1540976131.016 * [misc]progress: [Phase 1 of 3] Setting up. 1540976131.016 * * * [misc]progress: [1/2] Preparing points 1540976131.016 * * * * [misc]points: Sampling 256 additional inputs, on iter 0 have 0 / 256 1540976131.141 * * * * [misc]points: Filtering points with unrepresentable outputs 1540976131.141 * * * * [misc]points: Sampling 205 additional inputs, on iter 1 have 51 / 256 1540976131.194 * * * * [misc]points: Filtering points with unrepresentable outputs 1540976131.194 * * * * [misc]points: Sampling 144 additional inputs, on iter 2 have 112 / 256 1540976131.265 * * * * [misc]points: Filtering points with unrepresentable outputs 1540976131.265 * * * * [misc]points: Sampling 104 additional inputs, on iter 3 have 152 / 256 1540976131.295 * * * * [misc]points: Filtering points with unrepresentable outputs 1540976131.296 * * * * [misc]points: Sampling 76 additional inputs, on iter 4 have 180 / 256 1540976131.317 * * * * [misc]points: Filtering points with unrepresentable outputs 1540976131.317 * * * * [misc]points: Sampling 56 additional inputs, on iter 5 have 200 / 256 1540976131.346 * * * * [misc]points: Filtering points with unrepresentable outputs 1540976131.346 * * * * [misc]points: Sampling 43 additional inputs, on iter 6 have 213 / 256 1540976131.427 * * * * [misc]points: Filtering points with unrepresentable outputs 1540976131.427 * * * * [misc]points: Sampling 27 additional inputs, on iter 7 have 229 / 256 1540976131.445 * * * * [misc]points: Filtering points with unrepresentable outputs 1540976131.445 * * * * [misc]points: Sampling 20 additional inputs, on iter 8 have 236 / 256 1540976131.459 * * * * [misc]points: Filtering points with unrepresentable outputs 1540976131.459 * * * * [misc]points: Sampling 16 additional inputs, on iter 9 have 240 / 256 1540976131.470 * * * * [misc]points: Filtering points with unrepresentable outputs 1540976131.470 * * * * [misc]points: Sampling 16 additional inputs, on iter 10 have 240 / 256 1540976131.482 * * * * [misc]points: Filtering points with unrepresentable outputs 1540976131.482 * * * * [misc]points: Sampling 13 additional inputs, on iter 11 have 243 / 256 1540976131.492 * * * * [misc]points: Filtering points with unrepresentable outputs 1540976131.492 * * * * [misc]points: Sampling 12 additional inputs, on iter 12 have 244 / 256 1540976131.503 * * * * [misc]points: Filtering points with unrepresentable outputs 1540976131.503 * * * * [misc]points: Sampling 6 additional inputs, on iter 13 have 250 / 256 1540976131.510 * * * * [misc]points: Filtering points with unrepresentable outputs 1540976131.510 * * * * [misc]points: Sampling 6 additional inputs, on iter 14 have 250 / 256 1540976131.518 * * * * [misc]points: Filtering points with unrepresentable outputs 1540976131.518 * * * * [misc]points: Sampling 5 additional inputs, on iter 15 have 251 / 256 1540976131.525 * * * * [misc]points: Filtering points with unrepresentable outputs 1540976131.525 * * * * [misc]points: Sampling 4 additional inputs, on iter 16 have 252 / 256 1540976131.531 * * * * [misc]points: Filtering points with unrepresentable outputs 1540976131.532 * * * * [misc]points: Sampling 4 additional inputs, on iter 17 have 254 / 256 1540976131.538 * * * * [misc]points: Filtering points with unrepresentable outputs 1540976131.538 * * * * [misc]points: Sampling 4 additional inputs, on iter 18 have 255 / 256 1540976131.544 * * * * [misc]points: Filtering points with unrepresentable outputs 1540976131.544 * * * * [misc]points: Sampling 4 additional inputs, on iter 19 have 255 / 256 1540976131.551 * * * * [misc]points: Filtering points with unrepresentable outputs 1540976131.551 * * * * [exit]points: Sampled 256 points with exact outputs 1540976131.551 * * * [misc]progress: [2/2] Setting up program. 1540976131.563 * [misc]progress: [Phase 2 of 3] Improving. 1540976131.563 * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) 1540976131.587 * * [misc]simplify: iters left: 6 (13 enodes) 1540976131.591 * * [misc]simplify: iters left: 5 (28 enodes) 1540976131.599 * * [misc]simplify: iters left: 4 (44 enodes) 1540976131.607 * * [misc]simplify: iters left: 3 (54 enodes) 1540976131.614 * * [misc]simplify: iters left: 2 (57 enodes) 1540976131.621 * * [misc]simplify: iters left: 1 (65 enodes) 1540976131.636 * [exit]simplify: Simplified to (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)) 1540976131.657 * * [misc]progress: iteration 1 / 4 1540976131.657 * * * [misc]progress: picking best candidate 1540976131.668 * * * * [misc]pick: Picked # 1540976131.668 * * * [misc]progress: localizing error 1540976131.699 * * * [misc]progress: generating rewritten candidates 1540976131.699 * * * * [misc]progress: [ 1 / 3 ] rewriting at (2 1) 1540976131.731 * * * * [misc]progress: [ 2 / 3 ] rewriting at (2 1 1) 1540976131.754 * * * * [misc]progress: [ 3 / 3 ] rewriting at (2) 1540976131.819 * * * [misc]progress: generating series expansions 1540976131.819 * * * * [misc]progress: [ 1 / 3 ] generating series at (2 1) 1540976131.819 * [misc]backup-simplify: Simplify (pow (* PI (* n 2)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 1540976131.819 * [misc]approximate: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 1540976131.819 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1540976131.819 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1540976131.819 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1540976131.819 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1540976131.819 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976131.819 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976131.819 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1540976131.819 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976131.819 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976131.819 * [misc]taylor: Taking taylor expansion of k in k 1540976131.819 * [misc]backup-simplify: Simplify 0 into 0 1540976131.819 * [misc]backup-simplify: Simplify 1 into 1 1540976131.819 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1540976131.819 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1540976131.819 * [misc]taylor: Taking taylor expansion of 2 in k 1540976131.819 * [misc]backup-simplify: Simplify 2 into 2 1540976131.819 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1540976131.819 * [misc]taylor: Taking taylor expansion of n in k 1540976131.819 * [misc]backup-simplify: Simplify n into n 1540976131.819 * [misc]taylor: Taking taylor expansion of PI in k 1540976131.819 * [misc]backup-simplify: Simplify PI into PI 1540976131.819 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1540976131.820 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1540976131.820 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1540976131.820 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1540976131.820 * [misc]backup-simplify: Simplify (- 0) into 0 1540976131.820 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1540976131.820 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1540976131.820 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1540976131.820 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1540976131.820 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1540976131.820 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1540976131.820 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1540976131.820 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976131.820 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976131.821 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1540976131.821 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976131.821 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976131.821 * [misc]taylor: Taking taylor expansion of k in n 1540976131.821 * [misc]backup-simplify: Simplify k into k 1540976131.821 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1540976131.821 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1540976131.821 * [misc]taylor: Taking taylor expansion of 2 in n 1540976131.821 * [misc]backup-simplify: Simplify 2 into 2 1540976131.821 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1540976131.821 * [misc]taylor: Taking taylor expansion of n in n 1540976131.821 * [misc]backup-simplify: Simplify 0 into 0 1540976131.821 * [misc]backup-simplify: Simplify 1 into 1 1540976131.821 * [misc]taylor: Taking taylor expansion of PI in n 1540976131.821 * [misc]backup-simplify: Simplify PI into PI 1540976131.821 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1540976131.821 * [misc]backup-simplify: Simplify (* 2 0) into 0 1540976131.822 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1540976131.822 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1540976131.822 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1540976131.822 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1540976131.822 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1540976131.823 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1540976131.823 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1540976131.823 * [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)))) 1540976131.824 * [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))))) 1540976131.824 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1540976131.824 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1540976131.824 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1540976131.824 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1540976131.824 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976131.824 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976131.824 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1540976131.824 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976131.824 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976131.824 * [misc]taylor: Taking taylor expansion of k in n 1540976131.824 * [misc]backup-simplify: Simplify k into k 1540976131.824 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1540976131.824 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1540976131.824 * [misc]taylor: Taking taylor expansion of 2 in n 1540976131.824 * [misc]backup-simplify: Simplify 2 into 2 1540976131.824 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1540976131.824 * [misc]taylor: Taking taylor expansion of n in n 1540976131.824 * [misc]backup-simplify: Simplify 0 into 0 1540976131.824 * [misc]backup-simplify: Simplify 1 into 1 1540976131.824 * [misc]taylor: Taking taylor expansion of PI in n 1540976131.824 * [misc]backup-simplify: Simplify PI into PI 1540976131.824 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1540976131.825 * [misc]backup-simplify: Simplify (* 2 0) into 0 1540976131.825 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1540976131.825 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1540976131.826 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1540976131.826 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1540976131.826 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1540976131.826 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1540976131.826 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1540976131.827 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 1540976131.827 * [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))))) 1540976131.827 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1540976131.827 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1540976131.828 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1540976131.828 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976131.828 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976131.828 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1540976131.828 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976131.828 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976131.828 * [misc]taylor: Taking taylor expansion of k in k 1540976131.828 * [misc]backup-simplify: Simplify 0 into 0 1540976131.828 * [misc]backup-simplify: Simplify 1 into 1 1540976131.828 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1540976131.828 * [misc]taylor: Taking taylor expansion of (log n) in k 1540976131.828 * [misc]taylor: Taking taylor expansion of n in k 1540976131.828 * [misc]backup-simplify: Simplify n into n 1540976131.828 * [misc]backup-simplify: Simplify (log n) into (log n) 1540976131.828 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1540976131.828 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1540976131.828 * [misc]taylor: Taking taylor expansion of 2 in k 1540976131.828 * [misc]backup-simplify: Simplify 2 into 2 1540976131.828 * [misc]taylor: Taking taylor expansion of PI in k 1540976131.828 * [misc]backup-simplify: Simplify PI into PI 1540976131.828 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1540976131.829 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1540976131.829 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1540976131.829 * [misc]backup-simplify: Simplify (- 0) into 0 1540976131.829 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1540976131.829 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1540976131.830 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1540976131.830 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1540976131.831 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1540976131.831 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1540976131.832 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1540976131.834 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1540976131.834 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1540976131.834 * [misc]backup-simplify: Simplify (- 0) into 0 1540976131.834 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976131.835 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1540976131.835 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1540976131.836 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1540976131.836 * [misc]taylor: Taking taylor expansion of 0 in k 1540976131.836 * [misc]backup-simplify: Simplify 0 into 0 1540976131.836 * [misc]backup-simplify: Simplify 0 into 0 1540976131.837 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1540976131.837 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1540976131.839 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1540976131.839 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976131.840 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1540976131.840 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1540976131.840 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1540976131.840 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1540976131.842 * [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))))))) 1540976131.843 * [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))))))) 1540976131.844 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1540976131.845 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1540976131.848 * [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 1540976131.848 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1540976131.848 * [misc]backup-simplify: Simplify (- 0) into 0 1540976131.849 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976131.849 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1540976131.850 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1540976131.851 * [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 1540976131.851 * [misc]taylor: Taking taylor expansion of 0 in k 1540976131.851 * [misc]backup-simplify: Simplify 0 into 0 1540976131.851 * [misc]backup-simplify: Simplify 0 into 0 1540976131.851 * [misc]backup-simplify: Simplify 0 into 0 1540976131.852 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1540976131.853 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1540976131.857 * [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 1540976131.857 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976131.857 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1540976131.857 * [misc]backup-simplify: Simplify (- 0) into 0 1540976131.857 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976131.858 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1540976131.860 * [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))))) 1540976131.863 * [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))))) 1540976131.869 * [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))))) 1540976131.869 * [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)))) 1540976131.869 * [misc]approximate: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 1540976131.869 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1540976131.869 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1540976131.869 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1540976131.869 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1540976131.869 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976131.869 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976131.869 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1540976131.869 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976131.869 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976131.869 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1540976131.869 * [misc]taylor: Taking taylor expansion of k in k 1540976131.869 * [misc]backup-simplify: Simplify 0 into 0 1540976131.869 * [misc]backup-simplify: Simplify 1 into 1 1540976131.869 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1540976131.869 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1540976131.869 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1540976131.869 * [misc]taylor: Taking taylor expansion of 2 in k 1540976131.869 * [misc]backup-simplify: Simplify 2 into 2 1540976131.869 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1540976131.869 * [misc]taylor: Taking taylor expansion of PI in k 1540976131.869 * [misc]backup-simplify: Simplify PI into PI 1540976131.869 * [misc]taylor: Taking taylor expansion of n in k 1540976131.869 * [misc]backup-simplify: Simplify n into n 1540976131.870 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1540976131.870 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1540976131.870 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1540976131.870 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1540976131.870 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1540976131.870 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1540976131.870 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1540976131.870 * [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)))) 1540976131.870 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1540976131.870 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1540976131.870 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1540976131.870 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1540976131.870 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976131.870 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976131.870 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1540976131.870 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976131.870 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976131.871 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1540976131.871 * [misc]taylor: Taking taylor expansion of k in n 1540976131.871 * [misc]backup-simplify: Simplify k into k 1540976131.871 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1540976131.871 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1540976131.871 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1540976131.871 * [misc]taylor: Taking taylor expansion of 2 in n 1540976131.871 * [misc]backup-simplify: Simplify 2 into 2 1540976131.871 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1540976131.871 * [misc]taylor: Taking taylor expansion of PI in n 1540976131.871 * [misc]backup-simplify: Simplify PI into PI 1540976131.871 * [misc]taylor: Taking taylor expansion of n in n 1540976131.871 * [misc]backup-simplify: Simplify 0 into 0 1540976131.871 * [misc]backup-simplify: Simplify 1 into 1 1540976131.871 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1540976131.871 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1540976131.872 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1540976131.872 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1540976131.872 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1540976131.872 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1540976131.872 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1540976131.873 * [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))) 1540976131.873 * [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)))) 1540976131.873 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1540976131.873 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1540976131.873 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1540976131.873 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1540976131.873 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976131.873 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976131.873 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1540976131.873 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976131.873 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976131.873 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1540976131.873 * [misc]taylor: Taking taylor expansion of k in n 1540976131.873 * [misc]backup-simplify: Simplify k into k 1540976131.873 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1540976131.873 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1540976131.873 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1540976131.873 * [misc]taylor: Taking taylor expansion of 2 in n 1540976131.873 * [misc]backup-simplify: Simplify 2 into 2 1540976131.873 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1540976131.873 * [misc]taylor: Taking taylor expansion of PI in n 1540976131.874 * [misc]backup-simplify: Simplify PI into PI 1540976131.874 * [misc]taylor: Taking taylor expansion of n in n 1540976131.874 * [misc]backup-simplify: Simplify 0 into 0 1540976131.874 * [misc]backup-simplify: Simplify 1 into 1 1540976131.874 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1540976131.874 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1540976131.874 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1540976131.874 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1540976131.874 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1540976131.874 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1540976131.875 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1540976131.875 * [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))) 1540976131.876 * [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)))) 1540976131.876 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1540976131.876 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1540976131.876 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1540976131.876 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976131.876 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976131.876 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1540976131.876 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976131.876 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976131.876 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1540976131.876 * [misc]taylor: Taking taylor expansion of k in k 1540976131.876 * [misc]backup-simplify: Simplify 0 into 0 1540976131.876 * [misc]backup-simplify: Simplify 1 into 1 1540976131.876 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1540976131.876 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1540976131.876 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1540976131.876 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1540976131.876 * [misc]taylor: Taking taylor expansion of 2 in k 1540976131.876 * [misc]backup-simplify: Simplify 2 into 2 1540976131.876 * [misc]taylor: Taking taylor expansion of PI in k 1540976131.876 * [misc]backup-simplify: Simplify PI into PI 1540976131.877 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1540976131.877 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1540976131.877 * [misc]taylor: Taking taylor expansion of (log n) in k 1540976131.877 * [misc]taylor: Taking taylor expansion of n in k 1540976131.877 * [misc]backup-simplify: Simplify n into n 1540976131.877 * [misc]backup-simplify: Simplify (log n) into (log n) 1540976131.877 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1540976131.877 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1540976131.877 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1540976131.877 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1540976131.878 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1540976131.878 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1540976131.879 * [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)))) 1540976131.882 * [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)))) 1540976131.882 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1540976131.883 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1540976131.885 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1540976131.885 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1540976131.885 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1540976131.885 * [misc]backup-simplify: Simplify (- 0) into 0 1540976131.885 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976131.886 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1540976131.886 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1540976131.887 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1540976131.887 * [misc]taylor: Taking taylor expansion of 0 in k 1540976131.887 * [misc]backup-simplify: Simplify 0 into 0 1540976131.887 * [misc]backup-simplify: Simplify 0 into 0 1540976131.887 * [misc]backup-simplify: Simplify 0 into 0 1540976131.888 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976131.889 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1540976131.892 * [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 1540976131.892 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1540976131.893 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1540976131.893 * [misc]backup-simplify: Simplify (- 0) into 0 1540976131.893 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976131.893 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1540976131.894 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1540976131.896 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1540976131.896 * [misc]taylor: Taking taylor expansion of 0 in k 1540976131.896 * [misc]backup-simplify: Simplify 0 into 0 1540976131.896 * [misc]backup-simplify: Simplify 0 into 0 1540976131.896 * [misc]backup-simplify: Simplify 0 into 0 1540976131.896 * [misc]backup-simplify: Simplify 0 into 0 1540976131.898 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976131.899 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1540976131.909 * [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 1540976131.909 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1540976131.909 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1540976131.910 * [misc]backup-simplify: Simplify (- 0) into 0 1540976131.910 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976131.911 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1540976131.912 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1540976131.916 * [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 1540976131.916 * [misc]taylor: Taking taylor expansion of 0 in k 1540976131.916 * [misc]backup-simplify: Simplify 0 into 0 1540976131.916 * [misc]backup-simplify: Simplify 0 into 0 1540976131.917 * [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))))) 1540976131.917 * [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)) 1540976131.917 * [misc]approximate: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 1540976131.917 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1540976131.918 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1540976131.918 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1540976131.918 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1540976131.918 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1540976131.918 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976131.918 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976131.918 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1540976131.918 * [misc]taylor: Taking taylor expansion of k in k 1540976131.918 * [misc]backup-simplify: Simplify 0 into 0 1540976131.918 * [misc]backup-simplify: Simplify 1 into 1 1540976131.918 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1540976131.918 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976131.918 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976131.918 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1540976131.918 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1540976131.918 * [misc]taylor: Taking taylor expansion of -2 in k 1540976131.918 * [misc]backup-simplify: Simplify -2 into -2 1540976131.918 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1540976131.918 * [misc]taylor: Taking taylor expansion of PI in k 1540976131.918 * [misc]backup-simplify: Simplify PI into PI 1540976131.918 * [misc]taylor: Taking taylor expansion of n in k 1540976131.918 * [misc]backup-simplify: Simplify n into n 1540976131.918 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1540976131.919 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1540976131.919 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1540976131.919 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1540976131.919 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1540976131.919 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1540976131.920 * [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))) 1540976131.920 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1540976131.920 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1540976131.920 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1540976131.920 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1540976131.920 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1540976131.920 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976131.920 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976131.920 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1540976131.920 * [misc]taylor: Taking taylor expansion of k in n 1540976131.920 * [misc]backup-simplify: Simplify k into k 1540976131.920 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1540976131.920 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976131.920 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976131.920 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1540976131.920 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1540976131.920 * [misc]taylor: Taking taylor expansion of -2 in n 1540976131.920 * [misc]backup-simplify: Simplify -2 into -2 1540976131.920 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1540976131.920 * [misc]taylor: Taking taylor expansion of PI in n 1540976131.920 * [misc]backup-simplify: Simplify PI into PI 1540976131.920 * [misc]taylor: Taking taylor expansion of n in n 1540976131.920 * [misc]backup-simplify: Simplify 0 into 0 1540976131.920 * [misc]backup-simplify: Simplify 1 into 1 1540976131.921 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1540976131.921 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1540976131.922 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1540976131.922 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1540976131.922 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1540976131.923 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1540976131.924 * [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))) 1540976131.924 * [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)))) 1540976131.924 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1540976131.925 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1540976131.925 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1540976131.925 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1540976131.925 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1540976131.925 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976131.925 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976131.925 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1540976131.925 * [misc]taylor: Taking taylor expansion of k in n 1540976131.925 * [misc]backup-simplify: Simplify k into k 1540976131.925 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1540976131.925 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976131.925 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976131.925 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1540976131.925 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1540976131.925 * [misc]taylor: Taking taylor expansion of -2 in n 1540976131.925 * [misc]backup-simplify: Simplify -2 into -2 1540976131.925 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1540976131.925 * [misc]taylor: Taking taylor expansion of PI in n 1540976131.925 * [misc]backup-simplify: Simplify PI into PI 1540976131.925 * [misc]taylor: Taking taylor expansion of n in n 1540976131.925 * [misc]backup-simplify: Simplify 0 into 0 1540976131.925 * [misc]backup-simplify: Simplify 1 into 1 1540976131.926 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1540976131.926 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1540976131.926 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1540976131.926 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1540976131.927 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1540976131.927 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1540976131.928 * [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))) 1540976131.929 * [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)))) 1540976131.929 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1540976131.929 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1540976131.929 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1540976131.929 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1540976131.929 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976131.929 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976131.929 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1540976131.929 * [misc]taylor: Taking taylor expansion of k in k 1540976131.929 * [misc]backup-simplify: Simplify 0 into 0 1540976131.929 * [misc]backup-simplify: Simplify 1 into 1 1540976131.929 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1540976131.929 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976131.929 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976131.929 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1540976131.929 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1540976131.929 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1540976131.929 * [misc]taylor: Taking taylor expansion of -2 in k 1540976131.930 * [misc]backup-simplify: Simplify -2 into -2 1540976131.930 * [misc]taylor: Taking taylor expansion of PI in k 1540976131.930 * [misc]backup-simplify: Simplify PI into PI 1540976131.930 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1540976131.930 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1540976131.930 * [misc]taylor: Taking taylor expansion of (log n) in k 1540976131.930 * [misc]taylor: Taking taylor expansion of n in k 1540976131.931 * [misc]backup-simplify: Simplify n into n 1540976131.931 * [misc]backup-simplify: Simplify (log n) into (log n) 1540976131.931 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1540976131.931 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1540976131.931 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1540976131.932 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1540976131.932 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1540976131.933 * [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)))) 1540976131.934 * [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)))) 1540976131.935 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1540976131.936 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1540976131.939 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1540976131.939 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1540976131.939 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1540976131.939 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976131.940 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1540976131.941 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1540976131.943 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1540976131.943 * [misc]taylor: Taking taylor expansion of 0 in k 1540976131.943 * [misc]backup-simplify: Simplify 0 into 0 1540976131.943 * [misc]backup-simplify: Simplify 0 into 0 1540976131.943 * [misc]backup-simplify: Simplify 0 into 0 1540976131.944 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976131.945 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1540976131.951 * [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 1540976131.951 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1540976131.952 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1540976131.952 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976131.953 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1540976131.954 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1540976131.956 * [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 1540976131.956 * [misc]taylor: Taking taylor expansion of 0 in k 1540976131.956 * [misc]backup-simplify: Simplify 0 into 0 1540976131.956 * [misc]backup-simplify: Simplify 0 into 0 1540976131.956 * [misc]backup-simplify: Simplify 0 into 0 1540976131.956 * [misc]backup-simplify: Simplify 0 into 0 1540976131.958 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976131.960 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1540976131.970 * [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 1540976131.970 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1540976131.970 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1540976131.971 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976131.971 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1540976131.972 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 1540976131.974 * [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 1540976131.974 * [misc]taylor: Taking taylor expansion of 0 in k 1540976131.974 * [misc]backup-simplify: Simplify 0 into 0 1540976131.974 * [misc]backup-simplify: Simplify 0 into 0 1540976131.975 * [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))))) 1540976131.975 * * * * [misc]progress: [ 2 / 3 ] generating series at (2 1 1) 1540976131.975 * [misc]backup-simplify: Simplify (* PI (* n 2)) into (* 2 (* n PI)) 1540976131.975 * [misc]approximate: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1540976131.975 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1540976131.976 * [misc]taylor: Taking taylor expansion of 2 in n 1540976131.976 * [misc]backup-simplify: Simplify 2 into 2 1540976131.976 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1540976131.976 * [misc]taylor: Taking taylor expansion of n in n 1540976131.976 * [misc]backup-simplify: Simplify 0 into 0 1540976131.976 * [misc]backup-simplify: Simplify 1 into 1 1540976131.976 * [misc]taylor: Taking taylor expansion of PI in n 1540976131.976 * [misc]backup-simplify: Simplify PI into PI 1540976131.976 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1540976131.976 * [misc]taylor: Taking taylor expansion of 2 in n 1540976131.976 * [misc]backup-simplify: Simplify 2 into 2 1540976131.976 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1540976131.976 * [misc]taylor: Taking taylor expansion of n in n 1540976131.976 * [misc]backup-simplify: Simplify 0 into 0 1540976131.976 * [misc]backup-simplify: Simplify 1 into 1 1540976131.976 * [misc]taylor: Taking taylor expansion of PI in n 1540976131.976 * [misc]backup-simplify: Simplify PI into PI 1540976131.976 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1540976131.976 * [misc]backup-simplify: Simplify (* 2 0) into 0 1540976131.976 * [misc]backup-simplify: Simplify 0 into 0 1540976131.977 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1540976131.977 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1540976131.977 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1540976131.978 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1540976131.979 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1540976131.979 * [misc]backup-simplify: Simplify 0 into 0 1540976131.980 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1540976131.981 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1540976131.981 * [misc]backup-simplify: Simplify 0 into 0 1540976131.982 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1540976131.983 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1540976131.983 * [misc]backup-simplify: Simplify 0 into 0 1540976131.985 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1540976131.987 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1540976131.987 * [misc]backup-simplify: Simplify 0 into 0 1540976131.989 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1540976131.991 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1540976131.991 * [misc]backup-simplify: Simplify 0 into 0 1540976131.993 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1540976131.996 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1540976131.996 * [misc]backup-simplify: Simplify 0 into 0 1540976131.996 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1540976131.996 * [misc]backup-simplify: Simplify (* PI (* (/ 1 n) 2)) into (* 2 (/ PI n)) 1540976131.996 * [misc]approximate: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1540976131.996 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1540976131.996 * [misc]taylor: Taking taylor expansion of 2 in n 1540976131.996 * [misc]backup-simplify: Simplify 2 into 2 1540976131.996 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1540976131.996 * [misc]taylor: Taking taylor expansion of PI in n 1540976131.996 * [misc]backup-simplify: Simplify PI into PI 1540976131.996 * [misc]taylor: Taking taylor expansion of n in n 1540976131.996 * [misc]backup-simplify: Simplify 0 into 0 1540976131.996 * [misc]backup-simplify: Simplify 1 into 1 1540976131.996 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1540976131.997 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1540976131.997 * [misc]taylor: Taking taylor expansion of 2 in n 1540976131.997 * [misc]backup-simplify: Simplify 2 into 2 1540976131.997 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1540976131.997 * [misc]taylor: Taking taylor expansion of PI in n 1540976131.997 * [misc]backup-simplify: Simplify PI into PI 1540976131.997 * [misc]taylor: Taking taylor expansion of n in n 1540976131.997 * [misc]backup-simplify: Simplify 0 into 0 1540976131.997 * [misc]backup-simplify: Simplify 1 into 1 1540976131.997 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1540976131.997 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1540976131.997 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1540976131.998 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1540976131.998 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1540976131.998 * [misc]backup-simplify: Simplify 0 into 0 1540976131.999 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976132.000 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1540976132.000 * [misc]backup-simplify: Simplify 0 into 0 1540976132.001 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976132.004 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1540976132.004 * [misc]backup-simplify: Simplify 0 into 0 1540976132.005 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976132.006 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1540976132.006 * [misc]backup-simplify: Simplify 0 into 0 1540976132.008 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976132.010 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1540976132.010 * [misc]backup-simplify: Simplify 0 into 0 1540976132.011 * [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 1540976132.014 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1540976132.014 * [misc]backup-simplify: Simplify 0 into 0 1540976132.014 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 1540976132.014 * [misc]backup-simplify: Simplify (* PI (* (/ 1 (- n)) 2)) into (* -2 (/ PI n)) 1540976132.014 * [misc]approximate: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1540976132.014 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1540976132.014 * [misc]taylor: Taking taylor expansion of -2 in n 1540976132.014 * [misc]backup-simplify: Simplify -2 into -2 1540976132.014 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1540976132.014 * [misc]taylor: Taking taylor expansion of PI in n 1540976132.014 * [misc]backup-simplify: Simplify PI into PI 1540976132.014 * [misc]taylor: Taking taylor expansion of n in n 1540976132.014 * [misc]backup-simplify: Simplify 0 into 0 1540976132.014 * [misc]backup-simplify: Simplify 1 into 1 1540976132.015 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1540976132.015 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1540976132.015 * [misc]taylor: Taking taylor expansion of -2 in n 1540976132.015 * [misc]backup-simplify: Simplify -2 into -2 1540976132.015 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1540976132.015 * [misc]taylor: Taking taylor expansion of PI in n 1540976132.015 * [misc]backup-simplify: Simplify PI into PI 1540976132.015 * [misc]taylor: Taking taylor expansion of n in n 1540976132.015 * [misc]backup-simplify: Simplify 0 into 0 1540976132.015 * [misc]backup-simplify: Simplify 1 into 1 1540976132.015 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1540976132.015 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1540976132.016 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1540976132.017 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1540976132.017 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1540976132.017 * [misc]backup-simplify: Simplify 0 into 0 1540976132.018 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976132.019 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1540976132.019 * [misc]backup-simplify: Simplify 0 into 0 1540976132.020 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976132.022 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1540976132.022 * [misc]backup-simplify: Simplify 0 into 0 1540976132.023 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976132.024 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1540976132.024 * [misc]backup-simplify: Simplify 0 into 0 1540976132.025 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976132.027 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1540976132.027 * [misc]backup-simplify: Simplify 0 into 0 1540976132.029 * [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 1540976132.031 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1540976132.031 * [misc]backup-simplify: Simplify 0 into 0 1540976132.031 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 1540976132.031 * * * * [misc]progress: [ 3 / 3 ] generating series at (2) 1540976132.032 * [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)))) 1540976132.032 * [misc]approximate: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (n k) around 0 1540976132.032 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 1540976132.032 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1540976132.032 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1540976132.032 * [misc]taylor: Taking taylor expansion of k in k 1540976132.032 * [misc]backup-simplify: Simplify 0 into 0 1540976132.032 * [misc]backup-simplify: Simplify 1 into 1 1540976132.032 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1540976132.032 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1540976132.032 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1540976132.032 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1540976132.032 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1540976132.032 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1540976132.032 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1540976132.032 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976132.032 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976132.032 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1540976132.032 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976132.032 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976132.032 * [misc]taylor: Taking taylor expansion of k in k 1540976132.032 * [misc]backup-simplify: Simplify 0 into 0 1540976132.032 * [misc]backup-simplify: Simplify 1 into 1 1540976132.032 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1540976132.032 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1540976132.032 * [misc]taylor: Taking taylor expansion of 2 in k 1540976132.032 * [misc]backup-simplify: Simplify 2 into 2 1540976132.032 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1540976132.033 * [misc]taylor: Taking taylor expansion of n in k 1540976132.033 * [misc]backup-simplify: Simplify n into n 1540976132.033 * [misc]taylor: Taking taylor expansion of PI in k 1540976132.033 * [misc]backup-simplify: Simplify PI into PI 1540976132.033 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1540976132.033 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1540976132.033 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1540976132.033 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1540976132.033 * [misc]backup-simplify: Simplify (- 0) into 0 1540976132.033 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1540976132.033 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1540976132.033 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1540976132.033 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 1540976132.033 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1540976132.033 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1540976132.033 * [misc]taylor: Taking taylor expansion of k in n 1540976132.033 * [misc]backup-simplify: Simplify k into k 1540976132.033 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1540976132.034 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1540976132.034 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1540976132.034 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1540976132.034 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1540976132.034 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1540976132.034 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1540976132.034 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1540976132.034 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976132.034 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976132.034 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1540976132.034 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976132.034 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976132.034 * [misc]taylor: Taking taylor expansion of k in n 1540976132.034 * [misc]backup-simplify: Simplify k into k 1540976132.034 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1540976132.034 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1540976132.034 * [misc]taylor: Taking taylor expansion of 2 in n 1540976132.034 * [misc]backup-simplify: Simplify 2 into 2 1540976132.034 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1540976132.034 * [misc]taylor: Taking taylor expansion of n in n 1540976132.034 * [misc]backup-simplify: Simplify 0 into 0 1540976132.034 * [misc]backup-simplify: Simplify 1 into 1 1540976132.034 * [misc]taylor: Taking taylor expansion of PI in n 1540976132.034 * [misc]backup-simplify: Simplify PI into PI 1540976132.034 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1540976132.034 * [misc]backup-simplify: Simplify (* 2 0) into 0 1540976132.035 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1540976132.035 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1540976132.036 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1540976132.036 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1540976132.036 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1540976132.036 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1540976132.037 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1540976132.038 * [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)))) 1540976132.038 * [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))))) 1540976132.038 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 1540976132.038 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1540976132.038 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1540976132.039 * [misc]taylor: Taking taylor expansion of k in n 1540976132.039 * [misc]backup-simplify: Simplify k into k 1540976132.039 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1540976132.039 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1540976132.039 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1540976132.039 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1540976132.039 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1540976132.039 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1540976132.039 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1540976132.039 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1540976132.039 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976132.039 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976132.039 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1540976132.039 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976132.039 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976132.039 * [misc]taylor: Taking taylor expansion of k in n 1540976132.039 * [misc]backup-simplify: Simplify k into k 1540976132.039 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1540976132.039 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1540976132.039 * [misc]taylor: Taking taylor expansion of 2 in n 1540976132.039 * [misc]backup-simplify: Simplify 2 into 2 1540976132.039 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1540976132.039 * [misc]taylor: Taking taylor expansion of n in n 1540976132.039 * [misc]backup-simplify: Simplify 0 into 0 1540976132.040 * [misc]backup-simplify: Simplify 1 into 1 1540976132.040 * [misc]taylor: Taking taylor expansion of PI in n 1540976132.040 * [misc]backup-simplify: Simplify PI into PI 1540976132.040 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1540976132.040 * [misc]backup-simplify: Simplify (* 2 0) into 0 1540976132.041 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1540976132.041 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1540976132.042 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1540976132.042 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1540976132.042 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1540976132.042 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1540976132.043 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1540976132.044 * [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)))) 1540976132.044 * [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))))) 1540976132.045 * [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))) 1540976132.045 * [misc]taylor: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k))) in k 1540976132.045 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1540976132.045 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1540976132.045 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1540976132.045 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976132.045 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976132.045 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1540976132.045 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976132.045 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976132.045 * [misc]taylor: Taking taylor expansion of k in k 1540976132.045 * [misc]backup-simplify: Simplify 0 into 0 1540976132.045 * [misc]backup-simplify: Simplify 1 into 1 1540976132.045 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1540976132.045 * [misc]taylor: Taking taylor expansion of (log n) in k 1540976132.046 * [misc]taylor: Taking taylor expansion of n in k 1540976132.046 * [misc]backup-simplify: Simplify n into n 1540976132.046 * [misc]backup-simplify: Simplify (log n) into (log n) 1540976132.046 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1540976132.046 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1540976132.046 * [misc]taylor: Taking taylor expansion of 2 in k 1540976132.046 * [misc]backup-simplify: Simplify 2 into 2 1540976132.046 * [misc]taylor: Taking taylor expansion of PI in k 1540976132.046 * [misc]backup-simplify: Simplify PI into PI 1540976132.046 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1540976132.047 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1540976132.047 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1540976132.047 * [misc]backup-simplify: Simplify (- 0) into 0 1540976132.047 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1540976132.048 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1540976132.048 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1540976132.049 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1540976132.049 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1540976132.049 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1540976132.049 * [misc]taylor: Taking taylor expansion of k in k 1540976132.049 * [misc]backup-simplify: Simplify 0 into 0 1540976132.049 * [misc]backup-simplify: Simplify 1 into 1 1540976132.049 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1540976132.050 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1540976132.050 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1540976132.051 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) into 0 1540976132.051 * [misc]backup-simplify: Simplify 0 into 0 1540976132.052 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1540976132.053 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1540976132.056 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1540976132.057 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1540976132.057 * [misc]backup-simplify: Simplify (- 0) into 0 1540976132.057 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976132.058 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1540976132.059 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1540976132.060 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1540976132.061 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 k)) 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))) into 0 1540976132.061 * [misc]taylor: Taking taylor expansion of 0 in k 1540976132.061 * [misc]backup-simplify: Simplify 0 into 0 1540976132.062 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1540976132.063 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1540976132.067 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1540976132.067 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976132.067 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1540976132.067 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1540976132.068 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1540976132.068 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1540976132.070 * [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))))))) 1540976132.073 * [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))))))) 1540976132.074 * [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))))))) 1540976132.076 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1540976132.077 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1540976132.083 * [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 1540976132.083 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1540976132.084 * [misc]backup-simplify: Simplify (- 0) into 0 1540976132.084 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976132.084 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1540976132.085 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1540976132.088 * [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 1540976132.088 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1540976132.089 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 1540976132.090 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))))) into 0 1540976132.090 * [misc]taylor: Taking taylor expansion of 0 in k 1540976132.090 * [misc]backup-simplify: Simplify 0 into 0 1540976132.090 * [misc]backup-simplify: Simplify 0 into 0 1540976132.090 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1540976132.092 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1540976132.093 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1540976132.094 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1540976132.100 * [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 1540976132.100 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976132.101 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1540976132.101 * [misc]backup-simplify: Simplify (- 0) into 0 1540976132.101 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976132.102 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1540976132.105 * [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))))) 1540976132.112 * [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)))))))) 1540976132.116 * [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)))))))) 1540976132.119 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1540976132.121 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1540976132.130 * [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 1540976132.131 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 1540976132.131 * [misc]backup-simplify: Simplify (- 0) into 0 1540976132.131 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976132.132 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1540976132.133 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 1540976132.139 * [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 1540976132.139 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1540976132.140 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 1540976132.141 * [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 1540976132.141 * [misc]taylor: Taking taylor expansion of 0 in k 1540976132.141 * [misc]backup-simplify: Simplify 0 into 0 1540976132.141 * [misc]backup-simplify: Simplify 0 into 0 1540976132.141 * [misc]backup-simplify: Simplify 0 into 0 1540976132.142 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976132.143 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1540976132.146 * [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 1540976132.148 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1540976132.157 * [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 1540976132.157 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976132.158 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1540976132.158 * [misc]backup-simplify: Simplify (- 0) into 0 1540976132.158 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976132.159 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 1540976132.166 * [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))))))) 1540976132.187 * [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)))))))))))))) 1540976132.199 * [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)))))))))))))) 1540976132.221 * [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)))))))))))))))))))))) 1540976132.221 * [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))))) 1540976132.221 * [misc]approximate: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0 1540976132.221 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 1540976132.221 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1540976132.221 * [misc]taylor: Taking taylor expansion of k in k 1540976132.221 * [misc]backup-simplify: Simplify 0 into 0 1540976132.221 * [misc]backup-simplify: Simplify 1 into 1 1540976132.222 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1540976132.222 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1540976132.222 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1540976132.222 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1540976132.222 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1540976132.222 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1540976132.223 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976132.223 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976132.223 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1540976132.223 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976132.223 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976132.223 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1540976132.223 * [misc]taylor: Taking taylor expansion of k in k 1540976132.223 * [misc]backup-simplify: Simplify 0 into 0 1540976132.223 * [misc]backup-simplify: Simplify 1 into 1 1540976132.223 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1540976132.223 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1540976132.223 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1540976132.223 * [misc]taylor: Taking taylor expansion of 2 in k 1540976132.223 * [misc]backup-simplify: Simplify 2 into 2 1540976132.223 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1540976132.223 * [misc]taylor: Taking taylor expansion of PI in k 1540976132.223 * [misc]backup-simplify: Simplify PI into PI 1540976132.223 * [misc]taylor: Taking taylor expansion of n in k 1540976132.223 * [misc]backup-simplify: Simplify n into n 1540976132.223 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1540976132.223 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1540976132.224 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1540976132.224 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1540976132.224 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1540976132.224 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1540976132.224 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1540976132.225 * [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)))) 1540976132.225 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1540976132.225 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1540976132.225 * [misc]taylor: Taking taylor expansion of k in n 1540976132.225 * [misc]backup-simplify: Simplify k into k 1540976132.225 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1540976132.225 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1540976132.225 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1540976132.225 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1540976132.225 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1540976132.225 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1540976132.225 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976132.225 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976132.225 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1540976132.225 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976132.225 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976132.225 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1540976132.225 * [misc]taylor: Taking taylor expansion of k in n 1540976132.225 * [misc]backup-simplify: Simplify k into k 1540976132.225 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1540976132.225 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1540976132.225 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1540976132.225 * [misc]taylor: Taking taylor expansion of 2 in n 1540976132.225 * [misc]backup-simplify: Simplify 2 into 2 1540976132.225 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1540976132.226 * [misc]taylor: Taking taylor expansion of PI in n 1540976132.226 * [misc]backup-simplify: Simplify PI into PI 1540976132.226 * [misc]taylor: Taking taylor expansion of n in n 1540976132.226 * [misc]backup-simplify: Simplify 0 into 0 1540976132.226 * [misc]backup-simplify: Simplify 1 into 1 1540976132.226 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1540976132.226 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1540976132.227 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1540976132.227 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1540976132.227 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1540976132.227 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1540976132.228 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1540976132.229 * [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))) 1540976132.229 * [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)))) 1540976132.229 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1540976132.230 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1540976132.230 * [misc]taylor: Taking taylor expansion of k in n 1540976132.230 * [misc]backup-simplify: Simplify k into k 1540976132.230 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1540976132.230 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1540976132.230 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1540976132.230 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1540976132.230 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1540976132.230 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1540976132.230 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976132.230 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976132.230 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1540976132.230 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976132.230 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976132.230 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1540976132.230 * [misc]taylor: Taking taylor expansion of k in n 1540976132.230 * [misc]backup-simplify: Simplify k into k 1540976132.230 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1540976132.230 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1540976132.230 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1540976132.230 * [misc]taylor: Taking taylor expansion of 2 in n 1540976132.230 * [misc]backup-simplify: Simplify 2 into 2 1540976132.230 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1540976132.230 * [misc]taylor: Taking taylor expansion of PI in n 1540976132.230 * [misc]backup-simplify: Simplify PI into PI 1540976132.230 * [misc]taylor: Taking taylor expansion of n in n 1540976132.230 * [misc]backup-simplify: Simplify 0 into 0 1540976132.230 * [misc]backup-simplify: Simplify 1 into 1 1540976132.231 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1540976132.231 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1540976132.232 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1540976132.232 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1540976132.232 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1540976132.232 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1540976132.233 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1540976132.233 * [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))) 1540976132.234 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 1540976132.235 * [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)) 1540976132.235 * [misc]taylor: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) in k 1540976132.235 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1540976132.235 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1540976132.235 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1540976132.235 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976132.235 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976132.235 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1540976132.235 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976132.235 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976132.235 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1540976132.236 * [misc]taylor: Taking taylor expansion of k in k 1540976132.236 * [misc]backup-simplify: Simplify 0 into 0 1540976132.236 * [misc]backup-simplify: Simplify 1 into 1 1540976132.236 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1540976132.236 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1540976132.236 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1540976132.236 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1540976132.236 * [misc]taylor: Taking taylor expansion of 2 in k 1540976132.236 * [misc]backup-simplify: Simplify 2 into 2 1540976132.236 * [misc]taylor: Taking taylor expansion of PI in k 1540976132.236 * [misc]backup-simplify: Simplify PI into PI 1540976132.236 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1540976132.237 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1540976132.237 * [misc]taylor: Taking taylor expansion of (log n) in k 1540976132.237 * [misc]taylor: Taking taylor expansion of n in k 1540976132.237 * [misc]backup-simplify: Simplify n into n 1540976132.237 * [misc]backup-simplify: Simplify (log n) into (log n) 1540976132.237 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1540976132.237 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1540976132.237 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1540976132.238 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1540976132.238 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1540976132.239 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1540976132.240 * [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)))) 1540976132.240 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1540976132.240 * [misc]taylor: Taking taylor expansion of k in k 1540976132.240 * [misc]backup-simplify: Simplify 0 into 0 1540976132.240 * [misc]backup-simplify: Simplify 1 into 1 1540976132.240 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1540976132.240 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1540976132.241 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) into 0 1540976132.241 * [misc]backup-simplify: Simplify 0 into 0 1540976132.242 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1540976132.243 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1540976132.246 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1540976132.247 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1540976132.247 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1540976132.247 * [misc]backup-simplify: Simplify (- 0) into 0 1540976132.247 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976132.248 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1540976132.249 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1540976132.250 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1540976132.251 * [misc]backup-simplify: Simplify (+ (* (sqrt k) 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0 1540976132.251 * [misc]taylor: Taking taylor expansion of 0 in k 1540976132.251 * [misc]backup-simplify: Simplify 0 into 0 1540976132.251 * [misc]backup-simplify: Simplify 0 into 0 1540976132.252 * [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)))))) 1540976132.253 * [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)))))) 1540976132.255 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976132.256 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1540976132.262 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1540976132.262 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1540976132.262 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1540976132.263 * [misc]backup-simplify: Simplify (- 0) into 0 1540976132.263 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976132.264 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1540976132.264 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1540976132.267 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1540976132.268 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 1540976132.269 * [misc]backup-simplify: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0 1540976132.269 * [misc]taylor: Taking taylor expansion of 0 in k 1540976132.269 * [misc]backup-simplify: Simplify 0 into 0 1540976132.269 * [misc]backup-simplify: Simplify 0 into 0 1540976132.269 * [misc]backup-simplify: Simplify 0 into 0 1540976132.270 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1540976132.272 * [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)))))) 1540976132.272 * [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)))))) 1540976132.274 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976132.276 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1540976132.288 * [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 1540976132.288 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1540976132.289 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1540976132.289 * [misc]backup-simplify: Simplify (- 0) into 0 1540976132.289 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976132.290 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1540976132.291 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1540976132.295 * [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 1540976132.295 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 1540976132.297 * [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 1540976132.297 * [misc]taylor: Taking taylor expansion of 0 in k 1540976132.297 * [misc]backup-simplify: Simplify 0 into 0 1540976132.297 * [misc]backup-simplify: Simplify 0 into 0 1540976132.297 * [misc]backup-simplify: Simplify 0 into 0 1540976132.297 * [misc]backup-simplify: Simplify 0 into 0 1540976132.298 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1540976132.299 * [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)))))) 1540976132.300 * [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)))))) 1540976132.304 * [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)))))))) 1540976132.304 * [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))) 1540976132.304 * [misc]approximate: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (n k) around 0 1540976132.304 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 1540976132.304 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1540976132.304 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1540976132.304 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1540976132.305 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1540976132.305 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1540976132.305 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976132.305 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976132.305 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1540976132.305 * [misc]taylor: Taking taylor expansion of k in k 1540976132.305 * [misc]backup-simplify: Simplify 0 into 0 1540976132.305 * [misc]backup-simplify: Simplify 1 into 1 1540976132.305 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1540976132.305 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976132.305 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976132.305 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1540976132.305 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1540976132.305 * [misc]taylor: Taking taylor expansion of -2 in k 1540976132.305 * [misc]backup-simplify: Simplify -2 into -2 1540976132.305 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1540976132.305 * [misc]taylor: Taking taylor expansion of PI in k 1540976132.305 * [misc]backup-simplify: Simplify PI into PI 1540976132.305 * [misc]taylor: Taking taylor expansion of n in k 1540976132.305 * [misc]backup-simplify: Simplify n into n 1540976132.305 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1540976132.306 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1540976132.306 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1540976132.306 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1540976132.306 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1540976132.306 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1540976132.307 * [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))) 1540976132.307 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1540976132.307 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1540976132.307 * [misc]taylor: Taking taylor expansion of -1 in k 1540976132.307 * [misc]backup-simplify: Simplify -1 into -1 1540976132.307 * [misc]taylor: Taking taylor expansion of k in k 1540976132.307 * [misc]backup-simplify: Simplify 0 into 0 1540976132.307 * [misc]backup-simplify: Simplify 1 into 1 1540976132.307 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1540976132.307 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1540976132.308 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1540976132.308 * [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)))) 1540976132.308 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 1540976132.308 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1540976132.308 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1540976132.308 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1540976132.308 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1540976132.308 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1540976132.308 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976132.308 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976132.308 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1540976132.308 * [misc]taylor: Taking taylor expansion of k in n 1540976132.308 * [misc]backup-simplify: Simplify k into k 1540976132.308 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1540976132.308 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976132.308 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976132.309 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1540976132.309 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1540976132.309 * [misc]taylor: Taking taylor expansion of -2 in n 1540976132.309 * [misc]backup-simplify: Simplify -2 into -2 1540976132.309 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1540976132.309 * [misc]taylor: Taking taylor expansion of PI in n 1540976132.309 * [misc]backup-simplify: Simplify PI into PI 1540976132.309 * [misc]taylor: Taking taylor expansion of n in n 1540976132.309 * [misc]backup-simplify: Simplify 0 into 0 1540976132.309 * [misc]backup-simplify: Simplify 1 into 1 1540976132.309 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1540976132.309 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1540976132.310 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1540976132.310 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1540976132.310 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1540976132.311 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1540976132.312 * [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))) 1540976132.312 * [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)))) 1540976132.312 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1540976132.313 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1540976132.313 * [misc]taylor: Taking taylor expansion of -1 in n 1540976132.313 * [misc]backup-simplify: Simplify -1 into -1 1540976132.313 * [misc]taylor: Taking taylor expansion of k in n 1540976132.313 * [misc]backup-simplify: Simplify k into k 1540976132.313 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1540976132.313 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1540976132.313 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1540976132.313 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1540976132.314 * [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))) 1540976132.314 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 1540976132.314 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1540976132.314 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1540976132.314 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1540976132.314 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1540976132.314 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1540976132.314 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976132.314 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976132.314 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1540976132.314 * [misc]taylor: Taking taylor expansion of k in n 1540976132.314 * [misc]backup-simplify: Simplify k into k 1540976132.314 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1540976132.314 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976132.314 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976132.314 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1540976132.314 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1540976132.314 * [misc]taylor: Taking taylor expansion of -2 in n 1540976132.315 * [misc]backup-simplify: Simplify -2 into -2 1540976132.315 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1540976132.315 * [misc]taylor: Taking taylor expansion of PI in n 1540976132.315 * [misc]backup-simplify: Simplify PI into PI 1540976132.315 * [misc]taylor: Taking taylor expansion of n in n 1540976132.315 * [misc]backup-simplify: Simplify 0 into 0 1540976132.315 * [misc]backup-simplify: Simplify 1 into 1 1540976132.315 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1540976132.315 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1540976132.316 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1540976132.316 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1540976132.316 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1540976132.317 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1540976132.318 * [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))) 1540976132.319 * [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)))) 1540976132.319 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1540976132.319 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1540976132.319 * [misc]taylor: Taking taylor expansion of -1 in n 1540976132.319 * [misc]backup-simplify: Simplify -1 into -1 1540976132.319 * [misc]taylor: Taking taylor expansion of k in n 1540976132.319 * [misc]backup-simplify: Simplify k into k 1540976132.319 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1540976132.319 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1540976132.319 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1540976132.319 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1540976132.320 * [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))) 1540976132.320 * [misc]taylor: Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) in k 1540976132.320 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1540976132.320 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1540976132.320 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1540976132.320 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1540976132.320 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976132.320 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976132.321 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1540976132.321 * [misc]taylor: Taking taylor expansion of k in k 1540976132.321 * [misc]backup-simplify: Simplify 0 into 0 1540976132.321 * [misc]backup-simplify: Simplify 1 into 1 1540976132.321 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1540976132.321 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976132.321 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976132.321 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1540976132.321 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1540976132.321 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1540976132.321 * [misc]taylor: Taking taylor expansion of -2 in k 1540976132.321 * [misc]backup-simplify: Simplify -2 into -2 1540976132.321 * [misc]taylor: Taking taylor expansion of PI in k 1540976132.321 * [misc]backup-simplify: Simplify PI into PI 1540976132.321 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1540976132.322 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1540976132.322 * [misc]taylor: Taking taylor expansion of (log n) in k 1540976132.322 * [misc]taylor: Taking taylor expansion of n in k 1540976132.322 * [misc]backup-simplify: Simplify n into n 1540976132.322 * [misc]backup-simplify: Simplify (log n) into (log n) 1540976132.322 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1540976132.322 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1540976132.322 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1540976132.323 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1540976132.324 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1540976132.324 * [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)))) 1540976132.324 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1540976132.324 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1540976132.325 * [misc]taylor: Taking taylor expansion of -1 in k 1540976132.325 * [misc]backup-simplify: Simplify -1 into -1 1540976132.325 * [misc]taylor: Taking taylor expansion of k in k 1540976132.325 * [misc]backup-simplify: Simplify 0 into 0 1540976132.325 * [misc]backup-simplify: Simplify 1 into 1 1540976132.325 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1540976132.325 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1540976132.325 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1540976132.326 * [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))))) 1540976132.327 * [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))))) 1540976132.328 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1540976132.329 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1540976132.332 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1540976132.332 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1540976132.333 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1540976132.333 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976132.333 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1540976132.334 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1540976132.336 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1540976132.338 * [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 1540976132.338 * [misc]taylor: Taking taylor expansion of 0 in k 1540976132.338 * [misc]backup-simplify: Simplify 0 into 0 1540976132.338 * [misc]backup-simplify: Simplify 0 into 0 1540976132.338 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1540976132.339 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1540976132.340 * [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)))))) 1540976132.341 * [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)))))) 1540976132.343 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976132.344 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1540976132.350 * [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 1540976132.350 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1540976132.350 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1540976132.350 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976132.351 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1540976132.352 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1540976132.354 * [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 1540976132.355 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1540976132.355 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 1540976132.357 * [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 1540976132.357 * [misc]taylor: Taking taylor expansion of 0 in k 1540976132.357 * [misc]backup-simplify: Simplify 0 into 0 1540976132.357 * [misc]backup-simplify: Simplify 0 into 0 1540976132.357 * [misc]backup-simplify: Simplify 0 into 0 1540976132.357 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976132.358 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1540976132.361 * [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)))))) 1540976132.362 * [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)))))) 1540976132.365 * [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))))))))))) 1540976132.365 * * * [misc]progress: simplifying candidates 1540976132.365 * * * * [misc]progress: [ 1 / 77 ] simplifiying candidate # 1540976132.365 * [enter]simplify: Simplifying (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) 1540976132.367 * * [misc]simplify: iters left: 6 (11 enodes) 1540976132.373 * * [misc]simplify: iters left: 5 (21 enodes) 1540976132.384 * * [misc]simplify: iters left: 4 (47 enodes) 1540976132.412 * * [misc]simplify: iters left: 3 (109 enodes) 1540976132.470 * * [misc]simplify: iters left: 2 (300 enodes) 1540976132.884 * [exit]simplify: Simplified to (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) 1540976132.884 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (exp (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI)))) (sqrt k))) 1540976132.885 * * * * [misc]progress: [ 2 / 77 ] simplifiying candidate # 1540976132.885 * * * * [misc]progress: [ 3 / 77 ] simplifiying candidate # 1540976132.885 * [enter]simplify: Simplifying (* PI (* n 2)) 1540976132.885 * * [misc]simplify: iters left: 4 (5 enodes) 1540976132.887 * * [misc]simplify: iters left: 3 (9 enodes) 1540976132.889 * * [misc]simplify: iters left: 2 (15 enodes) 1540976132.891 * * [misc]simplify: iters left: 1 (17 enodes) 1540976132.894 * [exit]simplify: Simplified to (* (* 2 n) PI) 1540976132.895 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* 2 n) PI) (* 1 (- 1/2 (/ k 2)))) (sqrt k))) 1540976132.895 * * * * [misc]progress: [ 4 / 77 ] simplifiying candidate # 1540976132.895 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (/ k 2)) 1540976132.895 * * [misc]simplify: iters left: 5 (8 enodes) 1540976132.897 * * [misc]simplify: iters left: 4 (12 enodes) 1540976132.901 * * [misc]simplify: iters left: 3 (18 enodes) 1540976132.904 * * [misc]simplify: iters left: 2 (20 enodes) 1540976132.907 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ k 2)) 1540976132.907 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (/ (pow (* PI (* n 2)) 1/2) (pow (* (* 2 n) PI) (/ k 2))) (sqrt k))) 1540976132.907 * * * * [misc]progress: [ 5 / 77 ] simplifiying candidate # 1540976132.907 * [enter]simplify: Simplifying (cbrt (- 1/2 (/ k 2))) 1540976132.908 * * [misc]simplify: iters left: 5 (6 enodes) 1540976132.909 * * [misc]simplify: iters left: 4 (8 enodes) 1540976132.910 * * [misc]simplify: iters left: 3 (11 enodes) 1540976132.912 * [exit]simplify: Simplified to (cbrt (- 1/2 (/ k 2))) 1540976132.912 * [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))) 1540976132.912 * * * * [misc]progress: [ 6 / 77 ] simplifiying candidate # 1540976132.912 * [enter]simplify: Simplifying (sqrt (- 1/2 (/ k 2))) 1540976132.913 * * [misc]simplify: iters left: 5 (6 enodes) 1540976132.914 * * [misc]simplify: iters left: 4 (8 enodes) 1540976132.915 * * [misc]simplify: iters left: 3 (11 enodes) 1540976132.917 * [exit]simplify: Simplified to (sqrt (- 1/2 (/ k 2))) 1540976132.917 * [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))) 1540976132.917 * * * * [misc]progress: [ 7 / 77 ] simplifiying candidate # 1540976132.917 * [enter]simplify: Simplifying (- 1/2 (/ k 2)) 1540976132.917 * * [misc]simplify: iters left: 4 (5 enodes) 1540976132.918 * * [misc]simplify: iters left: 3 (7 enodes) 1540976132.922 * * [misc]simplify: iters left: 2 (10 enodes) 1540976132.925 * [exit]simplify: Simplified to (- 1/2 (/ k 2)) 1540976132.925 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (pow (pow (* PI (* n 2)) 1) (- 1/2 (/ k 2))) (sqrt k))) 1540976132.925 * * * * [misc]progress: [ 8 / 77 ] simplifiying candidate # 1540976132.925 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1540976132.926 * * [misc]simplify: iters left: 5 (9 enodes) 1540976132.930 * * [misc]simplify: iters left: 4 (15 enodes) 1540976132.936 * * [misc]simplify: iters left: 3 (21 enodes) 1540976132.943 * * [misc]simplify: iters left: 2 (22 enodes) 1540976132.951 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1540976132.951 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2)))) (sqrt k))) 1540976132.951 * * * * [misc]progress: [ 9 / 77 ] simplifiying candidate # 1540976132.951 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1540976132.952 * * [misc]simplify: iters left: 5 (9 enodes) 1540976132.956 * * [misc]simplify: iters left: 4 (15 enodes) 1540976132.962 * * [misc]simplify: iters left: 3 (21 enodes) 1540976132.968 * * [misc]simplify: iters left: 2 (22 enodes) 1540976132.976 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1540976132.976 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2)))) (sqrt k))) 1540976132.976 * * * * [misc]progress: [ 10 / 77 ] simplifiying candidate # 1540976132.976 * [enter]simplify: Simplifying (pow PI (- 1/2 (/ k 2))) 1540976132.977 * * [misc]simplify: iters left: 5 (7 enodes) 1540976132.979 * * [misc]simplify: iters left: 4 (9 enodes) 1540976132.983 * * [misc]simplify: iters left: 3 (12 enodes) 1540976132.987 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1540976132.987 * [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))) 1540976132.987 * * * * [misc]progress: [ 11 / 77 ] simplifiying candidate # 1540976132.987 * * * * [misc]progress: [ 12 / 77 ] simplifiying candidate # 1540976132.987 * * * * [misc]progress: [ 13 / 77 ] simplifiying candidate # 1540976132.987 * * * * [misc]progress: [ 14 / 77 ] simplifiying candidate # 1540976132.987 * * * * [misc]progress: [ 15 / 77 ] simplifiying candidate # 1540976132.987 * * * * [misc]progress: [ 16 / 77 ] simplifiying candidate # 1540976132.987 * * * * [misc]progress: [ 17 / 77 ] simplifiying candidate # 1540976132.987 * * * * [misc]progress: [ 18 / 77 ] simplifiying candidate # 1540976132.987 * * * * [misc]progress: [ 19 / 77 ] simplifiying candidate # 1540976132.987 * * * * [misc]progress: [ 20 / 77 ] simplifiying candidate # 1540976132.988 * * * * [misc]progress: [ 21 / 77 ] simplifiying candidate # 1540976132.988 * * * * [misc]progress: [ 22 / 77 ] simplifiying candidate # 1540976132.988 * * * * [misc]progress: [ 23 / 77 ] simplifiying candidate # 1540976132.988 * * * * [misc]progress: [ 24 / 77 ] simplifiying candidate # 1540976132.988 * * * * [misc]progress: [ 25 / 77 ] simplifiying candidate # 1540976132.988 * * * * [misc]progress: [ 26 / 77 ] simplifiying candidate # 1540976132.988 * * * * [misc]progress: [ 27 / 77 ] simplifiying candidate # 1540976132.988 * * * * [misc]progress: [ 28 / 77 ] simplifiying candidate # 1540976132.988 * [enter]simplify: Simplifying (- (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) (log (sqrt k))) 1540976132.989 * * [misc]simplify: iters left: 6 (14 enodes) 1540976132.995 * * [misc]simplify: iters left: 5 (26 enodes) 1540976133.010 * * [misc]simplify: iters left: 4 (53 enodes) 1540976133.044 * * [misc]simplify: iters left: 3 (137 enodes) 1540976133.165 * * [misc]simplify: iters left: 2 (487 enodes) 1540976134.217 * [exit]simplify: Simplified to (- (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) (log (sqrt k))) 1540976134.217 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) (log (sqrt k))))) 1540976134.217 * * * * [misc]progress: [ 29 / 77 ] simplifiying candidate # 1540976134.217 * [enter]simplify: Simplifying (- (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) (log (sqrt k))) 1540976134.219 * * [misc]simplify: iters left: 6 (14 enodes) 1540976134.225 * * [misc]simplify: iters left: 5 (26 enodes) 1540976134.239 * * [misc]simplify: iters left: 4 (53 enodes) 1540976134.272 * * [misc]simplify: iters left: 3 (137 enodes) 1540976134.415 * * [misc]simplify: iters left: 2 (487 enodes) 1540976135.337 * [exit]simplify: Simplified to (- (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) (log (sqrt k))) 1540976135.338 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) (log (sqrt k))))) 1540976135.338 * * * * [misc]progress: [ 30 / 77 ] simplifiying candidate # 1540976135.338 * [enter]simplify: Simplifying (- (log (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (log (sqrt k))) 1540976135.340 * * [misc]simplify: iters left: 6 (14 enodes) 1540976135.348 * * [misc]simplify: iters left: 5 (24 enodes) 1540976135.359 * * [misc]simplify: iters left: 4 (42 enodes) 1540976135.379 * * [misc]simplify: iters left: 3 (71 enodes) 1540976135.408 * * [misc]simplify: iters left: 2 (208 enodes) 1540976135.775 * [exit]simplify: Simplified to (- (* (log (* (* 2 n) PI)) (- 1/2 (/ k 2))) (log (sqrt k))) 1540976135.775 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (log (* (* 2 n) PI)) (- 1/2 (/ k 2))) (log (sqrt k))))) 1540976135.775 * * * * [misc]progress: [ 31 / 77 ] simplifiying candidate # 1540976135.775 * * * * [misc]progress: [ 32 / 77 ] simplifiying candidate # 1540976135.775 * * * * [misc]progress: [ 33 / 77 ] simplifiying candidate # 1540976135.776 * [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))) 1540976135.778 * * [misc]simplify: iters left: 6 (16 enodes) 1540976135.786 * * [misc]simplify: iters left: 5 (31 enodes) 1540976135.802 * * [misc]simplify: iters left: 4 (67 enodes) 1540976135.819 * * [misc]simplify: iters left: 3 (124 enodes) 1540976135.851 * * [misc]simplify: iters left: 2 (195 enodes) 1540976135.906 * * [misc]simplify: iters left: 1 (309 enodes) 1540976136.049 * [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)))) 1540976136.049 * [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)))))) 1540976136.049 * * * * [misc]progress: [ 34 / 77 ] simplifiying candidate # 1540976136.050 * * * * [misc]progress: [ 35 / 77 ] simplifiying candidate # 1540976136.050 * * * * [misc]progress: [ 36 / 77 ] simplifiying candidate # 1540976136.050 * * * * [misc]progress: [ 37 / 77 ] simplifiying candidate # 1540976136.050 * * * * [misc]progress: [ 38 / 77 ] simplifiying candidate # 1540976136.050 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1540976136.051 * * [misc]simplify: iters left: 6 (12 enodes) 1540976136.054 * * [misc]simplify: iters left: 5 (19 enodes) 1540976136.057 * * [misc]simplify: iters left: 4 (25 enodes) 1540976136.061 * * [misc]simplify: iters left: 3 (26 enodes) 1540976136.066 * [exit]simplify: Simplified to (/ (sqrt (* (* 2 n) PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1540976136.066 * [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))))) 1540976136.066 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (sqrt k))) 1540976136.067 * * [misc]simplify: iters left: 6 (12 enodes) 1540976136.069 * * [misc]simplify: iters left: 5 (18 enodes) 1540976136.072 * * [misc]simplify: iters left: 4 (24 enodes) 1540976136.077 * * [misc]simplify: iters left: 3 (25 enodes) 1540976136.081 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt k))) 1540976136.081 * [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))))) 1540976136.081 * * * * [misc]progress: [ 39 / 77 ] simplifiying candidate # 1540976136.081 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (sqrt (sqrt k))) 1540976136.082 * * [misc]simplify: iters left: 6 (11 enodes) 1540976136.084 * * [misc]simplify: iters left: 5 (16 enodes) 1540976136.087 * * [misc]simplify: iters left: 4 (22 enodes) 1540976136.091 * * [misc]simplify: iters left: 3 (24 enodes) 1540976136.098 * [exit]simplify: Simplified to (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) 1540976136.098 * [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))))) 1540976136.098 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k))) 1540976136.100 * * [misc]simplify: iters left: 6 (12 enodes) 1540976136.105 * * [misc]simplify: iters left: 5 (18 enodes) 1540976136.113 * * [misc]simplify: iters left: 4 (24 enodes) 1540976136.123 * * [misc]simplify: iters left: 3 (25 enodes) 1540976136.132 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k))) 1540976136.133 * [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))))) 1540976136.133 * * * * [misc]progress: [ 40 / 77 ] simplifiying candidate # 1540976136.133 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) 1) 1540976136.134 * * [misc]simplify: iters left: 6 (9 enodes) 1540976136.139 * * [misc]simplify: iters left: 5 (16 enodes) 1540976136.146 * * [misc]simplify: iters left: 4 (24 enodes) 1540976136.153 * * [misc]simplify: iters left: 3 (26 enodes) 1540976136.160 * [exit]simplify: Simplified to (sqrt (* (* PI 2) n)) 1540976136.160 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) 1540976136.161 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)) 1540976136.162 * * [misc]simplify: iters left: 6 (11 enodes) 1540976136.166 * * [misc]simplify: iters left: 5 (17 enodes) 1540976136.173 * * [misc]simplify: iters left: 4 (23 enodes) 1540976136.180 * * [misc]simplify: iters left: 3 (24 enodes) 1540976136.189 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)) 1540976136.189 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)))) 1540976136.189 * * * * [misc]progress: [ 41 / 77 ] simplifiying candidate # 1540976136.190 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1540976136.191 * * [misc]simplify: iters left: 6 (12 enodes) 1540976136.197 * * [misc]simplify: iters left: 5 (19 enodes) 1540976136.204 * * [misc]simplify: iters left: 4 (25 enodes) 1540976136.213 * * [misc]simplify: iters left: 3 (26 enodes) 1540976136.222 * [exit]simplify: Simplified to (/ (sqrt (* (* 2 n) PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1540976136.222 * [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))))) 1540976136.222 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (sqrt k))) 1540976136.223 * * [misc]simplify: iters left: 6 (12 enodes) 1540976136.228 * * [misc]simplify: iters left: 5 (18 enodes) 1540976136.236 * * [misc]simplify: iters left: 4 (24 enodes) 1540976136.243 * * [misc]simplify: iters left: 3 (25 enodes) 1540976136.252 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt k))) 1540976136.252 * [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))))) 1540976136.252 * * * * [misc]progress: [ 42 / 77 ] simplifiying candidate # 1540976136.252 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (sqrt (sqrt k))) 1540976136.255 * * [misc]simplify: iters left: 6 (11 enodes) 1540976136.260 * * [misc]simplify: iters left: 5 (16 enodes) 1540976136.266 * * [misc]simplify: iters left: 4 (22 enodes) 1540976136.273 * * [misc]simplify: iters left: 3 (24 enodes) 1540976136.281 * [exit]simplify: Simplified to (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) 1540976136.281 * [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))))) 1540976136.282 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k))) 1540976136.283 * * [misc]simplify: iters left: 6 (12 enodes) 1540976136.288 * * [misc]simplify: iters left: 5 (18 enodes) 1540976136.295 * * [misc]simplify: iters left: 4 (24 enodes) 1540976136.303 * * [misc]simplify: iters left: 3 (25 enodes) 1540976136.312 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k))) 1540976136.312 * [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))))) 1540976136.312 * * * * [misc]progress: [ 43 / 77 ] simplifiying candidate # 1540976136.312 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) 1) 1540976136.313 * * [misc]simplify: iters left: 6 (9 enodes) 1540976136.317 * * [misc]simplify: iters left: 5 (16 enodes) 1540976136.324 * * [misc]simplify: iters left: 4 (24 enodes) 1540976136.331 * * [misc]simplify: iters left: 3 (26 enodes) 1540976136.338 * [exit]simplify: Simplified to (sqrt (* (* PI 2) n)) 1540976136.338 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) 1540976136.338 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)) 1540976136.339 * * [misc]simplify: iters left: 6 (11 enodes) 1540976136.344 * * [misc]simplify: iters left: 5 (17 enodes) 1540976136.350 * * [misc]simplify: iters left: 4 (23 enodes) 1540976136.357 * * [misc]simplify: iters left: 3 (24 enodes) 1540976136.364 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)) 1540976136.364 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)))) 1540976136.364 * * * * [misc]progress: [ 44 / 77 ] simplifiying candidate # 1540976136.365 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1540976136.366 * * [misc]simplify: iters left: 6 (11 enodes) 1540976136.370 * * [misc]simplify: iters left: 5 (15 enodes) 1540976136.376 * * [misc]simplify: iters left: 4 (18 enodes) 1540976136.383 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1540976136.383 * [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))))) 1540976136.383 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1540976136.387 * * [misc]simplify: iters left: 6 (11 enodes) 1540976136.391 * * [misc]simplify: iters left: 5 (14 enodes) 1540976136.397 * * [misc]simplify: iters left: 4 (17 enodes) 1540976136.403 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1540976136.403 * [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))))) 1540976136.403 * * * * [misc]progress: [ 45 / 77 ] simplifiying candidate # 1540976136.404 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1540976136.405 * * [misc]simplify: iters left: 6 (10 enodes) 1540976136.408 * * [misc]simplify: iters left: 5 (12 enodes) 1540976136.413 * * [misc]simplify: iters left: 4 (15 enodes) 1540976136.418 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1540976136.418 * [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))))) 1540976136.419 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1540976136.420 * * [misc]simplify: iters left: 6 (11 enodes) 1540976136.424 * * [misc]simplify: iters left: 5 (14 enodes) 1540976136.429 * * [misc]simplify: iters left: 4 (17 enodes) 1540976136.435 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1540976136.435 * [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))))) 1540976136.435 * * * * [misc]progress: [ 46 / 77 ] simplifiying candidate # 1540976136.436 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) 1) 1540976136.436 * * [misc]simplify: iters left: 6 (9 enodes) 1540976136.440 * * [misc]simplify: iters left: 5 (13 enodes) 1540976136.446 * * [misc]simplify: iters left: 4 (18 enodes) 1540976136.451 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1540976136.451 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1540976136.451 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)) 1540976136.452 * * [misc]simplify: iters left: 6 (10 enodes) 1540976136.456 * * [misc]simplify: iters left: 5 (13 enodes) 1540976136.461 * * [misc]simplify: iters left: 4 (16 enodes) 1540976136.466 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)) 1540976136.466 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1540976136.467 * * * * [misc]progress: [ 47 / 77 ] simplifiying candidate # 1540976136.467 * [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)))) 1540976136.468 * * [misc]simplify: iters left: 6 (16 enodes) 1540976136.472 * * [misc]simplify: iters left: 5 (28 enodes) 1540976136.478 * * [misc]simplify: iters left: 4 (46 enodes) 1540976136.486 * * [misc]simplify: iters left: 3 (50 enodes) 1540976136.493 * * [misc]simplify: iters left: 2 (53 enodes) 1540976136.505 * [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)))) 1540976136.505 * [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))))) 1540976136.505 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1540976136.506 * * [misc]simplify: iters left: 6 (14 enodes) 1540976136.509 * * [misc]simplify: iters left: 5 (20 enodes) 1540976136.513 * * [misc]simplify: iters left: 4 (29 enodes) 1540976136.517 * * [misc]simplify: iters left: 3 (30 enodes) 1540976136.522 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1540976136.523 * [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))))) 1540976136.523 * * * * [misc]progress: [ 48 / 77 ] simplifiying candidate # 1540976136.523 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) 1540976136.524 * * [misc]simplify: iters left: 6 (15 enodes) 1540976136.527 * * [misc]simplify: iters left: 5 (23 enodes) 1540976136.532 * * [misc]simplify: iters left: 4 (34 enodes) 1540976136.537 * * [misc]simplify: iters left: 3 (37 enodes) 1540976136.548 * [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)))))) 1540976136.548 * [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))))) 1540976136.549 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1540976136.550 * * [misc]simplify: iters left: 6 (14 enodes) 1540976136.556 * * [misc]simplify: iters left: 5 (20 enodes) 1540976136.563 * * [misc]simplify: iters left: 4 (29 enodes) 1540976136.572 * * [misc]simplify: iters left: 3 (30 enodes) 1540976136.581 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1540976136.581 * [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))))) 1540976136.581 * * * * [misc]progress: [ 49 / 77 ] simplifiying candidate # 1540976136.581 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1) 1540976136.585 * * [misc]simplify: iters left: 6 (14 enodes) 1540976136.592 * * [misc]simplify: iters left: 5 (24 enodes) 1540976136.602 * * [misc]simplify: iters left: 4 (39 enodes) 1540976136.614 * * [misc]simplify: iters left: 3 (54 enodes) 1540976136.631 * * [misc]simplify: iters left: 2 (80 enodes) 1540976136.651 * [exit]simplify: Simplified to (* (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))) 1540976136.652 * [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)))) 1540976136.652 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt k)) 1540976136.653 * * [misc]simplify: iters left: 6 (13 enodes) 1540976136.658 * * [misc]simplify: iters left: 5 (19 enodes) 1540976136.665 * * [misc]simplify: iters left: 4 (28 enodes) 1540976136.673 * * [misc]simplify: iters left: 3 (30 enodes) 1540976136.683 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt k)) 1540976136.683 * [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)))) 1540976136.683 * * * * [misc]progress: [ 50 / 77 ] simplifiying candidate # 1540976136.684 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1540976136.685 * * [misc]simplify: iters left: 6 (15 enodes) 1540976136.691 * * [misc]simplify: iters left: 5 (23 enodes) 1540976136.699 * * [misc]simplify: iters left: 4 (32 enodes) 1540976136.711 * * [misc]simplify: iters left: 3 (34 enodes) 1540976136.721 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1540976136.721 * [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))))) 1540976136.721 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1540976136.722 * * [misc]simplify: iters left: 6 (14 enodes) 1540976136.725 * * [misc]simplify: iters left: 5 (20 enodes) 1540976136.729 * * [misc]simplify: iters left: 4 (29 enodes) 1540976136.734 * * [misc]simplify: iters left: 3 (30 enodes) 1540976136.739 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1540976136.739 * [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))))) 1540976136.739 * * * * [misc]progress: [ 51 / 77 ] simplifiying candidate # 1540976136.740 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1540976136.741 * * [misc]simplify: iters left: 6 (14 enodes) 1540976136.744 * * [misc]simplify: iters left: 5 (20 enodes) 1540976136.748 * * [misc]simplify: iters left: 4 (29 enodes) 1540976136.752 * * [misc]simplify: iters left: 3 (30 enodes) 1540976136.757 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1540976136.757 * [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))))) 1540976136.757 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1540976136.758 * * [misc]simplify: iters left: 6 (14 enodes) 1540976136.761 * * [misc]simplify: iters left: 5 (20 enodes) 1540976136.765 * * [misc]simplify: iters left: 4 (29 enodes) 1540976136.771 * * [misc]simplify: iters left: 3 (30 enodes) 1540976136.777 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1540976136.777 * [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))))) 1540976136.777 * * * * [misc]progress: [ 52 / 77 ] simplifiying candidate # 1540976136.777 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1) 1540976136.778 * * [misc]simplify: iters left: 6 (13 enodes) 1540976136.781 * * [misc]simplify: iters left: 5 (21 enodes) 1540976136.788 * * [misc]simplify: iters left: 4 (32 enodes) 1540976136.792 * * [misc]simplify: iters left: 3 (33 enodes) 1540976136.797 * [exit]simplify: Simplified to (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) 1540976136.797 * [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)))) 1540976136.797 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt k)) 1540976136.798 * * [misc]simplify: iters left: 6 (13 enodes) 1540976136.801 * * [misc]simplify: iters left: 5 (19 enodes) 1540976136.804 * * [misc]simplify: iters left: 4 (28 enodes) 1540976136.809 * * [misc]simplify: iters left: 3 (30 enodes) 1540976136.814 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt k)) 1540976136.814 * [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)))) 1540976136.814 * * * * [misc]progress: [ 53 / 77 ] simplifiying candidate # 1540976136.814 * [enter]simplify: Simplifying (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1540976136.815 * * [misc]simplify: iters left: 6 (6 enodes) 1540976136.816 * * [misc]simplify: iters left: 5 (10 enodes) 1540976136.818 * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) 1540976136.818 * [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))))) 1540976136.818 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1540976136.819 * * [misc]simplify: iters left: 6 (13 enodes) 1540976136.821 * * [misc]simplify: iters left: 5 (19 enodes) 1540976136.825 * * [misc]simplify: iters left: 4 (28 enodes) 1540976136.830 * * [misc]simplify: iters left: 3 (30 enodes) 1540976136.834 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1540976136.835 * [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))))) 1540976136.835 * * * * [misc]progress: [ 54 / 77 ] simplifiying candidate # 1540976136.835 * [enter]simplify: Simplifying (/ 1 (sqrt (sqrt k))) 1540976136.835 * * [misc]simplify: iters left: 4 (5 enodes) 1540976136.836 * * [misc]simplify: iters left: 3 (7 enodes) 1540976136.837 * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt k))) 1540976136.837 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) 1540976136.837 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1540976136.838 * * [misc]simplify: iters left: 6 (13 enodes) 1540976136.841 * * [misc]simplify: iters left: 5 (19 enodes) 1540976136.845 * * [misc]simplify: iters left: 4 (28 enodes) 1540976136.850 * * [misc]simplify: iters left: 3 (30 enodes) 1540976136.856 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1540976136.856 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) 1540976136.856 * * * * [misc]progress: [ 55 / 77 ] simplifiying candidate # 1540976136.856 * [enter]simplify: Simplifying (/ 1 1) 1540976136.856 * * [misc]simplify: iters left: 2 (2 enodes) 1540976136.857 * * [misc]simplify: iters left: 1 (4 enodes) 1540976136.857 * [exit]simplify: Simplified to 1 1540976136.857 * [misc]simplify: Simplified (2 1) to (λ (k n) (* 1 (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))) 1540976136.857 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)) 1540976136.858 * * [misc]simplify: iters left: 6 (12 enodes) 1540976136.861 * * [misc]simplify: iters left: 5 (18 enodes) 1540976136.864 * * [misc]simplify: iters left: 4 (27 enodes) 1540976136.869 * * [misc]simplify: iters left: 3 (29 enodes) 1540976136.874 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k)) 1540976136.874 * [misc]simplify: Simplified (2 2) to (λ (k n) (* 1 (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k)))) 1540976136.874 * * * * [misc]progress: [ 56 / 77 ] simplifiying candidate # 1540976136.874 * * * * [misc]progress: [ 57 / 77 ] simplifiying candidate # 1540976136.874 * * * * [misc]progress: [ 58 / 77 ] simplifiying candidate # 1540976136.874 * * * * [misc]progress: [ 59 / 77 ] simplifiying candidate # 1540976136.874 * [enter]simplify: Simplifying (cbrt (sqrt k)) 1540976136.874 * * [misc]simplify: iters left: 2 (3 enodes) 1540976136.875 * [exit]simplify: Simplified to (cbrt (sqrt k)) 1540976136.875 * [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)))) 1540976136.875 * * * * [misc]progress: [ 60 / 77 ] simplifiying candidate # 1540976136.875 * [enter]simplify: Simplifying (sqrt (sqrt k)) 1540976136.875 * * [misc]simplify: iters left: 2 (3 enodes) 1540976136.876 * [exit]simplify: Simplified to (sqrt (sqrt k)) 1540976136.876 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k)))) 1540976136.876 * * * * [misc]progress: [ 61 / 77 ] simplifiying candidate # 1540976136.876 * [enter]simplify: Simplifying (sqrt k) 1540976136.876 * * [misc]simplify: iters left: 1 (2 enodes) 1540976136.877 * [exit]simplify: Simplified to (sqrt k) 1540976136.877 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) 1) (sqrt k))) 1540976136.877 * * * * [misc]progress: [ 62 / 77 ] simplifiying candidate # 1540976136.877 * [enter]simplify: Simplifying (pow (* PI (* n 2)) 1/2) 1540976136.877 * * [misc]simplify: iters left: 5 (7 enodes) 1540976136.879 * * [misc]simplify: iters left: 4 (12 enodes) 1540976136.881 * * [misc]simplify: iters left: 3 (18 enodes) 1540976136.885 * * [misc]simplify: iters left: 2 (20 enodes) 1540976136.892 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1540976136.892 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2)))))) 1540976136.892 * * * * [misc]progress: [ 63 / 77 ] simplifiying candidate # 1540976136.892 * [enter]simplify: Simplifying (pow (* PI (* n 2)) 1/2) 1540976136.893 * * [misc]simplify: iters left: 5 (7 enodes) 1540976136.896 * * [misc]simplify: iters left: 4 (12 enodes) 1540976136.901 * * [misc]simplify: iters left: 3 (18 enodes) 1540976136.907 * * [misc]simplify: iters left: 2 (20 enodes) 1540976136.913 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1540976136.913 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2)))))) 1540976136.914 * * * * [misc]progress: [ 64 / 77 ] simplifiying candidate # 1540976136.914 * [enter]simplify: Simplifying (pow PI (- 1/2 (/ k 2))) 1540976136.914 * * [misc]simplify: iters left: 5 (7 enodes) 1540976136.917 * * [misc]simplify: iters left: 4 (9 enodes) 1540976136.921 * * [misc]simplify: iters left: 3 (12 enodes) 1540976136.925 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1540976136.925 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (pow PI (- 1/2 (/ k 2))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2)))))) 1540976136.925 * * * * [misc]progress: [ 65 / 77 ] simplifiying candidate # 1540976136.925 * [enter]simplify: Simplifying (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1540976136.927 * * [misc]simplify: iters left: 6 (12 enodes) 1540976136.932 * * [misc]simplify: iters left: 5 (18 enodes) 1540976136.939 * * [misc]simplify: iters left: 4 (27 enodes) 1540976136.949 * * [misc]simplify: iters left: 3 (29 enodes) 1540976136.958 * [exit]simplify: Simplified to (* (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) 1540976136.958 * [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))))))) 1540976136.958 * * * * [misc]progress: [ 66 / 77 ] simplifiying candidate # 1540976136.958 * [enter]simplify: Simplifying (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1540976136.959 * * [misc]simplify: iters left: 6 (11 enodes) 1540976136.965 * * [misc]simplify: iters left: 5 (17 enodes) 1540976136.972 * * [misc]simplify: iters left: 4 (26 enodes) 1540976136.980 * * [misc]simplify: iters left: 3 (27 enodes) 1540976136.989 * [exit]simplify: Simplified to (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) 1540976136.989 * [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))))))) 1540976136.989 * * * * [misc]progress: [ 67 / 77 ] simplifiying candidate # 1540976136.989 * * * * [misc]progress: [ 68 / 77 ] simplifiying candidate # 1540976136.989 * [enter]simplify: Simplifying (pow (* PI (* n 2)) 1/2) 1540976136.990 * * [misc]simplify: iters left: 5 (7 enodes) 1540976136.993 * * [misc]simplify: iters left: 4 (12 enodes) 1540976136.999 * * [misc]simplify: iters left: 3 (18 enodes) 1540976137.005 * * [misc]simplify: iters left: 2 (20 enodes) 1540976137.012 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1540976137.012 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2))))) 1540976137.012 * * * * [misc]progress: [ 69 / 77 ] simplifiying candidate # 1540976137.012 * [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))))) 1540976137.016 * * [misc]simplify: iters left: 6 (37 enodes) 1540976137.043 * * [misc]simplify: iters left: 5 (105 enodes) 1540976137.088 * * [misc]simplify: iters left: 4 (339 enodes) 1540976137.639 * [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))))) 1540976137.640 * [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))) 1540976137.640 * * * * [misc]progress: [ 70 / 77 ] simplifiying candidate # 1540976137.640 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 1540976137.641 * * [misc]simplify: iters left: 6 (15 enodes) 1540976137.650 * * [misc]simplify: iters left: 5 (33 enodes) 1540976137.667 * * [misc]simplify: iters left: 4 (64 enodes) 1540976137.707 * * [misc]simplify: iters left: 3 (171 enodes) 1540976137.889 * [exit]simplify: Simplified to (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow n (- 1/2 (* 1/2 k)))) 1540976137.889 * [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))) 1540976137.889 * * * * [misc]progress: [ 71 / 77 ] simplifiying candidate # 1540976137.889 