]taylor: Taking taylor expansion of PI in n 1547111157.657 * [misc]backup-simplify: Simplify PI into PI 1547111157.657 * [misc]taylor: Taking taylor expansion of n in n 1547111157.657 * [misc]backup-simplify: Simplify 0 into 0 1547111157.657 * [misc]backup-simplify: Simplify 1 into 1 1547111157.657 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547111157.658 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547111157.658 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547111157.658 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1547111157.658 * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 1547111157.658 * [misc]backup-simplify: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k))) 1547111157.659 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547111157.660 * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 1547111157.660 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 1547111157.660 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1547111157.660 * [misc]taylor: Taking taylor expansion of k in n 1547111157.660 * [misc]backup-simplify: Simplify k into k 1547111157.660 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1547111157.661 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1547111157.661 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k 1547111157.661 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k 1547111157.661 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1547111157.661 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1547111157.661 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k 1547111157.661 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111157.661 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111157.661 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k 1547111157.661 * [misc]taylor: Taking taylor expansion of 1 in k 1547111157.661 * [misc]backup-simplify: Simplify 1 into 1 1547111157.661 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547111157.661 * [misc]taylor: Taking taylor expansion of k in k 1547111157.661 * [misc]backup-simplify: Simplify 0 into 0 1547111157.661 * [misc]backup-simplify: Simplify 1 into 1 1547111157.661 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547111157.661 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1547111157.661 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1547111157.661 * [misc]taylor: Taking taylor expansion of 2 in k 1547111157.661 * [misc]backup-simplify: Simplify 2 into 2 1547111157.661 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1547111157.661 * [misc]taylor: Taking taylor expansion of PI in k 1547111157.661 * [misc]backup-simplify: Simplify PI into PI 1547111157.661 * [misc]taylor: Taking taylor expansion of n in k 1547111157.661 * [misc]backup-simplify: Simplify n into n 1547111157.661 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1547111157.661 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1547111157.662 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1547111157.662 * [misc]backup-simplify: Simplify (- 1) into -1 1547111157.662 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 1547111157.662 * [misc]backup-simplify: Simplify (* 1/2 -1) into -1/2 1547111157.662 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1547111157.662 * [misc]backup-simplify: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 1547111157.662 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1547111157.662 * [misc]taylor: Taking taylor expansion of k in k 1547111157.662 * [misc]backup-simplify: Simplify 0 into 0 1547111157.663 * [misc]backup-simplify: Simplify 1 into 1 1547111157.663 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547111157.663 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1547111157.663 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k 1547111157.663 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k 1547111157.663 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1547111157.663 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1547111157.663 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k 1547111157.663 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111157.663 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111157.663 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k 1547111157.663 * [misc]taylor: Taking taylor expansion of 1 in k 1547111157.663 * [misc]backup-simplify: Simplify 1 into 1 1547111157.663 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547111157.663 * [misc]taylor: Taking taylor expansion of k in k 1547111157.663 * [misc]backup-simplify: Simplify 0 into 0 1547111157.663 * [misc]backup-simplify: Simplify 1 into 1 1547111157.664 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547111157.664 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1547111157.664 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1547111157.664 * [misc]taylor: Taking taylor expansion of 2 in k 1547111157.664 * [misc]backup-simplify: Simplify 2 into 2 1547111157.664 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1547111157.664 * [misc]taylor: Taking taylor expansion of PI in k 1547111157.664 * [misc]backup-simplify: Simplify PI into PI 1547111157.664 * [misc]taylor: Taking taylor expansion of n in k 1547111157.664 * [misc]backup-simplify: Simplify n into n 1547111157.664 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1547111157.664 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1547111157.664 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1547111157.664 * [misc]backup-simplify: Simplify (- 1) into -1 1547111157.664 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 1547111157.665 * [misc]backup-simplify: Simplify (* 1/2 -1) into -1/2 1547111157.665 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1547111157.665 * [misc]backup-simplify: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 1547111157.665 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1547111157.665 * [misc]taylor: Taking taylor expansion of k in k 1547111157.665 * [misc]backup-simplify: Simplify 0 into 0 1547111157.665 * [misc]backup-simplify: Simplify 1 into 1 1547111157.665 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547111157.666 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1547111157.666 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 0) into 0 1547111157.666 * [misc]taylor: Taking taylor expansion of 0 in n 1547111157.666 * [misc]backup-simplify: Simplify 0 into 0 1547111157.666 * [misc]backup-simplify: Simplify 0 into 0 1547111157.666 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) 1547111157.666 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n 1547111157.667 * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n 1547111157.667 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1547111157.667 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547111157.667 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n 1547111157.667 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n 1547111157.667 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111157.667 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111157.667 * [misc]taylor: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n 1547111157.667 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n 1547111157.667 * [misc]taylor: Taking taylor expansion of 1 in n 1547111157.667 * [misc]backup-simplify: Simplify 1 into 1 1547111157.667 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547111157.667 * [misc]taylor: Taking taylor expansion of k in n 1547111157.667 * [misc]backup-simplify: Simplify k into k 1547111157.667 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547111157.667 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1547111157.667 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1547111157.667 * [misc]taylor: Taking taylor expansion of 2 in n 1547111157.667 * [misc]backup-simplify: Simplify 2 into 2 1547111157.667 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547111157.667 * [misc]taylor: Taking taylor expansion of PI in n 1547111157.667 * [misc]backup-simplify: Simplify PI into PI 1547111157.667 * [misc]taylor: Taking taylor expansion of n in n 1547111157.667 * [misc]backup-simplify: Simplify 0 into 0 1547111157.667 * [misc]backup-simplify: Simplify 1 into 1 1547111157.667 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547111157.668 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547111157.668 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547111157.668 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1547111157.668 * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 1547111157.669 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547111157.670 * [misc]backup-simplify: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) 1547111157.670 * [misc]backup-simplify: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 1547111157.671 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 1547111157.672 * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) 1547111157.672 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 1547111157.673 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 1547111157.673 * [misc]backup-simplify: Simplify 0 into 0 1547111157.674 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1547111157.675 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) 1547111157.675 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n 1547111157.675 * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n 1547111157.675 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1547111157.675 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547111157.675 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n 1547111157.675 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n 1547111157.675 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111157.675 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111157.675 * [misc]taylor: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n 1547111157.675 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n 1547111157.675 * [misc]taylor: Taking taylor expansion of 1 in n 1547111157.675 * [misc]backup-simplify: Simplify 1 into 1 1547111157.675 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547111157.675 * [misc]taylor: Taking taylor expansion of k in n 1547111157.675 * [misc]backup-simplify: Simplify k into k 1547111157.675 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547111157.675 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1547111157.675 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1547111157.675 * [misc]taylor: Taking taylor expansion of 2 in n 1547111157.675 * [misc]backup-simplify: Simplify 2 into 2 1547111157.675 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547111157.675 * [misc]taylor: Taking taylor expansion of PI in n 1547111157.675 * [misc]backup-simplify: Simplify PI into PI 1547111157.675 * [misc]taylor: Taking taylor expansion of n in n 1547111157.675 * [misc]backup-simplify: Simplify 0 into 0 1547111157.675 * [misc]backup-simplify: Simplify 1 into 1 1547111157.676 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547111157.676 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547111157.676 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547111157.676 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1547111157.677 * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 1547111157.677 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547111157.678 * [misc]backup-simplify: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) 1547111157.678 * [misc]backup-simplify: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 1547111157.679 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 1547111157.680 * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) 1547111157.680 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 1547111157.681 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 1547111157.682 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1547111157.683 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1547111157.686 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1547111157.686 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1547111157.686 * [misc]backup-simplify: Simplify (- 0) into 0 1547111157.686 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111157.687 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547111157.687 * [misc]backup-simplify: Simplify (+ (* (- 1 (/ 1 k)) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1547111157.688 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into 0 1547111157.690 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1547111157.691 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into 0 1547111157.691 * [misc]backup-simplify: Simplify (- 0) into 0 1547111157.691 * [misc]backup-simplify: Simplify 0 into 0 1547111157.691 * [misc]backup-simplify: Simplify 0 into 0 1547111157.692 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1547111157.693 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) 1547111157.693 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n 1547111157.693 * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n 1547111157.693 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1547111157.693 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547111157.693 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n 1547111157.693 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n 1547111157.693 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111157.693 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111157.693 * [misc]taylor: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n 1547111157.693 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n 1547111157.693 * [misc]taylor: Taking taylor expansion of 1 in n 1547111157.693 * [misc]backup-simplify: Simplify 1 into 1 1547111157.693 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547111157.693 * [misc]taylor: Taking taylor expansion of k in n 1547111157.693 * [misc]backup-simplify: Simplify k into k 1547111157.693 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547111157.693 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1547111157.693 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1547111157.693 * [misc]taylor: Taking taylor expansion of 2 in n 1547111157.693 * [misc]backup-simplify: Simplify 2 into 2 1547111157.693 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547111157.693 * [misc]taylor: Taking taylor expansion of PI in n 1547111157.693 * [misc]backup-simplify: Simplify PI into PI 1547111157.693 * [misc]taylor: Taking taylor expansion of n in n 1547111157.693 * [misc]backup-simplify: Simplify 0 into 0 1547111157.693 * [misc]backup-simplify: Simplify 1 into 1 1547111157.694 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547111157.694 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547111157.694 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547111157.695 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1547111157.695 * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 1547111157.695 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547111157.696 * [misc]backup-simplify: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) 1547111157.696 * [misc]backup-simplify: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 1547111157.697 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 1547111157.698 * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) 1547111157.698 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 1547111157.699 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 1547111157.701 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3)))))))) 1547111157.702 * [misc]backup-simplify: Simplify (* (pow (/ 1 (- k)) -1/2) (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2))) into (* (sqrt (/ k -1)) (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1)))) 1547111157.702 * [misc]approximate: Taking taylor expansion of (* (sqrt (/ k -1)) (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1)))) in (k n) around 0 1547111157.702 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ k -1)) (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1)))) in n 1547111157.702 * [misc]taylor: Taking taylor expansion of (sqrt (/ k -1)) in n 1547111157.702 * [misc]taylor: Taking taylor expansion of (/ k -1) in n 1547111157.702 * [misc]taylor: Taking taylor expansion of k in n 1547111157.702 * [misc]backup-simplify: Simplify k into k 1547111157.702 * [misc]taylor: Taking taylor expansion of -1 in n 1547111157.702 * [misc]backup-simplify: Simplify -1 into -1 1547111157.702 * [misc]backup-simplify: Simplify (/ k -1) into (* -1 k) 1547111157.703 * [misc]backup-simplify: Simplify (sqrt (* -1 k)) into (sqrt (* -1 k)) 1547111157.703 * [misc]backup-simplify: Simplify (- (/ 0 -1) (+ (* (* -1 k) (/ 0 -1)))) into 0 1547111157.703 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (* -1 k)))) into 0 1547111157.703 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n 1547111157.703 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n 1547111157.703 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n 1547111157.703 * [misc]taylor: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n 1547111157.703 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111157.703 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111157.703 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in n 1547111157.703 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547111157.703 * [misc]taylor: Taking taylor expansion of k in n 1547111157.703 * [misc]backup-simplify: Simplify k into k 1547111157.703 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547111157.703 * [misc]taylor: Taking taylor expansion of 1 in n 1547111157.703 * [misc]backup-simplify: Simplify 1 into 1 1547111157.703 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1547111157.703 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1547111157.704 * [misc]taylor: Taking taylor expansion of -2 in n 1547111157.704 * [misc]backup-simplify: Simplify -2 into -2 1547111157.704 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547111157.704 * [misc]taylor: Taking taylor expansion of PI in n 1547111157.704 * [misc]backup-simplify: Simplify PI into PI 1547111157.704 * [misc]taylor: Taking taylor expansion of n in n 1547111157.704 * [misc]backup-simplify: Simplify 0 into 0 1547111157.704 * [misc]backup-simplify: Simplify 1 into 1 1547111157.704 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547111157.704 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547111157.705 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1547111157.705 * [misc]backup-simplify: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 1547111157.705 * [misc]backup-simplify: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1)) 1547111157.706 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547111157.706 * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 1547111157.707 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 1547111157.707 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ k -1)) (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1)))) in k 1547111157.707 * [misc]taylor: Taking taylor expansion of (sqrt (/ k -1)) in k 1547111157.707 * [misc]taylor: Taking taylor expansion of (/ k -1) in k 1547111157.707 * [misc]taylor: Taking taylor expansion of k in k 1547111157.707 * [misc]backup-simplify: Simplify 0 into 0 1547111157.707 * [misc]backup-simplify: Simplify 1 into 1 1547111157.707 * [misc]taylor: Taking taylor expansion of -1 in k 1547111157.707 * [misc]backup-simplify: Simplify -1 into -1 1547111157.707 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 1547111157.707 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547111157.708 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1547111157.708 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k 1547111157.708 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k 1547111157.708 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k 1547111157.708 * [misc]taylor: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k 1547111157.708 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111157.708 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111157.708 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in k 1547111157.708 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547111157.708 * [misc]taylor: Taking taylor expansion of k in k 1547111157.708 * [misc]backup-simplify: Simplify 0 into 0 1547111157.708 * [misc]backup-simplify: Simplify 1 into 1 1547111157.708 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547111157.708 * [misc]taylor: Taking taylor expansion of 1 in k 1547111157.708 * [misc]backup-simplify: Simplify 1 into 1 1547111157.708 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1547111157.708 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1547111157.708 * [misc]taylor: Taking taylor expansion of -2 in k 1547111157.708 * [misc]backup-simplify: Simplify -2 into -2 1547111157.708 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1547111157.708 * [misc]taylor: Taking taylor expansion of PI in k 1547111157.709 * [misc]backup-simplify: Simplify PI into PI 1547111157.709 * [misc]taylor: Taking taylor expansion of n in k 1547111157.709 * [misc]backup-simplify: Simplify n into n 1547111157.709 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1547111157.709 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1547111157.709 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1547111157.709 * [misc]backup-simplify: Simplify (+ 1 0) into 1 1547111157.709 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1547111157.709 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1547111157.710 * [misc]backup-simplify: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) 1547111157.710 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ k -1)) (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1)))) in k 1547111157.710 * [misc]taylor: Taking taylor expansion of (sqrt (/ k -1)) in k 1547111157.710 * [misc]taylor: Taking taylor expansion of (/ k -1) in k 1547111157.710 * [misc]taylor: Taking taylor expansion of k in k 1547111157.710 * [misc]backup-simplify: Simplify 0 into 0 1547111157.710 * [misc]backup-simplify: Simplify 1 into 1 1547111157.710 * [misc]taylor: Taking taylor expansion of -1 in k 1547111157.710 * [misc]backup-simplify: Simplify -1 into -1 1547111157.710 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 1547111157.710 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547111157.711 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1547111157.711 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k 1547111157.711 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k 1547111157.711 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k 1547111157.711 * [misc]taylor: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k 1547111157.711 