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 1540976137.891 * * [misc]simplify: iters left: 6 (15 enodes) 1540976137.896 * * [misc]simplify: iters left: 5 (30 enodes) 1540976137.905 * * [misc]simplify: iters left: 4 (65 enodes) 1540976137.939 * * [misc]simplify: iters left: 3 (200 enodes) 1540976138.223 * [exit]simplify: Simplified to (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))) 1540976138.223 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))) (sqrt k))) 1540976138.223 * * * * [misc]progress: [ 72 / 77 ] simplifiying candidate # 1540976138.224 * [enter]simplify: Simplifying (* 2 (* n PI)) 1540976138.224 * * [misc]simplify: iters left: 4 (5 enodes) 1540976138.227 * * [misc]simplify: iters left: 3 (9 enodes) 1540976138.231 * * [misc]simplify: iters left: 2 (15 enodes) 1540976138.236 * * [misc]simplify: iters left: 1 (17 enodes) 1540976138.242 * [exit]simplify: Simplified to (* (* PI n) 2) 1540976138.242 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt k))) 1540976138.242 * * * * [misc]progress: [ 73 / 77 ] simplifiying candidate # 1540976138.242 * [enter]simplify: Simplifying (* 2 (* n PI)) 1540976138.243 * * [misc]simplify: iters left: 4 (5 enodes) 1540976138.245 * * [misc]simplify: iters left: 3 (9 enodes) 1540976138.249 * * [misc]simplify: iters left: 2 (15 enodes) 1540976138.255 * * [misc]simplify: iters left: 1 (17 enodes) 1540976138.260 * [exit]simplify: Simplified to (* (* PI n) 2) 1540976138.260 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt k))) 1540976138.260 * * * * [misc]progress: [ 74 / 77 ] simplifiying candidate # 1540976138.261 * [enter]simplify: Simplifying (* 2 (* n PI)) 1540976138.261 * * [misc]simplify: iters left: 4 (5 enodes) 1540976138.264 * * [misc]simplify: iters left: 3 (9 enodes) 1540976138.267 * * [misc]simplify: iters left: 2 (15 enodes) 1540976138.270 * * [misc]simplify: iters left: 1 (17 enodes) 1540976138.273 * [exit]simplify: Simplified to (* (* PI n) 2) 1540976138.273 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt k))) 1540976138.273 * * * * [misc]progress: [ 75 / 77 ] simplifiying candidate # 1540976138.273 * [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)))))))))))))))))))))) 1540976138.273 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1540976138.273 * * * * [misc]progress: [ 76 / 77 ] simplifiying candidate # 1540976138.273 * [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)))))))) 1540976138.273 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1540976138.273 * * * * [misc]progress: [ 77 / 77 ] simplifiying candidate # 1540976138.273 * [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))))))))))) 1540976138.273 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1540976138.273 * * * [misc]progress: adding candidates to table 1540976140.077 * * [misc]progress: iteration 2 / 4 1540976140.077 * * * [misc]progress: picking best candidate 1540976140.152 * * * * [misc]pick: Picked # 1540976140.153 * * * [misc]progress: localizing error 1540976140.167 * * * [misc]progress: generating rewritten candidates 1540976140.167 * * * * [misc]progress: [ 1 / 4 ] rewriting at (2 2 2) 1540976140.206 * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 2 2 1) 1540976140.229 * * * * [misc]progress: [ 3 / 4 ] rewriting at (2) 1540976140.304 * * * * [misc]progress: [ 4 / 4 ] rewriting at (2 2) 1540976140.351 * * * [misc]progress: generating series expansions 1540976140.351 * * * * [misc]progress: [ 1 / 4 ] generating series at (2 2 2) 1540976140.351 * [misc]backup-simplify: Simplify (pow (* PI (* n 2)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 1540976140.352 * [misc]approximate: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 1540976140.352 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1540976140.352 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1540976140.352 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1540976140.352 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1540976140.352 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976140.352 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.352 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1540976140.352 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976140.352 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.352 * [misc]taylor: Taking taylor expansion of k in k 1540976140.352 * [misc]backup-simplify: Simplify 0 into 0 1540976140.352 * [misc]backup-simplify: Simplify 1 into 1 1540976140.352 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1540976140.352 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1540976140.352 * [misc]taylor: Taking taylor expansion of 2 in k 1540976140.352 * [misc]backup-simplify: Simplify 2 into 2 1540976140.352 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1540976140.352 * [misc]taylor: Taking taylor expansion of n in k 1540976140.352 * [misc]backup-simplify: Simplify n into n 1540976140.352 * [misc]taylor: Taking taylor expansion of PI in k 1540976140.352 * [misc]backup-simplify: Simplify PI into PI 1540976140.352 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1540976140.352 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1540976140.353 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1540976140.353 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1540976140.353 * [misc]backup-simplify: Simplify (- 0) into 0 1540976140.353 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1540976140.353 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1540976140.354 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1540976140.354 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1540976140.354 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1540976140.354 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1540976140.354 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1540976140.354 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976140.354 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.354 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1540976140.354 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976140.354 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.354 * [misc]taylor: Taking taylor expansion of k in n 1540976140.354 * [misc]backup-simplify: Simplify k into k 1540976140.354 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1540976140.354 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1540976140.354 * [misc]taylor: Taking taylor expansion of 2 in n 1540976140.354 * [misc]backup-simplify: Simplify 2 into 2 1540976140.354 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1540976140.354 * [misc]taylor: Taking taylor expansion of n in n 1540976140.354 * [misc]backup-simplify: Simplify 0 into 0 1540976140.354 * [misc]backup-simplify: Simplify 1 into 1 1540976140.354 * [misc]taylor: Taking taylor expansion of PI in n 1540976140.354 * [misc]backup-simplify: Simplify PI into PI 1540976140.355 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1540976140.355 * [misc]backup-simplify: Simplify (* 2 0) into 0 1540976140.355 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1540976140.356 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1540976140.357 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1540976140.357 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1540976140.357 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1540976140.357 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1540976140.358 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1540976140.358 * [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)))) 1540976140.359 * [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))))) 1540976140.359 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1540976140.360 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1540976140.360 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1540976140.360 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1540976140.360 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976140.360 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.360 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1540976140.360 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976140.360 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.360 * [misc]taylor: Taking taylor expansion of k in n 1540976140.360 * [misc]backup-simplify: Simplify k into k 1540976140.360 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1540976140.360 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1540976140.360 * [misc]taylor: Taking taylor expansion of 2 in n 1540976140.360 * [misc]backup-simplify: Simplify 2 into 2 1540976140.360 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1540976140.360 * [misc]taylor: Taking taylor expansion of n in n 1540976140.360 * [misc]backup-simplify: Simplify 0 into 0 1540976140.360 * [misc]backup-simplify: Simplify 1 into 1 1540976140.360 * [misc]taylor: Taking taylor expansion of PI in n 1540976140.360 * [misc]backup-simplify: Simplify PI into PI 1540976140.361 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1540976140.361 * [misc]backup-simplify: Simplify (* 2 0) into 0 1540976140.361 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1540976140.362 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1540976140.363 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1540976140.363 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1540976140.363 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1540976140.363 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1540976140.364 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1540976140.365 * [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)))) 1540976140.365 * [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))))) 1540976140.365 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1540976140.365 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1540976140.365 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1540976140.366 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976140.366 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.366 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1540976140.366 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976140.366 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.366 * [misc]taylor: Taking taylor expansion of k in k 1540976140.366 * [misc]backup-simplify: Simplify 0 into 0 1540976140.366 * [misc]backup-simplify: Simplify 1 into 1 1540976140.366 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1540976140.366 * [misc]taylor: Taking taylor expansion of (log n) in k 1540976140.366 * [misc]taylor: Taking taylor expansion of n in k 1540976140.366 * [misc]backup-simplify: Simplify n into n 1540976140.366 * [misc]backup-simplify: Simplify (log n) into (log n) 1540976140.366 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1540976140.366 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1540976140.366 * [misc]taylor: Taking taylor expansion of 2 in k 1540976140.366 * [misc]backup-simplify: Simplify 2 into 2 1540976140.366 * [misc]taylor: Taking taylor expansion of PI in k 1540976140.366 * [misc]backup-simplify: Simplify PI into PI 1540976140.366 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1540976140.367 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1540976140.367 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1540976140.367 * [misc]backup-simplify: Simplify (- 0) into 0 1540976140.367 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1540976140.368 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1540976140.369 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1540976140.370 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1540976140.370 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1540976140.371 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1540976140.373 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1540976140.376 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1540976140.377 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1540976140.377 * [misc]backup-simplify: Simplify (- 0) into 0 1540976140.377 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976140.378 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1540976140.378 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1540976140.380 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1540976140.380 * [misc]taylor: Taking taylor expansion of 0 in k 1540976140.380 * [misc]backup-simplify: Simplify 0 into 0 1540976140.380 * [misc]backup-simplify: Simplify 0 into 0 1540976140.381 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1540976140.382 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1540976140.385 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1540976140.385 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976140.386 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1540976140.386 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1540976140.386 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1540976140.387 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1540976140.389 * [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))))))) 1540976140.390 * [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))))))) 1540976140.392 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1540976140.394 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1540976140.400 * [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 1540976140.400 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1540976140.400 * [misc]backup-simplify: Simplify (- 0) into 0 1540976140.400 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976140.401 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1540976140.402 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1540976140.405 * [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 1540976140.405 * [misc]taylor: Taking taylor expansion of 0 in k 1540976140.405 * [misc]backup-simplify: Simplify 0 into 0 1540976140.405 * [misc]backup-simplify: Simplify 0 into 0 1540976140.405 * [misc]backup-simplify: Simplify 0 into 0 1540976140.411 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1540976140.413 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1540976140.419 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1540976140.419 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976140.419 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1540976140.419 * [misc]backup-simplify: Simplify (- 0) into 0 1540976140.419 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976140.420 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1540976140.424 * [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))))) 1540976140.427 * [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))))) 1540976140.435 * [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))))) 1540976140.435 * [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)))) 1540976140.435 * [misc]approximate: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 1540976140.435 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1540976140.436 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1540976140.436 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1540976140.436 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1540976140.436 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976140.436 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.436 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1540976140.436 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976140.436 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.436 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1540976140.436 * [misc]taylor: Taking taylor expansion of k in k 1540976140.436 * [misc]backup-simplify: Simplify 0 into 0 1540976140.436 * [misc]backup-simplify: Simplify 1 into 1 1540976140.436 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1540976140.436 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1540976140.436 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1540976140.436 * [misc]taylor: Taking taylor expansion of 2 in k 1540976140.436 * [misc]backup-simplify: Simplify 2 into 2 1540976140.436 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1540976140.436 * [misc]taylor: Taking taylor expansion of PI in k 1540976140.436 * [misc]backup-simplify: Simplify PI into PI 1540976140.436 * [misc]taylor: Taking taylor expansion of n in k 1540976140.436 * [misc]backup-simplify: Simplify n into n 1540976140.437 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1540976140.437 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1540976140.437 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1540976140.437 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1540976140.437 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1540976140.437 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1540976140.438 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1540976140.438 * [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)))) 1540976140.438 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1540976140.438 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1540976140.438 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1540976140.438 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1540976140.438 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976140.438 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.438 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1540976140.438 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976140.438 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.438 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1540976140.438 * [misc]taylor: Taking taylor expansion of k in n 1540976140.438 * [misc]backup-simplify: Simplify k into k 1540976140.438 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1540976140.438 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1540976140.439 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1540976140.439 * [misc]taylor: Taking taylor expansion of 2 in n 1540976140.439 * [misc]backup-simplify: Simplify 2 into 2 1540976140.439 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1540976140.439 * [misc]taylor: Taking taylor expansion of PI in n 1540976140.439 * [misc]backup-simplify: Simplify PI into PI 1540976140.439 * [misc]taylor: Taking taylor expansion of n in n 1540976140.439 * [misc]backup-simplify: Simplify 0 into 0 1540976140.439 * [misc]backup-simplify: Simplify 1 into 1 1540976140.439 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1540976140.440 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1540976140.440 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1540976140.440 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1540976140.441 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1540976140.441 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1540976140.441 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1540976140.442 * [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))) 1540976140.443 * [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)))) 1540976140.443 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1540976140.443 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1540976140.443 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1540976140.443 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1540976140.443 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976140.443 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.443 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1540976140.443 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976140.443 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.443 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1540976140.443 * [misc]taylor: Taking taylor expansion of k in n 1540976140.443 * [misc]backup-simplify: Simplify k into k 1540976140.443 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1540976140.443 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1540976140.443 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1540976140.443 * [misc]taylor: Taking taylor expansion of 2 in n 1540976140.443 * [misc]backup-simplify: Simplify 2 into 2 1540976140.444 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1540976140.444 * [misc]taylor: Taking taylor expansion of PI in n 1540976140.444 * [misc]backup-simplify: Simplify PI into PI 1540976140.444 * [misc]taylor: Taking taylor expansion of n in n 1540976140.444 * [misc]backup-simplify: Simplify 0 into 0 1540976140.444 * [misc]backup-simplify: Simplify 1 into 1 1540976140.444 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1540976140.444 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1540976140.445 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1540976140.445 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1540976140.445 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1540976140.445 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1540976140.446 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1540976140.447 * [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))) 1540976140.447 * [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)))) 1540976140.448 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1540976140.448 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1540976140.448 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1540976140.448 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976140.448 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.448 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1540976140.448 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976140.448 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.448 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1540976140.448 * [misc]taylor: Taking taylor expansion of k in k 1540976140.448 * [misc]backup-simplify: Simplify 0 into 0 1540976140.448 * [misc]backup-simplify: Simplify 1 into 1 1540976140.448 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1540976140.448 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1540976140.448 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1540976140.448 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1540976140.448 * [misc]taylor: Taking taylor expansion of 2 in k 1540976140.448 * [misc]backup-simplify: Simplify 2 into 2 1540976140.448 * [misc]taylor: Taking taylor expansion of PI in k 1540976140.448 * [misc]backup-simplify: Simplify PI into PI 1540976140.449 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1540976140.449 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1540976140.449 * [misc]taylor: Taking taylor expansion of (log n) in k 1540976140.449 * [misc]taylor: Taking taylor expansion of n in k 1540976140.449 * [misc]backup-simplify: Simplify n into n 1540976140.450 * [misc]backup-simplify: Simplify (log n) into (log n) 1540976140.450 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1540976140.450 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1540976140.450 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1540976140.450 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1540976140.451 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1540976140.451 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1540976140.452 * [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)))) 1540976140.453 * [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)))) 1540976140.454 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1540976140.455 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1540976140.458 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1540976140.458 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1540976140.459 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1540976140.459 * [misc]backup-simplify: Simplify (- 0) into 0 1540976140.459 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976140.460 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1540976140.461 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1540976140.463 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1540976140.463 * [misc]taylor: Taking taylor expansion of 0 in k 1540976140.463 * [misc]backup-simplify: Simplify 0 into 0 1540976140.463 * [misc]backup-simplify: Simplify 0 into 0 1540976140.463 * [misc]backup-simplify: Simplify 0 into 0 1540976140.464 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976140.465 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1540976140.468 * [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 1540976140.469 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1540976140.469 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1540976140.469 * [misc]backup-simplify: Simplify (- 0) into 0 1540976140.469 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976140.469 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1540976140.470 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1540976140.472 * [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 1540976140.472 * [misc]taylor: Taking taylor expansion of 0 in k 1540976140.472 * [misc]backup-simplify: Simplify 0 into 0 1540976140.472 * [misc]backup-simplify: Simplify 0 into 0 1540976140.472 * [misc]backup-simplify: Simplify 0 into 0 1540976140.472 * [misc]backup-simplify: Simplify 0 into 0 1540976140.473 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976140.474 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1540976140.479 * [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 1540976140.479 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1540976140.480 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1540976140.480 * [misc]backup-simplify: Simplify (- 0) into 0 1540976140.480 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976140.480 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1540976140.481 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1540976140.483 * [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 1540976140.483 * [misc]taylor: Taking taylor expansion of 0 in k 1540976140.483 * [misc]backup-simplify: Simplify 0 into 0 1540976140.483 * [misc]backup-simplify: Simplify 0 into 0 1540976140.484 * [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))))) 1540976140.484 * [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)) 1540976140.484 * [misc]approximate: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 1540976140.484 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1540976140.484 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1540976140.484 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1540976140.484 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1540976140.484 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1540976140.484 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976140.484 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.484 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1540976140.484 * [misc]taylor: Taking taylor expansion of k in k 1540976140.484 * [misc]backup-simplify: Simplify 0 into 0 1540976140.484 * [misc]backup-simplify: Simplify 1 into 1 1540976140.485 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1540976140.485 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976140.485 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.485 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1540976140.485 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1540976140.485 * [misc]taylor: Taking taylor expansion of -2 in k 1540976140.485 * [misc]backup-simplify: Simplify -2 into -2 1540976140.485 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1540976140.485 * [misc]taylor: Taking taylor expansion of PI in k 1540976140.485 * [misc]backup-simplify: Simplify PI into PI 1540976140.485 * [misc]taylor: Taking taylor expansion of n in k 1540976140.485 * [misc]backup-simplify: Simplify n into n 1540976140.485 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1540976140.485 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1540976140.485 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1540976140.485 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1540976140.485 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1540976140.485 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1540976140.486 * [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))) 1540976140.486 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1540976140.486 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1540976140.486 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1540976140.486 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1540976140.486 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1540976140.486 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976140.486 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.486 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1540976140.486 * [misc]taylor: Taking taylor expansion of k in n 1540976140.486 * [misc]backup-simplify: Simplify k into k 1540976140.486 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1540976140.486 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976140.486 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.486 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1540976140.486 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1540976140.486 * [misc]taylor: Taking taylor expansion of -2 in n 1540976140.486 * [misc]backup-simplify: Simplify -2 into -2 1540976140.486 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1540976140.486 * [misc]taylor: Taking taylor expansion of PI in n 1540976140.486 * [misc]backup-simplify: Simplify PI into PI 1540976140.486 * [misc]taylor: Taking taylor expansion of n in n 1540976140.486 * [misc]backup-simplify: Simplify 0 into 0 1540976140.486 * [misc]backup-simplify: Simplify 1 into 1 1540976140.486 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1540976140.486 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1540976140.487 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1540976140.487 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1540976140.487 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1540976140.487 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1540976140.488 * [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))) 1540976140.488 * [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)))) 1540976140.488 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1540976140.488 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1540976140.488 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1540976140.488 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1540976140.488 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1540976140.488 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976140.488 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.488 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1540976140.488 * [misc]taylor: Taking taylor expansion of k in n 1540976140.488 * [misc]backup-simplify: Simplify k into k 1540976140.488 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1540976140.488 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976140.489 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.489 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1540976140.489 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1540976140.489 * [misc]taylor: Taking taylor expansion of -2 in n 1540976140.489 * [misc]backup-simplify: Simplify -2 into -2 1540976140.489 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1540976140.489 * [misc]taylor: Taking taylor expansion of PI in n 1540976140.489 * [misc]backup-simplify: Simplify PI into PI 1540976140.489 * [misc]taylor: Taking taylor expansion of n in n 1540976140.489 * [misc]backup-simplify: Simplify 0 into 0 1540976140.489 * [misc]backup-simplify: Simplify 1 into 1 1540976140.489 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1540976140.489 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1540976140.489 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1540976140.490 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1540976140.490 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1540976140.490 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1540976140.491 * [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))) 1540976140.491 * [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)))) 1540976140.491 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1540976140.491 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1540976140.491 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1540976140.491 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1540976140.491 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976140.491 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.491 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1540976140.491 * [misc]taylor: Taking taylor expansion of k in k 1540976140.491 * [misc]backup-simplify: Simplify 0 into 0 1540976140.491 * [misc]backup-simplify: Simplify 1 into 1 1540976140.491 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1540976140.491 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976140.491 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.491 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1540976140.491 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1540976140.491 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1540976140.491 * [misc]taylor: Taking taylor expansion of -2 in k 1540976140.491 * [misc]backup-simplify: Simplify -2 into -2 1540976140.491 * [misc]taylor: Taking taylor expansion of PI in k 1540976140.492 * [misc]backup-simplify: Simplify PI into PI 1540976140.492 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1540976140.492 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1540976140.492 * [misc]taylor: Taking taylor expansion of (log n) in k 1540976140.492 * [misc]taylor: Taking taylor expansion of n in k 1540976140.492 * [misc]backup-simplify: Simplify n into n 1540976140.492 * [misc]backup-simplify: Simplify (log n) into (log n) 1540976140.492 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1540976140.492 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1540976140.492 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1540976140.493 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1540976140.493 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1540976140.494 * [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)))) 1540976140.494 * [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)))) 1540976140.495 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1540976140.495 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1540976140.497 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1540976140.497 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1540976140.497 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1540976140.497 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976140.498 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1540976140.498 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1540976140.500 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1540976140.500 * [misc]taylor: Taking taylor expansion of 0 in k 1540976140.500 * [misc]backup-simplify: Simplify 0 into 0 1540976140.500 * [misc]backup-simplify: Simplify 0 into 0 1540976140.500 * [misc]backup-simplify: Simplify 0 into 0 1540976140.501 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976140.502 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1540976140.506 * [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 1540976140.506 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1540976140.507 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1540976140.507 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976140.507 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1540976140.508 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1540976140.509 * [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 1540976140.509 * [misc]taylor: Taking taylor expansion of 0 in k 1540976140.509 * [misc]backup-simplify: Simplify 0 into 0 1540976140.509 * [misc]backup-simplify: Simplify 0 into 0 1540976140.509 * [misc]backup-simplify: Simplify 0 into 0 1540976140.509 * [misc]backup-simplify: Simplify 0 into 0 1540976140.510 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976140.511 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1540976140.517 * [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 1540976140.517 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1540976140.517 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1540976140.517 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976140.518 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1540976140.519 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 1540976140.521 * [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 1540976140.521 * [misc]taylor: Taking taylor expansion of 0 in k 1540976140.521 * [misc]backup-simplify: Simplify 0 into 0 1540976140.521 * [misc]backup-simplify: Simplify 0 into 0 1540976140.521 * [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))))) 1540976140.521 * * * * [misc]progress: [ 2 / 4 ] generating series at (2 2 2 1) 1540976140.523 * [misc]backup-simplify: Simplify (* PI (* n 2)) into (* 2 (* n PI)) 1540976140.523 * [misc]approximate: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1540976140.523 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1540976140.523 * [misc]taylor: Taking taylor expansion of 2 in n 1540976140.523 * [misc]backup-simplify: Simplify 2 into 2 1540976140.523 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1540976140.523 * [misc]taylor: Taking taylor expansion of n in n 1540976140.523 * [misc]backup-simplify: Simplify 0 into 0 1540976140.523 * [misc]backup-simplify: Simplify 1 into 1 1540976140.524 * [misc]taylor: Taking taylor expansion of PI in n 1540976140.524 * [misc]backup-simplify: Simplify PI into PI 1540976140.524 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1540976140.524 * [misc]taylor: Taking taylor expansion of 2 in n 1540976140.524 * [misc]backup-simplify: Simplify 2 into 2 1540976140.524 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1540976140.524 * [misc]taylor: Taking taylor expansion of n in n 1540976140.524 * [misc]backup-simplify: Simplify 0 into 0 1540976140.524 * [misc]backup-simplify: Simplify 1 into 1 1540976140.524 * [misc]taylor: Taking taylor expansion of PI in n 1540976140.524 * [misc]backup-simplify: Simplify PI into PI 1540976140.524 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1540976140.524 * [misc]backup-simplify: Simplify (* 2 0) into 0 1540976140.524 * [misc]backup-simplify: Simplify 0 into 0 1540976140.525 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1540976140.525 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1540976140.526 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1540976140.526 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1540976140.527 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1540976140.527 * [misc]backup-simplify: Simplify 0 into 0 1540976140.528 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1540976140.530 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1540976140.530 * [misc]backup-simplify: Simplify 0 into 0 1540976140.532 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1540976140.534 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1540976140.535 * [misc]backup-simplify: Simplify 0 into 0 1540976140.537 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1540976140.540 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1540976140.540 * [misc]backup-simplify: Simplify 0 into 0 1540976140.544 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1540976140.547 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1540976140.547 * [misc]backup-simplify: Simplify 0 into 0 1540976140.551 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1540976140.556 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1540976140.556 * [misc]backup-simplify: Simplify 0 into 0 1540976140.556 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1540976140.556 * [misc]backup-simplify: Simplify (* PI (* (/ 1 n) 2)) into (* 2 (/ PI n)) 1540976140.556 * [misc]approximate: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1540976140.556 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1540976140.556 * [misc]taylor: Taking taylor expansion of 2 in n 1540976140.556 * [misc]backup-simplify: Simplify 2 into 2 1540976140.556 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1540976140.556 * [misc]taylor: Taking taylor expansion of PI in n 1540976140.556 * [misc]backup-simplify: Simplify PI into PI 1540976140.556 * [misc]taylor: Taking taylor expansion of n in n 1540976140.556 * [misc]backup-simplify: Simplify 0 into 0 1540976140.556 * [misc]backup-simplify: Simplify 1 into 1 1540976140.557 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1540976140.557 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1540976140.557 * [misc]taylor: Taking taylor expansion of 2 in n 1540976140.557 * [misc]backup-simplify: Simplify 2 into 2 1540976140.557 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1540976140.557 * [misc]taylor: Taking taylor expansion of PI in n 1540976140.557 * [misc]backup-simplify: Simplify PI into PI 1540976140.557 * [misc]taylor: Taking taylor expansion of n in n 1540976140.557 * [misc]backup-simplify: Simplify 0 into 0 1540976140.557 * [misc]backup-simplify: Simplify 1 into 1 1540976140.558 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1540976140.558 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1540976140.558 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1540976140.559 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1540976140.560 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1540976140.560 * [misc]backup-simplify: Simplify 0 into 0 1540976140.561 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976140.563 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1540976140.563 * [misc]backup-simplify: Simplify 0 into 0 1540976140.564 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976140.565 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1540976140.565 * [misc]backup-simplify: Simplify 0 into 0 1540976140.566 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976140.568 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1540976140.568 * [misc]backup-simplify: Simplify 0 into 0 1540976140.570 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976140.573 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1540976140.573 * [misc]backup-simplify: Simplify 0 into 0 1540976140.576 * [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 1540976140.580 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1540976140.580 * [misc]backup-simplify: Simplify 0 into 0 1540976140.580 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 1540976140.580 * [misc]backup-simplify: Simplify (* PI (* (/ 1 (- n)) 2)) into (* -2 (/ PI n)) 1540976140.580 * [misc]approximate: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1540976140.580 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1540976140.580 * [misc]taylor: Taking taylor expansion of -2 in n 1540976140.580 * [misc]backup-simplify: Simplify -2 into -2 1540976140.580 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1540976140.581 * [misc]taylor: Taking taylor expansion of PI in n 1540976140.581 * [misc]backup-simplify: Simplify PI into PI 1540976140.581 * [misc]taylor: Taking taylor expansion of n in n 1540976140.581 * [misc]backup-simplify: Simplify 0 into 0 1540976140.581 * [misc]backup-simplify: Simplify 1 into 1 1540976140.581 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1540976140.581 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1540976140.581 * [misc]taylor: Taking taylor expansion of -2 in n 1540976140.581 * [misc]backup-simplify: Simplify -2 into -2 1540976140.581 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1540976140.581 * [misc]taylor: Taking taylor expansion of PI in n 1540976140.581 * [misc]backup-simplify: Simplify PI into PI 1540976140.581 * [misc]taylor: Taking taylor expansion of n in n 1540976140.581 * [misc]backup-simplify: Simplify 0 into 0 1540976140.581 * [misc]backup-simplify: Simplify 1 into 1 1540976140.582 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1540976140.582 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1540976140.583 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1540976140.584 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1540976140.584 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1540976140.584 * [misc]backup-simplify: Simplify 0 into 0 1540976140.586 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976140.587 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1540976140.587 * [misc]backup-simplify: Simplify 0 into 0 1540976140.589 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976140.591 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1540976140.591 * [misc]backup-simplify: Simplify 0 into 0 1540976140.593 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976140.595 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1540976140.595 * [misc]backup-simplify: Simplify 0 into 0 1540976140.597 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976140.600 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1540976140.600 * [misc]backup-simplify: Simplify 0 into 0 1540976140.603 * [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 1540976140.606 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1540976140.607 * [misc]backup-simplify: Simplify 0 into 0 1540976140.607 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 1540976140.607 * * * * [misc]progress: [ 3 / 4 ] generating series at (2) 1540976140.608 * [misc]backup-simplify: Simplify (/ 1 (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) into (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) 1540976140.608 * [misc]approximate: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (k n) around 0 1540976140.608 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 1540976140.608 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1540976140.608 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1540976140.608 * [misc]taylor: Taking taylor expansion of k in n 1540976140.608 * [misc]backup-simplify: Simplify k into k 1540976140.608 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1540976140.608 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1540976140.608 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1540976140.608 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1540976140.608 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1540976140.608 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1540976140.609 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1540976140.609 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1540976140.609 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976140.609 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.609 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1540976140.609 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976140.609 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.609 * [misc]taylor: Taking taylor expansion of k in n 1540976140.609 * [misc]backup-simplify: Simplify k into k 1540976140.609 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1540976140.609 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1540976140.609 * [misc]taylor: Taking taylor expansion of 2 in n 1540976140.609 * [misc]backup-simplify: Simplify 2 into 2 1540976140.609 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1540976140.609 * [misc]taylor: Taking taylor expansion of n in n 1540976140.609 * [misc]backup-simplify: Simplify 0 into 0 1540976140.609 * [misc]backup-simplify: Simplify 1 into 1 1540976140.609 * [misc]taylor: Taking taylor expansion of PI in n 1540976140.609 * [misc]backup-simplify: Simplify PI into PI 1540976140.609 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1540976140.610 * [misc]backup-simplify: Simplify (* 2 0) into 0 1540976140.610 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1540976140.611 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1540976140.612 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1540976140.612 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1540976140.612 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1540976140.612 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1540976140.613 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1540976140.614 * [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)))) 1540976140.614 * [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))))) 1540976140.614 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 1540976140.614 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1540976140.614 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1540976140.614 * [misc]taylor: Taking taylor expansion of k in k 1540976140.614 * [misc]backup-simplify: Simplify 0 into 0 1540976140.615 * [misc]backup-simplify: Simplify 1 into 1 1540976140.615 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1540976140.615 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1540976140.615 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1540976140.615 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1540976140.615 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1540976140.615 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1540976140.615 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1540976140.616 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976140.616 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.616 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1540976140.616 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976140.616 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.616 * [misc]taylor: Taking taylor expansion of k in k 1540976140.616 * [misc]backup-simplify: Simplify 0 into 0 1540976140.616 * [misc]backup-simplify: Simplify 1 into 1 1540976140.616 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1540976140.616 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1540976140.616 * [misc]taylor: Taking taylor expansion of 2 in k 1540976140.616 * [misc]backup-simplify: Simplify 2 into 2 1540976140.616 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1540976140.616 * [misc]taylor: Taking taylor expansion of n in k 1540976140.616 * [misc]backup-simplify: Simplify n into n 1540976140.616 * [misc]taylor: Taking taylor expansion of PI in k 1540976140.616 * [misc]backup-simplify: Simplify PI into PI 1540976140.616 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1540976140.616 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1540976140.616 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1540976140.617 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1540976140.617 * [misc]backup-simplify: Simplify (- 0) into 0 1540976140.617 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1540976140.617 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1540976140.617 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1540976140.617 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 1540976140.617 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1540976140.618 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1540976140.618 * [misc]taylor: Taking taylor expansion of k in k 1540976140.618 * [misc]backup-simplify: Simplify 0 into 0 1540976140.618 * [misc]backup-simplify: Simplify 1 into 1 1540976140.618 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1540976140.618 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1540976140.618 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1540976140.618 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1540976140.619 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1540976140.619 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1540976140.619 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1540976140.619 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976140.619 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.619 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1540976140.619 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976140.619 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.619 * [misc]taylor: Taking taylor expansion of k in k 1540976140.619 * [misc]backup-simplify: Simplify 0 into 0 1540976140.619 * [misc]backup-simplify: Simplify 1 into 1 1540976140.619 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1540976140.619 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1540976140.619 * [misc]taylor: Taking taylor expansion of 2 in k 1540976140.619 * [misc]backup-simplify: Simplify 2 into 2 1540976140.619 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1540976140.619 * [misc]taylor: Taking taylor expansion of n in k 1540976140.619 * [misc]backup-simplify: Simplify n into n 1540976140.619 * [misc]taylor: Taking taylor expansion of PI in k 1540976140.619 * [misc]backup-simplify: Simplify PI into PI 1540976140.619 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1540976140.619 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1540976140.620 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1540976140.620 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1540976140.620 * [misc]backup-simplify: Simplify (- 0) into 0 1540976140.620 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1540976140.620 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1540976140.621 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1540976140.621 * [misc]backup-simplify: Simplify (* 0 (pow (* 2 (* n PI)) 1/2)) into 0 1540976140.621 * [misc]taylor: Taking taylor expansion of 0 in n 1540976140.621 * [misc]backup-simplify: Simplify 0 into 0 1540976140.621 * [misc]backup-simplify: Simplify 0 into 0 1540976140.622 * [misc]backup-simplify: Simplify (+ (* n 0) (* 0 PI)) into 0 1540976140.622 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0 1540976140.623 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 1540976140.624 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1540976140.624 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1540976140.624 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1540976140.624 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI))))) 1540976140.626 * [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))))) 1540976140.627 * [misc]backup-simplify: Simplify (+ (* 0 (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI)))))) (* +nan.0 (pow (* 2 (* n PI)) 1/2))) into (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) 1540976140.627 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 1540976140.627 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 1540976140.627 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1540976140.627 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1540976140.627 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1540976140.627 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1540976140.627 * [misc]taylor: Taking taylor expansion of 2 in n 1540976140.627 * [misc]backup-simplify: Simplify 2 into 2 1540976140.627 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1540976140.628 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1540976140.628 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1540976140.628 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1540976140.628 * [misc]taylor: Taking taylor expansion of n in n 1540976140.628 * [misc]backup-simplify: Simplify 0 into 0 1540976140.628 * [misc]backup-simplify: Simplify 1 into 1 1540976140.628 * [misc]taylor: Taking taylor expansion of PI in n 1540976140.628 * [misc]backup-simplify: Simplify PI into PI 1540976140.628 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1540976140.629 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1540976140.629 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1540976140.629 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1540976140.630 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1540976140.630 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1540976140.630 * [misc]backup-simplify: Simplify (- 0) into 0 1540976140.630 * [misc]backup-simplify: Simplify 0 into 0 1540976140.630 * [misc]backup-simplify: Simplify 0 into 0 1540976140.631 * [misc]backup-simplify: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 1540976140.631 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 1540976140.634 * [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 1540976140.634 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1540976140.634 * [misc]backup-simplify: Simplify (- 0) into 0 1540976140.634 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976140.635 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0 1540976140.637 * [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))) 1540976140.638 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1540976140.639 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1540976140.641 * [misc]backup-simplify: Simplify (+ (* 0 (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2)))) (+ (* +nan.0 (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI)))))) (* +nan.0 (pow (* 2 (* n PI)) 1/2)))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) 1540976140.641 * [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 1540976140.641 * [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 1540976140.641 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n 1540976140.641 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1540976140.641 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1540976140.641 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n 1540976140.641 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n 1540976140.641 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1540976140.641 * [misc]taylor: Taking taylor expansion of 2 in n 1540976140.641 * [misc]backup-simplify: Simplify 2 into 2 1540976140.641 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1540976140.642 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1540976140.642 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1540976140.642 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1540976140.642 * [misc]taylor: Taking taylor expansion of 2 in n 1540976140.642 * [misc]backup-simplify: Simplify 2 into 2 1540976140.642 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1540976140.642 * [misc]taylor: Taking taylor expansion of n in n 1540976140.642 * [misc]backup-simplify: Simplify 0 into 0 1540976140.642 * [misc]backup-simplify: Simplify 1 into 1 1540976140.642 * [misc]taylor: Taking taylor expansion of PI in n 1540976140.642 * [misc]backup-simplify: Simplify PI into PI 1540976140.642 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1540976140.642 * [misc]backup-simplify: Simplify (* 2 0) into 0 1540976140.643 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1540976140.644 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1540976140.644 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1540976140.644 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1540976140.645 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1540976140.645 * [misc]taylor: Taking taylor expansion of n in n 1540976140.645 * [misc]backup-simplify: Simplify 0 into 0 1540976140.645 * [misc]backup-simplify: Simplify 1 into 1 1540976140.645 * [misc]taylor: Taking taylor expansion of PI in n 1540976140.645 * [misc]backup-simplify: Simplify PI into PI 1540976140.645 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1540976140.646 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1540976140.646 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1540976140.646 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1540976140.646 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 1540976140.646 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 1540976140.647 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1540976140.647 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1540976140.647 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1540976140.647 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1540976140.647 * [misc]taylor: Taking taylor expansion of 2 in n 1540976140.647 * [misc]backup-simplify: Simplify 2 into 2 1540976140.647 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1540976140.647 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1540976140.647 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1540976140.647 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1540976140.647 * [misc]taylor: Taking taylor expansion of n in n 1540976140.647 * [misc]backup-simplify: Simplify 0 into 0 1540976140.647 * [misc]backup-simplify: Simplify 1 into 1 1540976140.647 * [misc]taylor: Taking taylor expansion of PI in n 1540976140.647 * [misc]backup-simplify: Simplify PI into PI 1540976140.648 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1540976140.648 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1540976140.649 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1540976140.649 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1540976140.650 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1540976140.651 * [misc]backup-simplify: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 1540976140.652 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0 1540976140.652 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1540976140.652 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1540976140.652 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1540976140.652 * [misc]backup-simplify: Simplify (- 0) into 0 1540976140.652 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976140.652 * [misc]backup-simplify: Simplify (- 0) into 0 1540976140.653 * [misc]backup-simplify: Simplify 0 into 0 1540976140.654 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1540976140.656 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1540976140.657 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 1540976140.658 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI))) 1540976140.659 * [misc]backup-simplify: Simplify 0 into 0 1540976140.660 * [misc]backup-simplify: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1540976140.660 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 1540976140.665 * [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 1540976140.665 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1540976140.666 * [misc]backup-simplify: Simplify (- 0) into 0 1540976140.666 