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111157.711 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111157.711 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in k 1547111157.711 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547111157.711 * [misc]taylor: Taking taylor expansion of k in k 1547111157.711 * [misc]backup-simplify: Simplify 0 into 0 1547111157.711 * [misc]backup-simplify: Simplify 1 into 1 1547111157.711 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547111157.711 * [misc]taylor: Taking taylor expansion of 1 in k 1547111157.711 * [misc]backup-simplify: Simplify 1 into 1 1547111157.711 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1547111157.711 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1547111157.711 * [misc]taylor: Taking taylor expansion of -2 in k 1547111157.712 * [misc]backup-simplify: Simplify -2 into -2 1547111157.712 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1547111157.712 * [misc]taylor: Taking taylor expansion of PI in k 1547111157.712 * [misc]backup-simplify: Simplify PI into PI 1547111157.712 * [misc]taylor: Taking taylor expansion of n in k 1547111157.712 * [misc]backup-simplify: Simplify n into n 1547111157.712 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1547111157.712 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1547111157.712 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1547111157.712 * [misc]backup-simplify: Simplify (+ 1 0) into 1 1547111157.712 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1547111157.712 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1547111157.713 * [misc]backup-simplify: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) 1547111157.713 * [misc]backup-simplify: Simplify (* 0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) into 0 1547111157.713 * [misc]taylor: Taking taylor expansion of 0 in n 1547111157.713 * [misc]backup-simplify: Simplify 0 into 0 1547111157.713 * [misc]backup-simplify: Simplify 0 into 0 1547111157.713 * [misc]backup-simplify: Simplify (+ (* 0 0) (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) into (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) 1547111157.713 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n 1547111157.713 * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n 1547111157.713 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1547111157.714 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547111157.714 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n 1547111157.714 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n 1547111157.714 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111157.714 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111157.714 * [misc]taylor: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n 1547111157.714 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1547111157.714 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1547111157.714 * [misc]taylor: Taking taylor expansion of -2 in n 1547111157.714 * [misc]backup-simplify: Simplify -2 into -2 1547111157.714 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547111157.714 * [misc]taylor: Taking taylor expansion of PI in n 1547111157.714 * [misc]backup-simplify: Simplify PI into PI 1547111157.714 * [misc]taylor: Taking taylor expansion of n in n 1547111157.714 * [misc]backup-simplify: Simplify 0 into 0 1547111157.714 * [misc]backup-simplify: Simplify 1 into 1 1547111157.714 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547111157.714 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547111157.715 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1547111157.715 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in n 1547111157.715 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547111157.715 * [misc]taylor: Taking taylor expansion of k in n 1547111157.715 * [misc]backup-simplify: Simplify k into k 1547111157.715 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547111157.715 * [misc]taylor: Taking taylor expansion of 1 in n 1547111157.715 * [misc]backup-simplify: Simplify 1 into 1 1547111157.716 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547111157.716 * [misc]backup-simplify: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 1547111157.717 * [misc]backup-simplify: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) 1547111157.717 * [misc]backup-simplify: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 1547111157.718 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 1547111157.719 * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) 1547111157.719 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) 1547111157.720 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) 1547111157.720 * [misc]backup-simplify: Simplify 0 into 0 1547111157.720 * [misc]backup-simplify: Simplify (- (/ 0 -1) (+ (* -1 (/ 0 -1)))) into 0 1547111157.721 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1547111157.722 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))))) into (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) 1547111157.722 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n 1547111157.722 * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n 1547111157.722 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1547111157.722 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547111157.722 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n 1547111157.722 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n 1547111157.722 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111157.722 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111157.722 * [misc]taylor: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n 1547111157.722 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1547111157.722 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1547111157.722 * [misc]taylor: Taking taylor expansion of -2 in n 1547111157.722 * [misc]backup-simplify: Simplify -2 into -2 1547111157.722 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547111157.722 * [misc]taylor: Taking taylor expansion of PI in n 1547111157.722 * [misc]backup-simplify: Simplify PI into PI 1547111157.722 * [misc]taylor: Taking taylor expansion of n in n 1547111157.722 * [misc]backup-simplify: Simplify 0 into 0 1547111157.722 * [misc]backup-simplify: Simplify 1 into 1 1547111157.723 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547111157.723 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547111157.723 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1547111157.723 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in n 1547111157.723 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547111157.724 * [misc]taylor: Taking taylor expansion of k in n 1547111157.724 * [misc]backup-simplify: Simplify k into k 1547111157.724 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547111157.724 * [misc]taylor: Taking taylor expansion of 1 in n 1547111157.724 * [misc]backup-simplify: Simplify 1 into 1 1547111157.724 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547111157.724 * [misc]backup-simplify: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 1547111157.725 * [misc]backup-simplify: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) 1547111157.726 * [misc]backup-simplify: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 1547111157.726 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 1547111157.727 * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) 1547111157.728 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) 1547111157.728 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) 1547111157.729 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547111157.729 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1547111157.729 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111157.730 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1547111157.731 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1547111157.734 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1547111157.734 * [misc]backup-simplify: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (/ 1 k) 1))) into 0 1547111157.735 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into 0 1547111157.737 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1547111157.737 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into 0 1547111157.738 * [misc]backup-simplify: Simplify (- 0) into 0 1547111157.738 * [misc]backup-simplify: Simplify 0 into 0 1547111157.738 * [misc]backup-simplify: Simplify 0 into 0 1547111157.738 * [misc]backup-simplify: Simplify (- (/ 0 -1) (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 1547111157.739 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1547111157.740 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* +nan.0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))))) into (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) 1547111157.740 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n 1547111157.740 * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n 1547111157.740 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1547111157.740 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547111157.740 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n 1547111157.740 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n 1547111157.740 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111157.740 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111157.740 * [misc]taylor: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n 1547111157.740 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1547111157.740 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1547111157.740 * [misc]taylor: Taking taylor expansion of -2 in n 1547111157.740 * [misc]backup-simplify: Simplify -2 into -2 1547111157.740 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547111157.740 * [misc]taylor: Taking taylor expansion of PI in n 1547111157.740 * [misc]backup-simplify: Simplify PI into PI 1547111157.740 * [misc]taylor: Taking taylor expansion of n in n 1547111157.740 * [misc]backup-simplify: Simplify 0 into 0 1547111157.741 * [misc]backup-simplify: Simplify 1 into 1 1547111157.741 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547111157.741 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547111157.741 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1547111157.742 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in n 1547111157.742 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547111157.742 * [misc]taylor: Taking taylor expansion of k in n 1547111157.742 * [misc]backup-simplify: Simplify k into k 1547111157.742 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547111157.742 * [misc]taylor: Taking taylor expansion of 1 in n 1547111157.742 * [misc]backup-simplify: Simplify 1 into 1 1547111157.742 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547111157.742 * [misc]backup-simplify: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 1547111157.743 * [misc]backup-simplify: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) 1547111157.744 * [misc]backup-simplify: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 1547111157.744 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 1547111157.745 * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) 1547111157.746 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) 1547111157.746 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) 1547111157.749 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 3)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 2)) (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (* 1 (/ 1 (- k)))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k))))))) 1547111157.749 * * * [misc]progress: simplifying candidates 1547111157.749 * * * * [misc]progress: [ 1 / 57 ] simplifiying candidate # 1547111157.749 * [enter]simplify: Simplifying (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)) 1547111157.750 * * [misc]simplify: iters left: 6 (11 enodes) 1547111157.754 * * [misc]simplify: iters left: 5 (29 enodes) 1547111157.763 * * [misc]simplify: iters left: 4 (59 enodes) 1547111157.783 * * [misc]simplify: iters left: 3 (142 enodes) 1547111157.839 * * [misc]simplify: iters left: 2 (497 enodes) 1547111158.299 * [exit]simplify: Simplified to (* (- 1/2 (/ k 2)) (log (* (* 2 PI) n))) 1547111158.299 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow k -1/2) (exp (* (- 1/2 (/ k 2)) (log (* (* 2 PI) n)))))) 1547111158.299 * * * * [misc]progress: [ 2 / 57 ] simplifiying candidate # 1547111158.299 * * * * [misc]progress: [ 3 / 57 ] simplifiying candidate # 1547111158.299 * [enter]simplify: Simplifying (* (* 2 PI) n) 1547111158.299 * * [misc]simplify: iters left: 4 (5 enodes) 1547111158.300 * * [misc]simplify: iters left: 3 (9 enodes) 1547111158.301 * * [misc]simplify: iters left: 2 (15 enodes) 1547111158.303 * * [misc]simplify: iters left: 1 (17 enodes) 1547111158.307 * [exit]simplify: Simplified to (* (* 2 PI) n) 1547111158.307 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow k -1/2) (pow (* (* 2 PI) n) (* 1 (/ (- 1 k) 2))))) 1547111158.307 * * * * [misc]progress: [ 4 / 57 ] simplifiying candidate # 1547111158.307 * [enter]simplify: Simplifying (pow (* (* 2 PI) n) (/ k 2)) 1547111158.308 * * [misc]simplify: iters left: 5 (8 enodes) 1547111158.310 * * [misc]simplify: iters left: 4 (12 enodes) 1547111158.313 * * [misc]simplify: iters left: 3 (18 enodes) 1547111158.318 * * [misc]simplify: iters left: 2 (20 enodes) 1547111158.322 * [exit]simplify: Simplified to (pow (* 2 (* n PI)) (/ k 2)) 1547111158.322 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow k -1/2) (/ (pow (* (* 2 PI) n) (/ 1 2)) (pow (* 2 (* n PI)) (/ k 2))))) 1547111158.322 * * * * [misc]progress: [ 5 / 57 ] simplifiying candidate # 1547111158.322 * [enter]simplify: Simplifying (cbrt (/ (- 1 k) 2)) 1547111158.323 * * [misc]simplify: iters left: 5 (6 enodes) 1547111158.325 * * [misc]simplify: iters left: 4 (14 enodes) 1547111158.328 * * [misc]simplify: iters left: 3 (17 enodes) 1547111158.332 * * [misc]simplify: iters left: 2 (19 enodes) 1547111158.336 * [exit]simplify: Simplified to (cbrt (/ (- 1 k) 2)) 1547111158.336 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow k -1/2) (pow (pow (* (* 2 PI) n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) (cbrt (/ (- 1 k) 2))))) 1547111158.336 * * * * [misc]progress: [ 6 / 57 ] simplifiying candidate # 1547111158.336 * [enter]simplify: Simplifying (sqrt (/ (- 1 k) 2)) 1547111158.336 * * [misc]simplify: iters left: 5 (6 enodes) 1547111158.339 * * [misc]simplify: iters left: 4 (14 enodes) 1547111158.342 * * [misc]simplify: iters left: 3 (17 enodes) 1547111158.345 * * [misc]simplify: iters left: 2 (19 enodes) 1547111158.349 * [exit]simplify: Simplified to (sqrt (/ (- 1 k) 2)) 1547111158.349 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow k -1/2) (pow (pow (* (* 2 PI) n) (sqrt (/ (- 1 k) 2))) (sqrt (/ (- 1 k) 2))))) 1547111158.349 * * * * [misc]progress: [ 7 / 57 ] simplifiying candidate # 1547111158.350 * [enter]simplify: Simplifying (/ (- 1 k) 2) 1547111158.350 * * [misc]simplify: iters left: 4 (5 enodes) 1547111158.352 * * [misc]simplify: iters left: 3 (13 enodes) 1547111158.355 * * [misc]simplify: iters left: 2 (16 enodes) 1547111158.358 * * [misc]simplify: iters left: 1 (18 enodes) 1547111158.361 * [exit]simplify: Simplified to (/ (- 1 k) 2) 1547111158.362 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow k -1/2) (pow (pow (* (* 2 PI) n) 1) (/ (- 1 k) 2)))) 1547111158.362 * * * * [misc]progress: [ 8 / 57 ] simplifiying candidate # 1547111158.362 * [enter]simplify: Simplifying (/ 1 2) 1547111158.362 * * [misc]simplify: iters left: 2 (3 enodes) 1547111158.363 * * [misc]simplify: iters left: 1 (6 enodes) 1547111158.364 * [exit]simplify: Simplified to 1/2 1547111158.364 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow k -1/2) (pow (pow (* (* 2 PI) n) (- 1 k)) 1/2))) 1547111158.364 * * * * [misc]progress: [ 9 / 57 ] simplifiying candidate # 1547111158.365 * [enter]simplify: Simplifying (pow (* 2 PI) (/ (- 1 k) 2)) 1547111158.365 * * [misc]simplify: iters left: 5 (8 enodes) 1547111158.368 * * [misc]simplify: iters left: 4 (17 enodes) 1547111158.372 * * [misc]simplify: iters left: 3 (20 enodes) 1547111158.376 * * [misc]simplify: iters left: 2 (22 enodes) 1547111158.380 * [exit]simplify: Simplified to (pow (* 2 PI) (- 1/2 (/ k 2))) 1547111158.381 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow k -1/2) (* (pow (* 2 PI) (- 1/2 (/ k 2))) (pow n (/ (- 1 k) 2))))) 1547111158.381 * * * * [misc]progress: [ 10 / 57 ] simplifiying candidate # 1547111158.381 * * * * [misc]progress: [ 11 / 57 ] simplifiying candidate # 1547111158.381 * * * * [misc]progress: [ 12 / 57 ] simplifiying candidate # 1547111158.381 * * * * [misc]progress: [ 13 / 57 ] simplifiying candidate # 1547111158.381 * * * * [misc]progress: [ 14 / 57 ] simplifiying candidate # 1547111158.381 * * * * [misc]progress: [ 15 / 57 ] simplifiying candidate # 1547111158.381 * * * * [misc]progress: [ 16 / 57 ] simplifiying candidate # 1547111158.381 * * * * [misc]progress: [ 17 / 57 ] simplifiying candidate # 1547111158.381 * * * * [misc]progress: [ 18 / 57 ] simplifiying candidate # 1547111158.381 * * * * [misc]progress: [ 19 / 57 ] simplifiying candidate # 1547111158.381 * * * * [misc]progress: [ 20 / 57 ] simplifiying candidate # 1547111158.381 * * * * [misc]progress: [ 21 / 57 ] simplifiying candidate # 1547111158.381 * * * * [misc]progress: [ 22 / 57 ] simplifiying candidate # 1547111158.381 * * * * [misc]progress: [ 23 / 57 ] simplifiying candidate # 1547111158.381 * * * * [misc]progress: [ 24 / 57 ] simplifiying candidate # 1547111158.381 * * * * [misc]progress: [ 25 / 57 ] simplifiying candidate # 1547111158.381 * * * * [misc]progress: [ 26 / 57 ] simplifiying candidate # 1547111158.382 * * * * [misc]progress: [ 27 / 57 ] simplifiying candidate # 1547111158.382 * [enter]simplify: Simplifying (+ (* (log k) -1/2) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))) 1547111158.382 * * [misc]simplify: iters left: 6 (15 enodes) 1547111158.387 * * [misc]simplify: iters left: 5 (35 enodes) 1547111158.397 * * [misc]simplify: iters left: 4 (65 enodes) 1547111158.416 * * [misc]simplify: iters left: 3 (156 enodes) 1547111158.512 * [exit]simplify: Simplified to (+ (* -1/2 (log k)) (/ (log (* (* n PI) 2)) (/ 2 (- 1 k)))) 1547111158.513 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (+ (* -1/2 (log k)) (/ (log (* (* n PI) 2)) (/ 2 (- 1 k)))))) 1547111158.513 * * * * [misc]progress: [ 28 / 57 ] simplifiying candidate # 1547111158.513 * [enter]simplify: Simplifying (+ (* (log k) -1/2) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))) 1547111158.513 * * [misc]simplify: iters left: 6 (15 enodes) 1547111158.519 * * [misc]simplify: iters left: 5 (35 enodes) 1547111158.529 * * [misc]simplify: iters left: 4 (65 enodes) 1547111158.551 * * [misc]simplify: iters left: 3 (156 enodes) 1547111158.609 * [exit]simplify: Simplified to (+ (* -1/2 (log k)) (/ (log (* (* n PI) 2)) (/ 2 (- 1 k)))) 1547111158.609 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (+ (* -1/2 (log k)) (/ (log (* (* n PI) 2)) (/ 2 (- 1 k)))))) 1547111158.609 * * * * [misc]progress: [ 29 / 57 ] simplifiying candidate # 1547111158.610 * [enter]simplify: Simplifying (+ (* (log k) -1/2) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) 1547111158.610 * * [misc]simplify: iters left: 6 (15 enodes) 1547111158.613 * * [misc]simplify: iters left: 5 (31 enodes) 1547111158.617 * * [misc]simplify: iters left: 4 (50 enodes) 1547111158.625 * * [misc]simplify: iters left: 3 (97 enodes) 1547111158.662 * * [misc]simplify: iters left: 2 (269 enodes) 1547111158.820 * [exit]simplify: Simplified to (+ (* -1/2 (log k)) (/ (log (* 2 (* n PI))) (/ 2 (- 1 k)))) 1547111158.820 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (+ (* -1/2 (log k)) (/ (log (* 2 (* n PI))) (/ 2 (- 1 k)))))) 1547111158.820 * * * * [misc]progress: [ 30 / 57 ] simplifiying candidate # 1547111158.820 * [enter]simplify: Simplifying (+ (log (pow k -1/2)) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))) 1547111158.820 * * [misc]simplify: iters left: 6 (15 enodes) 1547111158.823 * * [misc]simplify: iters left: 5 (36 enodes) 1547111158.828 * * [misc]simplify: iters left: 4 (67 enodes) 1547111158.843 * * [misc]simplify: iters left: 3 (157 enodes) 1547111158.893 * [exit]simplify: Simplified to (+ (* -1/2 (log k)) (* (log (* PI (* n 2))) (- 1/2 (/ k 2)))) 1547111158.893 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (+ (* -1/2 (log k)) (* (log (* PI (* n 2))) (- 1/2 (/ k 2)))))) 1547111158.893 * * * * [misc]progress: [ 31 / 57 ] simplifiying candidate # 1547111158.893 * [enter]simplify: Simplifying (+ (log (pow k -1/2)) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))) 1547111158.894 * * [misc]simplify: iters left: 6 (15 enodes) 1547111158.896 * * [misc]simplify: iters left: 5 (36 enodes) 1547111158.904 * * [misc]simplify: iters left: 4 (67 enodes) 1547111158.923 * * [misc]simplify: iters left: 3 (157 enodes) 1547111158.990 * [exit]simplify: Simplified to (+ (* -1/2 (log k)) (* (log (* PI (* n 2))) (- 1/2 (/ k 2)))) 1547111158.990 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (+ (* -1/2 (log k)) (* (log (* PI (* n 2))) (- 1/2 (/ k 2)))))) 1547111158.990 * * * * [misc]progress: [ 32 / 57 ] simplifiying candidate # 1547111158.990 * [enter]simplify: Simplifying (+ (log (pow k -1/2)) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) 1547111158.991 * * [misc]simplify: iters left: 6 (15 enodes) 1547111158.993 * * [misc]simplify: iters left: 5 (32 enodes) 1547111159.000 * * [misc]simplify: iters left: 4 (52 enodes) 1547111159.007 * * [misc]simplify: iters left: 3 (99 enodes) 1547111159.030 * * [misc]simplify: iters left: 2 (271 enodes) 1547111159.176 * [exit]simplify: Simplified to (+ (* (log k) -1/2) (* (/ (- 1 k) 2) (log (* 2 (* n PI))))) 1547111159.176 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (+ (* (log k) -1/2) (* (/ (- 1 k) 2) (log (* 2 (* n PI))))))) 1547111159.176 * * * * [misc]progress: [ 33 / 57 ] simplifiying candidate # 1547111159.177 * * * * [misc]progress: [ 34 / 57 ] simplifiying candidate # 1547111159.177 * * * * [misc]progress: [ 35 / 57 ] simplifiying candidate # 1547111159.177 * [enter]simplify: Simplifying (* (* (* (pow k -1/2) (pow k -1/2)) (pow k -1/2)) (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) 1547111159.177 * * [misc]simplify: iters left: 6 (17 enodes) 1547111159.184 * * [misc]simplify: iters left: 5 (36 enodes) 1547111159.194 * * [misc]simplify: iters left: 4 (70 enodes) 1547111159.216 * * [misc]simplify: iters left: 3 (105 enodes) 1547111159.244 * * [misc]simplify: iters left: 2 (126 enodes) 1547111159.262 * * [misc]simplify: iters left: 1 (129 enodes) 1547111159.285 * [exit]simplify: Simplified to (pow (* (pow k -1/2) (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) 3) 1547111159.285 * [misc]simplify: Simplified (2 1) to (λ (k n) (cbrt (pow (* (pow k -1/2) (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) 3))) 1547111159.285 * * * * [misc]progress: [ 36 / 57 ] simplifiying candidate # 1547111159.285 * * * * [misc]progress: [ 37 / 57 ] simplifiying candidate # 1547111159.285 * * * * [misc]progress: [ 38 / 57 ] simplifiying candidate # 1547111159.285 * * * * [misc]progress: [ 39 / 57 ] simplifiying candidate # 1547111159.285 * * * * [misc]progress: [ 40 / 57 ] simplifiying candidate # 1547111159.286 * [enter]simplify: Simplifying (pow n (/ (- 1 k) 2)) 1547111159.286 * * [misc]simplify: iters left: 5 (7 enodes) 1547111159.289 * * [misc]simplify: iters left: 4 (15 enodes) 1547111159.292 * * [misc]simplify: iters left: 3 (18 enodes) 1547111159.297 * * [misc]simplify: iters left: 2 (20 enodes) 1547111159.301 * [exit]simplify: Simplified to (pow n (- 1/2 (/ k 2))) 1547111159.301 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow k -1/2) (pow (* 2 PI) (/ (- 1 k) 2))) (pow n (- 1/2 (/ k 2))))) 1547111159.301 * * * * [misc]progress: [ 41 / 57 ] simplifiying candidate # 1547111159.302 * [enter]simplify: Simplifying (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) 1547111159.302 * * [misc]simplify: iters left: 6 (11 enodes) 1547111159.306 * * [misc]simplify: iters left: 5 (23 enodes) 1547111159.312 * * [misc]simplify: iters left: 4 (32 enodes) 1547111159.320 * * [misc]simplify: iters left: 3 (35 enodes) 1547111159.328 * [exit]simplify: Simplified to (cbrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) 1547111159.328 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow k -1/2) (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) (cbrt (pow (* PI (* n 2)) (/ (- 1 k) 2))))) 1547111159.328 * * * * [misc]progress: [ 42 / 57 ] simplifiying candidate # 1547111159.328 * [enter]simplify: Simplifying (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) 1547111159.328 * * [misc]simplify: iters left: 6 (11 enodes) 1547111159.330 * * [misc]simplify: iters left: 5 (23 enodes) 1547111159.333 * * [misc]simplify: iters left: 4 (32 enodes) 1547111159.337 * * [misc]simplify: iters left: 3 (35 enodes) 1547111159.341 * [exit]simplify: Simplified to (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) 1547111159.341 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow k -1/2) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))))) 1547111159.341 * * * * [misc]progress: [ 43 / 57 ] simplifiying candidate # 1547111159.341 * [enter]simplify: Simplifying (pow (* (* 2 PI) n) (/ (- 1 k) 2)) 1547111159.341 * * [misc]simplify: iters left: 5 (10 enodes) 1547111159.343 * * [misc]simplify: iters left: 4 (22 enodes) 1547111159.346 * * [misc]simplify: iters left: 3 (31 enodes) 1547111159.349 * * [misc]simplify: iters left: 2 (34 enodes) 1547111159.353 * [exit]simplify: Simplified to (pow (* (* n 2) PI) (/ (- 1 k) 2)) 1547111159.353 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow k -1/2) 1) (pow (* (* n 2) PI) (/ (- 1 k) 2)))) 1547111159.353 * * * * [misc]progress: [ 44 / 57 ] simplifiying candidate # 1547111159.353 * [enter]simplify: Simplifying (* (cbrt (pow k -1/2)) (cbrt (pow k -1/2))) 1547111159.354 * * [misc]simplify: iters left: 4 (5 enodes) 1547111159.354 * [exit]simplify: Simplified to (* (cbrt (pow k -1/2)) (cbrt (pow k -1/2))) 1547111159.354 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (* (cbrt (pow k -1/2)) (cbrt (pow k -1/2))) (* (cbrt (pow k -1/2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) 1547111159.354 * * * * [misc]progress: [ 45 / 57 ] simplifiying candidate # 1547111159.354 * [enter]simplify: Simplifying (sqrt (pow k -1/2)) 1547111159.354 * * [misc]simplify: iters left: 2 (4 enodes) 1547111159.355 * [exit]simplify: Simplified to (sqrt (pow k -1/2)) 1547111159.355 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (pow k -1/2)) (* (sqrt (pow k -1/2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) 1547111159.355 * * * * [misc]progress: [ 46 / 57 ] simplifiying candidate # 1547111159.355 * * * * [misc]progress: [ 47 / 57 ] simplifiying candidate # 1547111159.355 * [enter]simplify: Simplifying (pow (* (* 2 PI) n) (/ k 2)) 1547111159.355 * * [misc]simplify: iters left: 5 (8 enodes) 1547111159.356 * * [misc]simplify: iters left: 4 (12 enodes) 1547111159.358 * * [misc]simplify: iters left: 3 (18 enodes) 1547111159.360 * * [misc]simplify: iters left: 2 (20 enodes) 1547111159.363 * [exit]simplify: Simplified to (pow (* 2 (* n PI)) (/ k 2)) 1547111159.363 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (* (pow k -1/2) (pow (* (* 2 PI) n) (/ 1 2))) (pow (* 2 (* n PI)) (/ k 2)))) 1547111159.363 * * * * [misc]progress: [ 48 / 57 ] simplifiying candidate # 1547111159.363 * * * * [misc]progress: [ 49 / 57 ] simplifiying candidate # 1547111159.363 * [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))))) 1547111159.363 * * [misc]simplify: iters left: 6 (37 enodes) 1547111159.371 * * [misc]simplify: iters left: 5 (105 enodes) 1547111159.400 * * [misc]simplify: iters left: 4 (339 enodes) 1547111159.583 * [exit]simplify: Simplified to (+ (+ (* (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) -1/2) (+ (* (* (* k (log n)) (* k (log n))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (pow (* PI 2) 1/2) (pow n 1/2)))) (* (* k k) (+ (* (* (log (* PI 2)) (log (* PI 2))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (* (* (log n) (pow n 1/2)) (pow (* PI 2) 1/2)) (* (log (* PI 2)) 1/4))))) 1547111159.583 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (pow k -1/2) (+ (+ (* (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) -1/2) (+ (* (* (* k (log n)) (* k (log n))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (pow (* PI 2) 1/2) (pow n 1/2)))) (* (* k k) (+ (* (* (log (* PI 2)) (log (* PI 2))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (* (* (log n) (pow n 1/2)) (pow (* PI 2) 1/2)) (* (log (* PI 2)) 1/4))))))) 1547111159.583 * * * * [misc]progress: [ 50 / 57 ] simplifiying candidate # 1547111159.584 * [enter]simplify: Simplifying (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) 1547111159.584 * * [misc]simplify: iters left: 6 (15 enodes) 1547111159.587 * * [misc]simplify: iters left: 5 (35 enodes) 1547111159.595 * * [misc]simplify: iters left: 4 (72 enodes) 1547111159.610 * * [misc]simplify: iters left: 3 (234 enodes) 1547111159.702 * [exit]simplify: Simplified to (* (pow n (- 1/2 (* 1/2 k))) (pow (* 2 PI) (- 1/2 (* 1/2 k)))) 1547111159.702 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (pow k -1/2) (* (pow n (- 1/2 (* 1/2 k))) (pow (* 2 PI) (- 1/2 (* 1/2 k)))))) 1547111159.702 * * * * [misc]progress: [ 51 / 57 ] simplifiying candidate # 1547111159.702 * [enter]simplify: Simplifying (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) 1547111159.703 * * [misc]simplify: iters left: 6 (16 enodes) 1547111159.709 * * [misc]simplify: iters left: 5 (35 enodes) 1547111159.723 * * [misc]simplify: iters left: 4 (76 enodes) 1547111159.745 * * [misc]simplify: iters left: 3 (272 enodes) 1547111159.924 * [exit]simplify: Simplified to (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))) 1547111159.924 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (pow k -1/2) (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))))) 1547111159.924 * * * * [misc]progress: [ 52 / 57 ] simplifiying candidate # 1547111159.924 * [enter]simplify: Simplifying (* 2 (* n PI)) 1547111159.924 * * [misc]simplify: iters left: 4 (5 enodes) 1547111159.926 * * [misc]simplify: iters left: 3 (9 enodes) 1547111159.928 * * [misc]simplify: iters left: 2 (15 enodes) 1547111159.933 * * [misc]simplify: iters left: 1 (17 enodes) 1547111159.936 * [exit]simplify: Simplified to (* (* PI n) 2) 1547111159.937 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow k -1/2) (pow (* (* PI n) 2) (/ (- 1 k) 2)))) 1547111159.937 * * * * [misc]progress: [ 53 / 57 ] simplifiying candidate # 1547111159.937 * [enter]simplify: Simplifying (* 2 (* n PI)) 1547111159.937 * * [misc]simplify: iters left: 4 (5 enodes) 1547111159.939 * * [misc]simplify: iters left: 3 (9 enodes) 1547111159.941 * * [misc]simplify: iters left: 2 (15 enodes) 1547111159.945 * * [misc]simplify: iters left: 1 (17 enodes) 1547111159.949 * [exit]simplify: Simplified to (* (* PI n) 2) 1547111159.950 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow k -1/2) (pow (* (* PI n) 2) (/ (- 1 k) 2)))) 1547111159.950 * * * * [misc]progress: [ 54 / 57 ] simplifiying candidate # 1547111159.950 * [enter]simplify: Simplifying (* 2 (* n PI)) 1547111159.950 * * [misc]simplify: iters left: 4 (5 enodes) 1547111159.952 * * [misc]simplify: iters left: 3 (9 enodes) 1547111159.954 * * [misc]simplify: iters left: 2 (15 enodes) 1547111159.962 * * [misc]simplify: iters left: 1 (17 enodes) 1547111159.966 * [exit]simplify: Simplified to (* (* PI n) 2) 1547111159.966 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow k -1/2) (pow (* (* PI n) 2) (/ (- 1 k) 2)))) 1547111159.966 * * * * [misc]progress: [ 55 / 57 ] simplifiying candidate # 1547111159.966 * [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))))))))))))) 1547111159.966 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1547111159.966 * * * * [misc]progress: [ 56 / 57 ] simplifiying candidate # 1547111159.967 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3)))))))) 1547111159.967 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1547111159.967 * * * * [misc]progress: [ 57 / 57 ] simplifiying candidate # 1547111159.967 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k))))))) 1547111159.967 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1547111159.967 * * * [misc]progress: adding candidates to table 1547111160.694 * * [misc]progress: iteration 4 / 4 1547111160.695 * * * [misc]progress: picking best candidate 1547111160.724 * * * * [misc]pick: Picked # 1547111160.724 * * * [misc]progress: localizing error 1547111160.739 * * * [misc]progress: generating rewritten candidates 1547111160.739 * * * * [misc]progress: [ 1 / 3 ] rewriting at (2 1) 1547111160.741 * * * * [misc]progress: [ 2 / 3 ] rewriting at (2 1 1 1) 1547111160.742 * * * * [misc]progress: [ 3 / 3 ] rewriting at (2) 1547111160.752 * * * [misc]progress: generating series expansions 1547111160.752 * * * * [misc]progress: [ 1 / 3 ] generating series at (2 1) 1547111160.752 * [misc]backup-simplify: Simplify (pow (* (* n PI) 2) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 1547111160.752 * [misc]approximate: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 1547111160.752 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1547111160.752 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1547111160.752 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1547111160.752 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1547111160.752 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111160.752 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111160.752 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1547111160.752 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111160.752 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111160.752 * [misc]taylor: Taking taylor expansion of k in k 1547111160.752 * [misc]backup-simplify: Simplify 0 into 0 1547111160.752 * [misc]backup-simplify: Simplify 1 into 1 1547111160.752 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1547111160.752 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1547111160.752 * [misc]taylor: Taking taylor expansion of 2 in k 1547111160.753 * [misc]backup-simplify: Simplify 2 into 2 1547111160.753 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1547111160.753 * [misc]taylor: Taking taylor expansion of n in k 1547111160.753 * [misc]backup-simplify: Simplify n into n 1547111160.753 * [misc]taylor: Taking taylor expansion of PI in k 1547111160.753 * [misc]backup-simplify: Simplify PI into PI 1547111160.753 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1547111160.753 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1547111160.753 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1547111160.753 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1547111160.753 * [misc]backup-simplify: Simplify (- 0) into 0 1547111160.754 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1547111160.754 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1547111160.754 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1547111160.754 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1547111160.754 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1547111160.754 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1547111160.754 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1547111160.754 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111160.754 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111160.754 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1547111160.754 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111160.754 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111160.754 * [misc]taylor: Taking taylor expansion of k in n 1547111160.754 * [misc]backup-simplify: Simplify k into k 1547111160.754 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1547111160.754 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1547111160.754 * [misc]taylor: Taking taylor expansion of 2 in n 1547111160.754 * [misc]backup-simplify: Simplify 2 into 2 1547111160.754 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547111160.754 * [misc]taylor: Taking taylor expansion of n in n 1547111160.754 * [misc]backup-simplify: Simplify 0 into 0 1547111160.754 * [misc]backup-simplify: Simplify 1 into 1 1547111160.754 * [misc]taylor: Taking taylor expansion of PI in n 1547111160.754 * [misc]backup-simplify: Simplify PI into PI 1547111160.755 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547111160.755 * [misc]backup-simplify: Simplify (* 2 0) into 0 1547111160.756 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547111160.756 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1547111160.757 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547111160.757 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1547111160.757 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1547111160.757 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1547111160.758 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547111160.758 * [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)))) 1547111160.759 * [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))))) 1547111160.759 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1547111160.759 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1547111160.759 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1547111160.759 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1547111160.759 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111160.759 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111160.759 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1547111160.759 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111160.759 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111160.759 * [misc]taylor: Taking taylor expansion of k in n 1547111160.759 * [misc]backup-simplify: Simplify k into k 1547111160.759 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1547111160.759 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1547111160.759 * [misc]taylor: Taking taylor expansion of 2 in n 1547111160.759 * [misc]backup-simplify: Simplify 2 into 2 1547111160.759 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547111160.759 * [misc]taylor: Taking taylor expansion of n in n 1547111160.759 * [misc]backup-simplify: Simplify 0 into 0 1547111160.759 * [misc]backup-simplify: Simplify 1 into 1 1547111160.759 * [misc]taylor: Taking taylor expansion of PI in n 1547111160.759 * [misc]backup-simplify: Simplify PI into PI 1547111160.760 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547111160.760 * [misc]backup-simplify: Simplify (* 2 0) into 0 1547111160.761 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547111160.761 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1547111160.762 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547111160.762 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1547111160.762 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1547111160.762 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1547111160.763 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547111160.763 * [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)))) 1547111160.764 * [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))))) 1547111160.764 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1547111160.764 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1547111160.764 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1547111160.764 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111160.764 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111160.764 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1547111160.764 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111160.764 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111160.764 * [misc]taylor: Taking taylor expansion of k in k 1547111160.764 * [misc]backup-simplify: Simplify 0 into 0 1547111160.764 * [misc]backup-simplify: Simplify 1 into 1 1547111160.764 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1547111160.764 * [misc]taylor: Taking taylor expansion of (log n) in k 1547111160.764 * [misc]taylor: Taking taylor expansion of n in k 1547111160.764 * [misc]backup-simplify: Simplify n into n 1547111160.764 * [misc]backup-simplify: Simplify (log n) into (log n) 1547111160.764 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1547111160.764 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1547111160.764 * [misc]taylor: Taking taylor expansion of 2 in k 1547111160.764 * [misc]backup-simplify: Simplify 2 into 2 1547111160.764 * [misc]taylor: Taking taylor expansion of PI in k 1547111160.765 * [misc]backup-simplify: Simplify PI into PI 1547111160.765 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547111160.765 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547111160.765 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1547111160.766 * [misc]backup-simplify: Simplify (- 0) into 0 1547111160.766 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1547111160.766 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547111160.767 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1547111160.767 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1547111160.768 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1547111160.769 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1547111160.770 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1547111160.773 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1547111160.773 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1547111160.774 * [misc]backup-simplify: Simplify (- 0) into 0 1547111160.774 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111160.774 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547111160.775 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1547111160.777 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1547111160.777 * [misc]taylor: Taking taylor expansion of 0 in k 1547111160.777 * [misc]backup-simplify: Simplify 0 into 0 1547111160.777 * [misc]backup-simplify: Simplify 0 into 0 1547111160.778 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1547111160.778 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1547111160.781 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1547111160.781 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111160.781 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1547111160.782 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1547111160.782 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1547111160.782 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1547111160.784 * [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))))))) 1547111160.785 * [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))))))) 1547111160.787 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1547111160.789 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1547111160.794 * [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 1547111160.794 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1547111160.794 * [misc]backup-simplify: Simplify (- 0) into 0 1547111160.795 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111160.795 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547111160.796 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1547111160.798 * [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 1547111160.799 * [misc]taylor: Taking taylor expansion of 0 in k 1547111160.799 * [misc]backup-simplify: Simplify 0 into 0 1547111160.799 * [misc]backup-simplify: Simplify 0 into 0 1547111160.799 * [misc]backup-simplify: Simplify 0 into 0 1547111160.800 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1547111160.801 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1547111160.806 * [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 1547111160.807 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111160.807 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1547111160.807 * [misc]backup-simplify: Simplify (- 0) into 0 1547111160.807 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111160.808 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1547111160.809 * [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))))) 1547111160.811 * [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))))) 1547111160.813 * [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))))) 1547111160.814 * [misc]backup-simplify: Simplify (pow (* (* (/ 1 n) PI) 2) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 1547111160.814 * [misc]approximate: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 1547111160.814 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1547111160.814 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1547111160.814 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1547111160.814 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1547111160.814 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111160.814 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111160.814 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1547111160.814 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111160.814 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111160.814 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547111160.814 * [misc]taylor: Taking taylor expansion of k in k 1547111160.814 * [misc]backup-simplify: Simplify 0 into 0 1547111160.814 * [misc]backup-simplify: Simplify 1 into 1 1547111160.814 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547111160.814 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1547111160.814 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1547111160.814 * [misc]taylor: Taking taylor expansion of 2 in k 1547111160.814 * [misc]backup-simplify: Simplify 2 into 2 1547111160.814 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1547111160.814 * [misc]taylor: Taking taylor expansion of PI in k 1547111160.814 * [misc]backup-simplify: Simplify PI into PI 1547111160.814 * [misc]taylor: Taking taylor expansion of n in k 1547111160.814 * [misc]backup-simplify: Simplify n into n 1547111160.814 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1547111160.814 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1547111160.814 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1547111160.814 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1547111160.814 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1547111160.815 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1547111160.815 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1547111160.815 * [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)))) 1547111160.815 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1547111160.815 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1547111160.815 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1547111160.815 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1547111160.815 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111160.815 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111160.815 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1547111160.815 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111160.815 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111160.815 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547111160.815 * [misc]taylor: Taking taylor expansion of k in n 1547111160.815 * [misc]backup-simplify: Simplify k into k 1547111160.815 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547111160.815 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1547111160.815 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1547111160.815 * [misc]taylor: Taking taylor expansion of 2 in n 1547111160.815 * [misc]backup-simplify: Simplify 2 into 2 1547111160.815 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547111160.815 * [misc]taylor: Taking taylor expansion of PI in n 1547111160.815 * [misc]backup-simplify: Simplify PI into PI 1547111160.815 * [misc]taylor: Taking taylor expansion of n in n 1547111160.815 * [misc]backup-simplify: Simplify 0 into 0 1547111160.815 * [misc]backup-simplify: Simplify 1 into 1 1547111160.815 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547111160.816 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547111160.816 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547111160.816 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1547111160.816 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1547111160.816 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1547111160.817 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547111160.817 * [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))) 1547111160.817 * [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)))) 1547111160.817 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1547111160.817 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1547111160.817 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1547111160.817 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1547111160.817 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111160.817 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111160.817 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1547111160.817 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111160.817 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111160.817 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547111160.817 * [misc]taylor: Taking taylor expansion of k in n 1547111160.817 * [misc]backup-simplify: Simplify k into k 1547111160.818 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547111160.818 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1547111160.818 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1547111160.818 * [misc]taylor: Taking taylor expansion of 2 in n 1547111160.818 * [misc]backup-simplify: Simplify 2 into 2 1547111160.818 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547111160.818 * [misc]taylor: Taking taylor expansion of PI in n 1547111160.818 * [misc]backup-simplify: Simplify PI into PI 1547111160.818 * [misc]taylor: Taking taylor expansion of n in n 1547111160.818 * [misc]backup-simplify: Simplify 0 into 0 1547111160.818 * [misc]backup-simplify: Simplify 1 into 1 1547111160.818 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547111160.818 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547111160.818 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547111160.818 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1547111160.818 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1547111160.818 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1547111160.819 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547111160.819 * [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))) 1547111160.820 * [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)))) 1547111160.820 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1547111160.820 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1547111160.820 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1547111160.820 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111160.820 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111160.820 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1547111160.820 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111160.820 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111160.820 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547111160.820 * [misc]taylor: Taking taylor expansion of k in k 1547111160.820 * [misc]backup-simplify: Simplify 0 into 0 1547111160.820 * [misc]backup-simplify: Simplify 1 into 1 1547111160.820 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547111160.820 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1547111160.820 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1547111160.820 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1547111160.820 * [misc]taylor: Taking taylor expansion of 2 in k 1547111160.820 * [misc]backup-simplify: Simplify 2 into 2 1547111160.820 * [misc]taylor: Taking taylor expansion of PI in k 1547111160.820 * [misc]backup-simplify: Simplify PI into PI 1547111160.820 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547111160.821 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547111160.821 * [misc]taylor: Taking taylor expansion of (log n) in k 1547111160.821 * [misc]taylor: Taking taylor expansion of n in k 1547111160.821 * [misc]backup-simplify: Simplify n into n 1547111160.821 * [misc]backup-simplify: Simplify (log n) into (log n) 1547111160.821 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1547111160.821 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1547111160.821 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1547111160.821 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1547111160.822 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1547111160.822 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1547111160.822 * [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)))) 1547111160.823 * [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)))) 1547111160.824 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1547111160.824 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1547111160.826 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1547111160.826 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1547111160.826 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1547111160.826 * [misc]backup-simplify: Simplify (- 0) into 0 1547111160.826 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111160.826 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547111160.827 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1547111160.828 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1547111160.828 * [misc]taylor: Taking taylor expansion of 0 in k 1547111160.828 * [misc]backup-simplify: Simplify 0 into 0 1547111160.828 * [misc]backup-simplify: Simplify 0 into 0 1547111160.828 * [misc]backup-simplify: Simplify 0 into 0 1547111160.829 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111160.829 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1547111160.832 * [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 1547111160.833 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1547111160.833 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1547111160.833 * [misc]backup-simplify: Simplify (- 0) into 0 1547111160.833 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111160.833 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547111160.834 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1547111160.835 * [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 1547111160.835 * [misc]taylor: Taking taylor expansion of 0 in k 1547111160.835 * [misc]backup-simplify: Simplify 0 into 0 1547111160.835 * [misc]backup-simplify: Simplify 0 into 0 1547111160.836 * [misc]backup-simplify: Simplify 0 into 0 1547111160.836 * [misc]backup-simplify: Simplify 0 into 0 1547111160.837 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111160.839 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1547111160.847 * [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 1547111160.847 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1547111160.848 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1547111160.848 * [misc]backup-simplify: Simplify (- 0) into 0 1547111160.848 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111160.849 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547111160.850 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1547111160.853 * [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 1547111160.853 * [misc]taylor: Taking taylor expansion of 0 in k 1547111160.854 * [misc]backup-simplify: Simplify 0 into 0 1547111160.854 * [misc]backup-simplify: Simplify 0 into 0 1547111160.854 * [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))))) 1547111160.855 * [misc]backup-simplify: Simplify (pow (* (* (/ 1 (- n)) PI) 2) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 1547111160.855 * [misc]approximate: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 1547111160.855 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1547111160.855 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1547111160.855 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1547111160.855 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1547111160.855 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1547111160.855 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111160.855 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111160.855 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547111160.855 * [misc]taylor: Taking taylor expansion of k in k 1547111160.855 * [misc]backup-simplify: Simplify 0 into 0 1547111160.855 * [misc]backup-simplify: Simplify 1 into 1 1547111160.855 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547111160.855 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111160.855 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111160.855 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1547111160.855 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1547111160.855 * [misc]taylor: Taking taylor expansion of -2 in k 1547111160.855 * [misc]backup-simplify: Simplify -2 into -2 1547111160.855 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1547111160.855 * [misc]taylor: Taking taylor expansion of PI in k 1547111160.855 * [misc]backup-simplify: Simplify PI into PI 1547111160.856 * [misc]taylor: Taking taylor expansion of n in k 1547111160.856 * [misc]backup-simplify: Simplify n into n 1547111160.856 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1547111160.856 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1547111160.856 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1547111160.856 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1547111160.856 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1547111160.856 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1547111160.856 * [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))) 1547111160.856 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1547111160.857 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1547111160.857 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1547111160.857 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1547111160.857 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1547111160.857 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111160.857 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111160.857 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547111160.857 * [misc]taylor: Taking taylor expansion of k in n 1547111160.857 * [misc]backup-simplify: Simplify k into k 1547111160.857 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547111160.857 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111160.857 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111160.857 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1547111160.857 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1547111160.857 * [misc]taylor: Taking taylor expansion of -2 in n 1547111160.857 * [misc]backup-simplify: Simplify -2 into -2 1547111160.857 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547111160.857 * [misc]taylor: Taking taylor expansion of PI in n 1547111160.857 * [misc]backup-simplify: Simplify PI into PI 1547111160.857 * [misc]taylor: Taking taylor expansion of n in n 1547111160.857 * [misc]backup-simplify: Simplify 0 into 0 1547111160.857 * [misc]backup-simplify: Simplify 1 into 1 1547111160.857 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547111160.858 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547111160.858 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1547111160.858 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1547111160.858 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1547111160.859 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547111160.860 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1547111160.860 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 1547111160.860 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1547111160.860 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1547111160.860 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1547111160.860 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1547111160.861 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1547111160.861 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111160.861 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111160.861 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547111160.861 * [misc]taylor: Taking taylor expansion of k in n 1547111160.861 * [misc]backup-simplify: Simplify k into k 1547111160.861 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547111160.861 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111160.861 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111160.861 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1547111160.861 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1547111160.861 * [misc]taylor: Taking taylor expansion of -2 in n 1547111160.861 * [misc]backup-simplify: Simplify -2 into -2 1547111160.861 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547111160.861 * [misc]taylor: Taking taylor expansion of PI in n 1547111160.861 * [misc]backup-simplify: Simplify PI into PI 1547111160.861 * [misc]taylor: Taking taylor expansion of n in n 1547111160.861 * [misc]backup-simplify: Simplify 0 into 0 1547111160.861 * [misc]backup-simplify: Simplify 1 into 1 1547111160.861 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547111160.862 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547111160.862 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1547111160.862 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1547111160.862 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1547111160.863 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547111160.863 * [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))) 1547111160.864 * [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)))) 1547111160.864 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1547111160.864 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1547111160.864 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1547111160.864 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1547111160.864 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111160.864 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111160.864 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547111160.864 * [misc]taylor: Taking taylor expansion of k in k 1547111160.864 * [misc]backup-simplify: Simplify 0 into 0 1547111160.864 * [misc]backup-simplify: Simplify 1 into 1 1547111160.865 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547111160.865 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111160.865 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111160.865 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1547111160.865 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1547111160.865 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1547111160.865 * [misc]taylor: Taking taylor expansion of -2 in k 1547111160.865 * [misc]backup-simplify: Simplify -2 into -2 1547111160.865 * [misc]taylor: Taking taylor expansion of PI in k 1547111160.865 * [misc]backup-simplify: Simplify PI into PI 1547111160.865 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547111160.866 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1547111160.866 * [misc]taylor: Taking taylor expansion of (log n) in k 1547111160.866 * [misc]taylor: Taking taylor expansion of n in k 1547111160.866 * [misc]backup-simplify: Simplify n into n 1547111160.866 * [misc]backup-simplify: Simplify (log n) into (log n) 1547111160.866 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1547111160.866 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1547111160.866 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1547111160.867 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1547111160.867 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1547111160.870 * [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)))) 1547111160.871 * [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)))) 1547111160.873 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1547111160.873 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1547111160.876 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1547111160.876 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1547111160.876 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1547111160.876 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111160.876 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547111160.877 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1547111160.878 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1547111160.878 * [misc]taylor: Taking taylor expansion of 0 in k 1547111160.878 * [misc]backup-simplify: Simplify 0 into 0 1547111160.878 * [misc]backup-simplify: Simplify 0 into 0 1547111160.878 * [misc]backup-simplify: Simplify 0 into 0 1547111160.879 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111160.879 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1547111160.882 * [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 1547111160.882 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1547111160.882 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1547111160.883 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111160.883 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547111160.883 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1547111160.885 * [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 1547111160.885 * [misc]taylor: Taking taylor expansion of 0 in k 1547111160.885 * [misc]backup-simplify: Simplify 0 into 0 1547111160.885 * [misc]backup-simplify: Simplify 0 into 0 1547111160.885 * [misc]backup-simplify: Simplify 0 into 0 1547111160.885 * [misc]backup-simplify: Simplify 0 into 0 1547111160.886 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111160.887 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1547111160.891 * [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 1547111160.891 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1547111160.892 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1547111160.892 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111160.892 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547111160.893 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 1547111160.895 * [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 1547111160.895 * [misc]taylor: Taking taylor expansion of 0 in k 1547111160.895 * [misc]backup-simplify: Simplify 0 into 0 1547111160.895 * [misc]backup-simplify: Simplify 0 into 0 1547111160.896 * [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))))) 1547111160.896 * * * * [misc]progress: [ 2 / 3 ] generating series at (2 1 1 1) 1547111160.896 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1547111160.896 * [misc]approximate: Taking taylor expansion of (* n PI) in (n) around 0 1547111160.896 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547111160.896 * [misc]taylor: Taking taylor expansion of n in n 1547111160.896 * [misc]backup-simplify: Simplify 0 into 0 1547111160.896 * [misc]backup-simplify: Simplify 1 into 1 1547111160.896 * [misc]taylor: Taking taylor expansion of PI in n 1547111160.896 * [misc]backup-simplify: Simplify PI into PI 1547111160.896 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547111160.896 * [misc]taylor: Taking taylor expansion of n in n 1547111160.896 * [misc]backup-simplify: Simplify 0 into 0 1547111160.896 * [misc]backup-simplify: Simplify 1 into 1 1547111160.896 * [misc]taylor: Taking taylor expansion of PI in n 1547111160.896 * [misc]backup-simplify: Simplify PI into PI 1547111160.896 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547111160.896 * [misc]backup-simplify: Simplify 0 into 0 1547111160.897 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547111160.897 * [misc]backup-simplify: Simplify PI into PI 1547111160.897 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1547111160.897 * [misc]backup-simplify: Simplify 0 into 0 1547111160.898 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1547111160.898 * [misc]backup-simplify: Simplify 0 into 0 1547111160.899 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1547111160.899 * [misc]backup-simplify: Simplify 0 into 0 1547111160.901 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1547111160.901 * [misc]backup-simplify: Simplify 0 into 0 1547111160.903 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1547111160.903 * [misc]backup-simplify: Simplify 0 into 0 1547111160.905 