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976140.669 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log (* 2 (* n PI))))))) into 0 1540976140.673 * [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))) 1540976140.673 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976140.674 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1540976140.679 * [misc]backup-simplify: Simplify (+ (* 0 (* -1/48 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 3)))) (+ (* +nan.0 (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2)))) (+ (* +nan.0 (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI)))))) (* +nan.0 (pow (* 2 (* n PI)) 1/2))))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))))) 1540976140.680 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))))) in n 1540976140.680 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))))) in n 1540976140.680 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n 1540976140.680 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1540976140.680 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1540976140.680 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n 1540976140.680 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n 1540976140.680 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1540976140.680 * [misc]taylor: Taking taylor expansion of 2 in n 1540976140.680 * [misc]backup-simplify: Simplify 2 into 2 1540976140.680 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1540976140.680 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1540976140.680 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1540976140.680 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1540976140.680 * [misc]taylor: Taking taylor expansion of 2 in n 1540976140.680 * [misc]backup-simplify: Simplify 2 into 2 1540976140.680 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1540976140.680 * [misc]taylor: Taking taylor expansion of n in n 1540976140.680 * [misc]backup-simplify: Simplify 0 into 0 1540976140.680 * [misc]backup-simplify: Simplify 1 into 1 1540976140.680 * [misc]taylor: Taking taylor expansion of PI in n 1540976140.680 * [misc]backup-simplify: Simplify PI into PI 1540976140.681 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1540976140.681 * [misc]backup-simplify: Simplify (* 2 0) into 0 1540976140.681 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1540976140.682 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1540976140.682 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1540976140.682 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1540976140.682 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1540976140.682 * [misc]taylor: Taking taylor expansion of n in n 1540976140.682 * [misc]backup-simplify: Simplify 0 into 0 1540976140.682 * [misc]backup-simplify: Simplify 1 into 1 1540976140.682 * [misc]taylor: Taking taylor expansion of PI in n 1540976140.682 * [misc]backup-simplify: Simplify PI into PI 1540976140.682 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1540976140.683 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1540976140.683 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1540976140.683 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1540976140.683 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) in n 1540976140.683 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))) in n 1540976140.683 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) in n 1540976140.683 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1540976140.683 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1540976140.683 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))) in n 1540976140.683 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) in n 1540976140.683 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1540976140.683 * [misc]taylor: Taking taylor expansion of 2 in n 1540976140.683 * [misc]backup-simplify: Simplify 2 into 2 1540976140.683 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1540976140.684 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1540976140.684 * [misc]taylor: Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n 1540976140.684 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1540976140.684 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1540976140.684 * [misc]taylor: Taking taylor expansion of 2 in n 1540976140.684 * [misc]backup-simplify: Simplify 2 into 2 1540976140.684 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1540976140.684 * [misc]taylor: Taking taylor expansion of n in n 1540976140.684 * [misc]backup-simplify: Simplify 0 into 0 1540976140.684 * [misc]backup-simplify: Simplify 1 into 1 1540976140.684 * [misc]taylor: Taking taylor expansion of PI in n 1540976140.684 * [misc]backup-simplify: Simplify PI into PI 1540976140.684 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1540976140.684 * [misc]backup-simplify: Simplify (* 2 0) into 0 1540976140.684 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1540976140.685 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1540976140.685 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1540976140.686 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1540976140.686 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1540976140.686 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1540976140.686 * [misc]taylor: Taking taylor expansion of n in n 1540976140.686 * [misc]backup-simplify: Simplify 0 into 0 1540976140.686 * [misc]backup-simplify: Simplify 1 into 1 1540976140.686 * [misc]taylor: Taking taylor expansion of PI in n 1540976140.686 * [misc]backup-simplify: Simplify PI into PI 1540976140.686 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1540976140.686 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1540976140.687 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1540976140.687 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1540976140.687 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 1540976140.687 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 1540976140.687 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1540976140.687 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1540976140.687 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1540976140.687 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1540976140.687 * [misc]taylor: Taking taylor expansion of 2 in n 1540976140.687 * [misc]backup-simplify: Simplify 2 into 2 1540976140.687 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1540976140.687 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1540976140.687 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1540976140.687 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1540976140.687 * [misc]taylor: Taking taylor expansion of n in n 1540976140.687 * [misc]backup-simplify: Simplify 0 into 0 1540976140.687 * [misc]backup-simplify: Simplify 1 into 1 1540976140.687 * [misc]taylor: Taking taylor expansion of PI in n 1540976140.687 * [misc]backup-simplify: Simplify PI into PI 1540976140.688 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1540976140.688 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1540976140.688 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1540976140.688 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1540976140.689 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1540976140.689 * [misc]backup-simplify: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 1540976140.690 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0 1540976140.690 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1540976140.691 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1540976140.691 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1540976140.692 * [misc]backup-simplify: Simplify (* (+ (log n) (log (* 2 PI))) (+ (log n) (log (* 2 PI)))) into (pow (+ (log n) (log (* 2 PI))) 2) 1540976140.693 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) into (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 1540976140.694 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 0) into 0 1540976140.694 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1540976140.695 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1540976140.695 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1540976140.695 * [misc]backup-simplify: Simplify (- 0) into 0 1540976140.695 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976140.695 * [misc]backup-simplify: Simplify (- 0) into 0 1540976140.695 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976140.695 * [misc]backup-simplify: Simplify (- 0) into 0 1540976140.695 * [misc]backup-simplify: Simplify 0 into 0 1540976140.696 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1540976140.697 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1540976140.699 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1540976140.699 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1540976140.700 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1540976140.701 * [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)))))))) 1540976140.702 * [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)))))))) 1540976140.703 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1540976140.704 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1540976140.705 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 1540976140.708 * [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)))))))))) 1540976140.710 * [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))))))) 1540976140.712 * [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))))))) 1540976140.713 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1540976140.714 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 1540976140.715 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1540976140.717 * [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)))) 1540976140.720 * [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)))) 1540976140.721 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 1540976140.722 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 1540976140.727 * [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))))))))))))) 1540976140.727 * [misc]backup-simplify: Simplify (/ 1 (/ (sqrt (/ 1 k)) (pow (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2))))) into (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 1540976140.727 * [misc]approximate: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (k n) around 0 1540976140.727 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1540976140.727 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1540976140.727 * [misc]taylor: Taking taylor expansion of k in n 1540976140.727 * [misc]backup-simplify: Simplify k into k 1540976140.728 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1540976140.728 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1540976140.728 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1540976140.728 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1540976140.728 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1540976140.728 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1540976140.728 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976140.728 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.728 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1540976140.728 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976140.728 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.728 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1540976140.728 * [misc]taylor: Taking taylor expansion of k in n 1540976140.728 * [misc]backup-simplify: Simplify k into k 1540976140.728 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1540976140.728 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1540976140.728 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1540976140.728 * [misc]taylor: Taking taylor expansion of 2 in n 1540976140.728 * [misc]backup-simplify: Simplify 2 into 2 1540976140.728 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1540976140.728 * [misc]taylor: Taking taylor expansion of PI in n 1540976140.728 * [misc]backup-simplify: Simplify PI into PI 1540976140.728 * [misc]taylor: Taking taylor expansion of n in n 1540976140.728 * [misc]backup-simplify: Simplify 0 into 0 1540976140.728 * [misc]backup-simplify: Simplify 1 into 1 1540976140.728 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1540976140.728 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1540976140.729 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1540976140.729 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1540976140.729 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1540976140.729 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1540976140.729 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1540976140.730 * [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))) 1540976140.731 * [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)))) 1540976140.731 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 1540976140.731 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1540976140.731 * [misc]taylor: Taking taylor expansion of k in k 1540976140.731 * [misc]backup-simplify: Simplify 0 into 0 1540976140.731 * [misc]backup-simplify: Simplify 1 into 1 1540976140.731 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1540976140.731 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1540976140.731 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1540976140.731 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1540976140.731 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1540976140.731 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1540976140.731 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976140.731 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.731 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1540976140.731 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976140.731 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.731 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1540976140.731 * [misc]taylor: Taking taylor expansion of k in k 1540976140.731 * [misc]backup-simplify: Simplify 0 into 0 1540976140.731 * [misc]backup-simplify: Simplify 1 into 1 1540976140.731 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1540976140.731 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1540976140.731 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1540976140.731 * [misc]taylor: Taking taylor expansion of 2 in k 1540976140.731 * [misc]backup-simplify: Simplify 2 into 2 1540976140.731 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1540976140.732 * [misc]taylor: Taking taylor expansion of PI in k 1540976140.732 * [misc]backup-simplify: Simplify PI into PI 1540976140.732 * [misc]taylor: Taking taylor expansion of n in k 1540976140.732 * [misc]backup-simplify: Simplify n into n 1540976140.732 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1540976140.732 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1540976140.732 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1540976140.732 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1540976140.732 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1540976140.732 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1540976140.732 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1540976140.732 * [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)))) 1540976140.732 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 1540976140.732 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1540976140.732 * [misc]taylor: Taking taylor expansion of k in k 1540976140.733 * [misc]backup-simplify: Simplify 0 into 0 1540976140.733 * [misc]backup-simplify: Simplify 1 into 1 1540976140.733 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1540976140.733 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1540976140.733 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1540976140.733 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1540976140.733 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1540976140.733 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1540976140.733 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976140.733 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.733 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1540976140.733 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976140.733 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.733 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1540976140.733 * [misc]taylor: Taking taylor expansion of k in k 1540976140.733 * [misc]backup-simplify: Simplify 0 into 0 1540976140.733 * [misc]backup-simplify: Simplify 1 into 1 1540976140.733 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1540976140.733 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1540976140.733 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1540976140.733 * [misc]taylor: Taking taylor expansion of 2 in k 1540976140.733 * [misc]backup-simplify: Simplify 2 into 2 1540976140.733 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1540976140.733 * [misc]taylor: Taking taylor expansion of PI in k 1540976140.733 * [misc]backup-simplify: Simplify PI into PI 1540976140.733 * [misc]taylor: Taking taylor expansion of n in k 1540976140.733 * [misc]backup-simplify: Simplify n into n 1540976140.733 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1540976140.734 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1540976140.734 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1540976140.734 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1540976140.734 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1540976140.734 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1540976140.734 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1540976140.734 * [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)))) 1540976140.734 * [misc]backup-simplify: Simplify (* 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) into 0 1540976140.734 * [misc]taylor: Taking taylor expansion of 0 in n 1540976140.734 * [misc]backup-simplify: Simplify 0 into 0 1540976140.734 * [misc]backup-simplify: Simplify 0 into 0 1540976140.735 * [misc]backup-simplify: Simplify (+ (* 0 0) (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) into (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) 1540976140.735 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 1540976140.735 * [misc]taylor: Taking taylor expansion of (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1540976140.735 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1540976140.735 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1540976140.735 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1540976140.735 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1540976140.735 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1540976140.735 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1540976140.735 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976140.735 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.735 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1540976140.735 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976140.735 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.735 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1540976140.735 * [misc]taylor: Taking taylor expansion of k in n 1540976140.735 * [misc]backup-simplify: Simplify k into k 1540976140.735 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1540976140.735 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1540976140.735 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1540976140.735 * [misc]taylor: Taking taylor expansion of 2 in n 1540976140.735 * [misc]backup-simplify: Simplify 2 into 2 1540976140.735 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1540976140.735 * [misc]taylor: Taking taylor expansion of PI in n 1540976140.735 * [misc]backup-simplify: Simplify PI into PI 1540976140.735 * [misc]taylor: Taking taylor expansion of n in n 1540976140.735 * [misc]backup-simplify: Simplify 0 into 0 1540976140.735 * [misc]backup-simplify: Simplify 1 into 1 1540976140.735 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1540976140.736 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1540976140.736 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1540976140.736 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1540976140.736 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1540976140.736 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1540976140.737 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1540976140.737 * [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))) 1540976140.738 * [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)))) 1540976140.738 * [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))))) 1540976140.739 * [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)))))) 1540976140.739 * [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)))))) 1540976140.739 * [misc]backup-simplify: Simplify 0 into 0 1540976140.740 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1540976140.741 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* +nan.0 0) (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) into (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) 1540976140.741 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 1540976140.741 * [misc]taylor: Taking taylor expansion of (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1540976140.741 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1540976140.741 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1540976140.741 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1540976140.741 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1540976140.741 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1540976140.741 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1540976140.741 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976140.741 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.741 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1540976140.741 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976140.741 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.741 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1540976140.741 * [misc]taylor: Taking taylor expansion of k in n 1540976140.741 * [misc]backup-simplify: Simplify k into k 1540976140.742 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1540976140.742 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1540976140.742 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1540976140.742 * [misc]taylor: Taking taylor expansion of 2 in n 1540976140.742 * [misc]backup-simplify: Simplify 2 into 2 1540976140.742 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1540976140.742 * [misc]taylor: Taking taylor expansion of PI in n 1540976140.742 * [misc]backup-simplify: Simplify PI into PI 1540976140.742 * [misc]taylor: Taking taylor expansion of n in n 1540976140.742 * [misc]backup-simplify: Simplify 0 into 0 1540976140.742 * [misc]backup-simplify: Simplify 1 into 1 1540976140.742 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1540976140.742 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1540976140.743 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1540976140.743 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1540976140.743 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1540976140.743 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1540976140.744 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1540976140.745 * [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))) 1540976140.746 * [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)))) 1540976140.746 * [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))))) 1540976140.747 * [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)))))) 1540976140.748 * [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)))))) 1540976140.749 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1540976140.750 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1540976140.753 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1540976140.753 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1540976140.754 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1540976140.754 * [misc]backup-simplify: Simplify (- 0) into 0 1540976140.754 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976140.755 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1540976140.755 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1540976140.756 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1540976140.757 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0 1540976140.757 * [misc]backup-simplify: Simplify (- 0) into 0 1540976140.757 * [misc]backup-simplify: Simplify 0 into 0 1540976140.757 * [misc]backup-simplify: Simplify 0 into 0 1540976140.758 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1540976140.758 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* +nan.0 0) (+ (* +nan.0 0) (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) 1540976140.758 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 1540976140.758 * [misc]taylor: Taking taylor expansion of (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1540976140.758 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1540976140.758 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1540976140.758 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1540976140.758 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1540976140.758 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1540976140.758 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1540976140.759 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976140.759 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.759 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1540976140.759 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976140.759 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.759 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1540976140.759 * [misc]taylor: Taking taylor expansion of k in n 1540976140.759 * [misc]backup-simplify: Simplify k into k 1540976140.759 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1540976140.759 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1540976140.759 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1540976140.759 * [misc]taylor: Taking taylor expansion of 2 in n 1540976140.759 * [misc]backup-simplify: Simplify 2 into 2 1540976140.759 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1540976140.759 * [misc]taylor: Taking taylor expansion of PI in n 1540976140.759 * [misc]backup-simplify: Simplify PI into PI 1540976140.759 * [misc]taylor: Taking taylor expansion of n in n 1540976140.759 * [misc]backup-simplify: Simplify 0 into 0 1540976140.759 * [misc]backup-simplify: Simplify 1 into 1 1540976140.759 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1540976140.759 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1540976140.760 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1540976140.760 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1540976140.760 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1540976140.760 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1540976140.760 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1540976140.761 * [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))) 1540976140.761 * [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)))) 1540976140.762 * [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))))) 1540976140.762 * [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)))))) 1540976140.763 * [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)))))) 1540976140.766 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))))))) 1540976140.766 * [misc]backup-simplify: Simplify (/ 1 (/ (sqrt (/ 1 (- k))) (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2))))) into (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) 1540976140.766 * [misc]approximate: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (k n) around 0 1540976140.766 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 1540976140.766 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1540976140.766 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1540976140.766 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1540976140.766 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1540976140.766 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1540976140.766 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976140.766 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.766 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1540976140.766 * [misc]taylor: Taking taylor expansion of k in n 1540976140.766 * [misc]backup-simplify: Simplify k into k 1540976140.766 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1540976140.766 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976140.766 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.766 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1540976140.766 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1540976140.766 * [misc]taylor: Taking taylor expansion of -2 in n 1540976140.766 * [misc]backup-simplify: Simplify -2 into -2 1540976140.766 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1540976140.766 * [misc]taylor: Taking taylor expansion of PI in n 1540976140.766 * [misc]backup-simplify: Simplify PI into PI 1540976140.766 * [misc]taylor: Taking taylor expansion of n in n 1540976140.766 * [misc]backup-simplify: Simplify 0 into 0 1540976140.766 * [misc]backup-simplify: Simplify 1 into 1 1540976140.767 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1540976140.767 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1540976140.767 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1540976140.767 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1540976140.768 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1540976140.768 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1540976140.768 * [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))) 1540976140.769 * [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)))) 1540976140.769 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1540976140.769 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1540976140.769 * [misc]taylor: Taking taylor expansion of -1 in n 1540976140.769 * [misc]backup-simplify: Simplify -1 into -1 1540976140.769 * [misc]taylor: Taking taylor expansion of k in n 1540976140.769 * [misc]backup-simplify: Simplify k into k 1540976140.769 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1540976140.769 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1540976140.769 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1540976140.769 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1540976140.770 * [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))) 1540976140.770 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 1540976140.770 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1540976140.770 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1540976140.770 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1540976140.770 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1540976140.770 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1540976140.770 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976140.770 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.770 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1540976140.770 * [misc]taylor: Taking taylor expansion of k in k 1540976140.770 * [misc]backup-simplify: Simplify 0 into 0 1540976140.770 * [misc]backup-simplify: Simplify 1 into 1 1540976140.770 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1540976140.770 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976140.770 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.770 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1540976140.770 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1540976140.770 * [misc]taylor: Taking taylor expansion of -2 in k 1540976140.770 * [misc]backup-simplify: Simplify -2 into -2 1540976140.770 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1540976140.770 * [misc]taylor: Taking taylor expansion of PI in k 1540976140.770 * [misc]backup-simplify: Simplify PI into PI 1540976140.770 * [misc]taylor: Taking taylor expansion of n in k 1540976140.770 * [misc]backup-simplify: Simplify n into n 1540976140.770 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1540976140.770 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1540976140.770 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1540976140.771 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1540976140.771 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1540976140.771 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1540976140.771 * [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))) 1540976140.771 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1540976140.771 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1540976140.771 * [misc]taylor: Taking taylor expansion of -1 in k 1540976140.771 * [misc]backup-simplify: Simplify -1 into -1 1540976140.771 * [misc]taylor: Taking taylor expansion of k in k 1540976140.771 * [misc]backup-simplify: Simplify 0 into 0 1540976140.771 * [misc]backup-simplify: Simplify 1 into 1 1540976140.771 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1540976140.771 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1540976140.772 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1540976140.772 * [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)))) 1540976140.772 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 1540976140.772 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1540976140.772 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1540976140.772 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1540976140.772 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1540976140.772 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1540976140.772 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976140.772 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.772 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1540976140.772 * [misc]taylor: Taking taylor expansion of k in k 1540976140.772 * [misc]backup-simplify: Simplify 0 into 0 1540976140.772 * [misc]backup-simplify: Simplify 1 into 1 1540976140.772 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1540976140.772 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976140.772 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.772 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1540976140.772 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1540976140.772 * [misc]taylor: Taking taylor expansion of -2 in k 1540976140.772 * [misc]backup-simplify: Simplify -2 into -2 1540976140.772 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1540976140.772 * [misc]taylor: Taking taylor expansion of PI in k 1540976140.772 * [misc]backup-simplify: Simplify PI into PI 1540976140.772 * [misc]taylor: Taking taylor expansion of n in k 1540976140.772 * [misc]backup-simplify: Simplify n into n 1540976140.772 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1540976140.772 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1540976140.773 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1540976140.773 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1540976140.773 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1540976140.773 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1540976140.773 * [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))) 1540976140.773 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1540976140.773 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1540976140.773 * [misc]taylor: Taking taylor expansion of -1 in k 1540976140.773 * [misc]backup-simplify: Simplify -1 into -1 1540976140.773 * [misc]taylor: Taking taylor expansion of k in k 1540976140.773 * [misc]backup-simplify: Simplify 0 into 0 1540976140.773 * [misc]backup-simplify: Simplify 1 into 1 1540976140.773 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1540976140.773 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1540976140.774 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1540976140.774 * [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)))) 1540976140.774 * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1540976140.774 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1540976140.774 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1540976140.774 * [misc]taylor: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1540976140.774 * [misc]taylor: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1540976140.774 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1540976140.774 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1540976140.774 * [misc]taylor: Taking taylor expansion of -2 in n 1540976140.774 * [misc]backup-simplify: Simplify -2 into -2 1540976140.774 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1540976140.774 * [misc]taylor: Taking taylor expansion of PI in n 1540976140.774 * [misc]backup-simplify: Simplify PI into PI 1540976140.774 * [misc]taylor: Taking taylor expansion of n in n 1540976140.774 * [misc]backup-simplify: Simplify 0 into 0 1540976140.774 * [misc]backup-simplify: Simplify 1 into 1 1540976140.774 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1540976140.775 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1540976140.775 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1540976140.775 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1540976140.775 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1540976140.775 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976140.775 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.775 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1540976140.775 * [misc]taylor: Taking taylor expansion of k in n 1540976140.775 * [misc]backup-simplify: Simplify k into k 1540976140.775 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1540976140.775 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976140.775 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.776 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1540976140.776 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1540976140.776 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1540976140.776 * [misc]backup-simplify: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1540976140.777 * [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)))) 1540976140.777 * [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))))) 1540976140.778 * [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))))) 1540976140.778 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1540976140.778 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1540976140.779 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) 1540976140.779 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 1540976140.779 * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1540976140.779 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1540976140.779 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1540976140.779 * [misc]taylor: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1540976140.779 * [misc]taylor: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1540976140.779 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1540976140.779 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1540976140.779 * [misc]taylor: Taking taylor expansion of -2 in n 1540976140.779 * [misc]backup-simplify: Simplify -2 into -2 1540976140.779 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1540976140.779 * [misc]taylor: Taking taylor expansion of PI in n 1540976140.779 * [misc]backup-simplify: Simplify PI into PI 1540976140.779 * [misc]taylor: Taking taylor expansion of n in n 1540976140.779 * [misc]backup-simplify: Simplify 0 into 0 1540976140.779 * [misc]backup-simplify: Simplify 1 into 1 1540976140.779 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1540976140.780 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1540976140.780 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1540976140.780 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1540976140.780 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1540976140.780 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976140.780 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.780 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1540976140.780 * [misc]taylor: Taking taylor expansion of k in n 1540976140.780 * [misc]backup-simplify: Simplify k into k 1540976140.780 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1540976140.780 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976140.780 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.781 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1540976140.781 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1540976140.781 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1540976140.781 * [misc]backup-simplify: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1540976140.782 * [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)))) 1540976140.782 * [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))))) 1540976140.783 * [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)))))) 1540976140.783 * [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)))))) 1540976140.784 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1540976140.784 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1540976140.784 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1540976140.784 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976140.785 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1540976140.785 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1540976140.787 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1540976140.788 * [misc]backup-simplify: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0 1540976140.789 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1540976140.790 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into 0 1540976140.790 * [misc]backup-simplify: Simplify 0 into 0 1540976140.790 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976140.791 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1540976140.791 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) 1540976140.791 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 1540976140.791 * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1540976140.791 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1540976140.791 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1540976140.791 * [misc]taylor: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1540976140.791 * [misc]taylor: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1540976140.791 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1540976140.791 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1540976140.792 * [misc]taylor: Taking taylor expansion of -2 in n 1540976140.792 * [misc]backup-simplify: Simplify -2 into -2 1540976140.792 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1540976140.792 * [misc]taylor: Taking taylor expansion of PI in n 1540976140.792 * [misc]backup-simplify: Simplify PI into PI 1540976140.792 * [misc]taylor: Taking taylor expansion of n in n 1540976140.792 * [misc]backup-simplify: Simplify 0 into 0 1540976140.792 * [misc]backup-simplify: Simplify 1 into 1 1540976140.792 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1540976140.792 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1540976140.792 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1540976140.792 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1540976140.792 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1540976140.792 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976140.792 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.792 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1540976140.792 * [misc]taylor: Taking taylor expansion of k in n 1540976140.792 * [misc]backup-simplify: Simplify k into k 1540976140.792 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1540976140.793 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976140.793 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.793 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1540976140.793 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1540976140.793 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1540976140.794 * [misc]backup-simplify: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1540976140.794 * [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)))) 1540976140.794 * [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))))) 1540976140.795 * [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)))))) 1540976140.795 * [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)))))) 1540976140.798 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (* 1 (/ 1 (- k)))) (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))) 1540976140.798 * * * * [misc]progress: [ 4 / 4 ] generating series at (2 2) 1540976140.798 * [misc]backup-simplify: Simplify (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) into (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) 1540976140.798 * [misc]approximate: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in (k n) around 0 1540976140.798 * [misc]taylor: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in n 1540976140.798 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 1540976140.798 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1540976140.798 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1540976140.798 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1540976140.798 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1540976140.798 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976140.798 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.798 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1540976140.798 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976140.798 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.798 * [misc]taylor: Taking taylor expansion of k in n 1540976140.798 * [misc]backup-simplify: Simplify k into k 1540976140.798 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1540976140.798 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1540976140.798 * [misc]taylor: Taking taylor expansion of 2 in n 1540976140.798 * [misc]backup-simplify: Simplify 2 into 2 1540976140.798 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1540976140.798 * [misc]taylor: Taking taylor expansion of n in n 1540976140.798 * [misc]backup-simplify: Simplify 0 into 0 1540976140.798 * [misc]backup-simplify: Simplify 1 into 1 1540976140.798 * [misc]taylor: Taking taylor expansion of PI in n 1540976140.798 * [misc]backup-simplify: Simplify PI into PI 1540976140.799 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1540976140.799 * [misc]backup-simplify: Simplify (* 2 0) into 0 1540976140.799 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1540976140.800 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1540976140.800 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1540976140.800 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1540976140.800 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1540976140.800 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1540976140.801 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1540976140.801 * [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)))) 1540976140.802 * [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))))) 1540976140.802 * [misc]backup-simplify: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (/ 1 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) 1540976140.802 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1540976140.802 * [misc]taylor: Taking taylor expansion of k in n 1540976140.802 * [misc]backup-simplify: Simplify k into k 1540976140.802 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1540976140.802 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1540976140.802 * [misc]taylor: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in k 1540976140.802 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 1540976140.802 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1540976140.802 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1540976140.802 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1540976140.802 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1540976140.802 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976140.802 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.802 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1540976140.802 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976140.802 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.802 * [misc]taylor: Taking taylor expansion of k in k 1540976140.802 * [misc]backup-simplify: Simplify 0 into 0 1540976140.802 * [misc]backup-simplify: Simplify 1 into 1 1540976140.802 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1540976140.802 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1540976140.802 * [misc]taylor: Taking taylor expansion of 2 in k 1540976140.802 * [misc]backup-simplify: Simplify 2 into 2 1540976140.802 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1540976140.802 * [misc]taylor: Taking taylor expansion of n in k 1540976140.802 * [misc]backup-simplify: Simplify n into n 1540976140.802 * [misc]taylor: Taking taylor expansion of PI in k 1540976140.803 * [misc]backup-simplify: Simplify PI into PI 1540976140.803 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1540976140.803 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1540976140.803 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1540976140.803 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1540976140.803 * [misc]backup-simplify: Simplify (- 0) into 0 1540976140.803 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1540976140.803 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1540976140.803 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1540976140.804 * [misc]backup-simplify: Simplify (/ 1 (pow (* 2 (* n PI)) 1/2)) into (sqrt (/ 1 (* PI (* n 2)))) 1540976140.804 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1540976140.804 * [misc]taylor: Taking taylor expansion of k in k 1540976140.804 * [misc]backup-simplify: Simplify 0 into 0 1540976140.804 * [misc]backup-simplify: Simplify 1 into 1 1540976140.804 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1540976140.804 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1540976140.804 * [misc]taylor: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in k 1540976140.804 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 1540976140.804 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1540976140.804 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1540976140.804 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1540976140.804 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1540976140.804 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976140.804 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.804 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1540976140.804 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976140.804 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.804 * [misc]taylor: Taking taylor expansion of k in k 1540976140.804 * [misc]backup-simplify: Simplify 0 into 0 1540976140.804 * [misc]backup-simplify: Simplify 1 into 1 1540976140.805 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1540976140.805 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1540976140.805 * [misc]taylor: Taking taylor expansion of 2 in k 1540976140.805 * [misc]backup-simplify: Simplify 2 into 2 1540976140.805 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1540976140.805 * [misc]taylor: Taking taylor expansion of n in k 1540976140.805 * [misc]backup-simplify: Simplify n into n 1540976140.805 * [misc]taylor: Taking taylor expansion of PI in k 1540976140.805 * [misc]backup-simplify: Simplify PI into PI 1540976140.805 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1540976140.805 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1540976140.805 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1540976140.805 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1540976140.805 * [misc]backup-simplify: Simplify (- 0) into 0 1540976140.805 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1540976140.805 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1540976140.806 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1540976140.806 * [misc]backup-simplify: Simplify (/ 1 (pow (* 2 (* n PI)) 1/2)) into (sqrt (/ 1 (* PI (* n 2)))) 1540976140.806 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1540976140.806 * [misc]taylor: Taking taylor expansion of k in k 1540976140.806 * [misc]backup-simplify: Simplify 0 into 0 1540976140.806 * [misc]backup-simplify: Simplify 1 into 1 1540976140.806 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1540976140.806 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1540976140.807 * [misc]backup-simplify: Simplify (* (sqrt (/ 1 (* PI (* n 2)))) 0) into 0 1540976140.807 * [misc]taylor: Taking taylor expansion of 0 in n 1540976140.807 * [misc]backup-simplify: Simplify 0 into 0 1540976140.807 * [misc]backup-simplify: Simplify 0 into 0 1540976140.807 * [misc]backup-simplify: Simplify (+ (* n 0) (* 0 PI)) into 0 1540976140.807 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0 1540976140.808 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 1540976140.808 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1540976140.808 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1540976140.808 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1540976140.808 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI))))) 1540976140.809 * [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))))) 1540976140.811 * [misc]backup-simplify: Simplify (- (+ (* (sqrt (/ 1 (* PI (* n 2)))) (/ (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) (pow (* 2 (* n PI)) 1/2))))) into (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) 1540976140.813 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 (* PI (* n 2)))) +nan.0) (* (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) 0)) into (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))) 1540976140.813 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))) in n 1540976140.813 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))) in n 1540976140.813 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1540976140.813 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1540976140.813 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)) in n 1540976140.813 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n 1540976140.813 * [misc]taylor: Taking taylor expansion of (/ 1 (* n PI)) in n 1540976140.813 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1540976140.813 * [misc]taylor: Taking taylor expansion of n in n 1540976140.813 * [misc]backup-simplify: Simplify 0 into 0 1540976140.813 * [misc]backup-simplify: Simplify 1 into 1 1540976140.813 * [misc]taylor: Taking taylor expansion of PI in n 1540976140.813 * [misc]backup-simplify: Simplify PI into PI 1540976140.814 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1540976140.814 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1540976140.815 * [misc]backup-simplify: Simplify (/ 1 PI) into (/ 1 PI) 1540976140.815 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1540976140.816 * [misc]backup-simplify: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI) 1540976140.816 * [misc]taylor: Taking taylor expansion of (sqrt 1/2) in n 1540976140.816 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976140.816 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.816 * [misc]backup-simplify: Simplify (sqrt 1/2) into (sqrt 1/2) 1540976140.816 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 1/2))) into 0 1540976140.817 * [misc]backup-simplify: Simplify (+ (* 0 0) (* (/ +nan.0 PI) (sqrt 1/2))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 1540976140.817 * [misc]backup-simplify: Simplify (* 0 (sqrt 1/2)) into 0 1540976140.819 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (sqrt 1/2) PI)))) (* 0 0)) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 1540976140.821 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (/ (sqrt 1/2) PI)))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 1540976140.822 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (sqrt 1/2) PI))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 1540976140.822 * [misc]backup-simplify: Simplify 0 into 0 1540976140.823 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1540976140.824 * [misc]backup-simplify: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 1540976140.824 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 1540976140.827 * [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 1540976140.827 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1540976140.827 * [misc]backup-simplify: Simplify (- 0) into 0 1540976140.827 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976140.828 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0 1540976140.830 * [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))) 1540976140.843 * [misc]backup-simplify: Simplify (- (+ (* (sqrt (/ 1 (* PI (* n 2)))) (/ (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) (pow (* 2 (* n PI)) 1/2))) (* (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (/ (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) (pow (* 2 (* n PI)) 1/2))))) into (- (* 1/4 (* (* (pow (sqrt 2) 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 3))) (sqrt (/ 1 (* n PI))))) (* 1/8 (* (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI)))))) 1540976140.856 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 (* PI (* n 2)))) +nan.0) (+ (* (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) +nan.0) (* (- (* 1/4 (* (* (pow (sqrt 2) 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 3))) (sqrt (/ 1 (* n PI))))) (* 1/8 (* (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI)))))) 0))) into (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))))) 1540976140.856 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))))) in n 1540976140.856 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))))) in n 1540976140.856 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) in n 1540976140.856 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1540976140.856 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1540976140.856 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI)))) in n 1540976140.856 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) in n 1540976140.856 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1540976140.856 * [misc]taylor: Taking taylor expansion of 2 in n 1540976140.856 * [misc]backup-simplify: Simplify 2 into 2 1540976140.857 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1540976140.857 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1540976140.857 * [misc]taylor: Taking taylor expansion of (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2)) in n 1540976140.857 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1540976140.857 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1540976140.857 * [misc]taylor: Taking taylor expansion of 2 in n 1540976140.857 * [misc]backup-simplify: Simplify 2 into 2 1540976140.857 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1540976140.857 * [misc]taylor: Taking taylor expansion of n in n 1540976140.857 * [misc]backup-simplify: Simplify 0 into 0 1540976140.857 * [misc]backup-simplify: Simplify 1 into 1 1540976140.857 * [misc]taylor: Taking taylor expansion of PI in n 1540976140.857 * [misc]backup-simplify: Simplify PI into PI 1540976140.857 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1540976140.858 * [misc]backup-simplify: Simplify (* 2 0) into 0 1540976140.858 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1540976140.859 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1540976140.860 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1540976140.860 * [misc]taylor: Taking taylor expansion of (pow (sqrt 1/2) 2) in n 1540976140.860 * [misc]taylor: Taking taylor expansion of (sqrt 1/2) in n 1540976140.860 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976140.860 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.860 * [misc]backup-simplify: Simplify (sqrt 1/2) into (sqrt 1/2) 1540976140.860 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 1/2))) into 0 1540976140.860 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n 1540976140.860 * [misc]taylor: Taking taylor expansion of (/ 1 (* n PI)) in n 1540976140.860 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1540976140.860 * [misc]taylor: Taking taylor expansion of n in n 1540976140.860 * [misc]backup-simplify: Simplify 0 into 0 1540976140.860 * [misc]backup-simplify: Simplify 1 into 1 1540976140.860 * [misc]taylor: Taking taylor expansion of PI in n 1540976140.860 * [misc]backup-simplify: Simplify PI into PI 1540976140.861 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1540976140.861 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1540976140.862 * [misc]backup-simplify: Simplify (/ 1 PI) into (/ 1 PI) 1540976140.862 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1540976140.862 * [misc]backup-simplify: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI) 1540976140.863 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))) in n 1540976140.863 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))) in n 1540976140.863 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1540976140.863 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1540976140.863 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)) in n 1540976140.863 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n 1540976140.863 * [misc]taylor: Taking taylor expansion of (/ 1 (* n PI)) in n 1540976140.863 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1540976140.863 * [misc]taylor: Taking taylor expansion of n in n 1540976140.863 * [misc]backup-simplify: Simplify 0 into 0 1540976140.863 * [misc]backup-simplify: Simplify 1 into 1 1540976140.863 * [misc]taylor: Taking taylor expansion of PI in n 1540976140.863 * [misc]backup-simplify: Simplify PI into PI 1540976140.863 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1540976140.864 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1540976140.864 * [misc]backup-simplify: Simplify (/ 1 PI) into (/ 1 PI) 1540976140.864 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1540976140.865 * [misc]backup-simplify: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI) 1540976140.865 * [misc]taylor: Taking taylor expansion of (sqrt 1/2) in n 1540976140.865 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976140.865 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.865 * [misc]backup-simplify: Simplify (sqrt 1/2) into (sqrt 1/2) 1540976140.866 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 1/2))) into 0 1540976140.866 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1540976140.867 * [misc]backup-simplify: Simplify (* (sqrt 1/2) (sqrt 1/2)) into (pow (sqrt 1/2) 2) 1540976140.869 * [misc]backup-simplify: Simplify (* (+ (log n) (log (* 2 PI))) (pow (sqrt 1/2) 2)) into (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI)))) 1540976140.870 * [misc]backup-simplify: Simplify (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) into (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) 1540976140.871 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1540976140.871 * [misc]backup-simplify: Simplify (+ (* (sqrt 1/2) 0) (* 0 (sqrt 1/2))) into 0 1540976140.873 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1540976140.874 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1540976140.877 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1540976140.881 * [misc]backup-simplify: Simplify (+ (* (+ (log n) (log (* 2 PI))) 0) (* 0 (pow (sqrt 1/2) 2))) into 0 1540976140.883 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI)))))) into 0 1540976140.887 * [misc]backup-simplify: Simplify (+ (* (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) (/ +nan.0 PI)) (* 0 0)) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))) 1540976140.889 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) 0) into 0 1540976140.901 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))) (* 0 0)) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))) 1540976140.903 * [misc]backup-simplify: Simplify (+ (* 0 0) (* (/ +nan.0 PI) (sqrt 1/2))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 1540976140.903 * [misc]backup-simplify: Simplify (* 0 (sqrt 1/2)) into 0 1540976140.905 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (sqrt 1/2) PI)))) (* 0 0)) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 1540976140.906 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (/ (sqrt 1/2) PI)))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 1540976140.918 * [misc]backup-simplify: Simplify (+ (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))) (- (* +nan.0 (/ (sqrt 1/2) PI)))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) 1540976140.932 * [misc]backup-simplify: Simplify (- (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) 1540976140.944 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) 1540976140.946 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1/2))) into 0 1540976140.947 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1540976140.949 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 PI) (/ 0 PI)))) into 0 1540976140.950 * [misc]backup-simplify: Simplify (/ (- 0 (pow (/ +nan.0 PI) 2) (+)) (* 2 0)) into (/ +nan.0 (pow PI 2)) 1540976140.954 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* (/ +nan.0 PI) 0) (* (/ +nan.0 (pow PI 2)) (sqrt 1/2)))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) 1540976140.959 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2))))) (+ (* 0 (- (* +nan.0 (/ (sqrt 1/2) PI)))) (* 0 0))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) 1540976140.961 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2))))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) 1540976140.963 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) 1540976140.985 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) (* n k)) (+ (* (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) (pow (* 1 k) 2)) (* (- (* +nan.0 (/ (sqrt 1/2) PI))) (* 1 k)))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow k 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI))))) PI)) (- (+ (* +nan.0 (/ (* (sqrt 1/2) (pow k 2)) PI)) (- (+ (* +nan.0 (/ (* n (* (sqrt 1/2) k)) (pow PI 2))) (- (+ (* +nan.0 (/ (* (log n) (* (sqrt 2) (* (pow (sqrt 1/2) 2) (pow k 2)))) PI)) (- (* +nan.0 (/ (* (sqrt 1/2) k) PI))))))))))) 1540976140.985 * [misc]backup-simplify: Simplify (/ (sqrt (/ 1 k)) (pow (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2)))) into (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) 1540976140.985 * [misc]approximate: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in (k n) around 0 1540976140.985 * [misc]taylor: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in n 1540976140.985 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1540976140.985 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1540976140.985 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1540976140.985 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1540976140.985 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1540976140.985 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976140.985 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.985 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1540976140.985 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976140.985 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.985 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1540976140.985 * [misc]taylor: Taking taylor expansion of k in n 1540976140.985 * [misc]backup-simplify: Simplify k into k 1540976140.985 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1540976140.986 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1540976140.986 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1540976140.986 * [misc]taylor: Taking taylor expansion of 2 in n 1540976140.986 * [misc]backup-simplify: Simplify 2 into 2 1540976140.986 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1540976140.986 * [misc]taylor: Taking taylor expansion of PI in n 1540976140.986 * [misc]backup-simplify: Simplify PI into PI 1540976140.986 * [misc]taylor: Taking taylor expansion of n in n 1540976140.986 * [misc]backup-simplify: Simplify 0 into 0 1540976140.986 * [misc]backup-simplify: Simplify 1 into 1 1540976140.986 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1540976140.986 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1540976140.987 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1540976140.987 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1540976140.987 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1540976140.987 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1540976140.988 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1540976140.989 * [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))) 1540976140.989 * [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)))) 1540976140.990 * [misc]backup-simplify: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 1540976140.990 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1540976140.990 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1540976140.990 * [misc]taylor: Taking taylor expansion of k in n 1540976140.990 * [misc]backup-simplify: Simplify k into k 1540976140.990 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1540976140.990 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1540976140.990 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1540976140.990 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1540976140.990 * [misc]taylor: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in k 1540976140.990 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 1540976140.990 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1540976140.991 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1540976140.991 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1540976140.991 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1540976140.991 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976140.991 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.991 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1540976140.991 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976140.991 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.991 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1540976140.991 * [misc]taylor: Taking taylor expansion of k in k 1540976140.991 * [misc]backup-simplify: Simplify 0 into 0 1540976140.991 * [misc]backup-simplify: Simplify 1 into 1 1540976140.991 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1540976140.991 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1540976140.991 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1540976140.991 * [misc]taylor: Taking taylor expansion of 2 in k 1540976140.991 * [misc]backup-simplify: Simplify 2 into 2 1540976140.991 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1540976140.991 * [misc]taylor: Taking taylor expansion of PI in k 1540976140.991 * [misc]backup-simplify: Simplify PI into PI 1540976140.991 * [misc]taylor: Taking taylor expansion of n in k 1540976140.991 * [misc]backup-simplify: Simplify n into n 1540976140.991 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1540976140.991 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1540976140.992 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1540976140.992 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1540976140.992 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1540976140.992 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1540976140.992 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1540976140.992 * [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)))) 1540976140.993 * [misc]backup-simplify: Simplify (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) into (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 1540976140.993 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1540976140.993 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1540976140.993 * [misc]taylor: Taking taylor expansion of k in k 1540976140.993 * [misc]backup-simplify: Simplify 0 into 0 1540976140.993 * [misc]backup-simplify: Simplify 1 into 1 1540976140.993 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1540976140.993 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1540976140.993 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1540976140.993 * [misc]taylor: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in k 1540976140.994 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 1540976140.994 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1540976140.994 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1540976140.994 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1540976140.994 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1540976140.994 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976140.994 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.994 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1540976140.994 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976140.994 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.994 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1540976140.994 * [misc]taylor: Taking taylor expansion of k in k 1540976140.994 * [misc]backup-simplify: Simplify 0 into 0 1540976140.994 * [misc]backup-simplify: Simplify 1 into 1 1540976140.994 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1540976140.994 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1540976140.994 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1540976140.994 * [misc]taylor: Taking taylor expansion of 2 in k 1540976140.994 * [misc]backup-simplify: Simplify 2 into 2 1540976140.994 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1540976140.994 * [misc]taylor: Taking taylor expansion of PI in k 1540976140.994 * [misc]backup-simplify: Simplify PI into PI 1540976140.994 * [misc]taylor: Taking taylor expansion of n in k 1540976140.994 * [misc]backup-simplify: Simplify n into n 1540976140.994 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1540976140.994 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1540976140.995 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1540976140.995 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1540976140.995 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1540976140.995 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1540976140.995 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1540976140.995 * [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)))) 1540976140.996 * [misc]backup-simplify: Simplify (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) into (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 1540976140.996 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1540976140.996 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1540976140.996 * [misc]taylor: Taking taylor expansion of k in k 1540976140.996 * [misc]backup-simplify: Simplify 0 into 0 1540976140.996 * [misc]backup-simplify: Simplify 1 into 1 1540976140.996 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1540976140.996 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1540976140.996 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1540976140.997 * [misc]backup-simplify: Simplify (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 0) into 0 1540976140.997 * [misc]taylor: Taking taylor expansion of 0 in n 1540976140.997 * [misc]backup-simplify: Simplify 0 into 0 1540976140.997 * [misc]backup-simplify: Simplify 0 into 0 1540976140.998 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 1540976140.998 * [misc]backup-simplify: Simplify (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (* 0 0)) into (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) 1540976140.998 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) in n 1540976140.998 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 1540976140.998 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1540976140.998 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1540976140.998 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1540976140.998 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1540976140.998 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1540976140.998 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1540976140.998 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1540976140.999 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976140.999 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.999 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1540976140.999 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976140.999 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976140.999 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1540976140.999 * [misc]taylor: Taking taylor expansion of k in n 1540976140.999 * [misc]backup-simplify: Simplify k into k 1540976140.999 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1540976140.999 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1540976140.999 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1540976140.999 * [misc]taylor: Taking taylor expansion of 2 in n 1540976140.999 * [misc]backup-simplify: Simplify 2 into 2 1540976140.999 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1540976140.999 * [misc]taylor: Taking taylor expansion of PI in n 1540976140.999 * [misc]backup-simplify: Simplify PI into PI 1540976140.999 * [misc]taylor: Taking taylor expansion of n in n 1540976140.999 * [misc]backup-simplify: Simplify 0 into 0 1540976140.999 * [misc]backup-simplify: Simplify 1 into 1 1540976140.999 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1540976141.000 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1540976141.000 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1540976141.000 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1540976141.000 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1540976141.000 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1540976141.001 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1540976141.002 * [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))) 1540976141.002 * [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)))) 1540976141.003 * [misc]backup-simplify: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 1540976141.004 * [misc]backup-simplify: Simplify (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 1540976141.004 * [misc]backup-simplify: Simplify (- (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 1540976141.005 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 1540976141.005 * [misc]backup-simplify: Simplify 0 into 0 1540976141.006 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1540976141.006 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1540976141.007 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) (* 0 (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 1540976141.008 * [misc]backup-simplify: Simplify (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) 1540976141.008 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) in n 1540976141.008 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 1540976141.008 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1540976141.008 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1540976141.008 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1540976141.008 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1540976141.008 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1540976141.008 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1540976141.008 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1540976141.008 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976141.008 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976141.008 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1540976141.008 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976141.008 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976141.008 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1540976141.008 * [misc]taylor: Taking taylor expansion of k in n 1540976141.008 * [misc]backup-simplify: Simplify k into k 1540976141.008 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1540976141.008 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1540976141.008 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1540976141.008 * [misc]taylor: Taking taylor expansion of 2 in n 1540976141.008 * [misc]backup-simplify: Simplify 2 into 2 1540976141.008 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1540976141.008 * [misc]taylor: Taking taylor expansion of PI in n 1540976141.008 * [misc]backup-simplify: Simplify PI into PI 1540976141.009 * [misc]taylor: Taking taylor expansion of n in n 1540976141.009 * [misc]backup-simplify: Simplify 0 into 0 1540976141.009 * [misc]backup-simplify: Simplify 1 into 1 1540976141.009 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1540976141.009 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1540976141.010 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1540976141.010 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1540976141.010 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1540976141.010 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1540976141.010 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1540976141.011 * [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))) 1540976141.012 * [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)))) 1540976141.012 * [misc]backup-simplify: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 1540976141.013 * [misc]backup-simplify: Simplify (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 1540976141.014 * [misc]backup-simplify: Simplify (- (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 1540976141.015 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 1540976141.016 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1540976141.016 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1540976141.021 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1540976141.021 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1540976141.022 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1540976141.022 * [misc]backup-simplify: Simplify (- 0) into 0 1540976141.022 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976141.023 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1540976141.023 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1540976141.025 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1540976141.026 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (/ 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))) into 0 1540976141.027 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0 1540976141.027 * [misc]backup-simplify: Simplify (- 0) into 0 1540976141.027 * [misc]backup-simplify: Simplify 0 into 0 1540976141.028 * [misc]backup-simplify: Simplify 0 into 0 1540976141.028 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976141.029 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1540976141.030 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) (* 0 (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) (* 0 (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 1540976141.031 * [misc]backup-simplify: Simplify (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) 1540976141.031 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) in n 1540976141.031 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 1540976141.031 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1540976141.031 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1540976141.031 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1540976141.031 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1540976141.031 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1540976141.031 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1540976141.031 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1540976141.031 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976141.031 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976141.031 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1540976141.031 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976141.031 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976141.031 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1540976141.031 * [misc]taylor: Taking taylor expansion of k in n 1540976141.031 * [misc]backup-simplify: Simplify k into k 1540976141.031 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1540976141.031 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1540976141.031 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1540976141.031 * [misc]taylor: Taking taylor expansion of 2 in n 1540976141.031 * [misc]backup-simplify: Simplify 2 into 2 1540976141.031 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1540976141.031 * [misc]taylor: Taking taylor expansion of PI in n 1540976141.031 * [misc]backup-simplify: Simplify PI into PI 1540976141.031 * [misc]taylor: Taking taylor expansion of n in n 1540976141.032 * [misc]backup-simplify: Simplify 0 into 0 1540976141.032 * [misc]backup-simplify: Simplify 1 into 1 1540976141.032 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1540976141.032 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1540976141.033 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1540976141.033 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1540976141.033 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1540976141.033 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1540976141.034 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1540976141.034 * [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))) 1540976141.035 * [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)))) 1540976141.036 * [misc]backup-simplify: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 1540976141.036 * [misc]backup-simplify: Simplify (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 1540976141.037 * [misc]backup-simplify: Simplify (- (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 1540976141.038 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 1540976141.041 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 2)) (+ (* (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (* 1 (/ 1 k))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))))))) into (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))))))))) 1540976141.041 * [misc]backup-simplify: Simplify (/ (sqrt (/ 1 (- k))) (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2)))) into (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) 1540976141.041 * [misc]approximate: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in (k n) around 0 1540976141.041 * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1540976141.042 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1540976141.042 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1540976141.042 * [misc]taylor: Taking taylor expansion of -1 in n 1540976141.042 * [misc]backup-simplify: Simplify -1 into -1 1540976141.042 * [misc]taylor: Taking taylor expansion of k in n 1540976141.042 * [misc]backup-simplify: Simplify k into k 1540976141.042 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1540976141.042 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1540976141.042 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1540976141.042 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1540976141.042 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1540976141.042 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1540976141.042 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1540976141.042 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1540976141.042 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1540976141.042 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976141.042 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976141.042 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1540976141.042 * [misc]taylor: Taking taylor expansion of k in n 1540976141.042 * [misc]backup-simplify: Simplify k into k 1540976141.042 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1540976141.042 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976141.042 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976141.042 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1540976141.042 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1540976141.042 * [misc]taylor: Taking taylor expansion of -2 in n 1540976141.042 * [misc]backup-simplify: Simplify -2 into -2 1540976141.042 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1540976141.042 * [misc]taylor: Taking taylor expansion of PI in n 1540976141.043 * [misc]backup-simplify: Simplify PI into PI 1540976141.043 * [misc]taylor: Taking taylor expansion of n in n 1540976141.043 * [misc]backup-simplify: Simplify 0 into 0 1540976141.043 * [misc]backup-simplify: Simplify 1 into 1 1540976141.043 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1540976141.043 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1540976141.044 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1540976141.044 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1540976141.044 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1540976141.045 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1540976141.045 * [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))) 1540976141.046 * [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)))) 1540976141.047 * [misc]backup-simplify: Simplify (/ (sqrt (/ -1 k)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ (sqrt (/ -1 k)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 1540976141.047 * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in k 1540976141.047 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1540976141.047 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1540976141.047 * [misc]taylor: Taking taylor expansion of -1 in k 1540976141.047 * [misc]backup-simplify: Simplify -1 into -1 1540976141.047 * [misc]taylor: Taking taylor expansion of k in k 1540976141.047 * [misc]backup-simplify: Simplify 0 into 0 1540976141.047 * [misc]backup-simplify: Simplify 1 into 1 1540976141.047 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1540976141.047 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1540976141.048 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1540976141.048 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1540976141.048 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1540976141.048 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1540976141.048 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1540976141.048 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1540976141.048 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976141.048 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976141.048 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1540976141.048 * [misc]taylor: Taking taylor expansion of k in k 1540976141.048 * [misc]backup-simplify: Simplify 0 into 0 1540976141.048 * [misc]backup-simplify: Simplify 1 into 1 1540976141.049 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1540976141.049 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976141.049 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976141.049 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1540976141.049 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1540976141.049 * [misc]taylor: Taking taylor expansion of -2 in k 1540976141.049 * [misc]backup-simplify: Simplify -2 into -2 1540976141.049 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1540976141.049 * [misc]taylor: Taking taylor expansion of PI in k 1540976141.049 * [misc]backup-simplify: Simplify PI into PI 1540976141.049 * [misc]taylor: Taking taylor expansion of n in k 1540976141.049 * [misc]backup-simplify: Simplify n into n 1540976141.049 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1540976141.049 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1540976141.049 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1540976141.049 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1540976141.050 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1540976141.050 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1540976141.050 * [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))) 1540976141.050 * [misc]backup-simplify: Simplify (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) into (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) 1540976141.050 * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in k 1540976141.050 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1540976141.051 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1540976141.051 * [misc]taylor: Taking taylor expansion of -1 in k 1540976141.051 * [misc]backup-simplify: Simplify -1 into -1 1540976141.051 * [misc]taylor: Taking taylor expansion of k in k 1540976141.051 * [misc]backup-simplify: Simplify 0 into 0 1540976141.051 * [misc]backup-simplify: Simplify 1 into 1 1540976141.051 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1540976141.051 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1540976141.052 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1540976141.052 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1540976141.052 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1540976141.052 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1540976141.052 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1540976141.052 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1540976141.052 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976141.052 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976141.052 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1540976141.052 * [misc]taylor: Taking taylor expansion of k in k 1540976141.052 * [misc]backup-simplify: Simplify 0 into 0 1540976141.052 * [misc]backup-simplify: Simplify 1 into 1 1540976141.052 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1540976141.052 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976141.052 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976141.052 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1540976141.052 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1540976141.052 * [misc]taylor: Taking taylor expansion of -2 in k 1540976141.052 * [misc]backup-simplify: Simplify -2 into -2 1540976141.052 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1540976141.052 * [misc]taylor: Taking taylor expansion of PI in k 1540976141.052 * [misc]backup-simplify: Simplify PI into PI 1540976141.052 * [misc]taylor: Taking taylor expansion of n in k 1540976141.052 * [misc]backup-simplify: Simplify n into n 1540976141.053 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1540976141.053 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1540976141.053 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1540976141.053 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1540976141.053 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1540976141.053 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1540976141.054 * [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))) 1540976141.054 * [misc]backup-simplify: Simplify (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) into (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) 1540976141.054 * [misc]taylor: Taking taylor expansion of (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1540976141.054 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1540976141.054 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1540976141.054 * [misc]taylor: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1540976141.054 * [misc]taylor: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1540976141.054 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1540976141.054 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1540976141.054 * [misc]taylor: Taking taylor expansion of -2 in n 1540976141.054 * [misc]backup-simplify: Simplify -2 into -2 1540976141.054 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1540976141.054 * [misc]taylor: Taking taylor expansion of PI in n 1540976141.054 * [misc]backup-simplify: Simplify PI into PI 1540976141.054 * [misc]taylor: Taking taylor expansion of n in n 1540976141.054 * [misc]backup-simplify: Simplify 0 into 0 1540976141.054 * [misc]backup-simplify: Simplify 1 into 1 1540976141.055 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1540976141.055 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1540976141.055 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1540976141.056 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1540976141.056 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1540976141.056 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976141.056 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976141.056 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1540976141.056 * [misc]taylor: Taking taylor expansion of k in n 1540976141.056 * [misc]backup-simplify: Simplify k into k 1540976141.056 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1540976141.056 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976141.056 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976141.056 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1540976141.057 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1540976141.057 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1540976141.057 * [misc]backup-simplify: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1540976141.058 * [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)))) 1540976141.059 * [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))))) 1540976141.059 * [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))))) 1540976141.060 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1540976141.061 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1540976141.062 * [misc]backup-simplify: Simplify (- (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (+ (* (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ 0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))))) into (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) 1540976141.062 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) in n 1540976141.062 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 1540976141.062 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1540976141.062 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1540976141.062 * [misc]taylor: Taking taylor expansion of (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1540976141.062 * [misc]taylor: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1540976141.062 * [misc]taylor: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1540976141.062 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1540976141.062 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1540976141.062 * [misc]taylor: Taking taylor expansion of -2 in n 1540976141.062 * [misc]backup-simplify: Simplify -2 into -2 1540976141.062 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1540976141.062 * [misc]taylor: Taking taylor expansion of PI in n 1540976141.062 * [misc]backup-simplify: Simplify PI into PI 1540976141.062 * [misc]taylor: Taking taylor expansion of n in n 1540976141.062 * [misc]backup-simplify: Simplify 0 into 0 1540976141.062 * [misc]backup-simplify: Simplify 1 into 1 1540976141.063 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1540976141.063 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1540976141.063 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1540976141.063 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1540976141.063 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1540976141.063 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976141.063 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976141.064 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1540976141.064 * [misc]taylor: Taking taylor expansion of k in n 1540976141.064 * [misc]backup-simplify: Simplify k into k 1540976141.064 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1540976141.064 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976141.064 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976141.064 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1540976141.064 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1540976141.065 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1540976141.065 * [misc]backup-simplify: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1540976141.066 * [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)))) 1540976141.067 * [misc]backup-simplify: Simplify (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 1540976141.067 * [misc]backup-simplify: Simplify (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 1540976141.068 * [misc]backup-simplify: Simplify (- (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) 1540976141.069 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) 1540976141.070 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1540976141.070 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1540976141.070 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1540976141.070 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976141.071 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1540976141.072 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1540976141.075 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1540976141.075 * [misc]backup-simplify: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0 1540976141.077 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1540976141.079 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (+ (* (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))))) into 0 1540976141.079 * [misc]backup-simplify: Simplify 0 into 0 1540976141.079 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976141.080 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1540976141.082 * [misc]backup-simplify: Simplify (- (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (+ (* (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ 0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) (* (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) (/ 0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))))) into (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) 1540976141.082 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) in n 1540976141.082 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 1540976141.082 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1540976141.082 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1540976141.082 * [misc]taylor: Taking taylor expansion of (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1540976141.082 * [misc]taylor: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1540976141.082 * [misc]taylor: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1540976141.082 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1540976141.082 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1540976141.082 * [misc]taylor: Taking taylor expansion of -2 in n 1540976141.082 * [misc]backup-simplify: Simplify -2 into -2 1540976141.082 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1540976141.082 * [misc]taylor: Taking taylor expansion of PI in n 1540976141.082 * [misc]backup-simplify: Simplify PI into PI 1540976141.082 * [misc]taylor: Taking taylor expansion of n in n 1540976141.082 * [misc]backup-simplify: Simplify 0 into 0 1540976141.082 * [misc]backup-simplify: Simplify 1 into 1 1540976141.083 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1540976141.083 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1540976141.083 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1540976141.084 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1540976141.084 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1540976141.084 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976141.084 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976141.084 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1540976141.084 * [misc]taylor: Taking taylor expansion of k in n 1540976141.084 * [misc]backup-simplify: Simplify k into k 1540976141.084 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1540976141.084 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976141.084 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976141.084 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1540976141.085 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1540976141.085 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1540976141.085 * [misc]backup-simplify: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1540976141.086 * [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)))) 1540976141.087 * [misc]backup-simplify: Simplify (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 1540976141.087 * [misc]backup-simplify: Simplify (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 1540976141.088 * [misc]backup-simplify: Simplify (- (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) 1540976141.089 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) 1540976141.093 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (* 1 (/ 1 (- k)))) (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) into (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))))))))) 1540976141.093 * * * [misc]progress: simplifying candidates 1540976141.093 * * * * [misc]progress: [ 1 / 120 ] simplifiying candidate # 1540976141.093 * [enter]simplify: Simplifying (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) 1540976141.094 * * [misc]simplify: iters left: 6 (11 enodes) 1540976141.100 * * [misc]simplify: iters left: 5 (21 enodes) 1540976141.111 * * [misc]simplify: iters left: 4 (47 enodes) 1540976141.138 * * [misc]simplify: iters left: 3 (109 enodes) 1540976141.221 * * [misc]simplify: iters left: 2 (300 enodes) 1540976141.625 * [exit]simplify: Simplified to (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) 1540976141.625 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ 1 (/ (sqrt k) (exp (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))))))) 1540976141.625 * * * * [misc]progress: [ 2 / 120 ] simplifiying candidate # 1540976141.625 * * * * [misc]progress: [ 3 / 120 ] simplifiying candidate # 1540976141.626 * [enter]simplify: Simplifying (* PI (* n 2)) 1540976141.626 * * [misc]simplify: iters left: 4 (5 enodes) 1540976141.628 * * [misc]simplify: iters left: 3 (9 enodes) 1540976141.630 * * [misc]simplify: iters left: 2 (15 enodes) 1540976141.633 * * [misc]simplify: iters left: 1 (17 enodes) 1540976141.636 * [exit]simplify: Simplified to (* (* 2 n) PI) 1540976141.636 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* 2 n) PI) (* 1 (- 1/2 (/ k 2))))))) 1540976141.636 * * * * [misc]progress: [ 4 / 120 ] simplifiying candidate # 1540976141.636 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (/ k 2)) 1540976141.637 * * [misc]simplify: iters left: 5 (8 enodes) 1540976141.639 * * [misc]simplify: iters left: 4 (12 enodes) 1540976141.642 * * [misc]simplify: iters left: 3 (18 enodes) 1540976141.645 * * [misc]simplify: iters left: 2 (20 enodes) 1540976141.648 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ k 2)) 1540976141.648 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (/ (sqrt k) (/ (pow (* PI (* n 2)) 1/2) (pow (* (* 2 n) PI) (/ k 2)))))) 1540976141.648 * * * * [misc]progress: [ 5 / 120 ] simplifiying candidate # 1540976141.649 * [enter]simplify: Simplifying (cbrt (- 1/2 (/ k 2))) 1540976141.649 * * [misc]simplify: iters left: 5 (6 enodes) 1540976141.650 * * [misc]simplify: iters left: 4 (8 enodes) 1540976141.651 * * [misc]simplify: iters left: 3 (11 enodes) 1540976141.653 * [exit]simplify: Simplified to (cbrt (- 1/2 (/ k 2))) 1540976141.653 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* PI (* n 2)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2))))))) 1540976141.653 * * * * [misc]progress: [ 6 / 120 ] simplifiying candidate # 1540976141.653 * [enter]simplify: Simplifying (sqrt (- 1/2 (/ k 2))) 1540976141.654 * * [misc]simplify: iters left: 5 (6 enodes) 1540976141.655 * * [misc]simplify: iters left: 4 (8 enodes) 1540976141.657 * * [misc]simplify: iters left: 3 (11 enodes) 1540976141.658 * [exit]simplify: Simplified to (sqrt (- 1/2 (/ k 2))) 1540976141.658 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* PI (* n 2)) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2))))))) 1540976141.658 * * * * [misc]progress: [ 7 / 120 ] simplifiying candidate # 1540976141.659 * [enter]simplify: Simplifying (- 1/2 (/ k 2)) 1540976141.659 * * [misc]simplify: iters left: 4 (5 enodes) 1540976141.660 * * [misc]simplify: iters left: 3 (7 enodes) 1540976141.664 * * [misc]simplify: iters left: 2 (10 enodes) 1540976141.665 * [exit]simplify: Simplified to (- 1/2 (/ k 2)) 1540976141.665 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* PI (* n 2)) 1) (- 1/2 (/ k 2)))))) 1540976141.666 * * * * [misc]progress: [ 8 / 120 ] simplifiying candidate # 1540976141.666 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1540976141.666 * * [misc]simplify: iters left: 5 (9 enodes) 1540976141.668 * * [misc]simplify: iters left: 4 (15 enodes) 1540976141.671 * * [misc]simplify: iters left: 3 (21 enodes) 1540976141.675 * * [misc]simplify: iters left: 2 (22 enodes) 1540976141.678 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1540976141.678 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (/ (sqrt k) (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2))))))) 1540976141.678 * * * * [misc]progress: [ 9 / 120 ] simplifiying candidate # 1540976141.679 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1540976141.679 * * [misc]simplify: iters left: 5 (9 enodes) 1540976141.681 * * [misc]simplify: iters left: 4 (15 enodes) 1540976141.684 * * [misc]simplify: iters left: 3 (21 enodes) 1540976141.687 * * [misc]simplify: iters left: 2 (22 enodes) 1540976141.691 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1540976141.691 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (/ (sqrt k) (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2))))))) 1540976141.691 * * * * [misc]progress: [ 10 / 120 ] simplifiying candidate # 1540976141.691 * [enter]simplify: Simplifying (pow PI (- 1/2 (/ k 2))) 1540976141.691 * * [misc]simplify: iters left: 5 (7 enodes) 1540976141.693 * * [misc]simplify: iters left: 4 (9 enodes) 1540976141.694 * * [misc]simplify: iters left: 3 (12 enodes) 1540976141.698 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1540976141.698 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ 1 (/ (sqrt k) (* (pow PI (- 1/2 (/ k 2))) (pow (* n 2) (- 1/2 (/ k 2))))))) 1540976141.698 * * * * [misc]progress: [ 11 / 120 ] simplifiying candidate # 1540976141.698 * * * * [misc]progress: [ 12 / 120 ] simplifiying candidate # 1540976141.698 * * * * [misc]progress: [ 13 / 120 ] simplifiying candidate # 1540976141.698 * * * * [misc]progress: [ 14 / 120 ] simplifiying candidate # 1540976141.698 * * * * [misc]progress: [ 15 / 120 ] simplifiying candidate # 1540976141.698 * * * * [misc]progress: [ 16 / 120 ] simplifiying candidate # 1540976141.698 * * * * [misc]progress: [ 17 / 120 ] simplifiying candidate # 1540976141.698 * * * * [misc]progress: [ 18 / 120 ] simplifiying candidate # 1540976141.698 * * * * [misc]progress: [ 19 / 120 ] simplifiying candidate # 1540976141.698 * * * * [misc]progress: [ 20 / 120 ] simplifiying candidate # 1540976141.698 * * * * [misc]progress: [ 21 / 120 ] simplifiying candidate # 1540976141.698 * * * * [misc]progress: [ 22 / 120 ] simplifiying candidate # 1540976141.699 * * * * [misc]progress: [ 23 / 120 ] simplifiying candidate # 1540976141.699 * * * * [misc]progress: [ 24 / 120 ] simplifiying candidate # 1540976141.699 * * * * [misc]progress: [ 25 / 120 ] simplifiying candidate # 1540976141.699 * * * * [misc]progress: [ 26 / 120 ] simplifiying candidate # 1540976141.699 * * * * [misc]progress: [ 27 / 120 ] simplifiying candidate # 1540976141.699 * * * * [misc]progress: [ 28 / 120 ] simplifiying candidate # 1540976141.699 * [enter]simplify: Simplifying (- 1) 1540976141.699 * * [misc]simplify: iters left: 2 (2 enodes) 1540976141.701 * * [misc]simplify: iters left: 1 (5 enodes) 1540976141.702 * [exit]simplify: Simplified to -1 1540976141.702 * [misc]simplify: Simplified (2 2) to (λ (k n) (pow (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) -1)) 1540976141.702 * * * * [misc]progress: [ 29 / 120 ] simplifiying candidate # 1540976141.702 * * * * [misc]progress: [ 30 / 120 ] simplifiying candidate # 1540976141.702 * * * * [misc]progress: [ 31 / 120 ] simplifiying candidate # 1540976141.702 * * * * [misc]progress: [ 32 / 120 ] simplifiying candidate # 1540976141.702 * * * * [misc]progress: [ 33 / 120 ] simplifiying candidate # 1540976141.702 * * * * [misc]progress: [ 34 / 120 ] simplifiying candidate # 1540976141.702 * * * * [misc]progress: [ 35 / 120 ] simplifiying candidate # 1540976141.703 * * * * [misc]progress: [ 36 / 120 ] simplifiying candidate # 1540976141.703 * * * * [misc]progress: [ 37 / 120 ] simplifiying candidate # 1540976141.703 * * * * [misc]progress: [ 38 / 120 ] simplifiying candidate # 1540976141.703 * * * * [misc]progress: [ 39 / 120 ] simplifiying candidate # 1540976141.703 * * * * [misc]progress: [ 40 / 120 ] simplifiying candidate # 1540976141.703 * * * * [misc]progress: [ 41 / 120 ] simplifiying candidate # 1540976141.703 * * * * [misc]progress: [ 42 / 120 ] simplifiying candidate # 1540976141.703 * * * * [misc]progress: [ 43 / 120 ] simplifiying candidate # 1540976141.703 * [enter]simplify: Simplifying (cbrt (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1540976141.704 * * [misc]simplify: iters left: 6 (13 enodes) 1540976141.710 * * [misc]simplify: iters left: 5 (19 enodes) 1540976141.718 * * [misc]simplify: iters left: 4 (28 enodes) 1540976141.727 * * [misc]simplify: iters left: 3 (30 enodes) 1540976141.737 * [exit]simplify: Simplified to (cbrt (/ (sqrt k) (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))) 1540976141.737 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (* (cbrt (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (cbrt (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))) (cbrt (/ (sqrt k) (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))))) 1540976141.737 * * * * [misc]progress: [ 44 / 120 ] simplifiying candidate # 1540976141.738 * [enter]simplify: Simplifying (sqrt (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1540976141.739 * * [misc]simplify: iters left: 6 (13 enodes) 1540976141.744 * * [misc]simplify: iters left: 5 (19 enodes) 1540976141.752 * * [misc]simplify: iters left: 4 (28 enodes) 1540976141.762 * * [misc]simplify: iters left: 3 (30 enodes) 1540976141.771 * [exit]simplify: Simplified to (sqrt (/ (sqrt k) (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))) 1540976141.771 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (sqrt (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) (sqrt (/ (sqrt k) (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))))) 1540976141.771 * * * * [misc]progress: [ 45 / 120 ] simplifiying candidate # 1540976141.772 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (pow (* PI (* n 2)) (- (/ k 2)))) 1540976141.772 * * [misc]simplify: iters left: 6 (12 enodes) 1540976141.775 * * [misc]simplify: iters left: 5 (18 enodes) 1540976141.779 * * [misc]simplify: iters left: 4 (24 enodes) 1540976141.783 * * [misc]simplify: iters left: 3 (25 enodes) 1540976141.787 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2)))) 1540976141.787 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* PI (* n 2)) 1/2))) (/ (cbrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2)))))) 1540976141.788 * * * * [misc]progress: [ 46 / 120 ] simplifiying candidate # 1540976141.788 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (pow (* PI (* n 2)) (- (/ k 2)))) 1540976141.788 * * [misc]simplify: iters left: 6 (12 enodes) 1540976141.791 * * [misc]simplify: iters left: 5 (18 enodes) 1540976141.794 * * [misc]simplify: iters left: 4 (24 enodes) 1540976141.798 * * [misc]simplify: iters left: 3 (25 enodes) 1540976141.803 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2)))) 1540976141.803 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* PI (* n 2)) 1/2))) (/ (cbrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2)))))) 1540976141.803 * * * * [misc]progress: [ 47 / 120 ] simplifiying candidate # 1540976141.803 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))) 1540976141.804 * * [misc]simplify: iters left: 6 (11 enodes) 1540976141.806 * * [misc]simplify: iters left: 5 (14 enodes) 1540976141.810 * * [misc]simplify: iters left: 4 (17 enodes) 1540976141.816 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))) 1540976141.816 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow PI (- 1/2 (/ k 2))))) (/ (cbrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))))) 1540976141.816 * * * * [misc]progress: [ 48 / 120 ] simplifiying candidate # 1540976141.817 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1540976141.818 * * [misc]simplify: iters left: 6 (14 enodes) 1540976141.825 * * [misc]simplify: iters left: 5 (20 enodes) 1540976141.834 * * [misc]simplify: iters left: 4 (29 enodes) 1540976141.843 * * [misc]simplify: iters left: 3 (30 enodes) 1540976141.853 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) 1540976141.853 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))) (/ (cbrt (sqrt k)) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))))) 1540976141.854 * * * * [misc]progress: [ 49 / 120 ] simplifiying candidate # 1540976141.854 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1540976141.855 * * [misc]simplify: iters left: 6 (14 enodes) 1540976141.861 * * [misc]simplify: iters left: 5 (20 enodes) 1540976141.871 * * [misc]simplify: iters left: 4 (29 enodes) 1540976141.880 * * [misc]simplify: iters left: 3 (30 enodes) 1540976141.891 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) 1540976141.891 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) (/ (cbrt (sqrt k)) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))))) 1540976141.892 * * * * [misc]progress: [ 50 / 120 ] simplifiying candidate # 1540976141.892 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1540976141.893 * * [misc]simplify: iters left: 6 (13 enodes) 1540976141.899 * * [misc]simplify: iters left: 5 (19 enodes) 1540976141.907 * * [misc]simplify: iters left: 4 (28 enodes) 1540976141.916 * * [misc]simplify: iters left: 3 (30 enodes) 1540976141.926 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (pow (* 2 (* PI n)) (- 1/2 (/ k 2)))) 1540976141.926 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1)) (/ (cbrt (sqrt k)) (pow (* 2 (* PI n)) (- 1/2 (/ k 2)))))) 1540976141.926 * * * * [misc]progress: [ 51 / 120 ] simplifiying candidate # 1540976141.927 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (pow (* PI (* n 2)) (- (/ k 2)))) 1540976141.928 * * [misc]simplify: iters left: 6 (12 enodes) 1540976141.933 * * [misc]simplify: iters left: 5 (18 enodes) 1540976141.940 * * [misc]simplify: iters left: 4 (24 enodes) 1540976141.948 * * [misc]simplify: iters left: 3 (25 enodes) 1540976141.957 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2)))) 1540976141.957 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (pow (* PI (* n 2)) 1/2))) (/ (sqrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2)))))) 1540976141.957 * * * * [misc]progress: [ 52 / 120 ] simplifiying candidate # 1540976141.957 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (pow (* PI (* n 2)) (- (/ k 2)))) 1540976141.958 * * [misc]simplify: iters left: 6 (12 enodes) 1540976141.964 * * [misc]simplify: iters left: 5 (18 enodes) 1540976141.971 * * [misc]simplify: iters left: 4 (24 enodes) 1540976141.980 * * [misc]simplify: iters left: 3 (25 enodes) 1540976141.989 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2)))) 1540976141.989 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (pow (* PI (* n 2)) 1/2))) (/ (sqrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2)))))) 1540976141.989 * * * * [misc]progress: [ 53 / 120 ] simplifiying candidate # 1540976141.989 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))) 1540976141.990 * * [misc]simplify: iters left: 6 (11 enodes) 1540976141.996 * * [misc]simplify: iters left: 5 (14 enodes) 1540976142.001 * * [misc]simplify: iters left: 4 (17 enodes) 1540976142.005 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))) 1540976142.005 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (pow PI (- 1/2 (/ k 2))))) (/ (sqrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))))) 1540976142.005 * * * * [misc]progress: [ 54 / 120 ] simplifiying candidate # 1540976142.007 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1540976142.007 * * [misc]simplify: iters left: 6 (14 enodes) 1540976142.010 * * [misc]simplify: iters left: 5 (20 enodes) 1540976142.015 * * [misc]simplify: iters left: 4 (29 enodes) 1540976142.020 * * [misc]simplify: iters left: 3 (30 enodes) 1540976142.025 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) 1540976142.025 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))) (/ (sqrt (sqrt k)) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))))) 1540976142.025 * * * * [misc]progress: [ 55 / 120 ] simplifiying candidate # 1540976142.025 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1540976142.026 * * [misc]simplify: iters left: 6 (14 enodes) 1540976142.029 * * [misc]simplify: iters left: 5 (20 enodes) 1540976142.033 * * [misc]simplify: iters left: 4 (29 enodes) 1540976142.037 * * [misc]simplify: iters left: 3 (30 enodes) 1540976142.042 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) 1540976142.042 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) (/ (sqrt (sqrt k)) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))))) 1540976142.042 * * * * [misc]progress: [ 56 / 120 ] simplifiying candidate # 1540976142.042 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1540976142.043 * * [misc]simplify: iters left: 6 (13 enodes) 1540976142.048 * * [misc]simplify: iters left: 5 (19 enodes) 1540976142.056 * * [misc]simplify: iters left: 4 (28 enodes) 1540976142.065 * * [misc]simplify: iters left: 3 (30 enodes) 1540976142.075 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (pow (* 2 (* PI n)) (- 1/2 (/ k 2)))) 1540976142.075 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) 1)) (/ (sqrt (sqrt k)) (pow (* 2 (* PI n)) (- 1/2 (/ k 2)))))) 1540976142.075 * * * * [misc]progress: [ 57 / 120 ] simplifiying candidate # 1540976142.076 * [enter]simplify: Simplifying (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2)))) 1540976142.077 * * [misc]simplify: iters left: 6 (11 enodes) 1540976142.081 * * [misc]simplify: iters left: 5 (17 enodes) 1540976142.088 * * [misc]simplify: iters left: 4 (23 enodes) 1540976142.096 * * [misc]simplify: iters left: 3 (24 enodes) 1540976142.106 * [exit]simplify: Simplified to (/ (sqrt k) (pow (* 2 (* PI n)) (- (/ k 2)))) 1540976142.106 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ 1 (pow (* PI (* n 2)) 1/2))) (/ (sqrt k) (pow (* 2 (* PI n)) (- (/ k 2)))))) 1540976142.106 * * * * [misc]progress: [ 58 / 120 ] simplifiying candidate # 1540976142.107 * [enter]simplify: Simplifying (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2)))) 1540976142.108 * * [misc]simplify: iters left: 6 (11 enodes) 1540976142.113 * * [misc]simplify: iters left: 5 (17 enodes) 1540976142.119 * * [misc]simplify: iters left: 4 (23 enodes) 1540976142.127 * * [misc]simplify: iters left: 3 (24 enodes) 1540976142.135 * [exit]simplify: Simplified to (/ (sqrt k) (pow (* 2 (* PI n)) (- (/ k 2)))) 1540976142.135 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ 1 (pow (* PI (* n 2)) 1/2))) (/ (sqrt k) (pow (* 2 (* PI n)) (- (/ k 2)))))) 1540976142.135 * * * * [misc]progress: [ 59 / 120 ] simplifiying candidate # 1540976142.136 * [enter]simplify: Simplifying (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2)))) 1540976142.137 * * [misc]simplify: iters left: 6 (10 enodes) 1540976142.140 * * [misc]simplify: iters left: 5 (13 enodes) 1540976142.145 * * [misc]simplify: iters left: 4 (16 enodes) 1540976142.151 * [exit]simplify: Simplified to (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2)))) 1540976142.151 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ 1 (pow PI (- 1/2 (/ k 2))))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2)))))) 1540976142.151 * * * * [misc]progress: [ 60 / 120 ] simplifiying candidate # 1540976142.152 * [enter]simplify: Simplifying (/ (sqrt k) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1540976142.153 * * [misc]simplify: iters left: 6 (13 enodes) 1540976142.157 * * [misc]simplify: iters left: 5 (19 enodes) 1540976142.161 * * [misc]simplify: iters left: 4 (28 enodes) 1540976142.166 * * [misc]simplify: iters left: 3 (30 enodes) 1540976142.171 * [exit]simplify: Simplified to (/ (sqrt k) (cbrt (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))) 1540976142.171 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ 1 (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))) (/ (sqrt k) (cbrt (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))))) 1540976142.171 * * * * [misc]progress: [ 61 / 120 ] simplifiying candidate # 1540976142.171 * [enter]simplify: Simplifying (/ (sqrt k) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1540976142.172 * * [misc]simplify: iters left: 6 (13 enodes) 1540976142.175 * * [misc]simplify: iters left: 5 (19 enodes) 1540976142.178 * * [misc]simplify: iters left: 4 (28 enodes) 1540976142.183 * * [misc]simplify: iters left: 3 (30 enodes) 1540976142.188 * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))) 1540976142.188 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ 1 (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) (/ (sqrt k) (sqrt (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))))) 1540976142.188 * * * * [misc]progress: [ 62 / 120 ] simplifiying candidate # 1540976142.188 * [enter]simplify: Simplifying (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1540976142.189 * * [misc]simplify: iters left: 6 (12 enodes) 1540976142.192 * * [misc]simplify: iters left: 5 (18 enodes) 1540976142.196 * * [misc]simplify: iters left: 4 (27 enodes) 1540976142.202 * * [misc]simplify: iters left: 3 (29 enodes) 1540976142.206 * [exit]simplify: Simplified to (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1540976142.206 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ 1 1)) (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) 1540976142.207 * * * * [misc]progress: [ 63 / 120 ] simplifiying candidate # 1540976142.207 * [enter]simplify: Simplifying (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1540976142.207 * * [misc]simplify: iters left: 6 (12 enodes) 1540976142.210 * * [misc]simplify: iters left: 5 (18 enodes) 1540976142.213 * * [misc]simplify: iters left: 4 (27 enodes) 1540976142.218 * * [misc]simplify: iters left: 3 (29 enodes) 1540976142.222 * [exit]simplify: Simplified to (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1540976142.222 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 1) (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) 1540976142.223 * * * * [misc]progress: [ 64 / 120 ] simplifiying candidate # 1540976142.223 * [enter]simplify: Simplifying (/ 1 (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1540976142.223 * * [misc]simplify: iters left: 6 (12 enodes) 1540976142.226 * * [misc]simplify: iters left: 5 (20 enodes) 1540976142.230 * * [misc]simplify: iters left: 4 (29 enodes) 1540976142.234 * * [misc]simplify: iters left: 3 (30 enodes) 1540976142.239 * [exit]simplify: Simplified to (/ 1 (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) 1540976142.239 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (sqrt k)) (/ 1 (pow (* (* n PI) 2) (- 1/2 (/ k 2)))))) 1540976142.239 * * * * [misc]progress: [ 65 / 120 ] simplifiying candidate # 1540976142.239 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (/ k 2)) 1540976142.239 * * [misc]simplify: iters left: 5 (8 enodes) 1540976142.241 * * [misc]simplify: iters left: 4 (12 enodes) 1540976142.244 * * [misc]simplify: iters left: 3 (18 enodes) 1540976142.247 * * [misc]simplify: iters left: 2 (20 enodes) 1540976142.250 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ k 2)) 1540976142.250 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (sqrt k) (pow (* PI (* n 2)) 1/2))) (pow (* (* 2 n) PI) (/ k 2)))) 1540976142.251 * * * * [misc]progress: [ 66 / 120 ] simplifiying candidate # 1540976142.251 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- 1/2 (/ k 2))) 1540976142.251 * * [misc]simplify: iters left: 5 (10 enodes) 1540976142.253 * * [misc]simplify: iters left: 4 (16 enodes) 1540976142.257 * * [misc]simplify: iters left: 3 (25 enodes) 1540976142.261 * * [misc]simplify: iters left: 2 (26 enodes) 1540976142.265 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) 1540976142.265 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) 1540976142.265 * * * * [misc]progress: [ 67 / 120 ] simplifiying candidate # 1540976142.265 * * * * [misc]progress: [ 68 / 120 ] simplifiying candidate # 1540976142.265 * [enter]simplify: Simplifying (- (log (sqrt k)) (* (log (* PI (* n 2))) (- 1/2 (/ k 2)))) 1540976142.267 * * [misc]simplify: iters left: 6 (14 enodes) 1540976142.271 * * [misc]simplify: iters left: 5 (26 enodes) 1540976142.279 * * [misc]simplify: iters left: 4 (59 enodes) 1540976142.304 * * [misc]simplify: iters left: 3 (164 enodes) 1540976142.394 * * [misc]simplify: iters left: 2 (488 enodes) 1540976142.922 * [exit]simplify: Simplified to (+ (log (sqrt k)) (* (+ -1/2 (/ k 2)) (log (* (* PI 2) n)))) 1540976142.923 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (exp (+ (log (sqrt k)) (* (+ -1/2 (/ k 2)) (log (* (* PI 2) n))))))) 1540976142.923 * * * * [misc]progress: [ 69 / 120 ] simplifiying candidate # 1540976142.923 * [enter]simplify: Simplifying (- (log (sqrt k)) (* (log (* PI (* n 2))) (- 1/2 (/ k 2)))) 1540976142.924 * * [misc]simplify: iters left: 6 (14 enodes) 1540976142.927 * * [misc]simplify: iters left: 5 (26 enodes) 1540976142.936 * * [misc]simplify: iters left: 4 (59 enodes) 1540976142.964 * * [misc]simplify: iters left: 3 (164 enodes) 1540976143.060 * * [misc]simplify: iters left: 2 (488 enodes) 1540976143.593 * [exit]simplify: Simplified to (+ (log (sqrt k)) (* (+ -1/2 (/ k 2)) (log (* (* PI 2) n)))) 1540976143.593 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (exp (+ (log (sqrt k)) (* (+ -1/2 (/ k 2)) (log (* (* PI 2) n))))))) 1540976143.593 * * * * [misc]progress: [ 70 / 120 ] simplifiying candidate # 1540976143.593 * [enter]simplify: Simplifying (- (log (sqrt k)) (log (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1540976143.595 * * [misc]simplify: iters left: 6 (14 enodes) 1540976143.602 * * [misc]simplify: iters left: 5 (24 enodes) 1540976143.614 * * [misc]simplify: iters left: 4 (46 enodes) 1540976143.640 * * [misc]simplify: iters left: 3 (103 enodes) 1540976143.720 * * [misc]simplify: iters left: 2 (336 enodes) 1540976144.160 * [exit]simplify: Simplified to (+ (* (log (* n (* PI 2))) (+ (/ k 2) -1/2)) (log (sqrt k))) 1540976144.160 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (exp (+ (* (log (* n (* PI 2))) (+ (/ k 2) -1/2)) (log (sqrt k)))))) 1540976144.160 * * * * [misc]progress: [ 71 / 120 ] simplifiying candidate # 1540976144.160 * * * * [misc]progress: [ 72 / 120 ] simplifiying candidate # 1540976144.160 * * * * [misc]progress: [ 73 / 120 ] simplifiying candidate # 1540976144.160 * [enter]simplify: Simplifying (/ (* (* (sqrt k) (sqrt k)) (sqrt k)) (* (* (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1540976144.162 * * [misc]simplify: iters left: 6 (16 enodes) 1540976144.170 * * [misc]simplify: iters left: 5 (31 enodes) 1540976144.178 * * [misc]simplify: iters left: 4 (70 enodes) 1540976144.205 * * [misc]simplify: iters left: 3 (130 enodes) 1540976144.241 * * [misc]simplify: iters left: 2 (206 enodes) 1540976144.319 * * [misc]simplify: iters left: 1 (288 enodes) 1540976144.494 * [exit]simplify: Simplified to (/ (/ (* k (sqrt k)) (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (* (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (pow (* (* 2 PI) n) (- 1/2 (/ k 2))))) 1540976144.494 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (cbrt (/ (/ (* k (sqrt k)) (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (* (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))))))) 1540976144.494 * * * * [misc]progress: [ 74 / 120 ] simplifiying candidate # 1540976144.494 * * * * [misc]progress: [ 75 / 120 ] simplifiying candidate # 1540976144.494 * * * * [misc]progress: [ 76 / 120 ] simplifiying candidate # 1540976144.494 * * * * [misc]progress: [ 77 / 120 ] simplifiying candidate # 1540976144.494 * * * * [misc]progress: [ 78 / 120 ] simplifiying candidate # 1540976144.495 * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* PI (* n 2)) 1/2)) 1540976144.496 * * [misc]simplify: iters left: 6 (12 enodes) 1540976144.500 * * [misc]simplify: iters left: 5 (19 enodes) 1540976144.509 * * [misc]simplify: iters left: 4 (27 enodes) 1540976144.518 * * [misc]simplify: iters left: 3 (29 enodes) 1540976144.528 * [exit]simplify: Simplified to (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (* (* n 2) PI))) 1540976144.528 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (* (* n 2) PI))) (/ (cbrt (sqrt k)) (pow (* PI (* n 2)) (- (/ k 2))))))) 1540976144.528 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (pow (* PI (* n 2)) (- (/ k 2)))) 1540976144.529 * * [misc]simplify: iters left: 6 (12 enodes) 1540976144.534 * * [misc]simplify: iters left: 5 (18 enodes) 1540976144.541 * * [misc]simplify: iters left: 4 (24 enodes) 1540976144.549 * * [misc]simplify: iters left: 3 (25 enodes) 1540976144.558 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2)))) 1540976144.558 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (* (* n 2) PI))) (/ (cbrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2))))))) 1540976144.558 * * * * [misc]progress: [ 79 / 120 ] simplifiying candidate # 1540976144.558 * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* PI (* n 2)) 1/2)) 1540976144.560 * * [misc]simplify: iters left: 6 (12 enodes) 1540976144.565 * * [misc]simplify: iters left: 5 (19 enodes) 1540976144.573 * * [misc]simplify: iters left: 4 (27 enodes) 1540976144.581 * * [misc]simplify: iters left: 3 (29 enodes) 1540976144.592 * [exit]simplify: Simplified to (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (* (* n 2) PI))) 1540976144.592 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (* (* n 2) PI))) (/ (cbrt (sqrt k)) (pow (* PI (* n 2)) (- (/ k 2))))))) 1540976144.592 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (pow (* PI (* n 2)) (- (/ k 2)))) 1540976144.594 * * [misc]simplify: iters left: 6 (12 enodes) 1540976144.599 * * [misc]simplify: iters left: 5 (18 enodes) 1540976144.605 * * [misc]simplify: iters left: 4 (24 enodes) 1540976144.613 * * [misc]simplify: iters left: 3 (25 enodes) 1540976144.621 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2)))) 1540976144.622 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (* (* n 2) PI))) (/ (cbrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2))))))) 1540976144.622 * * * * [misc]progress: [ 80 / 120 ] simplifiying candidate # 1540976144.622 * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow PI (- 1/2 (/ k 2)))) 1540976144.623 * * [misc]simplify: iters left: 6 (11 enodes) 1540976144.628 * * [misc]simplify: iters left: 5 (15 enodes) 1540976144.634 * * [misc]simplify: iters left: 4 (20 enodes) 1540976144.640 * * [misc]simplify: iters left: 3 (21 enodes) 1540976144.648 * [exit]simplify: Simplified to (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow PI (- 1/2 (/ k 2)))) 1540976144.648 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow PI (- 1/2 (/ k 2)))) (/ (cbrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2))))))) 1540976144.648 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))) 1540976144.649 * * [misc]simplify: iters left: 6 (11 enodes) 1540976144.653 * * [misc]simplify: iters left: 5 (14 enodes) 1540976144.658 * * [misc]simplify: iters left: 4 (17 enodes) 1540976144.664 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))) 1540976144.664 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow PI (- 1/2 (/ k 2)))) (/ (cbrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2))))))) 1540976144.664 * * * * [misc]progress: [ 81 / 120 ] simplifiying candidate # 1540976144.665 * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) 1540976144.666 * * [misc]simplify: iters left: 6 (16 enodes) 1540976144.674 * * [misc]simplify: iters left: 5 (28 enodes) 1540976144.687 * * [misc]simplify: iters left: 4 (46 enodes) 1540976144.703 * * [misc]simplify: iters left: 3 (50 enodes) 1540976144.718 * * [misc]simplify: iters left: 2 (53 enodes) 1540976144.740 * [exit]simplify: Simplified to (* (/ (cbrt (sqrt k)) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) (/ (cbrt (sqrt k)) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))))) 1540976144.740 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (* (/ (cbrt (sqrt k)) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) (/ (cbrt (sqrt k)) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))))) (/ (cbrt (sqrt k)) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))))) 1540976144.740 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1540976144.742 * * [misc]simplify: iters left: 6 (14 enodes) 1540976144.747 * * [misc]simplify: iters left: 5 (20 enodes) 1540976144.755 * * [misc]simplify: iters left: 4 (29 enodes) 1540976144.765 * * [misc]simplify: iters left: 3 (30 enodes) 1540976144.775 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) 1540976144.775 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) (/ (cbrt (sqrt k)) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))))))) 1540976144.775 * * * * [misc]progress: [ 82 / 120 ] simplifiying candidate # 1540976144.775 * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1540976144.778 * * [misc]simplify: iters left: 6 (15 enodes) 1540976144.784 * * [misc]simplify: iters left: 5 (23 enodes) 1540976144.793 * * [misc]simplify: iters left: 4 (34 enodes) 1540976144.804 * * [misc]simplify: iters left: 3 (36 enodes) 1540976144.818 * [exit]simplify: Simplified to (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) 1540976144.818 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) (/ (cbrt (sqrt k)) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))))) 1540976144.818 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1540976144.819 * * [misc]simplify: iters left: 6 (14 enodes) 1540976144.825 * * [misc]simplify: iters left: 5 (20 enodes) 1540976144.835 * * [misc]simplify: iters left: 4 (29 enodes) 1540976144.844 * * [misc]simplify: iters left: 3 (30 enodes) 1540976144.854 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) 1540976144.854 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (/ (cbrt (sqrt k)) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))))))) 1540976144.854 * * * * [misc]progress: [ 83 / 120 ] simplifiying candidate # 1540976144.855 * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1) 1540976144.855 * * [misc]simplify: iters left: 6 (6 enodes) 1540976144.856 * * [misc]simplify: iters left: 5 (10 enodes) 1540976144.859 * * [misc]simplify: iters left: 4 (16 enodes) 1540976144.862 * * [misc]simplify: iters left: 3 (18 enodes) 1540976144.864 * * [misc]simplify: iters left: 2 (23 enodes) 1540976144.867 * [exit]simplify: Simplified to (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1540976144.867 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (cbrt (sqrt k)) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))) 1540976144.867 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1540976144.868 * * [misc]simplify: iters left: 6 (13 enodes) 1540976144.871 * * [misc]simplify: iters left: 5 (19 enodes) 1540976144.874 * * [misc]simplify: iters left: 4 (28 enodes) 1540976144.879 * * [misc]simplify: iters left: 3 (30 enodes) 1540976144.884 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (pow (* 2 (* PI n)) (- 1/2 (/ k 2)))) 1540976144.884 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (cbrt (sqrt k)) (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))))) 1540976144.884 * * * * [misc]progress: [ 84 / 120 ] simplifiying candidate # 1540976144.884 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (pow (* PI (* n 2)) 1/2)) 1540976144.885 * * [misc]simplify: iters left: 6 (11 enodes) 1540976144.887 * * [misc]simplify: iters left: 5 (16 enodes) 1540976144.891 * * [misc]simplify: iters left: 4 (22 enodes) 1540976144.894 * * [misc]simplify: iters left: 3 (23 enodes) 1540976144.899 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (sqrt (* (* PI n) 2))) 1540976144.899 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (sqrt (* (* PI n) 2))) (/ (sqrt (sqrt k)) (pow (* PI (* n 2)) (- (/ k 2))))))) 1540976144.899 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (pow (* PI (* n 2)) (- (/ k 2)))) 1540976144.901 * * [misc]simplify: iters left: 6 (12 enodes) 1540976144.903 * * [misc]simplify: iters left: 5 (18 enodes) 1540976144.907 * * [misc]simplify: iters left: 4 (24 enodes) 1540976144.911 * * [misc]simplify: iters left: 3 (25 enodes) 1540976144.916 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2)))) 1540976144.917 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (sqrt (* (* PI n) 2))) (/ (sqrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2))))))) 1540976144.917 * * * * [misc]progress: [ 85 / 120 ] simplifiying candidate # 1540976144.917 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (pow (* PI (* n 2)) 1/2)) 1540976144.917 * * [misc]simplify: iters left: 6 (11 enodes) 1540976144.920 * * [misc]simplify: iters left: 5 (16 enodes) 1540976144.923 * * [misc]simplify: iters left: 4 (22 enodes) 1540976144.927 * * [misc]simplify: iters left: 3 (23 enodes) 1540976144.931 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (sqrt (* (* PI n) 2))) 1540976144.931 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (sqrt (* (* PI n) 2))) (/ (sqrt (sqrt k)) (pow (* PI (* n 2)) (- (/ k 2))))))) 1540976144.931 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (pow (* PI (* n 2)) (- (/ k 2)))) 1540976144.932 * * [misc]simplify: iters left: 6 (12 enodes) 1540976144.935 * * [misc]simplify: iters left: 5 (18 enodes) 1540976144.938 * * [misc]simplify: iters left: 4 (24 enodes) 1540976144.942 * * [misc]simplify: iters left: 3 (25 enodes) 1540976144.946 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2)))) 1540976144.946 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (sqrt (* (* PI n) 2))) (/ (sqrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2))))))) 1540976144.946 * * * * [misc]progress: [ 86 / 120 ] simplifiying candidate # 1540976144.946 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (pow PI (- 1/2 (/ k 2)))) 1540976144.947 * * [misc]simplify: iters left: 6 (10 enodes) 1540976144.949 * * [misc]simplify: iters left: 5 (12 enodes) 1540976144.951 * * [misc]simplify: iters left: 4 (15 enodes) 1540976144.953 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (pow PI (- 1/2 (/ k 2)))) 1540976144.953 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (pow PI (- 1/2 (/ k 2)))) (/ (sqrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2))))))) 1540976144.953 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))) 1540976144.954 * * [misc]simplify: iters left: 6 (11 enodes) 1540976144.956 * * [misc]simplify: iters left: 5 (14 enodes) 1540976144.958 * * [misc]simplify: iters left: 4 (17 enodes) 1540976144.961 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))) 1540976144.961 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (pow PI (- 1/2 (/ k 2)))) (/ (sqrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2))))))) 1540976144.961 * * * * [misc]progress: [ 87 / 120 ] simplifiying candidate # 1540976144.961 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) 1540976144.962 * * [misc]simplify: iters left: 6 (15 enodes) 1540976144.965 * * [misc]simplify: iters left: 5 (23 enodes) 1540976144.970 * * [misc]simplify: iters left: 4 (32 enodes) 1540976144.975 * * [misc]simplify: iters left: 3 (34 enodes) 1540976144.981 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (* (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))))) 1540976144.981 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (* (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))))) (/ (sqrt (sqrt k)) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))))) 1540976144.981 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1540976144.984 * * [misc]simplify: iters left: 6 (14 enodes) 1540976144.989 * * [misc]simplify: iters left: 5 (20 enodes) 1540976144.997 * * [misc]simplify: iters left: 4 (29 enodes) 1540976145.007 * * [misc]simplify: iters left: 3 (30 enodes) 1540976145.016 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) 1540976145.016 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) (/ (sqrt (sqrt k)) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))))))) 1540976145.016 * * * * [misc]progress: [ 88 / 120 ] simplifiying candidate # 1540976145.016 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1540976145.018 * * [misc]simplify: iters left: 6 (14 enodes) 1540976145.023 * * [misc]simplify: iters left: 5 (20 enodes) 1540976145.030 * * [misc]simplify: iters left: 4 (29 enodes) 1540976145.038 * * [misc]simplify: iters left: 3 (30 enodes) 1540976145.048 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) 1540976145.048 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) (/ (sqrt (sqrt k)) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))))) 1540976145.048 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1540976145.050 * * [misc]simplify: iters left: 6 (14 enodes) 1540976145.055 * * [misc]simplify: iters left: 5 (20 enodes) 1540976145.063 * * [misc]simplify: iters left: 4 (29 enodes) 1540976145.072 * * [misc]simplify: iters left: 3 (30 enodes) 1540976145.082 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) 1540976145.082 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (/ (sqrt (sqrt k)) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))))))) 1540976145.083 * * * * [misc]progress: [ 89 / 120 ] simplifiying candidate # 1540976145.083 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) 1) 1540976145.083 * * [misc]simplify: iters left: 4 (5 enodes) 1540976145.085 * * [misc]simplify: iters left: 3 (7 enodes) 1540976145.088 * * [misc]simplify: iters left: 2 (9 enodes) 1540976145.090 * [exit]simplify: Simplified to (sqrt (sqrt k)) 1540976145.090 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))) 1540976145.091 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1540976145.092 * * [misc]simplify: iters left: 6 (13 enodes) 1540976145.098 * * [misc]simplify: iters left: 5 (19 enodes) 1540976145.105 * * [misc]simplify: iters left: 4 (28 enodes) 1540976145.120 * * [misc]simplify: iters left: 3 (30 enodes) 1540976145.130 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (pow (* 2 (* PI n)) (- 1/2 (/ k 2)))) 1540976145.130 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))))) 1540976145.130 * * * * [misc]progress: [ 90 / 120 ] simplifiying candidate # 1540976145.131 * [enter]simplify: Simplifying (/ 1 (pow (* PI (* n 2)) 1/2)) 1540976145.131 * * [misc]simplify: iters left: 6 (9 enodes) 1540976145.135 * * [misc]simplify: iters left: 5 (16 enodes) 1540976145.150 * * [misc]simplify: iters left: 4 (22 enodes) 1540976145.156 * * [misc]simplify: iters left: 3 (23 enodes) 1540976145.164 * [exit]simplify: Simplified to (/ 1 (sqrt (* n (* 2 PI)))) 1540976145.164 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ 1 (sqrt (* n (* 2 PI)))) (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2))))))) 1540976145.165 * [enter]simplify: Simplifying (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2)))) 1540976145.166 * * [misc]simplify: iters left: 6 (11 enodes) 1540976145.171 * * [misc]simplify: iters left: 5 (17 enodes) 1540976145.177 * * [misc]simplify: iters left: 4 (23 enodes) 1540976145.185 * * [misc]simplify: iters left: 3 (24 enodes) 1540976145.193 * [exit]simplify: Simplified to (/ (sqrt k) (pow (* 2 (* PI n)) (- (/ k 2)))) 1540976145.193 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ 1 (sqrt (* n (* 2 PI)))) (/ (sqrt k) (pow (* 2 (* PI n)) (- (/ k 2))))))) 1540976145.193 * * * * [misc]progress: [ 91 / 120 ] simplifiying candidate # 1540976145.193 * [enter]simplify: Simplifying (/ 1 (pow (* PI (* n 2)) 1/2)) 1540976145.194 * * [misc]simplify: iters left: 6 (9 enodes) 1540976145.198 * * [misc]simplify: iters left: 5 (16 enodes) 1540976145.204 * * [misc]simplify: iters left: 4 (22 enodes) 1540976145.211 * * [misc]simplify: iters left: 3 (23 enodes) 1540976145.218 * [exit]simplify: Simplified to (/ 1 (sqrt (* n (* 2 PI)))) 1540976145.218 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ 1 (sqrt (* n (* 2 PI)))) (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2))))))) 1540976145.218 * [enter]simplify: Simplifying (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2)))) 1540976145.219 * * [misc]simplify: iters left: 6 (11 enodes) 1540976145.223 * * [misc]simplify: iters left: 5 (17 enodes) 1540976145.230 * * [misc]simplify: iters left: 4 (23 enodes) 1540976145.236 * * [misc]simplify: iters left: 3 (24 enodes) 1540976145.243 * [exit]simplify: Simplified to (/ (sqrt k) (pow (* 2 (* PI n)) (- (/ k 2)))) 1540976145.243 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ 1 (sqrt (* n (* 2 PI)))) (/ (sqrt k) (pow (* 2 (* PI n)) (- (/ k 2))))))) 1540976145.244 * * * * [misc]progress: [ 92 / 120 ] simplifiying candidate # 1540976145.244 * [enter]simplify: Simplifying (/ 1 (pow PI (- 1/2 (/ k 2)))) 1540976145.244 * * [misc]simplify: iters left: 6 (9 enodes) 1540976145.247 * * [misc]simplify: iters left: 5 (13 enodes) 1540976145.253 * * [misc]simplify: iters left: 4 (16 enodes) 1540976145.258 * [exit]simplify: Simplified to (/ 1 (pow PI (- 1/2 (/ k 2)))) 1540976145.258 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ 1 (pow PI (- 1/2 (/ k 2)))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))))) 1540976145.258 * [enter]simplify: Simplifying (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2)))) 1540976145.259 * * [misc]simplify: iters left: 6 (10 enodes) 1540976145.262 * * [misc]simplify: iters left: 5 (13 enodes) 1540976145.264 * * [misc]simplify: iters left: 4 (16 enodes) 1540976145.267 * [exit]simplify: Simplified to (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2)))) 1540976145.267 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ 1 (pow PI (- 1/2 (/ k 2)))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))))) 1540976145.267 * * * * [misc]progress: [ 93 / 120 ] simplifiying candidate # 1540976145.267 * [enter]simplify: Simplifying (/ 1 (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) 1540976145.268 * * [misc]simplify: iters left: 6 (14 enodes) 1540976145.272 * * [misc]simplify: iters left: 5 (24 enodes) 1540976145.276 * * [misc]simplify: iters left: 4 (33 enodes) 1540976145.281 * * [misc]simplify: iters left: 3 (34 enodes) 1540976145.288 * [exit]simplify: Simplified to (/ (/ 1 (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) 1540976145.288 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ (/ 1 (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) (/ (sqrt k) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))))) 1540976145.288 * [enter]simplify: Simplifying (/ (sqrt k) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1540976145.289 * * [misc]simplify: iters left: 6 (13 enodes) 1540976145.295 * * [misc]simplify: iters left: 5 (19 enodes) 1540976145.302 * * [misc]simplify: iters left: 4 (28 enodes) 1540976145.312 * * [misc]simplify: iters left: 3 (30 enodes) 1540976145.322 * [exit]simplify: Simplified to (/ (sqrt k) (cbrt (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))) 1540976145.322 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ 1 (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) (/ (sqrt k) (cbrt (pow (* 2 (* PI n)) (- 1/2 (/ k 2)))))))) 1540976145.322 * * * * [misc]progress: [ 94 / 120 ] simplifiying candidate # 1540976145.322 * [enter]simplify: Simplifying (/ 1 (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1540976145.323 * * [misc]simplify: iters left: 6 (13 enodes) 1540976145.330 * * [misc]simplify: iters left: 5 (21 enodes) 1540976145.338 * * [misc]simplify: iters left: 4 (30 enodes) 1540976145.347 * * [misc]simplify: iters left: 3 (31 enodes) 1540976145.358 * [exit]simplify: Simplified to (/ 1 (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2))))) 1540976145.358 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ 1 (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2))))) (/ (sqrt k) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))))) 1540976145.358 * [enter]simplify: Simplifying (/ (sqrt k) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1540976145.362 * * [misc]simplify: iters left: 6 (13 enodes) 1540976145.365 * * [misc]simplify: iters left: 5 (19 enodes) 1540976145.369 * * [misc]simplify: iters left: 4 (28 enodes) 1540976145.373 * * [misc]simplify: iters left: 3 (30 enodes) 1540976145.378 * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))) 1540976145.378 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ 1 (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (/ (sqrt k) (sqrt (pow (* 2 (* PI n)) (- 1/2 (/ k 2)))))))) 1540976145.378 * * * * [misc]progress: [ 95 / 120 ] simplifiying candidate # 1540976145.378 * [enter]simplify: Simplifying (/ 1 1) 1540976145.378 * * [misc]simplify: iters left: 2 (2 enodes) 1540976145.379 * * [misc]simplify: iters left: 1 (4 enodes) 1540976145.379 * [exit]simplify: Simplified to 1 1540976145.379 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* 1 (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))) 1540976145.379 * [enter]simplify: Simplifying (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1540976145.380 * * [misc]simplify: iters left: 6 (12 enodes) 1540976145.382 * * [misc]simplify: iters left: 5 (18 enodes) 1540976145.386 * * [misc]simplify: iters left: 4 (27 enodes) 1540976145.394 * * [misc]simplify: iters left: 3 (29 enodes) 1540976145.404 * [exit]simplify: Simplified to (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1540976145.404 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* 1 (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))) 1540976145.404 * * * * [misc]progress: [ 96 / 120 ] simplifiying candidate # 1540976145.404 * * * * [misc]progress: [ 97 / 120 ] simplifiying candidate # 1540976145.404 * * * * [misc]progress: [ 98 / 120 ] simplifiying candidate # 1540976145.404 * * * * [misc]progress: [ 99 / 120 ] simplifiying candidate # 1540976145.404 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1540976145.405 * * [misc]simplify: iters left: 5 (9 enodes) 1540976145.409 * * [misc]simplify: iters left: 4 (15 enodes) 1540976145.415 * * [misc]simplify: iters left: 3 (21 enodes) 1540976145.422 * * [misc]simplify: iters left: 2 (22 enodes) 1540976145.430 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1540976145.430 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (/ (/ (sqrt k) (pow (* PI (* n 2)) 1/2)) (pow (* (* PI n) 2) (- (/ k 2)))))) 1540976145.430 * * * * [misc]progress: [ 100 / 120 ] simplifiying candidate # 1540976145.431 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1540976145.431 * * [misc]simplify: iters left: 5 (9 enodes) 1540976145.436 * * [misc]simplify: iters left: 4 (15 enodes) 1540976145.443 * * [misc]simplify: iters left: 3 (21 enodes) 1540976145.450 * * [misc]simplify: iters left: 2 (22 enodes) 1540976145.457 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1540976145.457 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (/ (/ (sqrt k) (pow (* PI (* n 2)) 1/2)) (pow (* (* PI n) 2) (- (/ k 2)))))) 1540976145.457 * * * * [misc]progress: [ 101 / 120 ] simplifiying candidate # 1540976145.458 * [enter]simplify: Simplifying (pow (* n 2) (- 1/2 (/ k 2))) 1540976145.458 * * [misc]simplify: iters left: 5 (8 enodes) 1540976145.461 * * [misc]simplify: iters left: 4 (11 enodes) 1540976145.465 * * [misc]simplify: iters left: 3 (14 enodes) 1540976145.470 * [exit]simplify: Simplified to (pow (* n 2) (- 1/2 (/ k 2))) 1540976145.470 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (/ (/ (sqrt k) (pow PI (- 1/2 (/ k 2)))) (pow (* n 2) (- 1/2 (/ k 2)))))) 1540976145.470 * * * * [misc]progress: [ 102 / 120 ] simplifiying candidate # 1540976145.470 * [enter]simplify: Simplifying (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1540976145.473 * * [misc]simplify: iters left: 6 (11 enodes) 1540976145.478 * * [misc]simplify: iters left: 5 (17 enodes) 1540976145.485 * * [misc]simplify: iters left: 4 (26 enodes) 1540976145.490 * * [misc]simplify: iters left: 3 (27 enodes) 1540976145.494 * [exit]simplify: Simplified to (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) 1540976145.494 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (/ (/ (sqrt k) (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))))) 1540976145.494 * * * * [misc]progress: [ 103 / 120 ] simplifiying candidate # 1540976145.495 * [enter]simplify: Simplifying (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1540976145.496 * * [misc]simplify: iters left: 6 (11 enodes) 1540976145.498 * * [misc]simplify: iters left: 5 (17 enodes) 1540976145.502 * * [misc]simplify: iters left: 4 (26 enodes) 1540976145.506 * * [misc]simplify: iters left: 3 (27 enodes) 1540976145.510 * [exit]simplify: Simplified to (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) 1540976145.510 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (/ (/ (sqrt k) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))))) 1540976145.510 * * * * [misc]progress: [ 104 / 120 ] simplifiying candidate # 1540976145.510 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- 1/2 (/ k 2))) 1540976145.511 * * [misc]simplify: iters left: 5 (10 enodes) 1540976145.513 * * [misc]simplify: iters left: 4 (16 enodes) 1540976145.517 * * [misc]simplify: iters left: 3 (25 enodes) 1540976145.525 * * [misc]simplify: iters left: 2 (26 enodes) 1540976145.533 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) 1540976145.533 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (/ (/ (sqrt k) 1) (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))))) 1540976145.533 * * * * [misc]progress: [ 105 / 120 ] simplifiying candidate # 1540976145.534 * [enter]simplify: Simplifying (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1540976145.534 * * [misc]simplify: iters left: 4 (4 enodes) 1540976145.536 * [exit]simplify: Simplified to (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1540976145.536 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (cbrt (sqrt k)))))) 1540976145.536 * * * * [misc]progress: [ 106 / 120 ] simplifiying candidate # 1540976145.536 * [enter]simplify: Simplifying (sqrt (sqrt k)) 1540976145.536 * * [misc]simplify: iters left: 2 (3 enodes) 1540976145.537 * [exit]simplify: Simplified to (sqrt (sqrt k)) 1540976145.537 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (/ (sqrt (sqrt k)) (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))) 1540976145.537 * * * * [misc]progress: [ 107 / 120 ] simplifiying candidate # 1540976145.537 * * * * [misc]progress: [ 108 / 120 ] simplifiying candidate # 1540976145.538 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (/ k 2)) 1540976145.538 * * [misc]simplify: iters left: 5 (8 enodes) 1540976145.542 * * [misc]simplify: iters left: 4 (12 enodes) 1540976145.547 * * [misc]simplify: iters left: 3 (18 enodes) 1540976145.553 * * [misc]simplify: iters left: 2 (20 enodes) 1540976145.560 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ k 2)) 1540976145.560 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (sqrt k) (pow (* PI (* n 2)) 1/2)) (pow (* (* 2 n) PI) (/ k 2))))) 1540976145.560 * * * * [misc]progress: [ 109 / 120 ] simplifiying candidate # 1540976145.561 * [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))))) 1540976145.565 * * [misc]simplify: iters left: 6 (37 enodes) 1540976145.591 * * [misc]simplify: iters left: 5 (105 enodes) 1540976145.634 * * [misc]simplify: iters left: 4 (339 enodes) 1540976146.090 * [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))))) 1540976146.090 * [misc]simplify: Simplified (2 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)))))))) 1540976146.090 * * * * [misc]progress: [ 110 / 120 ] simplifiying candidate # 1540976146.090 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 1540976146.091 * * [misc]simplify: iters left: 6 (15 enodes) 1540976146.097 * * [misc]simplify: iters left: 5 (33 enodes) 1540976146.106 * * [misc]simplify: iters left: 4 (64 enodes) 1540976146.130 * * [misc]simplify: iters left: 3 (171 enodes) 1540976146.321 * [exit]simplify: Simplified to (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow n (- 1/2 (* 1/2 k)))) 1540976146.321 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (/ (sqrt k) (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow n (- 1/2 (* 1/2 k))))))) 1540976146.321 * * * * [misc]progress: [ 111 / 120 ] simplifiying candidate # 1540976146.321 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 1540976146.322 * * [misc]simplify: iters left: 6 (15 enodes) 1540976146.327 * * [misc]simplify: iters left: 5 (30 enodes) 1540976146.342 * * [misc]simplify: iters left: 4 (65 enodes) 1540976146.386 * * [misc]simplify: iters left: 3 (200 enodes) 1540976146.619 * [exit]simplify: Simplified to (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))) 1540976146.619 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (/ (sqrt k) (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n))))))) 1540976146.619 * * * * [misc]progress: [ 112 / 120 ] simplifiying candidate # 1540976146.619 * [enter]simplify: Simplifying (* 2 (* n PI)) 1540976146.620 * * [misc]simplify: iters left: 4 (5 enodes) 1540976146.621 * * [misc]simplify: iters left: 3 (9 enodes) 1540976146.623 * * [misc]simplify: iters left: 2 (15 enodes) 1540976146.626 * * [misc]simplify: iters left: 1 (17 enodes) 1540976146.628 * [exit]simplify: Simplified to (* (* PI n) 2) 1540976146.628 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* PI n) 2) (- 1/2 (/ k 2)))))) 1540976146.628 * * * * [misc]progress: [ 113 / 120 ] simplifiying candidate # 1540976146.628 * [enter]simplify: Simplifying (* 2 (* n PI)) 1540976146.629 * * [misc]simplify: iters left: 4 (5 enodes) 1540976146.630 * * [misc]simplify: iters left: 3 (9 enodes) 1540976146.632 * * [misc]simplify: iters left: 2 (15 enodes) 1540976146.635 * * [misc]simplify: iters left: 1 (17 enodes) 1540976146.637 * [exit]simplify: Simplified to (* (* PI n) 2) 1540976146.637 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* PI n) 2) (- 1/2 (/ k 2)))))) 1540976146.638 * * * * [misc]progress: [ 114 / 120 ] simplifiying candidate # 1540976146.638 * [enter]simplify: Simplifying (* 2 (* n PI)) 1540976146.638 * * [misc]simplify: iters left: 4 (5 enodes) 1540976146.639 * * [misc]simplify: iters left: 3 (9 enodes) 1540976146.641 * * [misc]simplify: iters left: 2 (15 enodes) 1540976146.644 * * [misc]simplify: iters left: 1 (17 enodes) 1540976146.646 * [exit]simplify: Simplified to (* (* PI n) 2) 1540976146.646 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* PI n) 2) (- 1/2 (/ k 2)))))) 1540976146.646 * * * * [misc]progress: [ 115 / 120 ] simplifiying candidate # 1540976146.647 * [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))))))))))))) 1540976146.647 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1540976146.647 * * * * [misc]progress: [ 116 / 120 ] simplifiying candidate # 1540976146.647 * [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)))))))) 1540976146.647 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1540976146.647 * * * * [misc]progress: [ 117 / 120 ] simplifiying candidate # 1540976146.647 * [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))))))))))) 1540976146.647 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1540976146.647 * * * * [misc]progress: [ 118 / 120 ] simplifiying candidate # 1540976146.647 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow k 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI))))) PI)) (- (+ (* +nan.0 (/ (* (sqrt 1/2) (pow k 2)) PI)) (- (+ (* +nan.0 (/ (* n (* (sqrt 1/2) k)) (pow PI 2))) (- (+ (* +nan.0 (/ (* (log n) (* (sqrt 2) (* (pow (sqrt 1/2) 2) (pow k 2)))) PI)) (- (* +nan.0 (/ (* (sqrt 1/2) k) PI))))))))))) 1540976146.647 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ 1 +nan.0)) 1540976146.647 * * * * [misc]progress: [ 119 / 120 ] simplifiying candidate # 1540976146.647 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))))))))) 1540976146.648 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ 1 +nan.0)) 1540976146.648 * * * * [misc]progress: [ 120 / 120 ] simplifiying candidate # 1540976146.648 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))))))))) 1540976146.648 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ 1 +nan.0)) 1540976146.648 * * * [misc]progress: adding candidates to table 1540976149.392 * * [misc]progress: iteration 3 / 4 1540976149.392 * * * [misc]progress: picking best candidate 1540976149.506 * * * * [misc]pick: Picked # 1540976149.506 * * * [misc]progress: localizing error 1540976149.519 * * * [misc]progress: generating rewritten candidates 1540976149.519 * * * * [misc]progress: [ 1 / 4 ] rewriting at (2 1 2 1) 1540976149.538 * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 1 1 1) 1540976149.557 * * * * [misc]progress: [ 3 / 4 ] rewriting at (2 1 2 1 1) 1540976149.580 * * * * [misc]progress: [ 4 / 4 ] rewriting at (2 1 1 1 1) 1540976149.593 * * * [misc]progress: generating series expansions 1540976149.593 * * * * [misc]progress: [ 1 / 4 ] generating series at (2 1 2 1) 1540976149.594 * [misc]backup-simplify: Simplify (pow (* PI (* n 2)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 1540976149.594 * [misc]approximate: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 1540976149.594 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1540976149.594 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1540976149.594 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1540976149.594 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1540976149.594 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976149.594 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976149.594 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1540976149.594 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976149.594 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976149.594 * [misc]taylor: Taking taylor expansion of k in k 1540976149.594 * [misc]backup-simplify: Simplify 0 into 0 1540976149.594 * [misc]backup-simplify: Simplify 1 into 1 1540976149.594 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1540976149.594 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1540976149.594 * [misc]taylor: Taking taylor expansion of 2 in k 1540976149.594 * [misc]backup-simplify: Simplify 2 into 2 1540976149.594 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1540976149.594 * [misc]taylor: Taking taylor expansion of n in k 1540976149.594 * [misc]backup-simplify: Simplify n into n 1540976149.594 * [misc]taylor: Taking taylor expansion of PI in k 1540976149.594 * [misc]backup-simplify: Simplify PI into PI 1540976149.594 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1540976149.594 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1540976149.594 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1540976149.594 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1540976149.595 * [misc]backup-simplify: Simplify (- 0) into 0 1540976149.595 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1540976149.595 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1540976149.595 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1540976149.595 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1540976149.595 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1540976149.595 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1540976149.595 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1540976149.595 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976149.595 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976149.595 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1540976149.595 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976149.595 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976149.595 * [misc]taylor: Taking taylor expansion of k in n 1540976149.595 * [misc]backup-simplify: Simplify k into k 1540976149.595 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1540976149.595 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1540976149.595 * [misc]taylor: Taking taylor expansion of 2 in n 1540976149.595 * [misc]backup-simplify: Simplify 2 into 2 1540976149.595 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1540976149.595 * [misc]taylor: Taking taylor expansion of n in n 1540976149.595 * [misc]backup-simplify: Simplify 0 into 0 1540976149.595 * [misc]backup-simplify: Simplify 1 into 1 1540976149.595 * [misc]taylor: Taking taylor expansion of PI in n 1540976149.595 * [misc]backup-simplify: Simplify PI into PI 1540976149.596 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1540976149.596 * [misc]backup-simplify: Simplify (* 2 0) into 0 1540976149.596 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1540976149.597 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1540976149.597 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1540976149.597 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1540976149.597 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1540976149.597 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1540976149.598 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1540976149.598 * [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)))) 1540976149.599 * [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))))) 1540976149.599 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1540976149.599 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1540976149.599 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1540976149.599 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1540976149.599 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976149.599 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976149.599 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1540976149.599 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976149.599 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976149.599 * [misc]taylor: Taking taylor expansion of k in n 1540976149.599 * [misc]backup-simplify: Simplify k into k 1540976149.599 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1540976149.599 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1540976149.599 * [misc]taylor: Taking taylor expansion of 2 in n 1540976149.599 * [misc]backup-simplify: Simplify 2 into 2 1540976149.599 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1540976149.599 * [misc]taylor: Taking taylor expansion of n in n 1540976149.599 * [misc]backup-simplify: Simplify 0 into 0 1540976149.599 * [misc]backup-simplify: Simplify 1 into 1 1540976149.599 * [misc]taylor: Taking taylor expansion of PI in n 1540976149.599 * [misc]backup-simplify: Simplify PI into PI 1540976149.599 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1540976149.599 * [misc]backup-simplify: Simplify (* 2 0) into 0 1540976149.600 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1540976149.600 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1540976149.601 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1540976149.601 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1540976149.601 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1540976149.601 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1540976149.601 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1540976149.602 * [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)))) 1540976149.602 * [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))))) 1540976149.602 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1540976149.602 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1540976149.602 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1540976149.602 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976149.602 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976149.602 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1540976149.602 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976149.602 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976149.602 * [misc]taylor: Taking taylor expansion of k in k 1540976149.602 * [misc]backup-simplify: Simplify 0 into 0 1540976149.602 * [misc]backup-simplify: Simplify 1 into 1 1540976149.602 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1540976149.602 * [misc]taylor: Taking taylor expansion of (log n) in k 1540976149.602 * [misc]taylor: Taking taylor expansion of n in k 1540976149.602 * [misc]backup-simplify: Simplify n into n 1540976149.602 * [misc]backup-simplify: Simplify (log n) into (log n) 1540976149.602 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1540976149.602 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1540976149.602 * [misc]taylor: Taking taylor expansion of 2 in k 1540976149.602 * [misc]backup-simplify: Simplify 2 into 2 1540976149.602 * [misc]taylor: Taking taylor expansion of PI in k 1540976149.603 * [misc]backup-simplify: Simplify PI into PI 1540976149.603 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1540976149.603 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1540976149.603 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1540976149.603 * [misc]backup-simplify: Simplify (- 0) into 0 1540976149.603 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1540976149.604 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1540976149.604 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1540976149.605 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1540976149.605 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1540976149.606 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1540976149.607 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1540976149.609 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1540976149.609 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1540976149.609 * [misc]backup-simplify: Simplify (- 0) into 0 1540976149.609 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976149.609 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1540976149.610 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1540976149.611 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1540976149.611 * [misc]taylor: Taking taylor expansion of 0 in k 1540976149.611 * [misc]backup-simplify: Simplify 0 into 0 1540976149.611 * [misc]backup-simplify: Simplify 0 into 0 1540976149.612 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1540976149.612 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1540976149.614 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1540976149.614 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976149.614 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1540976149.614 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1540976149.614 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1540976149.615 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1540976149.617 * [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))))))) 1540976149.619 * [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))))))) 1540976149.621 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1540976149.622 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1540976149.629 * [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 1540976149.629 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1540976149.629 * [misc]backup-simplify: Simplify (- 0) into 0 1540976149.629 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976149.630 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1540976149.631 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1540976149.634 * [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 1540976149.634 * [misc]taylor: Taking taylor expansion of 0 in k 1540976149.634 * [misc]backup-simplify: Simplify 0 into 0 1540976149.635 * [misc]backup-simplify: Simplify 0 into 0 1540976149.635 * [misc]backup-simplify: Simplify 0 into 0 1540976149.637 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1540976149.638 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1540976149.644 * [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 1540976149.644 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976149.644 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1540976149.644 * [misc]backup-simplify: Simplify (- 0) into 0 1540976149.645 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976149.646 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1540976149.650 * [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))))) 1540976149.654 * [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))))) 1540976149.663 * [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))))) 1540976149.664 * [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)))) 1540976149.664 * [misc]approximate: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 1540976149.664 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1540976149.664 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1540976149.664 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1540976149.664 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1540976149.664 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976149.664 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976149.664 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1540976149.664 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976149.664 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976149.664 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1540976149.664 * [misc]taylor: Taking taylor expansion of k in k 1540976149.664 * [misc]backup-simplify: Simplify 0 into 0 1540976149.664 * [misc]backup-simplify: Simplify 1 into 1 1540976149.664 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1540976149.664 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1540976149.664 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1540976149.664 * [misc]taylor: Taking taylor expansion of 2 in k 1540976149.664 * [misc]backup-simplify: Simplify 2 into 2 1540976149.664 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1540976149.664 * [misc]taylor: Taking taylor expansion of PI in k 1540976149.664 * [misc]backup-simplify: Simplify PI into PI 1540976149.664 * [misc]taylor: Taking taylor expansion of n in k 1540976149.665 * [misc]backup-simplify: Simplify n into n 1540976149.665 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1540976149.665 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1540976149.665 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1540976149.665 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1540976149.665 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1540976149.665 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1540976149.666 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1540976149.666 * [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)))) 1540976149.666 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1540976149.666 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1540976149.666 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1540976149.666 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1540976149.666 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976149.666 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976149.666 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1540976149.666 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976149.666 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976149.666 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1540976149.666 * [misc]taylor: Taking taylor expansion of k in n 1540976149.666 * [misc]backup-simplify: Simplify k into k 1540976149.666 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1540976149.666 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1540976149.666 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1540976149.666 * [misc]taylor: Taking taylor expansion of 2 in n 1540976149.666 * [misc]backup-simplify: Simplify 2 into 2 1540976149.667 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1540976149.667 * [misc]taylor: Taking taylor expansion of PI in n 1540976149.667 * [misc]backup-simplify: Simplify PI into PI 1540976149.667 * [misc]taylor: Taking taylor expansion of n in n 1540976149.667 * [misc]backup-simplify: Simplify 0 into 0 1540976149.667 * [misc]backup-simplify: Simplify 1 into 1 1540976149.667 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1540976149.667 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1540976149.668 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1540976149.668 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1540976149.668 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1540976149.668 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1540976149.669 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1540976149.670 * [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))) 1540976149.671 * [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)))) 1540976149.671 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1540976149.671 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1540976149.671 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1540976149.671 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1540976149.671 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976149.671 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976149.671 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1540976149.671 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976149.671 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976149.671 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1540976149.671 * [misc]taylor: Taking taylor expansion of k in n 1540976149.671 * [misc]backup-simplify: Simplify k into k 1540976149.671 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1540976149.671 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1540976149.671 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1540976149.671 * [misc]taylor: Taking taylor expansion of 2 in n 1540976149.671 * [misc]backup-simplify: Simplify 2 into 2 1540976149.671 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1540976149.671 * [misc]taylor: Taking taylor expansion of PI in n 1540976149.671 * [misc]backup-simplify: Simplify PI into PI 1540976149.671 * [misc]taylor: Taking taylor expansion of n in n 1540976149.671 * [misc]backup-simplify: Simplify 0 into 0 1540976149.671 * [misc]backup-simplify: Simplify 1 into 1 1540976149.672 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1540976149.672 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1540976149.673 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1540976149.673 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1540976149.673 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1540976149.673 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1540976149.674 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1540976149.674 * [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))) 1540976149.675 * [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)))) 1540976149.675 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1540976149.675 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1540976149.675 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1540976149.675 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976149.675 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976149.675 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1540976149.675 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976149.675 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976149.675 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1540976149.675 * [misc]taylor: Taking taylor expansion of k in k 1540976149.675 * [misc]backup-simplify: Simplify 0 into 0 1540976149.675 * [misc]backup-simplify: Simplify 1 into 1 1540976149.676 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1540976149.676 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1540976149.676 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1540976149.676 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1540976149.676 * [misc]taylor: Taking taylor expansion of 2 in k 1540976149.676 * [misc]backup-simplify: Simplify 2 into 2 1540976149.676 * [misc]taylor: Taking taylor expansion of PI in k 1540976149.676 * [misc]backup-simplify: Simplify PI into PI 1540976149.676 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1540976149.677 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1540976149.677 * [misc]taylor: Taking taylor expansion of (log n) in k 1540976149.677 * [misc]taylor: Taking taylor expansion of n in k 1540976149.677 * [misc]backup-simplify: Simplify n into n 1540976149.677 * [misc]backup-simplify: Simplify (log n) into (log n) 1540976149.677 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1540976149.677 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1540976149.677 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1540976149.677 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1540976149.678 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1540976149.679 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1540976149.679 * [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)))) 1540976149.680 * [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)))) 1540976149.681 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1540976149.682 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1540976149.688 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1540976149.688 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1540976149.689 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1540976149.689 * [misc]backup-simplify: Simplify (- 0) into 0 1540976149.689 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976149.690 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1540976149.690 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1540976149.692 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1540976149.692 * [misc]taylor: Taking taylor expansion of 0 in k 1540976149.692 * [misc]backup-simplify: Simplify 0 into 0 1540976149.692 * [misc]backup-simplify: Simplify 0 into 0 1540976149.692 * [misc]backup-simplify: Simplify 0 into 0 1540976149.694 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976149.695 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1540976149.701 * [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 1540976149.701 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1540976149.702 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1540976149.702 * [misc]backup-simplify: Simplify (- 0) into 0 1540976149.702 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976149.703 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1540976149.704 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1540976149.707 * [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 1540976149.707 * [misc]taylor: Taking taylor expansion of 0 in k 1540976149.707 * [misc]backup-simplify: Simplify 0 into 0 1540976149.707 * [misc]backup-simplify: Simplify 0 into 0 1540976149.707 * [misc]backup-simplify: Simplify 0 into 0 1540976149.707 * [misc]backup-simplify: Simplify 0 into 0 1540976149.709 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976149.710 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1540976149.719 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 1540976149.720 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1540976149.720 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1540976149.720 * [misc]backup-simplify: Simplify (- 0) into 0 1540976149.720 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976149.721 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1540976149.722 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1540976149.726 * [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 1540976149.726 * [misc]taylor: Taking taylor expansion of 0 in k 1540976149.726 * [misc]backup-simplify: Simplify 0 into 0 1540976149.726 * [misc]backup-simplify: Simplify 0 into 0 1540976149.727 * [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))))) 1540976149.727 * [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)) 1540976149.727 * [misc]approximate: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 1540976149.727 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1540976149.727 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1540976149.727 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1540976149.728 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1540976149.728 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1540976149.728 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976149.728 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976149.728 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1540976149.728 * [misc]taylor: Taking taylor expansion of k in k 1540976149.728 * [misc]backup-simplify: Simplify 0 into 0 1540976149.728 * [misc]backup-simplify: Simplify 1 into 1 1540976149.728 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1540976149.728 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976149.728 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976149.728 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1540976149.728 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1540976149.728 * [misc]taylor: Taking taylor expansion of -2 in k 1540976149.728 * [misc]backup-simplify: Simplify -2 into -2 1540976149.728 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1540976149.728 * [misc]taylor: Taking taylor expansion of PI in k 1540976149.728 * [misc]backup-simplify: Simplify PI into PI 1540976149.728 * [misc]taylor: Taking taylor expansion of n in k 1540976149.728 * [misc]backup-simplify: Simplify n into n 1540976149.728 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1540976149.728 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1540976149.729 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1540976149.729 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1540976149.729 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1540976149.729 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1540976149.729 * [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))) 1540976149.730 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1540976149.730 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1540976149.730 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1540976149.730 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1540976149.730 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1540976149.730 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976149.730 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976149.730 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1540976149.730 * [misc]taylor: Taking taylor expansion of k in n 1540976149.730 * [misc]backup-simplify: Simplify k into k 1540976149.730 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1540976149.730 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976149.730 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976149.730 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1540976149.730 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1540976149.730 * [misc]taylor: Taking taylor expansion of -2 in n 1540976149.730 * [misc]backup-simplify: Simplify -2 into -2 1540976149.730 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1540976149.730 * [misc]taylor: Taking taylor expansion of PI in n 1540976149.730 * [misc]backup-simplify: Simplify PI into PI 1540976149.730 * [misc]taylor: Taking taylor expansion of n in n 1540976149.730 * [misc]backup-simplify: Simplify 0 into 0 1540976149.730 * [misc]backup-simplify: Simplify 1 into 1 1540976149.731 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1540976149.731 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1540976149.732 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1540976149.732 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1540976149.732 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1540976149.733 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1540976149.733 * [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))) 1540976149.734 * [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)))) 1540976149.734 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1540976149.734 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1540976149.734 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1540976149.734 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1540976149.734 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1540976149.734 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976149.734 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976149.734 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1540976149.734 * [misc]taylor: Taking taylor expansion of k in n 1540976149.734 * [misc]backup-simplify: Simplify k into k 1540976149.734 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1540976149.734 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976149.734 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976149.734 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1540976149.734 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1540976149.734 * [misc]taylor: Taking taylor expansion of -2 in n 1540976149.735 * [misc]backup-simplify: Simplify -2 into -2 1540976149.735 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1540976149.735 * [misc]taylor: Taking taylor expansion of PI in n 1540976149.735 * [misc]backup-simplify: Simplify PI into PI 1540976149.735 * [misc]taylor: Taking taylor expansion of n in n 1540976149.735 * [misc]backup-simplify: Simplify 0 into 0 1540976149.735 * [misc]backup-simplify: Simplify 1 into 1 1540976149.735 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1540976149.735 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1540976149.736 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1540976149.736 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1540976149.736 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1540976149.737 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1540976149.737 * [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))) 1540976149.738 * [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)))) 1540976149.738 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1540976149.738 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1540976149.738 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1540976149.738 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1540976149.738 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976149.738 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976149.739 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1540976149.739 * [misc]taylor: Taking taylor expansion of k in k 1540976149.739 * [misc]backup-simplify: Simplify 0 into 0 1540976149.739 * [misc]backup-simplify: Simplify 1 into 1 1540976149.739 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1540976149.739 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976149.739 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976149.739 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1540976149.739 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1540976149.739 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1540976149.739 * [misc]taylor: Taking taylor expansion of -2 in k 1540976149.739 * [misc]backup-simplify: Simplify -2 into -2 1540976149.739 * [misc]taylor: Taking taylor expansion of PI in k 1540976149.739 * [misc]backup-simplify: Simplify PI into PI 1540976149.739 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1540976149.740 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1540976149.740 * [misc]taylor: Taking taylor expansion of (log n) in k 1540976149.740 * [misc]taylor: Taking taylor expansion of n in k 1540976149.740 * [misc]backup-simplify: Simplify n into n 1540976149.740 * [misc]backup-simplify: Simplify (log n) into (log n) 1540976149.740 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1540976149.740 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1540976149.740 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1540976149.741 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1540976149.742 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1540976149.743 * [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)))) 1540976149.743 * [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)))) 1540976149.745 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1540976149.745 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1540976149.748 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1540976149.748 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1540976149.749 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1540976149.749 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976149.750 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1540976149.750 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1540976149.752 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1540976149.752 * [misc]taylor: Taking taylor expansion of 0 in k 1540976149.752 * [misc]backup-simplify: Simplify 0 into 0 1540976149.752 * [misc]backup-simplify: Simplify 0 into 0 1540976149.752 * [misc]backup-simplify: Simplify 0 into 0 1540976149.754 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976149.755 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1540976149.761 * [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 1540976149.761 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1540976149.761 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1540976149.762 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976149.762 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1540976149.763 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1540976149.766 * [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 1540976149.766 * [misc]taylor: Taking taylor expansion of 0 in k 1540976149.766 * [misc]backup-simplify: Simplify 0 into 0 1540976149.766 * [misc]backup-simplify: Simplify 0 into 0 1540976149.766 * [misc]backup-simplify: Simplify 0 into 0 1540976149.766 * [misc]backup-simplify: Simplify 0 into 0 1540976149.768 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976149.769 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1540976149.779 * [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 1540976149.779 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1540976149.779 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1540976149.780 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976149.780 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1540976149.781 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 1540976149.785 * [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 1540976149.785 * [misc]taylor: Taking taylor expansion of 0 in k 1540976149.785 * [misc]backup-simplify: Simplify 0 into 0 1540976149.785 * [misc]backup-simplify: Simplify 0 into 0 1540976149.786 * [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))))) 1540976149.786 * * * * [misc]progress: [ 2 / 4 ] generating series at (2 1 1 1) 1540976149.787 * [misc]backup-simplify: Simplify (pow (* PI (* n 2)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 1540976149.787 * [misc]approximate: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 1540976149.787 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1540976149.787 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1540976149.787 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1540976149.787 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1540976149.787 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976149.787 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976149.787 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1540976149.787 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976149.787 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976149.787 * [misc]taylor: Taking taylor expansion of k in k 1540976149.787 * [misc]backup-simplify: Simplify 0 into 0 1540976149.787 * [misc]backup-simplify: Simplify 1 into 1 1540976149.788 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1540976149.788 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1540976149.788 * [misc]taylor: Taking taylor expansion of 2 in k 1540976149.788 * [misc]backup-simplify: Simplify 2 into 2 1540976149.788 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1540976149.788 * [misc]taylor: Taking taylor expansion of n in k 1540976149.788 * [misc]backup-simplify: Simplify n into n 1540976149.788 * [misc]taylor: Taking taylor expansion of PI in k 1540976149.788 * [misc]backup-simplify: Simplify PI into PI 1540976149.788 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1540976149.788 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1540976149.788 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1540976149.788 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1540976149.789 * [misc]backup-simplify: Simplify (- 0) into 0 1540976149.789 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1540976149.789 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1540976149.789 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1540976149.789 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1540976149.789 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1540976149.789 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1540976149.789 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1540976149.789 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976149.789 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976149.789 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1540976149.789 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976149.789 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976149.789 * [misc]taylor: Taking taylor expansion of k in n 1540976149.789 * [misc]backup-simplify: Simplify k into k 1540976149.790 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1540976149.790 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1540976149.790 * [misc]taylor: Taking taylor expansion of 2 in n 1540976149.790 * [misc]backup-simplify: Simplify 2 into 2 1540976149.790 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1540976149.790 * [misc]taylor: Taking taylor expansion of n in n 1540976149.790 * [misc]backup-simplify: Simplify 0 into 0 1540976149.790 * [misc]backup-simplify: Simplify 1 into 1 1540976149.790 * [misc]taylor: Taking taylor expansion of PI in n 1540976149.790 * [misc]backup-simplify: Simplify PI into PI 1540976149.790 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1540976149.790 * [misc]backup-simplify: Simplify (* 2 0) into 0 1540976149.791 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1540976149.792 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1540976149.792 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1540976149.792 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1540976149.792 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1540976149.793 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1540976149.793 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1540976149.794 * [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)))) 1540976149.795 * [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))))) 1540976149.795 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1540976149.795 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1540976149.795 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1540976149.795 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1540976149.795 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976149.795 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976149.795 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1540976149.795 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976149.795 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976149.795 * [misc]taylor: Taking taylor expansion of k in n 1540976149.795 * [misc]backup-simplify: Simplify k into k 1540976149.795 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1540976149.795 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1540976149.795 * [misc]taylor: Taking taylor expansion of 2 in n 1540976149.795 * [misc]backup-simplify: Simplify 2 into 2 1540976149.795 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1540976149.795 * [misc]taylor: Taking taylor expansion of n in n 1540976149.795 * [misc]backup-simplify: Simplify 0 into 0 1540976149.795 * [misc]backup-simplify: Simplify 1 into 1 1540976149.795 * [misc]taylor: Taking taylor expansion of PI in n 1540976149.795 * [misc]backup-simplify: Simplify PI into PI 1540976149.796 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1540976149.796 * [misc]backup-simplify: Simplify (* 2 0) into 0 1540976149.797 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1540976149.797 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1540976149.798 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1540976149.798 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1540976149.798 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1540976149.798 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1540976149.799 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1540976149.800 * [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)))) 1540976149.800 * [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))))) 1540976149.801 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1540976149.801 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1540976149.801 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1540976149.801 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976149.801 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976149.801 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1540976149.801 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976149.801 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976149.801 * [misc]taylor: Taking taylor expansion of k in k 1540976149.801 * [misc]backup-simplify: Simplify 0 into 0 1540976149.801 * [misc]backup-simplify: Simplify 1 into 1 1540976149.801 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1540976149.801 * [misc]taylor: Taking taylor expansion of (log n) in k 1540976149.801 * [misc]taylor: Taking taylor expansion of n in k 1540976149.801 * [misc]backup-simplify: Simplify n into n 1540976149.801 * [misc]backup-simplify: Simplify (log n) into (log n) 1540976149.801 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1540976149.801 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1540976149.801 * [misc]taylor: Taking taylor expansion of 2 in k 1540976149.801 * [misc]backup-simplify: Simplify 2 into 2 1540976149.801 * [misc]taylor: Taking taylor expansion of PI in k 1540976149.801 * [misc]backup-simplify: Simplify PI into PI 1540976149.802 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1540976149.802 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1540976149.802 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1540976149.802 * [misc]backup-simplify: Simplify (- 0) into 0 1540976149.803 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1540976149.803 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1540976149.804 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1540976149.804 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1540976149.805 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1540976149.807 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1540976149.808 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1540976149.811 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1540976149.811 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1540976149.811 * [misc]backup-simplify: Simplify (- 0) into 0 1540976149.812 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976149.812 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1540976149.813 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1540976149.815 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1540976149.815 * [misc]taylor: Taking taylor expansion of 0 in k 1540976149.815 * [misc]backup-simplify: Simplify 0 into 0 1540976149.815 * [misc]backup-simplify: Simplify 0 into 0 1540976149.816 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1540976149.817 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1540976149.821 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1540976149.821 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976149.821 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1540976149.821 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1540976149.821 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1540976149.822 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1540976149.825 * [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))))))) 1540976149.826 * [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))))))) 1540976149.828 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1540976149.830 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1540976149.836 * [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 1540976149.836 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1540976149.836 * [misc]backup-simplify: Simplify (- 0) into 0 1540976149.836 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976149.837 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1540976149.838 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1540976149.843 * [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 1540976149.843 * [misc]taylor: Taking taylor expansion of 0 in k 1540976149.843 * [misc]backup-simplify: Simplify 0 into 0 1540976149.843 * [misc]backup-simplify: Simplify 0 into 0 1540976149.843 * [misc]backup-simplify: Simplify 0 into 0 1540976149.845 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1540976149.846 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1540976149.852 * [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 1540976149.852 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976149.853 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1540976149.853 * [misc]backup-simplify: Simplify (- 0) into 0 1540976149.853 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976149.854 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1540976149.858 * [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))))) 1540976149.862 * [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))))) 1540976149.871 * [misc]backup-simplify: Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (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))))) 1540976149.871 * [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)))) 1540976149.871 * [misc]approximate: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 1540976149.871 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1540976149.871 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1540976149.871 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1540976149.871 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1540976149.871 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976149.871 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976149.871 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1540976149.871 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976149.871 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976149.871 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1540976149.872 * [misc]taylor: Taking taylor expansion of k in k 1540976149.872 * [misc]backup-simplify: Simplify 0 into 0 1540976149.872 * [misc]backup-simplify: Simplify 1 into 1 1540976149.872 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1540976149.872 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1540976149.872 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1540976149.872 * [misc]taylor: Taking taylor expansion of 2 in k 1540976149.872 * [misc]backup-simplify: Simplify 2 into 2 1540976149.872 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1540976149.872 * [misc]taylor: Taking taylor expansion of PI in k 1540976149.872 * [misc]backup-simplify: Simplify PI into PI 1540976149.872 * [misc]taylor: Taking taylor expansion of n in k 1540976149.872 * [misc]backup-simplify: Simplify n into n 1540976149.872 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1540976149.872 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1540976149.872 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1540976149.873 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1540976149.873 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1540976149.873 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1540976149.873 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1540976149.873 * [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)))) 1540976149.873 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1540976149.874 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1540976149.874 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1540976149.874 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1540976149.874 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976149.874 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976149.874 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1540976149.874 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976149.874 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976149.874 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1540976149.874 * [misc]taylor: Taking taylor expansion of k in n 1540976149.874 * [misc]backup-simplify: Simplify k into k 1540976149.874 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1540976149.874 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1540976149.874 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1540976149.874 * [misc]taylor: Taking taylor expansion of 2 in n 1540976149.874 * [misc]backup-simplify: Simplify 2 into 2 1540976149.874 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1540976149.874 * [misc]taylor: Taking taylor expansion of PI in n 1540976149.874 * [misc]backup-simplify: Simplify PI into PI 1540976149.874 * [misc]taylor: Taking taylor expansion of n in n 1540976149.874 * [misc]backup-simplify: Simplify 0 into 0 1540976149.874 * [misc]backup-simplify: Simplify 1 into 1 1540976149.875 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1540976149.875 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1540976149.875 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1540976149.876 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1540976149.876 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1540976149.876 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1540976149.877 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1540976149.877 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 1540976149.878 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 1540976149.878 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1540976149.878 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1540976149.878 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1540976149.878 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1540976149.878 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976149.878 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976149.878 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1540976149.878 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976149.878 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976149.878 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1540976149.878 * [misc]taylor: Taking taylor expansion of k in n 1540976149.878 * [misc]backup-simplify: Simplify k into k 1540976149.878 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1540976149.878 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1540976149.878 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1540976149.878 * [misc]taylor: Taking taylor expansion of 2 in n 1540976149.879 * [misc]backup-simplify: Simplify 2 into 2 1540976149.879 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1540976149.879 * [misc]taylor: Taking taylor expansion of PI in n 1540976149.879 * [misc]backup-simplify: Simplify PI into PI 1540976149.879 * [misc]taylor: Taking taylor expansion of n in n 1540976149.879 * [misc]backup-simplify: Simplify 0 into 0 1540976149.879 * [misc]backup-simplify: Simplify 1 into 1 1540976149.879 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1540976149.879 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1540976149.880 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1540976149.880 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1540976149.880 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1540976149.880 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1540976149.881 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1540976149.882 * [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))) 1540976149.882 * [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)))) 1540976149.882 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1540976149.882 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1540976149.882 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1540976149.883 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976149.883 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976149.883 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1540976149.883 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976149.883 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976149.883 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1540976149.883 * [misc]taylor: Taking taylor expansion of k in k 1540976149.883 * [misc]backup-simplify: Simplify 0 into 0 1540976149.883 * [misc]backup-simplify: Simplify 1 into 1 1540976149.883 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1540976149.883 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1540976149.883 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1540976149.883 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1540976149.883 * [misc]taylor: Taking taylor expansion of 2 in k 1540976149.883 * [misc]backup-simplify: Simplify 2 into 2 1540976149.883 * [misc]taylor: Taking taylor expansion of PI in k 1540976149.883 * [misc]backup-simplify: Simplify PI into PI 1540976149.883 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1540976149.884 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1540976149.884 * [misc]taylor: Taking taylor expansion of (log n) in k 1540976149.884 * [misc]taylor: Taking taylor expansion of n in k 1540976149.884 * [misc]backup-simplify: Simplify n into n 1540976149.884 * [misc]backup-simplify: Simplify (log n) into (log n) 1540976149.884 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1540976149.885 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1540976149.885 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1540976149.885 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1540976149.885 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1540976149.886 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1540976149.887 * [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)))) 1540976149.887 * [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)))) 1540976149.889 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1540976149.889 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1540976149.892 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1540976149.893 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1540976149.893 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1540976149.893 * [misc]backup-simplify: Simplify (- 0) into 0 1540976149.893 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976149.894 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1540976149.895 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1540976149.896 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1540976149.896 * [misc]taylor: Taking taylor expansion of 0 in k 1540976149.897 * [misc]backup-simplify: Simplify 0 into 0 1540976149.897 * [misc]backup-simplify: Simplify 0 into 0 1540976149.897 * [misc]backup-simplify: Simplify 0 into 0 1540976149.898 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976149.899 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1540976149.905 * [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 1540976149.905 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1540976149.906 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1540976149.906 * [misc]backup-simplify: Simplify (- 0) into 0 1540976149.906 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976149.907 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1540976149.908 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1540976149.910 * [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 1540976149.910 * [misc]taylor: Taking taylor expansion of 0 in k 1540976149.910 * [misc]backup-simplify: Simplify 0 into 0 1540976149.910 * [misc]backup-simplify: Simplify 0 into 0 1540976149.910 * [misc]backup-simplify: Simplify 0 into 0 1540976149.910 * [misc]backup-simplify: Simplify 0 into 0 1540976149.912 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976149.914 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1540976149.924 * [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 1540976149.924 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1540976149.924 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1540976149.925 * [misc]backup-simplify: Simplify (- 0) into 0 1540976149.925 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976149.926 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1540976149.927 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1540976149.931 * [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 1540976149.931 * [misc]taylor: Taking taylor expansion of 0 in k 1540976149.931 * [misc]backup-simplify: Simplify 0 into 0 1540976149.931 * [misc]backup-simplify: Simplify 0 into 0 1540976149.932 * [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))))) 1540976149.932 * [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)) 1540976149.932 * [misc]approximate: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 1540976149.932 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1540976149.932 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1540976149.932 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1540976149.932 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1540976149.932 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1540976149.932 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976149.932 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976149.932 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1540976149.932 * [misc]taylor: Taking taylor expansion of k in k 1540976149.932 * [misc]backup-simplify: Simplify 0 into 0 1540976149.932 * [misc]backup-simplify: Simplify 1 into 1 1540976149.933 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1540976149.933 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976149.933 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976149.933 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1540976149.933 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1540976149.933 * [misc]taylor: Taking taylor expansion of -2 in k 1540976149.933 * [misc]backup-simplify: Simplify -2 into -2 1540976149.933 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1540976149.933 * [misc]taylor: Taking taylor expansion of PI in k 1540976149.933 * [misc]backup-simplify: Simplify PI into PI 1540976149.933 * [misc]taylor: Taking taylor expansion of n in k 1540976149.933 * [misc]backup-simplify: Simplify n into n 1540976149.933 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1540976149.933 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1540976149.933 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1540976149.934 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1540976149.934 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1540976149.934 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1540976149.934 * [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))) 1540976149.934 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1540976149.934 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1540976149.934 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1540976149.934 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1540976149.934 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1540976149.935 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976149.935 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976149.935 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1540976149.935 * [misc]taylor: Taking taylor expansion of k in n 1540976149.935 * [misc]backup-simplify: Simplify k into k 1540976149.935 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1540976149.935 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976149.935 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976149.935 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1540976149.935 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1540976149.935 * [misc]taylor: Taking taylor expansion of -2 in n 1540976149.935 * [misc]backup-simplify: Simplify -2 into -2 1540976149.935 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1540976149.935 * [misc]taylor: Taking taylor expansion of PI in n 1540976149.935 * [misc]backup-simplify: Simplify PI into PI 1540976149.935 * [misc]taylor: Taking taylor expansion of n in n 1540976149.935 * [misc]backup-simplify: Simplify 0 into 0 1540976149.935 * [misc]backup-simplify: Simplify 1 into 1 1540976149.936 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1540976149.936 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1540976149.936 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1540976149.936 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1540976149.937 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1540976149.937 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1540976149.938 * [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))) 1540976149.939 * [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)))) 1540976149.939 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1540976149.939 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1540976149.939 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1540976149.939 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1540976149.939 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1540976149.939 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976149.939 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976149.939 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1540976149.939 * [misc]taylor: Taking taylor expansion of k in n 1540976149.939 * [misc]backup-simplify: Simplify k into k 1540976149.939 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1540976149.939 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976149.939 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976149.939 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1540976149.939 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1540976149.939 * [misc]taylor: Taking taylor expansion of -2 in n 1540976149.939 * [misc]backup-simplify: Simplify -2 into -2 1540976149.939 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1540976149.939 * [misc]taylor: Taking taylor expansion of PI in n 1540976149.940 * [misc]backup-simplify: Simplify PI into PI 1540976149.940 * [misc]taylor: Taking taylor expansion of n in n 1540976149.940 * [misc]backup-simplify: Simplify 0 into 0 1540976149.940 * [misc]backup-simplify: Simplify 1 into 1 1540976149.940 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1540976149.940 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1540976149.941 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1540976149.941 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1540976149.941 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1540976149.942 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1540976149.942 * [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))) 1540976149.943 * [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)))) 1540976149.943 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1540976149.943 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1540976149.943 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1540976149.943 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1540976149.943 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976149.943 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976149.943 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1540976149.944 * [misc]taylor: Taking taylor expansion of k in k 1540976149.944 * [misc]backup-simplify: Simplify 0 into 0 1540976149.944 * [misc]backup-simplify: Simplify 1 into 1 1540976149.944 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1540976149.944 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976149.944 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976149.944 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1540976149.944 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1540976149.944 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1540976149.944 * [misc]taylor: Taking taylor expansion of -2 in k 1540976149.944 * [misc]backup-simplify: Simplify -2 into -2 1540976149.944 * [misc]taylor: Taking taylor expansion of PI in k 1540976149.944 * [misc]backup-simplify: Simplify PI into PI 1540976149.944 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1540976149.945 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1540976149.945 * [misc]taylor: Taking taylor expansion of (log n) in k 1540976149.945 * [misc]taylor: Taking taylor expansion of n in k 1540976149.945 * [misc]backup-simplify: Simplify n into n 1540976149.945 * [misc]backup-simplify: Simplify (log n) into (log n) 1540976149.945 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1540976149.945 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1540976149.945 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1540976149.946 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1540976149.947 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1540976149.947 * [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)))) 1540976149.948 * [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)))) 1540976149.949 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1540976149.950 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1540976149.953 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1540976149.953 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1540976149.954 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1540976149.954 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976149.955 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1540976149.955 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1540976149.957 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1540976149.957 * [misc]taylor: Taking taylor expansion of 0 in k 1540976149.957 * [misc]backup-simplify: Simplify 0 into 0 1540976149.957 * [misc]backup-simplify: Simplify 0 into 0 1540976149.957 * [misc]backup-simplify: Simplify 0 into 0 1540976149.959 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976149.960 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1540976149.966 * [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 1540976149.966 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1540976149.966 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1540976149.967 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976149.967 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1540976149.968 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1540976149.971 * [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 1540976149.971 * [misc]taylor: Taking taylor expansion of 0 in k 1540976149.971 * [misc]backup-simplify: Simplify 0 into 0 1540976149.971 * [misc]backup-simplify: Simplify 0 into 0 1540976149.971 * [misc]backup-simplify: Simplify 0 into 0 1540976149.971 * [misc]backup-simplify: Simplify 0 into 0 1540976149.973 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976149.975 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1540976149.984 * [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 1540976149.985 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1540976149.985 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1540976149.985 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976149.986 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1540976149.987 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 1540976149.991 * [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 1540976149.991 * [misc]taylor: Taking taylor expansion of 0 in k 1540976149.991 * [misc]backup-simplify: Simplify 0 into 0 1540976149.991 * [misc]backup-simplify: Simplify 0 into 0 1540976149.992 * [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))))) 1540976149.992 * * * * [misc]progress: [ 3 / 4 ] generating series at (2 1 2 1 1) 1540976149.995 * [misc]backup-simplify: Simplify (* PI (* n 2)) into (* 2 (* n PI)) 1540976149.995 * [misc]approximate: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1540976149.995 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1540976149.995 * [misc]taylor: Taking taylor expansion of 2 in n 1540976149.995 * [misc]backup-simplify: Simplify 2 into 2 1540976149.995 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1540976149.995 * [misc]taylor: Taking taylor expansion of n in n 1540976149.995 * [misc]backup-simplify: Simplify 0 into 0 1540976149.995 * [misc]backup-simplify: Simplify 1 into 1 1540976149.995 * [misc]taylor: Taking taylor expansion of PI in n 1540976149.995 * [misc]backup-simplify: Simplify PI into PI 1540976149.995 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1540976149.995 * [misc]taylor: Taking taylor expansion of 2 in n 1540976149.995 * [misc]backup-simplify: Simplify 2 into 2 1540976149.995 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1540976149.995 * [misc]taylor: Taking taylor expansion of n in n 1540976149.995 * [misc]backup-simplify: Simplify 0 into 0 1540976149.995 * [misc]backup-simplify: Simplify 1 into 1 1540976149.995 * [misc]taylor: Taking taylor expansion of PI in n 1540976149.995 * [misc]backup-simplify: Simplify PI into PI 1540976149.996 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1540976149.996 * [misc]backup-simplify: Simplify (* 2 0) into 0 1540976149.996 * [misc]backup-simplify: Simplify 0 into 0 1540976149.997 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1540976149.998 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1540976149.998 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1540976149.999 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1540976150.001 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1540976150.001 * [misc]backup-simplify: Simplify 0 into 0 1540976150.003 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1540976150.004 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1540976150.004 * [misc]backup-simplify: Simplify 0 into 0 1540976150.007 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1540976150.009 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1540976150.009 * [misc]backup-simplify: Simplify 0 into 0 1540976150.012 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1540976150.015 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1540976150.015 * [misc]backup-simplify: Simplify 0 into 0 1540976150.018 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1540976150.022 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1540976150.022 * [misc]backup-simplify: Simplify 0 into 0 1540976150.027 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1540976150.031 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1540976150.031 * [misc]backup-simplify: Simplify 0 into 0 1540976150.032 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1540976150.032 * [misc]backup-simplify: Simplify (* PI (* (/ 1 n) 2)) into (* 2 (/ PI n)) 1540976150.032 * [misc]approximate: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1540976150.032 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1540976150.032 * [misc]taylor: Taking taylor expansion of 2 in n 1540976150.032 * [misc]backup-simplify: Simplify 2 into 2 1540976150.032 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1540976150.032 * [misc]taylor: Taking taylor expansion of PI in n 1540976150.032 * [misc]backup-simplify: Simplify PI into PI 1540976150.032 * [misc]taylor: Taking taylor expansion of n in n 1540976150.032 * [misc]backup-simplify: Simplify 0 into 0 1540976150.032 * [misc]backup-simplify: Simplify 1 into 1 1540976150.033 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1540976150.033 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1540976150.033 * [misc]taylor: Taking taylor expansion of 2 in n 1540976150.033 * [misc]backup-simplify: Simplify 2 into 2 1540976150.033 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1540976150.033 * [misc]taylor: Taking taylor expansion of PI in n 1540976150.033 * [misc]backup-simplify: Simplify PI into PI 1540976150.033 * [misc]taylor: Taking taylor expansion of n in n 1540976150.033 * [misc]backup-simplify: Simplify 0 into 0 1540976150.033 * [misc]backup-simplify: Simplify 1 into 1 1540976150.033 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1540976150.034 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1540976150.034 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1540976150.035 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1540976150.036 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1540976150.036 * [misc]backup-simplify: Simplify 0 into 0 1540976150.037 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976150.038 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1540976150.038 * [misc]backup-simplify: Simplify 0 into 0 1540976150.040 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976150.042 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1540976150.042 * [misc]backup-simplify: Simplify 0 into 0 1540976150.044 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976150.046 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1540976150.046 * [misc]backup-simplify: Simplify 0 into 0 1540976150.048 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976150.051 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1540976150.051 * [misc]backup-simplify: Simplify 0 into 0 1540976150.053 * [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 1540976150.057 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1540976150.057 * [misc]backup-simplify: Simplify 0 into 0 1540976150.057 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 1540976150.058 * [misc]backup-simplify: Simplify (* PI (* (/ 1 (- n)) 2)) into (* -2 (/ PI n)) 1540976150.058 * [misc]approximate: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1540976150.058 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1540976150.058 * [misc]taylor: Taking taylor expansion of -2 in n 1540976150.058 * [misc]backup-simplify: Simplify -2 into -2 1540976150.058 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1540976150.058 * [misc]taylor: Taking taylor expansion of PI in n 1540976150.058 * [misc]backup-simplify: Simplify PI into PI 1540976150.058 * [misc]taylor: Taking taylor expansion of n in n 1540976150.058 * [misc]backup-simplify: Simplify 0 into 0 1540976150.058 * [misc]backup-simplify: Simplify 1 into 1 1540976150.058 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1540976150.058 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1540976150.058 * [misc]taylor: Taking taylor expansion of -2 in n 1540976150.058 * [misc]backup-simplify: Simplify -2 into -2 1540976150.058 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1540976150.058 * [misc]taylor: Taking taylor expansion of PI in n 1540976150.059 * [misc]backup-simplify: Simplify PI into PI 1540976150.059 * [misc]taylor: Taking taylor expansion of n in n 1540976150.059 * [misc]backup-simplify: Simplify 0 into 0 1540976150.059 * [misc]backup-simplify: Simplify 1 into 1 1540976150.059 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1540976150.059 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1540976150.060 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1540976150.061 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1540976150.061 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1540976150.061 * [misc]backup-simplify: Simplify 0 into 0 1540976150.063 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976150.064 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1540976150.064 * [misc]backup-simplify: Simplify 0 into 0 1540976150.066 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976150.067 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1540976150.068 * [misc]backup-simplify: Simplify 0 into 0 1540976150.070 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976150.072 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1540976150.072 * [misc]backup-simplify: Simplify 0 into 0 1540976150.074 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976150.077 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1540976150.077 * [misc]backup-simplify: Simplify 0 into 0 1540976150.080 * [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 1540976150.083 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1540976150.084 * [misc]backup-simplify: Simplify 0 into 0 1540976150.084 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 1540976150.084 * * * * [misc]progress: [ 4 / 4 ] generating series at (2 1 1 1 1) 1540976150.085 * [misc]backup-simplify: Simplify (* PI (* n 2)) into (* 2 (* n PI)) 1540976150.085 * [misc]approximate: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1540976150.085 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1540976150.085 * [misc]taylor: Taking taylor expansion of 2 in n 1540976150.085 * [misc]backup-simplify: Simplify 2 into 2 1540976150.085 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1540976150.085 * [misc]taylor: Taking taylor expansion of n in n 1540976150.085 * [misc]backup-simplify: Simplify 0 into 0 1540976150.085 * [misc]backup-simplify: Simplify 1 into 1 1540976150.085 * [misc]taylor: Taking taylor expansion of PI in n 1540976150.085 * [misc]backup-simplify: Simplify PI into PI 1540976150.085 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1540976150.085 * [misc]taylor: Taking taylor expansion of 2 in n 1540976150.085 * [misc]backup-simplify: Simplify 2 into 2 1540976150.085 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1540976150.085 * [misc]taylor: Taking taylor expansion of n in n 1540976150.085 * [misc]backup-simplify: Simplify 0 into 0 1540976150.085 * [misc]backup-simplify: Simplify 1 into 1 1540976150.085 * [misc]taylor: Taking taylor expansion of PI in n 1540976150.085 * [misc]backup-simplify: Simplify PI into PI 1540976150.086 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1540976150.086 * [misc]backup-simplify: Simplify (* 2 0) into 0 1540976150.086 * [misc]backup-simplify: Simplify 0 into 0 1540976150.086 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1540976150.087 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1540976150.088 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1540976150.089 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1540976150.090 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1540976150.090 * [misc]backup-simplify: Simplify 0 into 0 1540976150.091 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1540976150.093 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1540976150.093 * [misc]backup-simplify: Simplify 0 into 0 1540976150.095 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1540976150.097 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1540976150.098 * [misc]backup-simplify: Simplify 0 into 0 1540976150.101 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1540976150.103 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1540976150.104 * [misc]backup-simplify: Simplify 0 into 0 1540976150.107 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1540976150.111 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1540976150.111 * [misc]backup-simplify: Simplify 0 into 0 1540976150.116 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1540976150.120 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1540976150.120 * [misc]backup-simplify: Simplify 0 into 0 1540976150.120 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1540976150.121 * [misc]backup-simplify: Simplify (* PI (* (/ 1 n) 2)) into (* 2 (/ PI n)) 1540976150.121 * [misc]approximate: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1540976150.121 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1540976150.121 * [misc]taylor: Taking taylor expansion of 2 in n 1540976150.121 * [misc]backup-simplify: Simplify 2 into 2 1540976150.121 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1540976150.121 * [misc]taylor: Taking taylor expansion of PI in n 1540976150.121 * [misc]backup-simplify: Simplify PI into PI 1540976150.121 * [misc]taylor: Taking taylor expansion of n in n 1540976150.121 * [misc]backup-simplify: Simplify 0 into 0 1540976150.121 * [misc]backup-simplify: Simplify 1 into 1 1540976150.121 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1540976150.121 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1540976150.121 * [misc]taylor: Taking taylor expansion of 2 in n 1540976150.121 * [misc]backup-simplify: Simplify 2 into 2 1540976150.121 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1540976150.121 * [misc]taylor: Taking taylor expansion of PI in n 1540976150.122 * [misc]backup-simplify: Simplify PI into PI 1540976150.122 * [misc]taylor: Taking taylor expansion of n in n 1540976150.122 * [misc]backup-simplify: Simplify 0 into 0 1540976150.122 * [misc]backup-simplify: Simplify 1 into 1 1540976150.122 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1540976150.122 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1540976150.123 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1540976150.124 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1540976150.125 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1540976150.125 * [misc]backup-simplify: Simplify 0 into 0 1540976150.126 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976150.127 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1540976150.127 * [misc]backup-simplify: Simplify 0 into 0 1540976150.129 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976150.131 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1540976150.131 * [misc]backup-simplify: Simplify 0 into 0 1540976150.133 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976150.136 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1540976150.136 * [misc]backup-simplify: Simplify 0 into 0 1540976150.138 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976150.141 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1540976150.141 * [misc]backup-simplify: Simplify 0 into 0 1540976150.145 * [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 1540976150.149 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1540976150.149 * [misc]backup-simplify: Simplify 0 into 0 1540976150.150 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 1540976150.150 * [misc]backup-simplify: Simplify (* PI (* (/ 1 (- n)) 2)) into (* -2 (/ PI n)) 1540976150.150 * [misc]approximate: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1540976150.150 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1540976150.150 * [misc]taylor: Taking taylor expansion of -2 in n 1540976150.150 * [misc]backup-simplify: Simplify -2 into -2 1540976150.150 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1540976150.150 * [misc]taylor: Taking taylor expansion of PI in n 1540976150.150 * [misc]backup-simplify: Simplify PI into PI 1540976150.150 * [misc]taylor: Taking taylor expansion of n in n 1540976150.150 * [misc]backup-simplify: Simplify 0 into 0 1540976150.150 * [misc]backup-simplify: Simplify 1 into 1 1540976150.151 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1540976150.151 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1540976150.151 * [misc]taylor: Taking taylor expansion of -2 in n 1540976150.151 * [misc]backup-simplify: Simplify -2 into -2 1540976150.151 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1540976150.151 * [misc]taylor: Taking taylor expansion of PI in n 1540976150.151 * [misc]backup-simplify: Simplify PI into PI 1540976150.151 * [misc]taylor: Taking taylor expansion of n in n 1540976150.151 * [misc]backup-simplify: Simplify 0 into 0 1540976150.151 * [misc]backup-simplify: Simplify 1 into 1 1540976150.151 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1540976150.152 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1540976150.152 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1540976150.153 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1540976150.153 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1540976150.153 * [misc]backup-simplify: Simplify 0 into 0 1540976150.154 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976150.155 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1540976150.155 * [misc]backup-simplify: Simplify 0 into 0 1540976150.156 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976150.157 