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1547111160.905 * [misc]backup-simplify: Simplify 0 into 0 1547111160.905 * [misc]backup-simplify: Simplify (* PI n) into (* n PI) 1547111160.905 * [misc]backup-simplify: Simplify (* (/ 1 n) PI) into (/ PI n) 1547111160.905 * [misc]approximate: Taking taylor expansion of (/ PI n) in (n) around 0 1547111160.905 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547111160.905 * [misc]taylor: Taking taylor expansion of PI in n 1547111160.905 * [misc]backup-simplify: Simplify PI into PI 1547111160.905 * [misc]taylor: Taking taylor expansion of n in n 1547111160.905 * [misc]backup-simplify: Simplify 0 into 0 1547111160.905 * [misc]backup-simplify: Simplify 1 into 1 1547111160.906 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547111160.906 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547111160.906 * [misc]taylor: Taking taylor expansion of PI in n 1547111160.906 * [misc]backup-simplify: Simplify PI into PI 1547111160.906 * [misc]taylor: Taking taylor expansion of n in n 1547111160.906 * [misc]backup-simplify: Simplify 0 into 0 1547111160.906 * [misc]backup-simplify: Simplify 1 into 1 1547111160.906 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547111160.906 * [misc]backup-simplify: Simplify PI into PI 1547111160.907 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1547111160.907 * [misc]backup-simplify: Simplify 0 into 0 1547111160.907 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111160.907 * [misc]backup-simplify: Simplify 0 into 0 1547111160.908 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111160.908 * [misc]backup-simplify: Simplify 0 into 0 1547111160.909 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111160.909 * [misc]backup-simplify: Simplify 0 into 0 1547111160.911 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111160.911 * [misc]backup-simplify: Simplify 0 into 0 1547111160.912 * [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 1547111160.912 * [misc]backup-simplify: Simplify 0 into 0 1547111160.912 * [misc]backup-simplify: Simplify (* PI (/ 1 (/ 1 n))) into (* n PI) 1547111160.912 * [misc]backup-simplify: Simplify (* (/ 1 (- n)) PI) into (* -1 (/ PI n)) 1547111160.912 * [misc]approximate: Taking taylor expansion of (* -1 (/ PI n)) in (n) around 0 1547111160.912 * [misc]taylor: Taking taylor expansion of (* -1 (/ PI n)) in n 1547111160.912 * [misc]taylor: Taking taylor expansion of -1 in n 1547111160.912 * [misc]backup-simplify: Simplify -1 into -1 1547111160.912 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547111160.912 * [misc]taylor: Taking taylor expansion of PI in n 1547111160.912 * [misc]backup-simplify: Simplify PI into PI 1547111160.912 * [misc]taylor: Taking taylor expansion of n in n 1547111160.912 * [misc]backup-simplify: Simplify 0 into 0 1547111160.912 * [misc]backup-simplify: Simplify 1 into 1 1547111160.912 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547111160.912 * [misc]taylor: Taking taylor expansion of (* -1 (/ PI n)) in n 1547111160.912 * [misc]taylor: Taking taylor expansion of -1 in n 1547111160.912 * [misc]backup-simplify: Simplify -1 into -1 1547111160.913 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547111160.913 * [misc]taylor: Taking taylor expansion of PI in n 1547111160.913 * [misc]backup-simplify: Simplify PI into PI 1547111160.913 * [misc]taylor: Taking taylor expansion of n in n 1547111160.913 * [misc]backup-simplify: Simplify 0 into 0 1547111160.913 * [misc]backup-simplify: Simplify 1 into 1 1547111160.913 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547111160.913 * [misc]backup-simplify: Simplify (* -1 PI) into (* -1 PI) 1547111160.913 * [misc]backup-simplify: Simplify (* -1 PI) into (* -1 PI) 1547111160.914 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1547111160.914 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 PI)) into 0 1547111160.914 * [misc]backup-simplify: Simplify 0 into 0 1547111160.915 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111160.916 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 PI))) into 0 1547111160.916 * [misc]backup-simplify: Simplify 0 into 0 1547111160.917 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111160.917 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1547111160.917 * [misc]backup-simplify: Simplify 0 into 0 1547111160.918 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111160.920 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1547111160.920 * [misc]backup-simplify: Simplify 0 into 0 1547111160.921 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111160.923 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1547111160.923 * [misc]backup-simplify: Simplify 0 into 0 1547111160.924 * [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 1547111160.926 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1547111160.926 * [misc]backup-simplify: Simplify 0 into 0 1547111160.926 * [misc]backup-simplify: Simplify (* (* -1 PI) (/ 1 (/ 1 (- n)))) into (* n PI) 1547111160.926 * * * * [misc]progress: [ 3 / 3 ] generating series at (2) 1547111160.926 * [misc]backup-simplify: Simplify (/ (pow (* (* n PI) 2) (- 1/2 (/ k 2))) (sqrt k)) into (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) 1547111160.926 * [misc]approximate: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (n k) around 0 1547111160.926 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 1547111160.926 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1547111160.926 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547111160.926 * [misc]taylor: Taking taylor expansion of k in k 1547111160.926 * [misc]backup-simplify: Simplify 0 into 0 1547111160.926 * [misc]backup-simplify: Simplify 1 into 1 1547111160.927 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547111160.927 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547111160.927 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1547111160.927 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1547111160.927 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1547111160.927 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1547111160.927 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1547111160.927 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111160.927 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111160.927 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1547111160.927 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111160.927 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111160.927 * [misc]taylor: Taking taylor expansion of k in k 1547111160.927 * [misc]backup-simplify: Simplify 0 into 0 1547111160.927 * [misc]backup-simplify: Simplify 1 into 1 1547111160.927 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1547111160.927 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1547111160.927 * [misc]taylor: Taking taylor expansion of 2 in k 1547111160.927 * [misc]backup-simplify: Simplify 2 into 2 1547111160.927 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1547111160.927 * [misc]taylor: Taking taylor expansion of n in k 1547111160.928 * [misc]backup-simplify: Simplify n into n 1547111160.928 * [misc]taylor: Taking taylor expansion of PI in k 1547111160.928 * [misc]backup-simplify: Simplify PI into PI 1547111160.928 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1547111160.928 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1547111160.928 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1547111160.928 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1547111160.928 * [misc]backup-simplify: Simplify (- 0) into 0 1547111160.928 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1547111160.929 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1547111160.929 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1547111160.929 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 1547111160.929 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1547111160.929 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547111160.929 * [misc]taylor: Taking taylor expansion of k in n 1547111160.929 * [misc]backup-simplify: Simplify k into k 1547111160.929 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547111160.929 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1547111160.929 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1547111160.929 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1547111160.929 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1547111160.929 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1547111160.929 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1547111160.929 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1547111160.929 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111160.929 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111160.929 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1547111160.929 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111160.929 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111160.929 * [misc]taylor: Taking taylor expansion of k in n 1547111160.930 * [misc]backup-simplify: Simplify k into k 1547111160.930 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1547111160.930 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1547111160.930 * [misc]taylor: Taking taylor expansion of 2 in n 1547111160.930 * [misc]backup-simplify: Simplify 2 into 2 1547111160.930 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547111160.930 * [misc]taylor: Taking taylor expansion of n in n 1547111160.930 * [misc]backup-simplify: Simplify 0 into 0 1547111160.930 * [misc]backup-simplify: Simplify 1 into 1 1547111160.930 * [misc]taylor: Taking taylor expansion of PI in n 1547111160.930 * [misc]backup-simplify: Simplify PI into PI 1547111160.930 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547111160.930 * [misc]backup-simplify: Simplify (* 2 0) into 0 1547111160.931 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547111160.931 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1547111160.932 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547111160.932 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1547111160.932 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1547111160.932 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1547111160.933 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547111160.933 * [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)))) 1547111160.934 * [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))))) 1547111160.934 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 1547111160.934 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1547111160.934 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547111160.934 * [misc]taylor: Taking taylor expansion of k in n 1547111160.934 * [misc]backup-simplify: Simplify k into k 1547111160.934 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547111160.934 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1547111160.935 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1547111160.935 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1547111160.935 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1547111160.935 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1547111160.935 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1547111160.935 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1547111160.935 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111160.935 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111160.935 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1547111160.935 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111160.935 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111160.935 * [misc]taylor: Taking taylor expansion of k in n 1547111160.935 * [misc]backup-simplify: Simplify k into k 1547111160.935 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1547111160.935 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1547111160.935 * [misc]taylor: Taking taylor expansion of 2 in n 1547111160.935 * [misc]backup-simplify: Simplify 2 into 2 1547111160.935 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547111160.935 * [misc]taylor: Taking taylor expansion of n in n 1547111160.935 * [misc]backup-simplify: Simplify 0 into 0 1547111160.935 * [misc]backup-simplify: Simplify 1 into 1 1547111160.935 * [misc]taylor: Taking taylor expansion of PI in n 1547111160.935 * [misc]backup-simplify: Simplify PI into PI 1547111160.936 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547111160.936 * [misc]backup-simplify: Simplify (* 2 0) into 0 1547111160.936 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547111160.937 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1547111160.938 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547111160.938 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1547111160.938 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1547111160.938 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1547111160.938 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547111160.939 * [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)))) 1547111160.940 * [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))))) 1547111160.940 * [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))) 1547111160.940 * [misc]taylor: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k))) in k 1547111160.940 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1547111160.940 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1547111160.941 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1547111160.941 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111160.941 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111160.941 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1547111160.941 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111160.941 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111160.941 * [misc]taylor: Taking taylor expansion of k in k 1547111160.941 * [misc]backup-simplify: Simplify 0 into 0 1547111160.941 * [misc]backup-simplify: Simplify 1 into 1 1547111160.941 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1547111160.941 * [misc]taylor: Taking taylor expansion of (log n) in k 1547111160.941 * [misc]taylor: Taking taylor expansion of n in k 1547111160.941 * [misc]backup-simplify: Simplify n into n 1547111160.941 * [misc]backup-simplify: Simplify (log n) into (log n) 1547111160.941 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1547111160.941 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1547111160.941 * [misc]taylor: Taking taylor expansion of 2 in k 1547111160.941 * [misc]backup-simplify: Simplify 2 into 2 1547111160.941 * [misc]taylor: Taking taylor expansion of PI in k 1547111160.941 * [misc]backup-simplify: Simplify PI into PI 1547111160.941 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547111160.942 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547111160.942 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1547111160.942 * [misc]backup-simplify: Simplify (- 0) into 0 1547111160.942 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1547111160.943 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547111160.943 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1547111160.944 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1547111160.944 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1547111160.944 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547111160.944 * [misc]taylor: Taking taylor expansion of k in k 1547111160.944 * [misc]backup-simplify: Simplify 0 into 0 1547111160.944 * [misc]backup-simplify: Simplify 1 into 1 1547111160.944 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547111160.944 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547111160.945 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1547111160.945 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) into 0 1547111160.945 * [misc]backup-simplify: Simplify 0 into 0 1547111160.946 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1547111160.947 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1547111160.950 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1547111160.950 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1547111160.950 * [misc]backup-simplify: Simplify (- 0) into 0 1547111160.951 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111160.951 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547111160.952 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1547111160.954 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1547111160.954 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 k)) 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))) into 0 1547111160.954 * [misc]taylor: Taking taylor expansion of 0 in k 1547111160.954 * [misc]backup-simplify: Simplify 0 into 0 1547111160.955 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1547111160.956 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1547111160.958 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1547111160.959 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111160.959 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1547111160.959 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1547111160.959 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1547111160.960 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1547111160.961 * [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))))))) 1547111160.963 * [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))))))) 1547111160.964 * [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))))))) 1547111160.965 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1547111160.967 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1547111160.972 * [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 1547111160.972 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1547111160.972 * [misc]backup-simplify: Simplify (- 0) into 0 1547111160.973 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111160.973 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547111160.974 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1547111160.976 * [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 1547111160.977 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1547111160.977 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 1547111160.978 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))))) into 0 1547111160.978 * [misc]taylor: Taking taylor expansion of 0 in k 1547111160.978 * [misc]backup-simplify: Simplify 0 into 0 1547111160.978 * [misc]backup-simplify: Simplify 0 into 0 1547111160.979 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1547111160.980 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1547111160.980 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1547111160.981 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1547111160.984 * [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 1547111160.984 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111160.984 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1547111160.984 * [misc]backup-simplify: Simplify (- 0) into 0 1547111160.984 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111160.985 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1547111160.986 * [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))))) 1547111160.989 * [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)))))))) 1547111160.991 * [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)))))))) 1547111160.992 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1547111160.994 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1547111160.998 * [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 1547111160.999 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 1547111160.999 * [misc]backup-simplify: Simplify (- 0) into 0 1547111160.999 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111160.999 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547111161.000 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 1547111161.002 * [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 1547111161.002 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1547111161.002 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 1547111161.003 * [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 1547111161.003 * [misc]taylor: Taking taylor expansion of 0 in k 1547111161.003 * [misc]backup-simplify: Simplify 0 into 0 1547111161.003 * [misc]backup-simplify: Simplify 0 into 0 1547111161.003 * [misc]backup-simplify: Simplify 0 into 0 1547111161.003 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111161.004 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1547111161.006 * [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 1547111161.007 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1547111161.014 * [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 1547111161.014 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111161.014 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1547111161.014 * [misc]backup-simplify: Simplify (- 0) into 0 1547111161.015 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111161.015 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 1547111161.019 * [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))))))) 1547111161.028 * [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)))))))))))))) 1547111161.034 * [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)))))))))))))) 1547111161.045 * [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)))))))))))))))))))))) 1547111161.045 * [misc]backup-simplify: Simplify (/ (pow (* (* (/ 1 n) PI) 2) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) into (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 1547111161.046 * [misc]approximate: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0 1547111161.046 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 1547111161.046 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1547111161.046 * [misc]taylor: Taking taylor expansion of k in k 1547111161.046 * [misc]backup-simplify: Simplify 0 into 0 1547111161.046 * [misc]backup-simplify: Simplify 1 into 1 1547111161.046 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547111161.046 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1547111161.046 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1547111161.047 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1547111161.047 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1547111161.047 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1547111161.047 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111161.047 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111161.047 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1547111161.047 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111161.047 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111161.047 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547111161.047 * [misc]taylor: Taking taylor expansion of k in k 1547111161.047 * [misc]backup-simplify: Simplify 0 into 0 1547111161.047 * [misc]backup-simplify: Simplify 1 into 1 1547111161.047 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547111161.047 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1547111161.047 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1547111161.047 * [misc]taylor: Taking taylor expansion of 2 in k 1547111161.047 * [misc]backup-simplify: Simplify 2 into 2 1547111161.047 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1547111161.047 * [misc]taylor: Taking taylor expansion of PI in k 1547111161.047 * [misc]backup-simplify: Simplify PI into PI 1547111161.047 * [misc]taylor: Taking taylor expansion of n in k 1547111161.047 * [misc]backup-simplify: Simplify n into n 1547111161.047 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1547111161.047 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1547111161.048 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1547111161.048 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1547111161.048 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1547111161.048 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1547111161.048 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1547111161.048 * [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)))) 1547111161.048 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1547111161.048 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1547111161.048 * [misc]taylor: Taking taylor expansion of k in n 1547111161.048 * [misc]backup-simplify: Simplify k into k 1547111161.049 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1547111161.049 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1547111161.049 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1547111161.049 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1547111161.049 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1547111161.049 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1547111161.049 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111161.049 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111161.049 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1547111161.049 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111161.049 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111161.049 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547111161.049 * [misc]taylor: Taking taylor expansion of k in n 1547111161.049 * [misc]backup-simplify: Simplify k into k 1547111161.049 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547111161.049 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1547111161.049 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1547111161.049 * [misc]taylor: Taking taylor expansion of 2 in n 1547111161.049 * [misc]backup-simplify: Simplify 2 into 2 1547111161.049 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547111161.049 * [misc]taylor: Taking taylor expansion of PI in n 1547111161.049 * [misc]backup-simplify: Simplify PI into PI 1547111161.049 * [misc]taylor: Taking taylor expansion of n in n 1547111161.049 * [misc]backup-simplify: Simplify 0 into 0 1547111161.049 * [misc]backup-simplify: Simplify 1 into 1 1547111161.049 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547111161.050 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547111161.050 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547111161.050 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1547111161.050 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1547111161.050 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1547111161.051 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547111161.052 * [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))) 1547111161.052 * [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)))) 1547111161.052 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1547111161.052 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1547111161.052 * [misc]taylor: Taking taylor expansion of k in n 1547111161.052 * [misc]backup-simplify: Simplify k into k 1547111161.053 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1547111161.053 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1547111161.053 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1547111161.053 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1547111161.053 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1547111161.053 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1547111161.053 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111161.053 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111161.053 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1547111161.053 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111161.053 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111161.053 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547111161.053 * [misc]taylor: Taking taylor expansion of k in n 1547111161.053 * [misc]backup-simplify: Simplify k into k 1547111161.053 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547111161.053 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1547111161.053 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1547111161.053 * [misc]taylor: Taking taylor expansion of 2 in n 1547111161.053 * [misc]backup-simplify: Simplify 2 into 2 1547111161.053 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547111161.053 * [misc]taylor: Taking taylor expansion of PI in n 1547111161.053 * [misc]backup-simplify: Simplify PI into PI 1547111161.053 * [misc]taylor: Taking taylor expansion of n in n 1547111161.053 * [misc]backup-simplify: Simplify 0 into 0 1547111161.053 * [misc]backup-simplify: Simplify 1 into 1 1547111161.054 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547111161.054 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547111161.054 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547111161.054 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1547111161.054 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1547111161.055 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1547111161.055 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547111161.056 * [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))) 1547111161.056 * [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)))) 1547111161.057 * [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)) 1547111161.057 * [misc]taylor: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) in k 1547111161.057 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1547111161.057 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1547111161.057 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1547111161.057 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111161.057 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111161.057 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1547111161.057 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111161.057 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111161.057 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547111161.057 * [misc]taylor: Taking taylor expansion of k in k 1547111161.057 * [misc]backup-simplify: Simplify 0 into 0 1547111161.057 * [misc]backup-simplify: Simplify 1 into 1 1547111161.058 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547111161.058 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1547111161.058 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1547111161.058 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1547111161.058 * [misc]taylor: Taking taylor expansion of 2 in k 1547111161.058 * [misc]backup-simplify: Simplify 2 into 2 1547111161.058 * [misc]taylor: Taking taylor expansion of PI in k 1547111161.058 * [misc]backup-simplify: Simplify PI into PI 1547111161.058 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547111161.058 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547111161.058 * [misc]taylor: Taking taylor expansion of (log n) in k 1547111161.059 * [misc]taylor: Taking taylor expansion of n in k 1547111161.059 * [misc]backup-simplify: Simplify n into n 1547111161.059 * [misc]backup-simplify: Simplify (log n) into (log n) 1547111161.059 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1547111161.059 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1547111161.059 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1547111161.059 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1547111161.060 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1547111161.060 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1547111161.061 * [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)))) 1547111161.061 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1547111161.061 * [misc]taylor: Taking taylor expansion of k in k 1547111161.061 * [misc]backup-simplify: Simplify 0 into 0 1547111161.061 * [misc]backup-simplify: Simplify 1 into 1 1547111161.061 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547111161.061 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1547111161.062 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) into 0 1547111161.062 * [misc]backup-simplify: Simplify 0 into 0 1547111161.063 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1547111161.064 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1547111161.066 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1547111161.066 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1547111161.066 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1547111161.067 * [misc]backup-simplify: Simplify (- 0) into 0 1547111161.067 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111161.067 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547111161.068 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1547111161.069 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1547111161.070 * [misc]backup-simplify: Simplify (+ (* (sqrt k) 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0 1547111161.070 * [misc]taylor: Taking taylor expansion of 0 in k 1547111161.070 * [misc]backup-simplify: Simplify 0 into 0 1547111161.070 * [misc]backup-simplify: Simplify 0 into 0 1547111161.071 * [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)))))) 1547111161.072 * [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)))))) 1547111161.073 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111161.074 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1547111161.079 * [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 1547111161.079 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1547111161.080 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1547111161.080 * [misc]backup-simplify: Simplify (- 0) into 0 1547111161.080 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111161.081 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547111161.081 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1547111161.084 * [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 1547111161.084 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 1547111161.085 * [misc]backup-simplify: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0 1547111161.085 * [misc]taylor: Taking taylor expansion of 0 in k 1547111161.085 * [misc]backup-simplify: Simplify 0 into 0 1547111161.085 * [misc]backup-simplify: Simplify 0 into 0 1547111161.085 * [misc]backup-simplify: Simplify 0 into 0 1547111161.086 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1547111161.087 * [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)))))) 1547111161.088 * [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)))))) 1547111161.090 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111161.091 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1547111161.097 * [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 1547111161.097 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1547111161.098 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1547111161.098 * [misc]backup-simplify: Simplify (- 0) into 0 1547111161.098 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111161.098 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547111161.099 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1547111161.101 * [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 1547111161.101 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 1547111161.102 * [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 1547111161.102 * [misc]taylor: Taking taylor expansion of 0 in k 1547111161.102 * [misc]backup-simplify: Simplify 0 into 0 1547111161.102 * [misc]backup-simplify: Simplify 0 into 0 1547111161.102 * [misc]backup-simplify: Simplify 0 into 0 1547111161.102 * [misc]backup-simplify: Simplify 0 into 0 1547111161.103 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1547111161.103 * [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)))))) 1547111161.104 * [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)))))) 1547111161.105 * [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)))))))) 1547111161.106 * [misc]backup-simplify: Simplify (/ (pow (* (* (/ 1 (- n)) PI) 2) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) into (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) 1547111161.106 * [misc]approximate: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (n k) around 0 1547111161.106 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 1547111161.106 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1547111161.106 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1547111161.106 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1547111161.106 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1547111161.106 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1547111161.106 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111161.106 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111161.106 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547111161.106 * [misc]taylor: Taking taylor expansion of k in k 1547111161.106 * [misc]backup-simplify: Simplify 0 into 0 1547111161.106 * [misc]backup-simplify: Simplify 1 into 1 1547111161.106 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547111161.106 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111161.106 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111161.106 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1547111161.106 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1547111161.106 * [misc]taylor: Taking taylor expansion of -2 in k 1547111161.106 * [misc]backup-simplify: Simplify -2 into -2 1547111161.106 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1547111161.106 * [misc]taylor: Taking taylor expansion of PI in k 1547111161.106 * [misc]backup-simplify: Simplify PI into PI 1547111161.106 * [misc]taylor: Taking taylor expansion of n in k 1547111161.106 * [misc]backup-simplify: Simplify n into n 1547111161.106 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1547111161.106 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1547111161.106 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1547111161.106 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1547111161.106 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1547111161.106 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1547111161.107 * [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))) 1547111161.107 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1547111161.107 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1547111161.107 * [misc]taylor: Taking taylor expansion of -1 in k 1547111161.107 * [misc]backup-simplify: Simplify -1 into -1 1547111161.107 * [misc]taylor: Taking taylor expansion of k in k 1547111161.107 * [misc]backup-simplify: Simplify 0 into 0 1547111161.107 * [misc]backup-simplify: Simplify 1 into 1 1547111161.107 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1547111161.107 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547111161.107 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1547111161.107 * [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)))) 1547111161.107 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 1547111161.108 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1547111161.108 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1547111161.108 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1547111161.108 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1547111161.108 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1547111161.108 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111161.108 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111161.108 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547111161.108 * [misc]taylor: Taking taylor expansion of k in n 1547111161.108 * [misc]backup-simplify: Simplify k into k 1547111161.108 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547111161.108 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111161.108 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111161.108 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1547111161.108 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1547111161.108 * [misc]taylor: Taking taylor expansion of -2 in n 1547111161.108 * [misc]backup-simplify: Simplify -2 into -2 1547111161.108 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547111161.108 * [misc]taylor: Taking taylor expansion of PI in n 1547111161.108 * [misc]backup-simplify: Simplify PI into PI 1547111161.108 * [misc]taylor: Taking taylor expansion of n in n 1547111161.108 * [misc]backup-simplify: Simplify 0 into 0 1547111161.108 * [misc]backup-simplify: Simplify 1 into 1 1547111161.108 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547111161.108 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547111161.108 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1547111161.109 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1547111161.109 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1547111161.109 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547111161.109 * [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))) 1547111161.110 * [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)))) 1547111161.110 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1547111161.110 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1547111161.110 * [misc]taylor: Taking taylor expansion of -1 in n 1547111161.110 * [misc]backup-simplify: Simplify -1 into -1 1547111161.110 * [misc]taylor: Taking taylor expansion of k in n 1547111161.110 * [misc]backup-simplify: Simplify k into k 1547111161.110 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1547111161.110 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1547111161.110 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1547111161.110 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1547111161.111 * [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))) 1547111161.111 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 1547111161.111 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1547111161.111 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1547111161.111 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1547111161.111 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1547111161.111 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1547111161.111 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111161.111 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111161.111 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547111161.111 * [misc]taylor: Taking taylor expansion of k in n 1547111161.111 * [misc]backup-simplify: Simplify k into k 1547111161.111 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547111161.111 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547111161.111 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111161.111 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1547111161.111 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1547111161.111 * [misc]taylor: Taking taylor expansion of -2 in n 1547111161.111 * [misc]backup-simplify: Simplify -2 into -2 1547111161.111 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547111161.111 * [misc]taylor: Taking taylor expansion of PI in n 1547111161.111 * [misc]backup-simplify: Simplify PI into PI 1547111161.111 * [misc]taylor: Taking taylor expansion of n in n 1547111161.111 * [misc]backup-simplify: Simplify 0 into 0 1547111161.111 * [misc]backup-simplify: Simplify 1 into 1 1547111161.111 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547111161.111 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547111161.112 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1547111161.112 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1547111161.112 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1547111161.112 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547111161.112 * [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))) 1547111161.113 * [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)))) 1547111161.113 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1547111161.113 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1547111161.113 * [misc]taylor: Taking taylor expansion of -1 in n 1547111161.113 * [misc]backup-simplify: Simplify -1 into -1 1547111161.113 * [misc]taylor: Taking taylor expansion of k in n 1547111161.113 * [misc]backup-simplify: Simplify k into k 1547111161.113 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1547111161.113 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1547111161.113 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1547111161.113 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1547111161.114 * [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))) 1547111161.114 * [misc]taylor: Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) in k 1547111161.114 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1547111161.114 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1547111161.114 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1547111161.114 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1547111161.114 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111161.114 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111161.114 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547111161.114 * [misc]taylor: Taking taylor expansion of k in k 1547111161.114 * [misc]backup-simplify: Simplify 0 into 0 1547111161.114 * [misc]backup-simplify: Simplify 1 into 1 1547111161.114 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547111161.114 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547111161.114 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547111161.114 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1547111161.114 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1547111161.114 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1547111161.114 * [misc]taylor: Taking taylor expansion of -2 in k 1547111161.114 * [misc]backup-simplify: Simplify -2 into -2 1547111161.114 * [misc]taylor: Taking taylor expansion of PI in k 1547111161.114 * [misc]backup-simplify: Simplify PI into PI 1547111161.114 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547111161.115 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1547111161.115 * [misc]taylor: Taking taylor expansion of (log n) in k 1547111161.115 * [misc]taylor: Taking taylor expansion of n in k 1547111161.115 * [misc]backup-simplify: Simplify n into n 1547111161.115 * [misc]backup-simplify: Simplify (log n) into (log n) 1547111161.115 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1547111161.115 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1547111161.115 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1547111161.115 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1547111161.116 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1547111161.117 * [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)))) 1547111161.117 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1547111161.117 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1547111161.117 * [misc]taylor: Taking taylor expansion of -1 in k 1547111161.117 * [misc]backup-simplify: Simplify -1 into -1 1547111161.117 * [misc]taylor: Taking taylor expansion of k in k 1547111161.117 * [misc]backup-simplify: Simplify 0 into 0 1547111161.117 * [misc]backup-simplify: Simplify 1 into 1 1547111161.117 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1547111161.117 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547111161.117 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1547111161.118 * [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))))) 1547111161.118 * [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))))) 1547111161.119 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1547111161.119 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1547111161.121 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1547111161.121 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1547111161.121 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1547111161.121 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111161.122 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547111161.122 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1547111161.123 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1547111161.124 * [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 1547111161.124 * [misc]taylor: Taking taylor expansion of 0 in k 1547111161.124 * [misc]backup-simplify: Simplify 0 into 0 1547111161.124 * [misc]backup-simplify: Simplify 0 into 0 1547111161.124 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1547111161.125 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1547111161.125 * [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)))))) 1547111161.126 * [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)))))) 1547111161.127 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111161.127 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1547111161.132 * [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 1547111161.132 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1547111161.133 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1547111161.133 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547111161.133 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547111161.134 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1547111161.136 * [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 1547111161.137 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1547111161.137 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 1547111161.138 * [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 1547111161.138 * [misc]taylor: Taking taylor expansion of 0 in k 1547111161.138 * [misc]backup-simplify: Simplify 0 into 0 1547111161.138 * [misc]backup-simplify: Simplify 0 into 0 1547111161.139 * [misc]backup-simplify: Simplify 0 into 0 1547111161.139 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547111161.140 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1547111161.142 * [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)))))) 1547111161.143 * [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)))))) 1547111161.145 * [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))))))))))) 1547111161.145 * * * [misc]progress: simplifying candidates 1547111161.145 * * * * [misc]progress: [ 1 / 76 ] simplifiying candidate # 1547111161.146 * [enter]simplify: Simplifying (* (log (* (* n PI) 2)) (- 1/2 (/ k 2))) 1547111161.146 * * [misc]simplify: iters left: 6 (11 enodes) 1547111161.150 * * [misc]simplify: iters left: 5 (21 enodes) 1547111161.156 * * [misc]simplify: iters left: 4 (47 enodes) 1547111161.164 * * [misc]simplify: iters left: 3 (107 enodes) 1547111161.188 * * [misc]simplify: iters left: 2 (308 enodes) 1547111161.394 * [exit]simplify: Simplified to (* (- 1/2 (/ k 2)) (log (* n (* 2 PI)))) 1547111161.394 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (exp (* (- 1/2 (/ k 2)) (log (* n (* 2 PI))))) (sqrt k))) 1547111161.395 * * * * [misc]progress: [ 2 / 76 ] simplifiying candidate # 1547111161.395 * * * * [misc]progress: [ 3 / 76 ] simplifiying candidate # 1547111161.395 * [enter]simplify: Simplifying (* (* n PI) 2) 1547111161.395 * * [misc]simplify: iters left: 4 (5 enodes) 1547111161.396 * * [misc]simplify: iters left: 3 (9 enodes) 1547111161.397 * * [misc]simplify: iters left: 2 (15 enodes) 1547111161.399 * * [misc]simplify: iters left: 1 (17 enodes) 1547111161.401 * [exit]simplify: Simplified to (* (* n PI) 2) 1547111161.401 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* n PI) 2) (* 1 (- 1/2 (/ k 2)))) (sqrt k))) 1547111161.401 * * * * [misc]progress: [ 4 / 76 ] simplifiying candidate # 1547111161.401 * [enter]simplify: Simplifying (pow (* (* n PI) 2) (/ k 2)) 1547111161.401 * * [misc]simplify: iters left: 5 (8 enodes) 1547111161.402 * * [misc]simplify: iters left: 4 (12 enodes) 1547111161.404 * * [misc]simplify: iters left: 3 (18 enodes) 1547111161.406 * * [misc]simplify: iters left: 2 (20 enodes) 1547111161.408 * [exit]simplify: Simplified to (pow (* n (* 2 PI)) (/ k 2)) 1547111161.408 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (/ (pow (* (* n PI) 2) 1/2) (pow (* n (* 2 PI)) (/ k 2))) (sqrt k))) 1547111161.409 * * * * [misc]progress: [ 5 / 76 ] simplifiying candidate # 1547111161.409 * [enter]simplify: Simplifying (cbrt (- 1/2 (/ k 2))) 1547111161.409 * * [misc]simplify: iters left: 5 (6 enodes) 1547111161.410 * * [misc]simplify: iters left: 4 (8 enodes) 1547111161.411 * * [misc]simplify: iters left: 3 (11 enodes) 1547111161.412 * [exit]simplify: Simplified to (cbrt (- 1/2 (/ k 2))) 1547111161.412 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (pow (pow (* (* n PI) 2) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))) (sqrt k))) 1547111161.412 * * * * [misc]progress: [ 6 / 76 ] simplifiying candidate # 1547111161.412 * [enter]simplify: Simplifying (sqrt (- 1/2 (/ k 2))) 1547111161.412 * * [misc]simplify: iters left: 5 (6 enodes) 1547111161.413 * * [misc]simplify: iters left: 4 (8 enodes) 1547111161.414 * * [misc]simplify: iters left: 3 (11 enodes) 1547111161.416 * [exit]simplify: Simplified to (sqrt (- 1/2 (/ k 2))) 1547111161.416 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (pow (pow (* (* n PI) 2) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))) (sqrt k))) 1547111161.416 * * * * [misc]progress: [ 7 / 76 ] simplifiying candidate # 1547111161.416 * [enter]simplify: Simplifying (- 1/2 (/ k 2)) 1547111161.416 * * [misc]simplify: iters left: 4 (5 enodes) 1547111161.418 * * [misc]simplify: iters left: 3 (7 enodes) 1547111161.420 * * [misc]simplify: iters left: 2 (10 enodes) 1547111161.423 * [exit]simplify: Simplified to (- 1/2 (/ k 2)) 1547111161.423 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (pow (pow (* (* n PI) 2) 1) (- 1/2 (/ k 2))) (sqrt k))) 1547111161.423 * * * * [misc]progress: [ 8 / 76 ] simplifiying candidate # 1547111161.423 * [enter]simplify: Simplifying (pow (* (* n PI) 2) (- (/ k 2))) 1547111161.423 * * [misc]simplify: iters left: 5 (9 enodes) 1547111161.427 * * [misc]simplify: iters left: 4 (15 enodes) 1547111161.431 * * [misc]simplify: iters left: 3 (21 enodes) 1547111161.436 * * [misc]simplify: iters left: 2 (22 enodes) 1547111161.442 * [exit]simplify: Simplified to (pow (* (* 2 PI) n) (- (/ k 2))) 1547111161.442 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (pow (* (* n PI) 2) 1/2) (pow (* (* 2 PI) n) (- (/ k 2)))) (sqrt k))) 1547111161.442 * * * * [misc]progress: [ 9 / 76 ] simplifiying candidate # 1547111161.442 * [enter]simplify: Simplifying (pow (* (* n PI) 2) (- (/ k 2))) 1547111161.442 * * [misc]simplify: iters left: 5 (9 enodes) 1547111161.445 * * [misc]simplify: iters left: 4 (15 enodes) 1547111161.450 * * [misc]simplify: iters left: 3 (21 enodes) 1547111161.453 * * [misc]simplify: iters left: 2 (22 enodes) 1547111161.458 * [exit]simplify: Simplified to (pow (* (* 2 PI) n) (- (/ k 2))) 1547111161.458 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (pow (* (* n PI) 2) 1/2) (pow (* (* 2 PI) n) (- (/ k 2)))) (sqrt k))) 1547111161.458 * * * * [misc]progress: [ 10 / 76 ] simplifiying candidate # 1547111161.458 * [enter]simplify: Simplifying (pow (* n PI) (- 1/2 (/ k 2))) 1547111161.458 * * [misc]simplify: iters left: 5 (9 enodes) 1547111161.460 * * [misc]simplify: iters left: 4 (12 enodes) 1547111161.461 * * [misc]simplify: iters left: 3 (15 enodes) 1547111161.463 * [exit]simplify: Simplified to (pow (* n PI) (- 1/2 (/ k 2))) 1547111161.463 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (* (pow (* n PI) (- 1/2 (/ k 2))) (pow 2 (- 1/2 (/ k 2)))) (sqrt k))) 1547111161.463 * * * * [misc]progress: [ 11 / 76 ] simplifiying candidate # 1547111161.463 * * * * [misc]progress: [ 12 / 76 ] simplifiying candidate # 1547111161.463 * * * * [misc]progress: [ 13 / 76 ] simplifiying candidate # 1547111161.463 * * * * [misc]progress: [ 14 / 76 ] simplifiying candidate # 1547111161.463 * * * * [misc]progress: [ 15 / 76 ] simplifiying candidate # 1547111161.463 * * * * [misc]progress: [ 16 / 76 ] simplifiying candidate # 1547111161.463 * * * * [misc]progress: [ 17 / 76 ] simplifiying candidate # 1547111161.463 * * * * [misc]progress: [ 18 / 76 ] simplifiying candidate # 1547111161.463 * * * * [misc]progress: [ 19 / 76 ] simplifiying candidate # 1547111161.464 * * * * [misc]progress: [ 20 / 76 ] simplifiying candidate # 1547111161.464 * * * * [misc]progress: [ 21 / 76 ] simplifiying candidate # 1547111161.464 * * * * [misc]progress: [ 22 / 76 ] simplifiying candidate # 1547111161.464 * * * * [misc]progress: [ 23 / 76 ] simplifiying candidate # 1547111161.464 * * * * [misc]progress: [ 24 / 76 ] simplifiying candidate # 1547111161.464 * * * * [misc]progress: [ 25 / 76 ] simplifiying candidate # 1547111161.464 * * * * [misc]progress: [ 26 / 76 ] simplifiying candidate # 1547111161.464 * * * * [misc]progress: [ 27 / 76 ] simplifiying candidate # 1547111161.464 * [enter]simplify: Simplifying (- (* (log (* (* n PI) 2)) (- 1/2 (/ k 2))) (log (sqrt k))) 1547111161.464 * * [misc]simplify: iters left: 6 (14 enodes) 1547111161.466 * * [misc]simplify: iters left: 5 (26 enodes) 1547111161.471 * * [misc]simplify: iters left: 4 (53 enodes) 1547111161.482 * * [misc]simplify: iters left: 3 (138 enodes) 1547111161.539 * * [misc]simplify: iters left: 2 (480 enodes) 1547111161.990 * [exit]simplify: Simplified to (- (* (- 1/2 (/ k 2)) (log (* n (* 2 PI)))) (log (sqrt k))) 1547111161.990 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (- 1/2 (/ k 2)) (log (* n (* 2 PI)))) (log (sqrt k))))) 1547111161.990 * * * * [misc]progress: [ 28 / 76 ] simplifiying candidate # 1547111161.991 * [enter]simplify: Simplifying (- (* (log (* (* n PI) 2)) (- 1/2 (/ k 2))) (log (sqrt k))) 1547111161.991 * * [misc]simplify: iters left: 6 (14 enodes) 1547111161.993 * * [misc]simplify: iters left: 5 (26 enodes) 1547111161.997 * * [misc]simplify: iters left: 4 (53 enodes) 1547111162.008 * * [misc]simplify: iters left: 3 (138 enodes) 1547111162.079 * * [misc]simplify: iters left: 2 (480 enodes) 1547111162.508 * [exit]simplify: Simplified to (- (* (- 1/2 (/ k 2)) (log (* n (* 2 PI)))) (log (sqrt k))) 1547111162.509 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (- 1/2 (/ k 2)) (log (* n (* 2 PI)))) (log (sqrt k))))) 1547111162.509 * * * * [misc]progress: [ 29 / 76 ] simplifiying candidate # 1547111162.509 * [enter]simplify: Simplifying (- (log (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (log (sqrt k))) 1547111162.509 * * [misc]simplify: iters left: 6 (14 enodes) 1547111162.511 * * [misc]simplify: iters left: 5 (24 enodes) 1547111162.515 * * [misc]simplify: iters left: 4 (42 enodes) 1547111162.521 * * [misc]simplify: iters left: 3 (71 enodes) 1547111162.552 * * [misc]simplify: iters left: 2 (208 enodes) 1547111162.724 * [exit]simplify: Simplified to (- (* (log (* (* n PI) 2)) (- 1/2 (/ k 2))) (log (sqrt k))) 1547111162.724 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (log (* (* n PI) 2)) (- 1/2 (/ k 2))) (log (sqrt k))))) 1547111162.724 * * * * [misc]progress: [ 30 / 76 ] simplifiying candidate # 1547111162.724 * * * * [misc]progress: [ 31 / 76 ] simplifiying candidate # 1547111162.724 * * * * [misc]progress: [ 32 / 76 ] simplifiying candidate # 1547111162.725 * [enter]simplify: Simplifying (/ (* (* (pow (* (* n PI) 2) (- 1/2 (/ k 2))) (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k))) 1547111162.725 * * [misc]simplify: iters left: 6 (16 enodes) 1547111162.731 * * [misc]simplify: iters left: 5 (31 enodes) 1547111162.740 * * [misc]simplify: iters left: 4 (67 enodes) 1547111162.756 * * [misc]simplify: iters left: 3 (124 enodes) 1547111162.777 * * [misc]simplify: iters left: 2 (195 enodes) 1547111162.854 * * [misc]simplify: iters left: 1 (309 enodes) 1547111162.977 * [exit]simplify: Simplified to (* (* (pow (* (* n PI) 2) (- 1/2 (/ k 2))) (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (/ (pow (* (* n PI) 2) (- 1/2 (/ k 2))) (* k (sqrt k)))) 1547111162.977 * [misc]simplify: Simplified (2 1) to (λ (k n) (cbrt (* (* (pow (* (* n PI) 2) (- 1/2 (/ k 2))) (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (/ (pow (* (* n PI) 2) (- 1/2 (/ k 2))) (* k (sqrt k)))))) 1547111162.977 * * * * [misc]progress: [ 33 / 76 ] simplifiying candidate # 1547111162.977 * * * * [misc]progress: [ 34 / 76 ] simplifiying candidate # 1547111162.977 * * * * [misc]progress: [ 35 / 76 ] simplifiying candidate # 1547111162.977 * * * * [misc]progress: [ 36 / 76 ] simplifiying candidate # 1547111162.977 * * * * [misc]progress: [ 37 / 76 ] simplifiying candidate # 1547111162.978 * [enter]simplify: Simplifying (/ (pow (* (* n PI) 2) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1547111162.978 * * [misc]simplify: iters left: 6 (12 enodes) 1547111162.979 * * [misc]simplify: iters left: 5 (19 enodes) 1547111162.982 * * [misc]simplify: iters left: 4 (25 enodes) 1547111162.985 * * [misc]simplify: iters left: 3 (26 enodes) 1547111162.988 * [exit]simplify: Simplified to (/ (sqrt (* (* n PI) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1547111162.988 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (* (* n PI) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* n PI) 2) (- (/ k 2))) (cbrt (sqrt k))))) 1547111162.989 * [enter]simplify: Simplifying (/ (pow (* (* n PI) 2) (- (/ k 2))) (cbrt (sqrt k))) 1547111162.989 * * [misc]simplify: iters left: 6 (12 enodes) 1547111162.990 * * [misc]simplify: iters left: 5 (18 enodes) 1547111162.993 * * [misc]simplify: iters left: 4 (24 enodes) 1547111162.996 * * [misc]simplify: iters left: 3 (25 enodes) 1547111162.999 * [exit]simplify: Simplified to (/ (pow (* n (* 2 PI)) (- (/ k 2))) (cbrt (sqrt k))) 1547111162.999 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (* (* n PI) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (cbrt (sqrt k))))) 1547111162.999 * * * * [misc]progress: [ 38 / 76 ] simplifiying candidate # 1547111162.999 * [enter]simplify: Simplifying (/ (pow (* (* n PI) 2) 1/2) (sqrt (sqrt k))) 1547111162.999 * * [misc]simplify: iters left: 6 (11 enodes) 1547111163.001 * * [misc]simplify: iters left: 5 (16 enodes) 1547111163.003 * * [misc]simplify: iters left: 4 (22 enodes) 1547111163.009 * * [misc]simplify: iters left: 3 (24 enodes) 1547111163.015 * [exit]simplify: Simplified to (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k))) 1547111163.015 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k))) (/ (pow (* (* n PI) 2) (- (/ k 2))) (sqrt (sqrt k))))) 1547111163.015 * [enter]simplify: Simplifying (/ (pow (* (* n PI) 2) (- (/ k 2))) (sqrt (sqrt k))) 1547111163.015 * * [misc]simplify: iters left: 6 (12 enodes) 1547111163.019 * * [misc]simplify: iters left: 5 (18 enodes) 1547111163.024 * * [misc]simplify: iters left: 4 (24 enodes) 1547111163.030 * * [misc]simplify: iters left: 3 (25 enodes) 1547111163.037 * [exit]simplify: Simplified to (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (sqrt k))) 1547111163.037 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (sqrt k))))) 1547111163.037 * * * * [misc]progress: [ 39 / 76 ] simplifiying candidate # 1547111163.037 * [enter]simplify: Simplifying (/ (pow (* (* n PI) 2) 1/2) 1) 1547111163.037 * * [misc]simplify: iters left: 6 (9 enodes) 1547111163.040 * * [misc]simplify: iters left: 5 (16 enodes) 1547111163.047 * * [misc]simplify: iters left: 4 (24 enodes) 1547111163.052 * * [misc]simplify: iters left: 3 (26 enodes) 1547111163.058 * [exit]simplify: Simplified to (sqrt (* (* 2 PI) n)) 1547111163.058 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (* (* 2 PI) n)) (/ (pow (* (* n PI) 2) (- (/ k 2))) (sqrt k)))) 1547111163.058 * [enter]simplify: Simplifying (/ (pow (* (* n PI) 2) (- (/ k 2))) (sqrt k)) 1547111163.059 * * [misc]simplify: iters left: 6 (11 enodes) 1547111163.063 * * [misc]simplify: iters left: 5 (17 enodes) 1547111163.065 * * [misc]simplify: iters left: 4 (23 enodes) 1547111163.068 * * [misc]simplify: iters left: 3 (24 enodes) 1547111163.071 * [exit]simplify: Simplified to (/ (pow (* (* n PI) 2) (- (/ k 2))) (sqrt k)) 1547111163.071 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (sqrt (* (* 2 PI) n)) (/ (pow (* (* n PI) 2) (- (/ k 2))) (sqrt k)))) 1547111163.071 * * * * [misc]progress: [ 40 / 76 ] simplifiying candidate # 1547111163.072 * [enter]simplify: Simplifying (/ (pow (* (* n PI) 2) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1547111163.072 * * [misc]simplify: iters left: 6 (12 enodes) 1547111163.073 * * [misc]simplify: iters left: 5 (19 enodes) 1547111163.076 * * [misc]simplify: iters left: 4 (25 enodes) 1547111163.079 * * [misc]simplify: iters left: 3 (26 enodes) 1547111163.082 * [exit]simplify: Simplified to (/ (sqrt (* (* n PI) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1547111163.082 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (* (* n PI) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* n PI) 2) (- (/ k 2))) (cbrt (sqrt k))))) 1547111163.083 * [enter]simplify: Simplifying (/ (pow (* (* n PI) 2) (- (/ k 2))) (cbrt (sqrt k))) 1547111163.083 * * [misc]simplify: iters left: 6 (12 enodes) 1547111163.084 * * [misc]simplify: iters left: 5 (18 enodes) 1547111163.087 * * [misc]simplify: iters left: 4 (24 enodes) 1547111163.090 * * [misc]simplify: iters left: 3 (25 enodes) 1547111163.093 * [exit]simplify: Simplified to (/ (pow (* n (* 2 PI)) (- (/ k 2))) (cbrt (sqrt k))) 1547111163.093 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (* (* n PI) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (cbrt (sqrt k))))) 1547111163.093 * * * * [misc]progress: [ 41 / 76 ] simplifiying candidate # 1547111163.093 * [enter]simplify: Simplifying (/ (pow (* (* n PI) 2) 1/2) (sqrt (sqrt k))) 1547111163.093 * * [misc]simplify: iters left: 6 (11 enodes) 1547111163.095 * * [misc]simplify: iters left: 5 (16 enodes) 1547111163.097 * * [misc]simplify: iters left: 4 (22 enodes) 1547111163.100 * * [misc]simplify: iters left: 3 (24 enodes) 1547111163.106 * [exit]simplify: Simplified to (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k))) 1547111163.106 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k))) (/ (pow (* (* n PI) 2) (- (/ k 2))) (sqrt (sqrt k))))) 1547111163.107 * [enter]simplify: Simplifying (/ (pow (* (* n PI) 2) (- (/ k 2))) (sqrt (sqrt k))) 1547111163.107 * * [misc]simplify: iters left: 6 (12 enodes) 1547111163.111 * * [misc]simplify: iters left: 5 (18 enodes) 1547111163.116 * * [misc]simplify: iters left: 4 (24 enodes) 1547111163.122 * * [misc]simplify: iters left: 3 (25 enodes) 1547111163.128 * [exit]simplify: Simplified to (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (sqrt k))) 1547111163.128 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (sqrt k))))) 1547111163.128 * * * * [misc]progress: [ 42 / 76 ] simplifiying candidate # 1547111163.129 * [enter]simplify: Simplifying (/ (pow (* (* n PI) 2) 1/2) 1) 1547111163.129 * * [misc]simplify: iters left: 6 (9 enodes) 1547111163.131 * * [misc]simplify: iters left: 5 (16 enodes) 1547111163.136 * * [misc]simplify: iters left: 4 (24 enodes) 1547111163.141 * * [misc]simplify: iters left: 3 (26 enodes) 1547111163.147 * [exit]simplify: Simplified to (sqrt (* (* 2 PI) n)) 1547111163.147 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (* (* 2 PI) n)) (/ (pow (* (* n PI) 2) (- (/ k 2))) (sqrt k)))) 1547111163.147 * [enter]simplify: Simplifying (/ (pow (* (* n PI) 2) (- (/ k 2))) (sqrt k)) 1547111163.147 * * [misc]simplify: iters left: 6 (11 enodes) 1547111163.151 * * [misc]simplify: iters left: 5 (17 enodes) 1547111163.155 * * [misc]simplify: iters left: 4 (23 enodes) 1547111163.163 * * [misc]simplify: iters left: 3 (24 enodes) 1547111163.169 * [exit]simplify: Simplified to (/ (pow (* (* n PI) 2) (- (/ k 2))) (sqrt k)) 1547111163.169 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (sqrt (* (* 2 PI) n)) (/ (pow (* (* n PI) 2) (- (/ k 2))) (sqrt k)))) 1547111163.169 * * * * [misc]progress: [ 43 / 76 ] simplifiying candidate # 1547111163.169 * [enter]simplify: Simplifying (/ (pow (* n PI) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1547111163.169 * * [misc]simplify: iters left: 6 (13 enodes) 1547111163.173 * * [misc]simplify: iters left: 5 (18 enodes) 1547111163.178 * * [misc]simplify: iters left: 4 (21 enodes) 1547111163.185 * [exit]simplify: Simplified to (/ (pow (* n PI) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1547111163.185 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (pow (* n PI) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow 2 (- 1/2 (/ k 2))) (cbrt (sqrt k))))) 1547111163.185 * [enter]simplify: Simplifying (/ (pow 2 (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1547111163.185 * * [misc]simplify: iters left: 6 (9 enodes) 1547111163.187 * * [misc]simplify: iters left: 5 (11 enodes) 1547111163.191 * * [misc]simplify: iters left: 4 (14 enodes) 1547111163.193 * [exit]simplify: Simplified to (/ (pow 2 (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1547111163.193 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (pow (* n PI) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow 2 (- 1/2 (/ k 2))) (cbrt (sqrt k))))) 1547111163.193 * * * * [misc]progress: [ 44 / 76 ] simplifiying candidate # 1547111163.193 * [enter]simplify: Simplifying (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1547111163.193 * * [misc]simplify: iters left: 6 (12 enodes) 1547111163.195 * * [misc]simplify: iters left: 5 (15 enodes) 1547111163.197 * * [misc]simplify: iters left: 4 (18 enodes) 1547111163.199 * [exit]simplify: Simplified to (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1547111163.199 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow 2 (- 1/2 (/ k 2))) (sqrt (sqrt k))))) 1547111163.199 * [enter]simplify: Simplifying (/ (pow 2 (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1547111163.199 * * [misc]simplify: iters left: 6 (9 enodes) 1547111163.200 * * [misc]simplify: iters left: 5 (11 enodes) 1547111163.202 * * [misc]simplify: iters left: 4 (14 enodes) 1547111163.204 * [exit]simplify: Simplified to (/ (pow 2 (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1547111163.204 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow 2 (- 1/2 (/ k 2))) (sqrt (sqrt k))))) 1547111163.204 * * * * [misc]progress: [ 45 / 76 ] simplifiying candidate # 1547111163.204 * [enter]simplify: Simplifying (/ (pow (* n PI) (- 1/2 (/ k 2))) 1) 1547111163.204 * * [misc]simplify: iters left: 6 (11 enodes) 1547111163.206 * * [misc]simplify: iters left: 5 (16 enodes) 1547111163.208 * * [misc]simplify: iters left: 4 (21 enodes) 1547111163.211 * [exit]simplify: Simplified to (pow (* n PI) (- 1/2 (/ k 2))) 1547111163.211 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (pow (* n PI) (- 1/2 (/ k 2))) (/ (pow 2 (- 1/2 (/ k 2))) (sqrt k)))) 1547111163.211 * [enter]simplify: Simplifying (/ (pow 2 (- 1/2 (/ k 2))) (sqrt k)) 1547111163.211 * * [misc]simplify: iters left: 6 (8 enodes) 1547111163.212 * * [misc]simplify: iters left: 5 (10 enodes) 1547111163.214 * * [misc]simplify: iters left: 4 (13 enodes) 1547111163.215 * [exit]simplify: Simplified to (/ (pow 2 (- 1/2 (/ k 2))) (sqrt k)) 1547111163.215 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (pow (* n PI) (- 1/2 (/ k 2))) (/ (pow 2 (- 1/2 (/ k 2))) (sqrt k)))) 1547111163.215 * * * * [misc]progress: [ 46 / 76 ] simplifiying candidate # 1547111163.216 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1547111163.216 * * [misc]simplify: iters left: 6 (16 enodes) 1547111163.218 * * [misc]simplify: iters left: 5 (28 enodes) 1547111163.222 * * [misc]simplify: iters left: 4 (46 enodes) 1547111163.228 * * [misc]simplify: iters left: 3 (50 enodes) 1547111163.234 * * [misc]simplify: iters left: 2 (53 enodes) 1547111163.241 * [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)))) 1547111163.241 * [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 (* (* n PI) 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))) 1547111163.241 * [enter]simplify: Simplifying (/ (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1547111163.241 * * [misc]simplify: iters left: 6 (14 enodes) 1547111163.243 * * [misc]simplify: iters left: 5 (20 enodes) 1547111163.246 * * [misc]simplify: iters left: 4 (29 enodes) 1547111163.250 * * [misc]simplify: iters left: 3 (30 enodes) 1547111163.254 * [exit]simplify: Simplified to (/ (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1547111163.254 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (* (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))) 1547111163.254 * * * * [misc]progress: [ 47 / 76 ] simplifiying candidate # 1547111163.254 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) 1547111163.254 * * [misc]simplify: iters left: 6 (15 enodes) 1547111163.257 * * [misc]simplify: iters left: 5 (23 enodes) 1547111163.260 * * [misc]simplify: iters left: 4 (34 enodes) 1547111163.264 * * [misc]simplify: iters left: 3 (36 enodes) 1547111163.270 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (/ (sqrt (sqrt k)) (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))))) 1547111163.271 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (/ (sqrt (sqrt k)) (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))))) (/ (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) 1547111163.271 * [enter]simplify: Simplifying (/ (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1547111163.271 * * [misc]simplify: iters left: 6 (14 enodes) 1547111163.275 * * [misc]simplify: iters left: 5 (20 enodes) 1547111163.281 * * [misc]simplify: iters left: 4 (29 enodes) 1547111163.288 * * [misc]simplify: iters left: 3 (30 enodes) 1547111163.296 * [exit]simplify: Simplified to (/ (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1547111163.296 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (* (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) (/ (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) 1547111163.296 * * * * [misc]progress: [ 48 / 76 ] simplifiying candidate # 1547111163.296 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2))))) 1) 1547111163.297 * * [misc]simplify: iters left: 6 (14 enodes) 1547111163.301 * * [misc]simplify: iters left: 5 (24 enodes) 1547111163.309 * * [misc]simplify: iters left: 4 (39 enodes) 1547111163.319 * * [misc]simplify: iters left: 3 (54 enodes) 1547111163.333 * * [misc]simplify: iters left: 2 (80 enodes) 1547111163.354 * [exit]simplify: Simplified to (* (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2))))) 1547111163.354 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (* (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2))))) (/ (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (sqrt k)))) 1547111163.354 * [enter]simplify: Simplifying (/ (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (sqrt k)) 1547111163.354 * * [misc]simplify: iters left: 6 (13 enodes) 1547111163.358 * * [misc]simplify: iters left: 5 (19 enodes) 1547111163.363 * * [misc]simplify: iters left: 4 (28 enodes) 1547111163.371 * * [misc]simplify: iters left: 3 (29 enodes) 1547111163.378 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (sqrt k)) 1547111163.378 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2))))) (/ (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (sqrt k)))) 1547111163.378 * * * * [misc]progress: [ 49 / 76 ] simplifiying candidate # 1547111163.378 * [enter]simplify: Simplifying (/ (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1547111163.378 * * [misc]simplify: iters left: 6 (15 enodes) 1547111163.382 * * [misc]simplify: iters left: 5 (23 enodes) 1547111163.385 * * [misc]simplify: iters left: 4 (32 enodes) 1547111163.390 * * [misc]simplify: iters left: 3 (33 enodes) 1547111163.394 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1547111163.394 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))) 1547111163.394 * [enter]simplify: Simplifying (/ (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1547111163.394 * * [misc]simplify: iters left: 6 (14 enodes) 1547111163.396 * * [misc]simplify: iters left: 5 (20 enodes) 1547111163.399 * * [misc]simplify: iters left: 4 (29 enodes) 1547111163.403 * * [misc]simplify: iters left: 3 (30 enodes) 1547111163.406 * [exit]simplify: Simplified to (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1547111163.406 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))) 1547111163.406 * * * * [misc]progress: [ 50 / 76 ] simplifiying candidate # 1547111163.406 * [enter]simplify: Simplifying (/ (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1547111163.406 * * [misc]simplify: iters left: 6 (14 enodes) 1547111163.408 * * [misc]simplify: iters left: 5 (20 enodes) 1547111163.411 * * [misc]simplify: iters left: 4 (29 enodes) 1547111163.415 * * [misc]simplify: iters left: 3 (30 enodes) 1547111163.419 * [exit]simplify: Simplified to (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1547111163.419 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) 1547111163.419 * [enter]simplify: Simplifying (/ (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1547111163.419 * * [misc]simplify: iters left: 6 (14 enodes) 1547111163.423 * * [misc]simplify: iters left: 5 (20 enodes) 1547111163.428 * * [misc]simplify: iters left: 4 (29 enodes) 1547111163.436 * * [misc]simplify: iters left: 3 (30 enodes) 1547111163.443 * [exit]simplify: Simplified to (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1547111163.443 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) 1547111163.443 * * * * [misc]progress: [ 51 / 76 ] simplifiying candidate # 1547111163.444 * [enter]simplify: Simplifying (/ (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) 1) 1547111163.444 * * [misc]simplify: iters left: 6 (13 enodes) 1547111163.447 * * [misc]simplify: iters left: 5 (21 enodes) 1547111163.451 * * [misc]simplify: iters left: 4 (32 enodes) 1547111163.455 * * [misc]simplify: iters left: 3 (33 enodes) 1547111163.458 * [exit]simplify: Simplified to (sqrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) 1547111163.458 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (/ (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (sqrt k)))) 1547111163.459 * [enter]simplify: Simplifying (/ (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (sqrt k)) 1547111163.459 * * [misc]simplify: iters left: 6 (13 enodes) 1547111163.460 * * [misc]simplify: iters left: 5 (19 enodes) 1547111163.463 * * [misc]simplify: iters left: 4 (28 enodes) 1547111163.467 * * [misc]simplify: iters left: 3 (29 enodes) 1547111163.471 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (sqrt k)) 1547111163.471 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (sqrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (/ (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (sqrt k)))) 1547111163.471 * * * * [misc]progress: [ 52 / 76 ] simplifiying candidate # 1547111163.471 * [enter]simplify: Simplifying (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1547111163.471 * * [misc]simplify: iters left: 6 (6 enodes) 1547111163.472 * * [misc]simplify: iters left: 5 (10 enodes) 1547111163.473 * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) 1547111163.473 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (pow (* (* n PI) 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))))) 1547111163.474 * [enter]simplify: Simplifying (/ (pow (* (* n PI) 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1547111163.474 * * [misc]simplify: iters left: 6 (13 enodes) 1547111163.475 * * [misc]simplify: iters left: 5 (19 enodes) 1547111163.478 * * [misc]simplify: iters left: 4 (28 enodes) 1547111163.482 * * [misc]simplify: iters left: 3 (29 enodes) 1547111163.487 * [exit]simplify: Simplified to (/ (pow (* (* n PI) 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1547111163.487 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* n PI) 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))))) 1547111163.488 * * * * [misc]progress: [ 53 / 76 ] simplifiying candidate # 1547111163.488 * [enter]simplify: Simplifying (/ 1 (sqrt (sqrt k))) 1547111163.488 * * [misc]simplify: iters left: 4 (5 enodes) 1547111163.489 * * [misc]simplify: iters left: 3 (7 enodes) 1547111163.491 * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt k))) 1547111163.491 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* (* n PI) 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) 1547111163.491 * [enter]simplify: Simplifying (/ (pow (* (* n PI) 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1547111163.491 * * [misc]simplify: iters left: 6 (13 enodes) 1547111163.495 * * [misc]simplify: iters left: 5 (19 enodes) 1547111163.501 * * [misc]simplify: iters left: 4 (28 enodes) 1547111163.508 * * [misc]simplify: iters left: 3 (29 enodes) 1547111163.515 * [exit]simplify: Simplified to (/ (pow (* (* n PI) 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1547111163.515 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* (* n PI) 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) 1547111163.515 * * * * [misc]progress: [ 54 / 76 ] simplifiying candidate # 1547111163.515 * [enter]simplify: Simplifying (/ 1 1) 1547111163.515 * * [misc]simplify: iters left: 2 (2 enodes) 1547111163.516 * * [misc]simplify: iters left: 1 (4 enodes) 1547111163.517 * [exit]simplify: Simplified to 1 1547111163.517 * [misc]simplify: Simplified (2 1) to (λ (k n) (* 1 (/ (pow (* (* n PI) 2) (- 1/2 (/ k 2))) (sqrt k)))) 1547111163.517 * [enter]simplify: Simplifying (/ (pow (* (* n PI) 2) (- 1/2 (/ k 2))) (sqrt k)) 1547111163.517 * * [misc]simplify: iters left: 6 (12 enodes) 1547111163.520 * * [misc]simplify: iters left: 5 (18 enodes) 1547111163.526 * * [misc]simplify: iters left: 4 (27 enodes) 1547111163.532 * * [misc]simplify: iters left: 3 (28 enodes) 1547111163.539 * [exit]simplify: Simplified to (/ (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (sqrt k)) 1547111163.540 * [misc]simplify: Simplified (2 2) to (λ (k n) (* 1 (/ (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (sqrt k)))) 1547111163.540 * * * * [misc]progress: [ 55 / 76 ] simplifiying candidate # 1547111163.540 * * * * [misc]progress: [ 56 / 76 ] simplifiying candidate # 1547111163.540 * * * * [misc]progress: [ 57 / 76 ] simplifiying candidate # 1547111163.540 * * * * [misc]progress: [ 58 / 76 ] simplifiying candidate # 1547111163.540 * [enter]simplify: Simplifying (cbrt (sqrt k)) 1547111163.540 * * [misc]simplify: iters left: 2 (3 enodes) 1547111163.541 * [exit]simplify: Simplified to (cbrt (sqrt k)) 1547111163.541 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (pow (* (* n PI) 2) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k)))) 1547111163.541 * * * * [misc]progress: [ 59 / 76 ] simplifiying candidate # 1547111163.541 * [enter]simplify: Simplifying (sqrt (sqrt k)) 1547111163.541 * * [misc]simplify: iters left: 2 (3 enodes) 1547111163.542 * [exit]simplify: Simplified to (sqrt (sqrt k)) 1547111163.542 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (pow (* (* n PI) 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k)))) 1547111163.542 * * * * [misc]progress: [ 60 / 76 ] simplifiying candidate # 1547111163.542 * [enter]simplify: Simplifying (sqrt k) 1547111163.543 * * [misc]simplify: iters left: 1 (2 enodes) 1547111163.543 * [exit]simplify: Simplified to (sqrt k) 1547111163.543 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (pow (* (* n PI) 2) (- 1/2 (/ k 2))) 1) (sqrt k))) 1547111163.543 * * * * [misc]progress: [ 61 / 76 ] simplifiying candidate # 1547111163.543 * [enter]simplify: Simplifying (pow (* (* n PI) 2) 1/2) 1547111163.544 * * [misc]simplify: iters left: 5 (7 enodes) 1547111163.546 * * [misc]simplify: iters left: 4 (12 enodes) 1547111163.549 * * [misc]simplify: iters left: 3 (18 enodes) 1547111163.552 * * [misc]simplify: iters left: 2 (20 enodes) 1547111163.555 * [exit]simplify: Simplified to (sqrt (* n (* 2 PI))) 1547111163.555 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* n (* 2 PI))) (/ (sqrt k) (pow (* (* n PI) 2) (- (/ k 2)))))) 1547111163.555 * * * * [misc]progress: [ 62 / 76 ] simplifiying candidate # 1547111163.555 * [enter]simplify: Simplifying (pow (* (* n PI) 2) 1/2) 1547111163.555 * * [misc]simplify: iters left: 5 (7 enodes) 1547111163.556 * * [misc]simplify: iters left: 4 (12 enodes) 1547111163.558 * * [misc]simplify: iters left: 3 (18 enodes) 1547111163.560 * * [misc]simplify: iters left: 2 (20 enodes) 1547111163.562 * [exit]simplify: Simplified to (sqrt (* n (* 2 PI))) 1547111163.562 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* n (* 2 PI))) (/ (sqrt k) (pow (* (* n PI) 2) (- (/ k 2)))))) 1547111163.562 * * * * [misc]progress: [ 63 / 76 ] simplifiying candidate # 1547111163.562 * [enter]simplify: Simplifying (pow (* n PI) (- 1/2 (/ k 2))) 1547111163.562 * * [misc]simplify: iters left: 5 (9 enodes) 1547111163.564 * * [misc]simplify: iters left: 4 (12 enodes) 1547111163.565 * * [misc]simplify: iters left: 3 (15 enodes) 1547111163.567 * [exit]simplify: Simplified to (pow (* n PI) (- 1/2 (/ k 2))) 1547111163.567 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (pow (* n PI) (- 1/2 (/ k 2))) (/ (sqrt k) (pow 2 (- 1/2 (/ k 2)))))) 1547111163.567 * * * * [misc]progress: [ 64 / 76 ] simplifiying candidate # 1547111163.567 * [enter]simplify: Simplifying (* (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2))))) 1547111163.568 * * [misc]simplify: iters left: 6 (12 enodes) 1547111163.569 * * [misc]simplify: iters left: 5 (18 enodes) 1547111163.572 * * [misc]simplify: iters left: 4 (27 enodes) 1547111163.575 * * [misc]simplify: iters left: 3 (28 enodes) 1547111163.579 * [exit]simplify: Simplified to (* (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2))))) 1547111163.579 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (* (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2))))) (/ (sqrt k) (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2))))))) 1547111163.579 * * * * [misc]progress: [ 65 / 76 ] simplifiying candidate # 1547111163.580 * [enter]simplify: Simplifying (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) 1547111163.580 * * [misc]simplify: iters left: 6 (11 enodes) 1547111163.581 * * [misc]simplify: iters left: 5 (17 enodes) 1547111163.584 * * [misc]simplify: iters left: 4 (26 enodes) 1547111163.587 * * [misc]simplify: iters left: 3 (27 enodes) 1547111163.590 * [exit]simplify: Simplified to (sqrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) 1547111163.590 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2))))))) 1547111163.590 * * * * [misc]progress: [ 66 / 76 ] simplifiying candidate # 1547111163.590 * * * * [misc]progress: [ 67 / 76 ] simplifiying candidate # 1547111163.590 * [enter]simplify: Simplifying (pow (* (* n PI) 2) 1/2) 1547111163.591 * * [misc]simplify: iters left: 5 (7 enodes) 1547111163.592 * * [misc]simplify: iters left: 4 (12 enodes) 1547111163.593 * * [misc]simplify: iters left: 3 (18 enodes) 1547111163.596 * * [misc]simplify: iters left: 2 (20 enodes) 1547111163.600 * [exit]simplify: Simplified to (sqrt (* n (* 2 PI))) 1547111163.600 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* n (* 2 PI))) (* (sqrt k) (pow (* (* n PI) 2) (/ k 2))))) 1547111163.601 * * * * [misc]progress: [ 68 / 76 ] simplifiying candidate # 1547111163.601 * [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))))) 1547111163.601 * * [misc]simplify: iters left: 6 (37 enodes) 1547111163.616 * * [misc]simplify: iters left: 5 (105 enodes) 1547111163.656 * * [misc]simplify: iters left: 4 (339 enodes) 1547111163.858 * [exit]simplify: Simplified to (+ (+ (* (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) -1/2) (+ (* (* (* k (log n)) (* k (log n))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (pow (* PI 2) 1/2) (pow n 1/2)))) (* (* k k) (+ (* (* (log (* PI 2)) (log (* PI 2))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (* (* (log n) (pow n 1/2)) (pow (* PI 2) 1/2)) (* (log (* PI 2)) 1/4))))) 1547111163.858 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (+ (+ (* (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) -1/2) (+ (* (* (* k (log n)) (* k (log n))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (pow (* PI 2) 1/2) (pow n 1/2)))) (* (* k k) (+ (* (* (log (* PI 2)) (log (* PI 2))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (* (* (log n) (pow n 1/2)) (pow (* PI 2) 1/2)) (* (log (* PI 2)) 1/4))))) (sqrt k))) 1547111163.858 * * * * [misc]progress: [ 69 / 76 ] simplifiying candidate # 1547111163.858 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 1547111163.859 * * [misc]simplify: iters left: 6 (15 enodes) 1547111163.864 * * [misc]simplify: iters left: 5 (33 enodes) 1547111163.875 * * [misc]simplify: iters left: 4 (64 enodes) 1547111163.898 * * [misc]simplify: iters left: 3 (171 enodes) 1547111163.983 * [exit]simplify: Simplified to (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow n (- 1/2 (* 1/2 k)))) 1547111163.983 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow n (- 1/2 (* 1/2 k)))) (sqrt k))) 1547111163.983 * * * * [misc]progress: [ 70 / 76 ] simplifiying candidate # 1547111163.984 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 1547111163.984 * * [misc]simplify: iters left: 6 (15 enodes) 1547111163.987 * * [misc]simplify: iters left: 5 (30 enodes) 1547111163.993 * * [misc]simplify: iters left: 4 (65 enodes) 1547111164.021 * * [misc]simplify: iters left: 3 (200 enodes) 1547111164.107 * [exit]simplify: Simplified to (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))) 1547111164.107 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))) (sqrt k))) 1547111164.107 * * * * [misc]progress: [ 71 / 76 ] simplifiying candidate # 1547111164.107 * [enter]simplify: Simplifying (* n PI) 1547111164.107 * * [misc]simplify: iters left: 2 (3 enodes) 1547111164.108 * * [misc]simplify: iters left: 1 (4 enodes) 1547111164.108 * [exit]simplify: Simplified to (* n PI) 1547111164.108 * [misc]simplify: Simplified (2 1 1 1) to (λ (k n) (/ (pow (* (* n PI) 2) (- 1/2 (/ k 2))) (sqrt k))) 1547111164.109 * * * * [misc]progress: [ 72 / 76 ] simplifiying candidate # 1547111164.109 * [enter]simplify: Simplifying (* n PI) 1547111164.109 * * [misc]simplify: iters left: 2 (3 enodes) 1547111164.109 * * [misc]simplify: iters left: 1 (4 enodes) 1547111164.110 * [exit]simplify: Simplified to (* n PI) 1547111164.110 * [misc]simplify: Simplified (2 1 1 1) to (λ (k n) (/ (pow (* (* n PI) 2) (- 1/2 (/ k 2))) (sqrt k))) 1547111164.110 * * * * [misc]progress: [ 73 / 76 ] simplifiying candidate # 1547111164.110 * [enter]simplify: Simplifying (* n PI) 1547111164.110 * * [misc]simplify: iters left: 2 (3 enodes) 1547111164.110 * * [misc]simplify: iters left: 1 (4 enodes) 1547111164.111 * [exit]simplify: Simplified to (* n PI) 1547111164.111 * [misc]simplify: Simplified (2 1 1 1) to (λ (k n) (/ (pow (* (* n PI) 2) (- 1/2 (/ k 2))) (sqrt k))) 1547111164.111 * * * * [misc]progress: [ 74 / 76 ] simplifiying candidate # 1547111164.111 * [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)))))))))))))))))))))) 1547111164.111 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1547111164.111 * * * * [misc]progress: [ 75 / 76 ] simplifiying candidate # 1547111164.111 * [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)))))))) 1547111164.111 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1547111164.111 * * * * [misc]progress: [ 76 / 76 ] simplifiying candidate # 1547111164.112 * [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))))))))))) 1547111164.112 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1547111164.112 * * * [misc]progress: adding candidates to table 1547111164.876 * [misc]progress: [Phase 3 of 3] Extracting. 1547111164.876 * * [misc]regime: Finding splitpoints for: (# # # # # #) 1547111164.877 * * * [misc]regime-changes: Trying 3 branch expressions: (n (* (* 2 PI) n) k) 1547111164.877 * * * * [misc]regimes: Trying to branch on n from (# # # # # #) 1547111164.938 * * * * [misc]regimes: Trying to branch on (* (* 2 PI) n) from (# # # # # #) 1547111165.014 * * * * [misc]regimes: Trying to branch on k from (# # # # # #) 1547111165.057 * * * [misc]regime: Found split indices: #