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1540976150.157 * [misc]backup-simplify: Simplify 0 into 0 1540976150.158 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976150.159 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1540976150.159 * [misc]backup-simplify: Simplify 0 into 0 1540976150.160 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976150.162 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1540976150.162 * [misc]backup-simplify: Simplify 0 into 0 1540976150.164 * [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 1540976150.166 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1540976150.166 * [misc]backup-simplify: Simplify 0 into 0 1540976150.166 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 1540976150.166 * * * [misc]progress: simplifying candidates 1540976150.166 * * * * [misc]progress: [ 1 / 64 ] simplifiying candidate # 1540976150.166 * [enter]simplify: Simplifying (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) 1540976150.167 * * [misc]simplify: iters left: 6 (11 enodes) 1540976150.170 * * [misc]simplify: iters left: 5 (21 enodes) 1540976150.177 * * [misc]simplify: iters left: 4 (47 enodes) 1540976150.202 * * [misc]simplify: iters left: 3 (109 enodes) 1540976150.268 * * [misc]simplify: iters left: 2 (300 enodes) 1540976150.651 * [exit]simplify: Simplified to (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) 1540976150.651 * [misc]simplify: Simplified (2 1 2 1 1) to (λ (k n) (/ (* (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (exp (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI)))))) (sqrt k))) 1540976150.651 * * * * [misc]progress: [ 2 / 64 ] simplifiying candidate # 1540976150.652 * * * * [misc]progress: [ 3 / 64 ] simplifiying candidate # 1540976150.652 * [enter]simplify: Simplifying (* PI (* n 2)) 1540976150.652 * * [misc]simplify: iters left: 4 (5 enodes) 1540976150.655 * * [misc]simplify: iters left: 3 (9 enodes) 1540976150.659 * * [misc]simplify: iters left: 2 (15 enodes) 1540976150.661 * * [misc]simplify: iters left: 1 (17 enodes) 1540976150.664 * [exit]simplify: Simplified to (* (* 2 n) PI) 1540976150.664 * [misc]simplify: Simplified (2 1 2 1 1) to (λ (k n) (/ (* (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (pow (* (* 2 n) PI) (* 1 (- 1/2 (/ k 2)))))) (sqrt k))) 1540976150.664 * * * * [misc]progress: [ 4 / 64 ] simplifiying candidate # 1540976150.664 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (/ k 2)) 1540976150.665 * * [misc]simplify: iters left: 5 (8 enodes) 1540976150.666 * * [misc]simplify: iters left: 4 (12 enodes) 1540976150.669 * * [misc]simplify: iters left: 3 (18 enodes) 1540976150.672 * * [misc]simplify: iters left: 2 (20 enodes) 1540976150.675 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ k 2)) 1540976150.675 * [misc]simplify: Simplified (2 1 2 1 2) to (λ (k n) (/ (* (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (/ (pow (* PI (* n 2)) 1/2) (pow (* (* 2 n) PI) (/ k 2))))) (sqrt k))) 1540976150.675 * * * * [misc]progress: [ 5 / 64 ] simplifiying candidate # 1540976150.675 * [enter]simplify: Simplifying (cbrt (- 1/2 (/ k 2))) 1540976150.676 * * [misc]simplify: iters left: 5 (6 enodes) 1540976150.677 * * [misc]simplify: iters left: 4 (8 enodes) 1540976150.678 * * [misc]simplify: iters left: 3 (11 enodes) 1540976150.680 * [exit]simplify: Simplified to (cbrt (- 1/2 (/ k 2))) 1540976150.680 * [misc]simplify: Simplified (2 1 2 1 2) to (λ (k n) (/ (* (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (pow (pow (* PI (* n 2)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))))) (sqrt k))) 1540976150.680 * * * * [misc]progress: [ 6 / 64 ] simplifiying candidate # 1540976150.681 * [enter]simplify: Simplifying (sqrt (- 1/2 (/ k 2))) 1540976150.681 * * [misc]simplify: iters left: 5 (6 enodes) 1540976150.682 * * [misc]simplify: iters left: 4 (8 enodes) 1540976150.683 * * [misc]simplify: iters left: 3 (11 enodes) 1540976150.685 * [exit]simplify: Simplified to (sqrt (- 1/2 (/ k 2))) 1540976150.685 * [misc]simplify: Simplified (2 1 2 1 2) to (λ (k n) (/ (* (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (pow (pow (* PI (* n 2)) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))))) (sqrt k))) 1540976150.685 * * * * [misc]progress: [ 7 / 64 ] simplifiying candidate # 1540976150.685 * [enter]simplify: Simplifying (- 1/2 (/ k 2)) 1540976150.685 * * [misc]simplify: iters left: 4 (5 enodes) 1540976150.686 * * [misc]simplify: iters left: 3 (7 enodes) 1540976150.688 * * [misc]simplify: iters left: 2 (10 enodes) 1540976150.692 * [exit]simplify: Simplified to (- 1/2 (/ k 2)) 1540976150.692 * [misc]simplify: Simplified (2 1 2 1 2) to (λ (k n) (/ (* (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (pow (pow (* PI (* n 2)) 1) (- 1/2 (/ k 2))))) (sqrt k))) 1540976150.692 * * * * [misc]progress: [ 8 / 64 ] simplifiying candidate # 1540976150.692 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1540976150.693 * * [misc]simplify: iters left: 5 (9 enodes) 1540976150.697 * * [misc]simplify: iters left: 4 (15 enodes) 1540976150.703 * * [misc]simplify: iters left: 3 (21 enodes) 1540976150.710 * * [misc]simplify: iters left: 2 (22 enodes) 1540976150.719 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1540976150.719 * [misc]simplify: Simplified (2 1 2 1 2) to (λ (k n) (/ (* (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2)))))) (sqrt k))) 1540976150.719 * * * * [misc]progress: [ 9 / 64 ] simplifiying candidate # 1540976150.719 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1540976150.720 * * [misc]simplify: iters left: 5 (9 enodes) 1540976150.724 * * [misc]simplify: iters left: 4 (15 enodes) 1540976150.729 * * [misc]simplify: iters left: 3 (21 enodes) 1540976150.736 * * [misc]simplify: iters left: 2 (22 enodes) 1540976150.739 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1540976150.739 * [misc]simplify: Simplified (2 1 2 1 2) to (λ (k n) (/ (* (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2)))))) (sqrt k))) 1540976150.739 * * * * [misc]progress: [ 10 / 64 ] simplifiying candidate # 1540976150.739 * [enter]simplify: Simplifying (pow PI (- 1/2 (/ k 2))) 1540976150.740 * * [misc]simplify: iters left: 5 (7 enodes) 1540976150.741 * * [misc]simplify: iters left: 4 (9 enodes) 1540976150.743 * * [misc]simplify: iters left: 3 (12 enodes) 1540976150.745 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1540976150.745 * [misc]simplify: Simplified (2 1 2 1 1) to (λ (k n) (/ (* (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (* (pow PI (- 1/2 (/ k 2))) (pow (* n 2) (- 1/2 (/ k 2)))))) (sqrt k))) 1540976150.745 * * * * [misc]progress: [ 11 / 64 ] simplifiying candidate # 1540976150.745 * * * * [misc]progress: [ 12 / 64 ] simplifiying candidate # 1540976150.745 * * * * [misc]progress: [ 13 / 64 ] simplifiying candidate # 1540976150.745 * * * * [misc]progress: [ 14 / 64 ] simplifiying candidate # 1540976150.745 * * * * [misc]progress: [ 15 / 64 ] simplifiying candidate # 1540976150.745 * * * * [misc]progress: [ 16 / 64 ] simplifiying candidate # 1540976150.745 * * * * [misc]progress: [ 17 / 64 ] simplifiying candidate # 1540976150.745 * * * * [misc]progress: [ 18 / 64 ] simplifiying candidate # 1540976150.745 * [enter]simplify: Simplifying (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) 1540976150.746 * * [misc]simplify: iters left: 6 (11 enodes) 1540976150.749 * * [misc]simplify: iters left: 5 (21 enodes) 1540976150.755 * * [misc]simplify: iters left: 4 (47 enodes) 1540976150.773 * * [misc]simplify: iters left: 3 (109 enodes) 1540976150.832 * * [misc]simplify: iters left: 2 (300 enodes) 1540976151.169 * [exit]simplify: Simplified to (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) 1540976151.169 * [misc]simplify: Simplified (2 1 1 1 1) to (λ (k n) (/ (* (sqrt (exp (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt k))) 1540976151.169 * * * * [misc]progress: [ 19 / 64 ] simplifiying candidate # 1540976151.169 * * * * [misc]progress: [ 20 / 64 ] simplifiying candidate # 1540976151.170 * [enter]simplify: Simplifying (* PI (* n 2)) 1540976151.170 * * [misc]simplify: iters left: 4 (5 enodes) 1540976151.173 * * [misc]simplify: iters left: 3 (9 enodes) 1540976151.178 * * [misc]simplify: iters left: 2 (15 enodes) 1540976151.183 * * [misc]simplify: iters left: 1 (17 enodes) 1540976151.188 * [exit]simplify: Simplified to (* (* 2 n) PI) 1540976151.188 * [misc]simplify: Simplified (2 1 1 1 1) to (λ (k n) (/ (* (sqrt (pow (* (* 2 n) PI) (* 1 (- 1/2 (/ k 2))))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt k))) 1540976151.188 * * * * [misc]progress: [ 21 / 64 ] simplifiying candidate # 1540976151.189 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (/ k 2)) 1540976151.189 * * [misc]simplify: iters left: 5 (8 enodes) 1540976151.193 * * [misc]simplify: iters left: 4 (12 enodes) 1540976151.198 * * [misc]simplify: iters left: 3 (18 enodes) 1540976151.204 * * [misc]simplify: iters left: 2 (20 enodes) 1540976151.210 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ k 2)) 1540976151.210 * [misc]simplify: Simplified (2 1 1 1 2) to (λ (k n) (/ (* (sqrt (/ (pow (* PI (* n 2)) 1/2) (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt k))) 1540976151.210 * * * * [misc]progress: [ 22 / 64 ] simplifiying candidate # 1540976151.211 * [enter]simplify: Simplifying (cbrt (- 1/2 (/ k 2))) 1540976151.211 * * [misc]simplify: iters left: 5 (6 enodes) 1540976151.213 * * [misc]simplify: iters left: 4 (8 enodes) 1540976151.216 * * [misc]simplify: iters left: 3 (11 enodes) 1540976151.220 * [exit]simplify: Simplified to (cbrt (- 1/2 (/ k 2))) 1540976151.220 * [misc]simplify: Simplified (2 1 1 1 2) to (λ (k n) (/ (* (sqrt (pow (pow (* PI (* n 2)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2))))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt k))) 1540976151.220 * * * * [misc]progress: [ 23 / 64 ] simplifiying candidate # 1540976151.220 * [enter]simplify: Simplifying (sqrt (- 1/2 (/ k 2))) 1540976151.221 * * [misc]simplify: iters left: 5 (6 enodes) 1540976151.223 * * [misc]simplify: iters left: 4 (8 enodes) 1540976151.227 * * [misc]simplify: iters left: 3 (11 enodes) 1540976151.231 * [exit]simplify: Simplified to (sqrt (- 1/2 (/ k 2))) 1540976151.231 * [misc]simplify: Simplified (2 1 1 1 2) to (λ (k n) (/ (* (sqrt (pow (pow (* PI (* n 2)) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2))))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt k))) 1540976151.231 * * * * [misc]progress: [ 24 / 64 ] simplifiying candidate # 1540976151.231 * [enter]simplify: Simplifying (- 1/2 (/ k 2)) 1540976151.232 * * [misc]simplify: iters left: 4 (5 enodes) 1540976151.234 * * [misc]simplify: iters left: 3 (7 enodes) 1540976151.237 * * [misc]simplify: iters left: 2 (10 enodes) 1540976151.240 * [exit]simplify: Simplified to (- 1/2 (/ k 2)) 1540976151.240 * [misc]simplify: Simplified (2 1 1 1 2) to (λ (k n) (/ (* (sqrt (pow (pow (* PI (* n 2)) 1) (- 1/2 (/ k 2)))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt k))) 1540976151.240 * * * * [misc]progress: [ 25 / 64 ] simplifiying candidate # 1540976151.240 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1540976151.241 * * [misc]simplify: iters left: 5 (9 enodes) 1540976151.246 * * [misc]simplify: iters left: 4 (15 enodes) 1540976151.252 * * [misc]simplify: iters left: 3 (21 enodes) 1540976151.256 * * [misc]simplify: iters left: 2 (22 enodes) 1540976151.260 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1540976151.260 * [misc]simplify: Simplified (2 1 1 1 2) to (λ (k n) (/ (* (sqrt (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2))))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt k))) 1540976151.260 * * * * [misc]progress: [ 26 / 64 ] simplifiying candidate # 1540976151.260 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1540976151.261 * * [misc]simplify: iters left: 5 (9 enodes) 1540976151.263 * * [misc]simplify: iters left: 4 (15 enodes) 1540976151.266 * * [misc]simplify: iters left: 3 (21 enodes) 1540976151.269 * * [misc]simplify: iters left: 2 (22 enodes) 1540976151.273 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1540976151.273 * [misc]simplify: Simplified (2 1 1 1 2) to (λ (k n) (/ (* (sqrt (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2))))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt k))) 1540976151.274 * * * * [misc]progress: [ 27 / 64 ] simplifiying candidate # 1540976151.274 * [enter]simplify: Simplifying (pow PI (- 1/2 (/ k 2))) 1540976151.274 * * [misc]simplify: iters left: 5 (7 enodes) 1540976151.276 * * [misc]simplify: iters left: 4 (9 enodes) 1540976151.278 * * [misc]simplify: iters left: 3 (12 enodes) 1540976151.280 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1540976151.280 * [misc]simplify: Simplified (2 1 1 1 1) to (λ (k n) (/ (* (sqrt (* (pow PI (- 1/2 (/ k 2))) (pow (* n 2) (- 1/2 (/ k 2))))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt k))) 1540976151.280 * * * * [misc]progress: [ 28 / 64 ] simplifiying candidate # 1540976151.280 * * * * [misc]progress: [ 29 / 64 ] simplifiying candidate # 1540976151.280 * * * * [misc]progress: [ 30 / 64 ] simplifiying candidate # 1540976151.280 * * * * [misc]progress: [ 31 / 64 ] simplifiying candidate # 1540976151.280 * * * * [misc]progress: [ 32 / 64 ] simplifiying candidate # 1540976151.280 * * * * [misc]progress: [ 33 / 64 ] simplifiying candidate # 1540976151.280 * * * * [misc]progress: [ 34 / 64 ] simplifiying candidate # 1540976151.280 * * * * [misc]progress: [ 35 / 64 ] simplifiying candidate # 1540976151.280 * * * * [misc]progress: [ 36 / 64 ] simplifiying candidate # 1540976151.280 * * * * [misc]progress: [ 37 / 64 ] simplifiying candidate # 1540976151.280 * * * * [misc]progress: [ 38 / 64 ] simplifiying candidate # 1540976151.280 * * * * [misc]progress: [ 39 / 64 ] simplifiying candidate # 1540976151.280 * * * * [misc]progress: [ 40 / 64 ] simplifiying candidate # 1540976151.281 * * * * [misc]progress: [ 41 / 64 ] simplifiying candidate # 1540976151.281 * * * * [misc]progress: [ 42 / 64 ] simplifiying candidate # 1540976151.281 * * * * [misc]progress: [ 43 / 64 ] simplifiying candidate # 1540976151.281 * * * * [misc]progress: [ 44 / 64 ] simplifiying candidate # 1540976151.281 * * * * [misc]progress: [ 45 / 64 ] simplifiying candidate # 1540976151.281 * * * * [misc]progress: [ 46 / 64 ] simplifiying candidate # 1540976151.281 * * * * [misc]progress: [ 47 / 64 ] simplifiying candidate # 1540976151.281 * * * * [misc]progress: [ 48 / 64 ] simplifiying candidate # 1540976151.281 * * * * [misc]progress: [ 49 / 64 ] simplifiying candidate # 1540976151.281 * * * * [misc]progress: [ 50 / 64 ] simplifiying candidate # 1540976151.281 * * * * [misc]progress: [ 51 / 64 ] simplifiying candidate # 1540976151.281 * * * * [misc]progress: [ 52 / 64 ] simplifiying candidate # 1540976151.281 * * * * [misc]progress: [ 53 / 64 ] simplifiying candidate # 1540976151.281 * [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))))) 1540976151.284 * * [misc]simplify: iters left: 6 (37 enodes) 1540976151.298 * * [misc]simplify: iters left: 5 (105 enodes) 1540976151.349 * * [misc]simplify: iters left: 4 (339 enodes) 1540976151.888 * [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))))) 1540976151.888 * [misc]simplify: Simplified (2 1 2 1) to (λ (k n) (/ (* (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (+ (+ (* (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) -1/2) (+ (* (* (* k (log n)) (* k (log n))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (pow (* PI 2) 1/2) (pow n 1/2)))) (* (* k k) (+ (* (* (log (* PI 2)) (log (* PI 2))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (* (* (log n) (pow n 1/2)) (pow (* PI 2) 1/2)) (* (log (* PI 2)) 1/4))))))) (sqrt k))) 1540976151.888 * * * * [misc]progress: [ 54 / 64 ] simplifiying candidate # 1540976151.889 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 1540976151.890 * * [misc]simplify: iters left: 6 (15 enodes) 1540976151.900 * * [misc]simplify: iters left: 5 (33 enodes) 1540976151.916 * * [misc]simplify: iters left: 4 (64 enodes) 1540976151.954 * * [misc]simplify: iters left: 3 (171 enodes) 1540976152.102 * [exit]simplify: Simplified to (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow n (- 1/2 (* 1/2 k)))) 1540976152.102 * [misc]simplify: Simplified (2 1 2 1) to (λ (k n) (/ (* (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow n (- 1/2 (* 1/2 k)))))) (sqrt k))) 1540976152.102 * * * * [misc]progress: [ 55 / 64 ] simplifiying candidate # 1540976152.103 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 1540976152.104 * * [misc]simplify: iters left: 6 (15 enodes) 1540976152.114 * * [misc]simplify: iters left: 5 (30 enodes) 1540976152.124 * * [misc]simplify: iters left: 4 (65 enodes) 1540976152.149 * * [misc]simplify: iters left: 3 (200 enodes) 1540976152.400 * [exit]simplify: Simplified to (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))) 1540976152.400 * [misc]simplify: Simplified (2 1 2 1) to (λ (k n) (/ (* (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))))) (sqrt k))) 1540976152.400 * * * * [misc]progress: [ 56 / 64 ] simplifiying candidate # 1540976152.400 * [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))))) 1540976152.405 * * [misc]simplify: iters left: 6 (37 enodes) 1540976152.432 * * [misc]simplify: iters left: 5 (105 enodes) 1540976152.481 * * [misc]simplify: iters left: 4 (339 enodes) 1540976152.961 * [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))))) 1540976152.961 * [misc]simplify: Simplified (2 1 1 1) to (λ (k n) (/ (* (sqrt (+ (+ (* (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) -1/2) (+ (* (* (* k (log n)) (* k (log n))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (pow (* PI 2) 1/2) (pow n 1/2)))) (* (* k k) (+ (* (* (log (* PI 2)) (log (* PI 2))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (* (* (log n) (pow n 1/2)) (pow (* PI 2) 1/2)) (* (log (* PI 2)) 1/4)))))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt k))) 1540976152.961 * * * * [misc]progress: [ 57 / 64 ] simplifiying candidate # 1540976152.961 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 1540976152.962 * * [misc]simplify: iters left: 6 (15 enodes) 1540976152.967 * * [misc]simplify: iters left: 5 (33 enodes) 1540976152.975 * * [misc]simplify: iters left: 4 (64 enodes) 1540976153.007 * * [misc]simplify: iters left: 3 (171 enodes) 1540976153.193 * [exit]simplify: Simplified to (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow n (- 1/2 (* 1/2 k)))) 1540976153.193 * [misc]simplify: Simplified (2 1 1 1) to (λ (k n) (/ (* (sqrt (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow n (- 1/2 (* 1/2 k))))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt k))) 1540976153.193 * * * * [misc]progress: [ 58 / 64 ] simplifiying candidate # 1540976153.193 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 1540976153.195 * * [misc]simplify: iters left: 6 (15 enodes) 1540976153.200 * * [misc]simplify: iters left: 5 (30 enodes) 1540976153.209 * * [misc]simplify: iters left: 4 (65 enodes) 1540976153.243 * * [misc]simplify: iters left: 3 (200 enodes) 1540976153.481 * [exit]simplify: Simplified to (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))) 1540976153.481 * [misc]simplify: Simplified (2 1 1 1) to (λ (k n) (/ (* (sqrt (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n))))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt k))) 1540976153.481 * * * * [misc]progress: [ 59 / 64 ] simplifiying candidate # 1540976153.481 * [enter]simplify: Simplifying (* 2 (* n PI)) 1540976153.482 * * [misc]simplify: iters left: 4 (5 enodes) 1540976153.484 * * [misc]simplify: iters left: 3 (9 enodes) 1540976153.488 * * [misc]simplify: iters left: 2 (15 enodes) 1540976153.494 * * [misc]simplify: iters left: 1 (17 enodes) 1540976153.499 * [exit]simplify: Simplified to (* (* PI n) 2) 1540976153.499 * [misc]simplify: Simplified (2 1 2 1 1) to (λ (k n) (/ (* (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) (sqrt k))) 1540976153.499 * * * * [misc]progress: [ 60 / 64 ] simplifiying candidate # 1540976153.500 * [enter]simplify: Simplifying (* 2 (* n PI)) 1540976153.500 * * [misc]simplify: iters left: 4 (5 enodes) 1540976153.503 * * [misc]simplify: iters left: 3 (9 enodes) 1540976153.507 * * [misc]simplify: iters left: 2 (15 enodes) 1540976153.512 * * [misc]simplify: iters left: 1 (17 enodes) 1540976153.517 * [exit]simplify: Simplified to (* (* PI n) 2) 1540976153.517 * [misc]simplify: Simplified (2 1 2 1 1) to (λ (k n) (/ (* (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) (sqrt k))) 1540976153.517 * * * * [misc]progress: [ 61 / 64 ] simplifiying candidate # 1540976153.517 * [enter]simplify: Simplifying (* 2 (* n PI)) 1540976153.518 * * [misc]simplify: iters left: 4 (5 enodes) 1540976153.520 * * [misc]simplify: iters left: 3 (9 enodes) 1540976153.524 * * [misc]simplify: iters left: 2 (15 enodes) 1540976153.530 * * [misc]simplify: iters left: 1 (17 enodes) 1540976153.535 * [exit]simplify: Simplified to (* (* PI n) 2) 1540976153.535 * [misc]simplify: Simplified (2 1 2 1 1) to (λ (k n) (/ (* (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) (sqrt k))) 1540976153.536 * * * * [misc]progress: [ 62 / 64 ] simplifiying candidate # 1540976153.536 * [enter]simplify: Simplifying (* 2 (* n PI)) 1540976153.536 * * [misc]simplify: iters left: 4 (5 enodes) 1540976153.539 * * [misc]simplify: iters left: 3 (9 enodes) 1540976153.543 * * [misc]simplify: iters left: 2 (15 enodes) 1540976153.548 * * [misc]simplify: iters left: 1 (17 enodes) 1540976153.553 * [exit]simplify: Simplified to (* (* PI n) 2) 1540976153.554 * [misc]simplify: Simplified (2 1 1 1 1) to (λ (k n) (/ (* (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt k))) 1540976153.554 * * * * [misc]progress: [ 63 / 64 ] simplifiying candidate # 1540976153.554 * [enter]simplify: Simplifying (* 2 (* n PI)) 1540976153.554 * * [misc]simplify: iters left: 4 (5 enodes) 1540976153.557 * * [misc]simplify: iters left: 3 (9 enodes) 1540976153.561 * * [misc]simplify: iters left: 2 (15 enodes) 1540976153.568 * * [misc]simplify: iters left: 1 (17 enodes) 1540976153.572 * [exit]simplify: Simplified to (* (* PI n) 2) 1540976153.572 * [misc]simplify: Simplified (2 1 1 1 1) to (λ (k n) (/ (* (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt k))) 1540976153.572 * * * * [misc]progress: [ 64 / 64 ] simplifiying candidate # 1540976153.573 * [enter]simplify: Simplifying (* 2 (* n PI)) 1540976153.573 * * [misc]simplify: iters left: 4 (5 enodes) 1540976153.574 * * [misc]simplify: iters left: 3 (9 enodes) 1540976153.576 * * [misc]simplify: iters left: 2 (15 enodes) 1540976153.578 * * [misc]simplify: iters left: 1 (17 enodes) 1540976153.581 * [exit]simplify: Simplified to (* (* PI n) 2) 1540976153.581 * [misc]simplify: Simplified (2 1 1 1 1) to (λ (k n) (/ (* (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt k))) 1540976153.581 * * * [misc]progress: adding candidates to table 1540976155.322 * * [misc]progress: iteration 4 / 4 1540976155.322 * * * [misc]progress: picking best candidate 1540976155.387 * * * * [misc]pick: Picked # 1540976155.387 * * * [misc]progress: localizing error 1540976155.411 * * * [misc]progress: generating rewritten candidates 1540976155.411 * * * * [misc]progress: [ 1 / 4 ] rewriting at (2 1 2 1) 1540976155.435 * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 1 1 1 2) 1540976155.451 * * * * [misc]progress: [ 3 / 4 ] rewriting at (2 1 1 1 1) 1540976155.461 * * * * [misc]progress: [ 4 / 4 ] rewriting at (2 1 2 1 1) 1540976155.481 * * * [misc]progress: generating series expansions 1540976155.481 * * * * [misc]progress: [ 1 / 4 ] generating series at (2 1 2 1) 1540976155.481 * [misc]backup-simplify: Simplify (pow (* PI (* n 2)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 1540976155.481 * [misc]approximate: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 1540976155.481 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1540976155.481 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1540976155.482 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1540976155.482 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1540976155.482 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976155.482 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976155.482 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1540976155.482 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976155.482 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976155.482 * [misc]taylor: Taking taylor expansion of k in k 1540976155.482 * [misc]backup-simplify: Simplify 0 into 0 1540976155.482 * [misc]backup-simplify: Simplify 1 into 1 1540976155.482 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1540976155.482 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1540976155.482 * [misc]taylor: Taking taylor expansion of 2 in k 1540976155.482 * [misc]backup-simplify: Simplify 2 into 2 1540976155.482 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1540976155.482 * [misc]taylor: Taking taylor expansion of n in k 1540976155.482 * [misc]backup-simplify: Simplify n into n 1540976155.482 * [misc]taylor: Taking taylor expansion of PI in k 1540976155.482 * [misc]backup-simplify: Simplify PI into PI 1540976155.482 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1540976155.482 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1540976155.483 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1540976155.483 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1540976155.483 * [misc]backup-simplify: Simplify (- 0) into 0 1540976155.483 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1540976155.484 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1540976155.484 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1540976155.484 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1540976155.484 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1540976155.484 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1540976155.484 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1540976155.484 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976155.484 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976155.484 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1540976155.484 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976155.484 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976155.484 * [misc]taylor: Taking taylor expansion of k in n 1540976155.484 * [misc]backup-simplify: Simplify k into k 1540976155.484 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1540976155.484 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1540976155.484 * [misc]taylor: Taking taylor expansion of 2 in n 1540976155.484 * [misc]backup-simplify: Simplify 2 into 2 1540976155.484 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1540976155.484 * [misc]taylor: Taking taylor expansion of n in n 1540976155.484 * [misc]backup-simplify: Simplify 0 into 0 1540976155.484 * [misc]backup-simplify: Simplify 1 into 1 1540976155.484 * [misc]taylor: Taking taylor expansion of PI in n 1540976155.485 * [misc]backup-simplify: Simplify PI into PI 1540976155.485 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1540976155.485 * [misc]backup-simplify: Simplify (* 2 0) into 0 1540976155.486 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1540976155.487 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1540976155.487 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1540976155.487 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1540976155.487 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1540976155.487 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1540976155.488 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1540976155.488 * [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)))) 1540976155.489 * [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))))) 1540976155.489 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1540976155.489 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1540976155.489 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1540976155.489 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1540976155.489 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976155.489 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976155.489 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1540976155.489 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976155.489 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976155.489 * [misc]taylor: Taking taylor expansion of k in n 1540976155.489 * [misc]backup-simplify: Simplify k into k 1540976155.489 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1540976155.489 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1540976155.489 * [misc]taylor: Taking taylor expansion of 2 in n 1540976155.489 * [misc]backup-simplify: Simplify 2 into 2 1540976155.489 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1540976155.489 * [misc]taylor: Taking taylor expansion of n in n 1540976155.489 * [misc]backup-simplify: Simplify 0 into 0 1540976155.489 * [misc]backup-simplify: Simplify 1 into 1 1540976155.489 * [misc]taylor: Taking taylor expansion of PI in n 1540976155.489 * [misc]backup-simplify: Simplify PI into PI 1540976155.489 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1540976155.489 * [misc]backup-simplify: Simplify (* 2 0) into 0 1540976155.490 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1540976155.490 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1540976155.491 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1540976155.491 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1540976155.491 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1540976155.491 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1540976155.491 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1540976155.492 * [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)))) 1540976155.492 * [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))))) 1540976155.492 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1540976155.492 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1540976155.492 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1540976155.492 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976155.492 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976155.492 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1540976155.492 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976155.492 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976155.492 * [misc]taylor: Taking taylor expansion of k in k 1540976155.492 * [misc]backup-simplify: Simplify 0 into 0 1540976155.493 * [misc]backup-simplify: Simplify 1 into 1 1540976155.493 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1540976155.493 * [misc]taylor: Taking taylor expansion of (log n) in k 1540976155.493 * [misc]taylor: Taking taylor expansion of n in k 1540976155.493 * [misc]backup-simplify: Simplify n into n 1540976155.493 * [misc]backup-simplify: Simplify (log n) into (log n) 1540976155.493 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1540976155.493 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1540976155.493 * [misc]taylor: Taking taylor expansion of 2 in k 1540976155.493 * [misc]backup-simplify: Simplify 2 into 2 1540976155.493 * [misc]taylor: Taking taylor expansion of PI in k 1540976155.493 * [misc]backup-simplify: Simplify PI into PI 1540976155.493 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1540976155.493 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1540976155.493 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1540976155.493 * [misc]backup-simplify: Simplify (- 0) into 0 1540976155.494 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1540976155.494 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1540976155.494 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1540976155.495 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1540976155.495 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1540976155.496 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1540976155.497 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1540976155.499 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1540976155.499 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1540976155.499 * [misc]backup-simplify: Simplify (- 0) into 0 1540976155.499 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976155.500 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1540976155.500 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1540976155.501 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1540976155.501 * [misc]taylor: Taking taylor expansion of 0 in k 1540976155.501 * [misc]backup-simplify: Simplify 0 into 0 1540976155.501 * [misc]backup-simplify: Simplify 0 into 0 1540976155.502 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1540976155.502 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1540976155.504 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1540976155.504 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976155.504 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1540976155.504 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1540976155.505 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1540976155.505 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1540976155.506 * [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))))))) 1540976155.507 * [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))))))) 1540976155.508 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1540976155.509 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1540976155.513 * [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 1540976155.513 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1540976155.513 * [misc]backup-simplify: Simplify (- 0) into 0 1540976155.513 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976155.513 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1540976155.514 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1540976155.516 * [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 1540976155.516 * [misc]taylor: Taking taylor expansion of 0 in k 1540976155.516 * [misc]backup-simplify: Simplify 0 into 0 1540976155.516 * [misc]backup-simplify: Simplify 0 into 0 1540976155.516 * [misc]backup-simplify: Simplify 0 into 0 1540976155.517 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1540976155.517 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1540976155.521 * [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 1540976155.521 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976155.521 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1540976155.521 * [misc]backup-simplify: Simplify (- 0) into 0 1540976155.521 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976155.522 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1540976155.524 * [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))))) 1540976155.526 * [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))))) 1540976155.533 * [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))))) 1540976155.534 * [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)))) 1540976155.534 * [misc]approximate: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 1540976155.534 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1540976155.534 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1540976155.534 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1540976155.534 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1540976155.534 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976155.534 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976155.534 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1540976155.534 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976155.534 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976155.534 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1540976155.534 * [misc]taylor: Taking taylor expansion of k in k 1540976155.534 * [misc]backup-simplify: Simplify 0 into 0 1540976155.534 * [misc]backup-simplify: Simplify 1 into 1 1540976155.534 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1540976155.534 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1540976155.534 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1540976155.534 * [misc]taylor: Taking taylor expansion of 2 in k 1540976155.534 * [misc]backup-simplify: Simplify 2 into 2 1540976155.534 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1540976155.534 * [misc]taylor: Taking taylor expansion of PI in k 1540976155.534 * [misc]backup-simplify: Simplify PI into PI 1540976155.534 * [misc]taylor: Taking taylor expansion of n in k 1540976155.534 * [misc]backup-simplify: Simplify n into n 1540976155.534 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1540976155.535 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1540976155.535 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1540976155.535 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1540976155.535 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1540976155.535 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1540976155.535 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1540976155.535 * [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)))) 1540976155.535 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1540976155.535 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1540976155.535 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1540976155.535 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1540976155.535 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976155.535 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976155.535 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1540976155.535 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976155.535 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976155.535 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1540976155.535 * [misc]taylor: Taking taylor expansion of k in n 1540976155.535 * [misc]backup-simplify: Simplify k into k 1540976155.535 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1540976155.535 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1540976155.536 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1540976155.536 * [misc]taylor: Taking taylor expansion of 2 in n 1540976155.536 * [misc]backup-simplify: Simplify 2 into 2 1540976155.536 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1540976155.536 * [misc]taylor: Taking taylor expansion of PI in n 1540976155.536 * [misc]backup-simplify: Simplify PI into PI 1540976155.536 * [misc]taylor: Taking taylor expansion of n in n 1540976155.536 * [misc]backup-simplify: Simplify 0 into 0 1540976155.536 * [misc]backup-simplify: Simplify 1 into 1 1540976155.536 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1540976155.536 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1540976155.537 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1540976155.537 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1540976155.537 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1540976155.537 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1540976155.537 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1540976155.538 * [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))) 1540976155.538 * [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)))) 1540976155.538 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1540976155.538 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1540976155.538 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1540976155.538 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1540976155.538 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976155.538 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976155.538 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1540976155.538 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976155.538 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976155.538 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1540976155.538 * [misc]taylor: Taking taylor expansion of k in n 1540976155.538 * [misc]backup-simplify: Simplify k into k 1540976155.538 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1540976155.538 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1540976155.538 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1540976155.538 * [misc]taylor: Taking taylor expansion of 2 in n 1540976155.538 * [misc]backup-simplify: Simplify 2 into 2 1540976155.538 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1540976155.538 * [misc]taylor: Taking taylor expansion of PI in n 1540976155.538 * [misc]backup-simplify: Simplify PI into PI 1540976155.538 * [misc]taylor: Taking taylor expansion of n in n 1540976155.539 * [misc]backup-simplify: Simplify 0 into 0 1540976155.539 * [misc]backup-simplify: Simplify 1 into 1 1540976155.539 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1540976155.539 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1540976155.539 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1540976155.539 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1540976155.539 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1540976155.539 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1540976155.540 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1540976155.540 * [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))) 1540976155.541 * [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)))) 1540976155.541 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1540976155.541 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1540976155.541 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1540976155.541 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976155.541 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976155.541 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1540976155.541 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976155.541 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976155.541 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1540976155.541 * [misc]taylor: Taking taylor expansion of k in k 1540976155.541 * [misc]backup-simplify: Simplify 0 into 0 1540976155.541 * [misc]backup-simplify: Simplify 1 into 1 1540976155.541 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1540976155.541 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1540976155.541 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1540976155.541 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1540976155.541 * [misc]taylor: Taking taylor expansion of 2 in k 1540976155.541 * [misc]backup-simplify: Simplify 2 into 2 1540976155.541 * [misc]taylor: Taking taylor expansion of PI in k 1540976155.541 * [misc]backup-simplify: Simplify PI into PI 1540976155.542 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1540976155.542 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1540976155.542 * [misc]taylor: Taking taylor expansion of (log n) in k 1540976155.542 * [misc]taylor: Taking taylor expansion of n in k 1540976155.542 * [misc]backup-simplify: Simplify n into n 1540976155.542 * [misc]backup-simplify: Simplify (log n) into (log n) 1540976155.542 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1540976155.542 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1540976155.542 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1540976155.542 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1540976155.543 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1540976155.543 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1540976155.544 * [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)))) 1540976155.544 * [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)))) 1540976155.545 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1540976155.545 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1540976155.547 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1540976155.547 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1540976155.547 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1540976155.548 * [misc]backup-simplify: Simplify (- 0) into 0 1540976155.548 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976155.548 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1540976155.549 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1540976155.550 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1540976155.550 * [misc]taylor: Taking taylor expansion of 0 in k 1540976155.550 * [misc]backup-simplify: Simplify 0 into 0 1540976155.550 * [misc]backup-simplify: Simplify 0 into 0 1540976155.550 * [misc]backup-simplify: Simplify 0 into 0 1540976155.551 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976155.552 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1540976155.555 * [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 1540976155.555 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1540976155.555 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1540976155.555 * [misc]backup-simplify: Simplify (- 0) into 0 1540976155.556 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976155.556 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1540976155.557 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1540976155.558 * [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 1540976155.558 * [misc]taylor: Taking taylor expansion of 0 in k 1540976155.558 * [misc]backup-simplify: Simplify 0 into 0 1540976155.558 * [misc]backup-simplify: Simplify 0 into 0 1540976155.558 * [misc]backup-simplify: Simplify 0 into 0 1540976155.558 * [misc]backup-simplify: Simplify 0 into 0 1540976155.559 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976155.560 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1540976155.566 * [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 1540976155.566 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1540976155.566 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1540976155.566 * [misc]backup-simplify: Simplify (- 0) into 0 1540976155.566 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976155.567 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1540976155.568 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1540976155.570 * [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 1540976155.570 * [misc]taylor: Taking taylor expansion of 0 in k 1540976155.570 * [misc]backup-simplify: Simplify 0 into 0 1540976155.570 * [misc]backup-simplify: Simplify 0 into 0 1540976155.571 * [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))))) 1540976155.571 * [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)) 1540976155.571 * [misc]approximate: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 1540976155.571 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1540976155.571 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1540976155.571 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1540976155.571 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1540976155.571 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1540976155.571 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976155.571 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976155.571 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1540976155.571 * [misc]taylor: Taking taylor expansion of k in k 1540976155.571 * [misc]backup-simplify: Simplify 0 into 0 1540976155.571 * [misc]backup-simplify: Simplify 1 into 1 1540976155.571 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1540976155.571 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976155.571 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976155.571 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1540976155.571 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1540976155.571 * [misc]taylor: Taking taylor expansion of -2 in k 1540976155.571 * [misc]backup-simplify: Simplify -2 into -2 1540976155.571 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1540976155.571 * [misc]taylor: Taking taylor expansion of PI in k 1540976155.571 * [misc]backup-simplify: Simplify PI into PI 1540976155.571 * [misc]taylor: Taking taylor expansion of n in k 1540976155.571 * [misc]backup-simplify: Simplify n into n 1540976155.572 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1540976155.572 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1540976155.572 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1540976155.572 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1540976155.572 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1540976155.572 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1540976155.572 * [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))) 1540976155.572 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1540976155.572 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1540976155.572 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1540976155.572 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1540976155.572 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1540976155.572 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976155.572 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976155.572 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1540976155.572 * [misc]taylor: Taking taylor expansion of k in n 1540976155.572 * [misc]backup-simplify: Simplify k into k 1540976155.572 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1540976155.572 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976155.572 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976155.572 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1540976155.573 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1540976155.573 * [misc]taylor: Taking taylor expansion of -2 in n 1540976155.573 * [misc]backup-simplify: Simplify -2 into -2 1540976155.573 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1540976155.573 * [misc]taylor: Taking taylor expansion of PI in n 1540976155.573 * [misc]backup-simplify: Simplify PI into PI 1540976155.573 * [misc]taylor: Taking taylor expansion of n in n 1540976155.573 * [misc]backup-simplify: Simplify 0 into 0 1540976155.573 * [misc]backup-simplify: Simplify 1 into 1 1540976155.573 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1540976155.573 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1540976155.573 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1540976155.573 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1540976155.574 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1540976155.574 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1540976155.574 * [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))) 1540976155.575 * [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)))) 1540976155.575 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1540976155.575 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1540976155.575 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1540976155.575 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1540976155.575 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1540976155.575 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976155.575 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976155.575 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1540976155.575 * [misc]taylor: Taking taylor expansion of k in n 1540976155.575 * [misc]backup-simplify: Simplify k into k 1540976155.575 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1540976155.575 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976155.575 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976155.575 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1540976155.575 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1540976155.575 * [misc]taylor: Taking taylor expansion of -2 in n 1540976155.575 * [misc]backup-simplify: Simplify -2 into -2 1540976155.575 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1540976155.575 * [misc]taylor: Taking taylor expansion of PI in n 1540976155.575 * [misc]backup-simplify: Simplify PI into PI 1540976155.575 * [misc]taylor: Taking taylor expansion of n in n 1540976155.575 * [misc]backup-simplify: Simplify 0 into 0 1540976155.575 * [misc]backup-simplify: Simplify 1 into 1 1540976155.576 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1540976155.576 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1540976155.576 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1540976155.576 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1540976155.576 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1540976155.577 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1540976155.577 * [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))) 1540976155.578 * [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)))) 1540976155.578 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1540976155.578 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1540976155.578 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1540976155.578 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1540976155.578 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976155.578 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976155.578 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1540976155.578 * [misc]taylor: Taking taylor expansion of k in k 1540976155.578 * [misc]backup-simplify: Simplify 0 into 0 1540976155.578 * [misc]backup-simplify: Simplify 1 into 1 1540976155.578 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1540976155.578 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976155.578 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976155.578 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1540976155.578 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1540976155.578 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1540976155.578 * [misc]taylor: Taking taylor expansion of -2 in k 1540976155.578 * [misc]backup-simplify: Simplify -2 into -2 1540976155.578 * [misc]taylor: Taking taylor expansion of PI in k 1540976155.578 * [misc]backup-simplify: Simplify PI into PI 1540976155.578 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1540976155.579 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1540976155.579 * [misc]taylor: Taking taylor expansion of (log n) in k 1540976155.579 * [misc]taylor: Taking taylor expansion of n in k 1540976155.579 * [misc]backup-simplify: Simplify n into n 1540976155.579 * [misc]backup-simplify: Simplify (log n) into (log n) 1540976155.579 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1540976155.579 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1540976155.579 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1540976155.579 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1540976155.580 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1540976155.580 * [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)))) 1540976155.581 * [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)))) 1540976155.581 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1540976155.582 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1540976155.584 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1540976155.584 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1540976155.584 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1540976155.584 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976155.585 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1540976155.585 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1540976155.586 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1540976155.586 * [misc]taylor: Taking taylor expansion of 0 in k 1540976155.586 * [misc]backup-simplify: Simplify 0 into 0 1540976155.586 * [misc]backup-simplify: Simplify 0 into 0 1540976155.586 * [misc]backup-simplify: Simplify 0 into 0 1540976155.587 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976155.588 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1540976155.591 * [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 1540976155.591 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1540976155.592 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1540976155.592 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976155.592 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1540976155.593 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1540976155.594 * [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 1540976155.594 * [misc]taylor: Taking taylor expansion of 0 in k 1540976155.594 * [misc]backup-simplify: Simplify 0 into 0 1540976155.594 * [misc]backup-simplify: Simplify 0 into 0 1540976155.594 * [misc]backup-simplify: Simplify 0 into 0 1540976155.594 * [misc]backup-simplify: Simplify 0 into 0 1540976155.595 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976155.596 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1540976155.602 * [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 1540976155.602 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1540976155.602 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1540976155.603 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976155.603 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1540976155.604 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 1540976155.606 * [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 1540976155.606 * [misc]taylor: Taking taylor expansion of 0 in k 1540976155.606 * [misc]backup-simplify: Simplify 0 into 0 1540976155.606 * [misc]backup-simplify: Simplify 0 into 0 1540976155.607 * [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))))) 1540976155.607 * * * * [misc]progress: [ 2 / 4 ] generating series at (2 1 1 1 2) 1540976155.607 * [misc]backup-simplify: Simplify (pow (* n 2) (- 1/2 (/ k 2))) into (pow (* 2 n) (- 1/2 (* 1/2 k))) 1540976155.607 * [misc]approximate: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in (n k) around 0 1540976155.607 * [misc]taylor: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in k 1540976155.607 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in k 1540976155.607 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in k 1540976155.607 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1540976155.607 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976155.607 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976155.607 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1540976155.607 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976155.607 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976155.607 * [misc]taylor: Taking taylor expansion of k in k 1540976155.607 * [misc]backup-simplify: Simplify 0 into 0 1540976155.607 * [misc]backup-simplify: Simplify 1 into 1 1540976155.607 * [misc]taylor: Taking taylor expansion of (log (* 2 n)) in k 1540976155.607 * [misc]taylor: Taking taylor expansion of (* 2 n) in k 1540976155.607 * [misc]taylor: Taking taylor expansion of 2 in k 1540976155.607 * [misc]backup-simplify: Simplify 2 into 2 1540976155.607 * [misc]taylor: Taking taylor expansion of n in k 1540976155.607 * [misc]backup-simplify: Simplify n into n 1540976155.607 * [misc]backup-simplify: Simplify (* 2 n) into (* 2 n) 1540976155.607 * [misc]backup-simplify: Simplify (log (* 2 n)) into (log (* 2 n)) 1540976155.608 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1540976155.608 * [misc]backup-simplify: Simplify (- 0) into 0 1540976155.608 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1540976155.608 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 n))) into (* 1/2 (log (* 2 n))) 1540976155.608 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 n)))) into (pow (* 2 n) 1/2) 1540976155.608 * [misc]taylor: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in n 1540976155.608 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in n 1540976155.608 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in n 1540976155.608 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1540976155.608 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976155.608 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976155.608 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1540976155.608 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976155.608 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976155.608 * [misc]taylor: Taking taylor expansion of k in n 1540976155.608 * [misc]backup-simplify: Simplify k into k 1540976155.608 * [misc]taylor: Taking taylor expansion of (log (* 2 n)) in n 1540976155.608 * [misc]taylor: Taking taylor expansion of (* 2 n) in n 1540976155.608 * [misc]taylor: Taking taylor expansion of 2 in n 1540976155.608 * [misc]backup-simplify: Simplify 2 into 2 1540976155.608 * [misc]taylor: Taking taylor expansion of n in n 1540976155.608 * [misc]backup-simplify: Simplify 0 into 0 1540976155.608 * [misc]backup-simplify: Simplify 1 into 1 1540976155.608 * [misc]backup-simplify: Simplify (* 2 0) into 0 1540976155.608 * [misc]backup-simplify: Simplify (+ (* 2 1) (* 0 0)) into 2 1540976155.608 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1540976155.609 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1540976155.609 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1540976155.609 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1540976155.609 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 1540976155.609 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (+ (log 2) (log n))) into (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) 1540976155.609 * [misc]backup-simplify: Simplify (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) into (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) 1540976155.609 * [misc]taylor: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in n 1540976155.609 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in n 1540976155.609 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in n 1540976155.609 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1540976155.609 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976155.609 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976155.609 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1540976155.609 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976155.609 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976155.609 * [misc]taylor: Taking taylor expansion of k in n 1540976155.609 * [misc]backup-simplify: Simplify k into k 1540976155.609 * [misc]taylor: Taking taylor expansion of (log (* 2 n)) in n 1540976155.609 * [misc]taylor: Taking taylor expansion of (* 2 n) in n 1540976155.609 * [misc]taylor: Taking taylor expansion of 2 in n 1540976155.609 * [misc]backup-simplify: Simplify 2 into 2 1540976155.610 * [misc]taylor: Taking taylor expansion of n in n 1540976155.610 * [misc]backup-simplify: Simplify 0 into 0 1540976155.610 * [misc]backup-simplify: Simplify 1 into 1 1540976155.610 * [misc]backup-simplify: Simplify (* 2 0) into 0 1540976155.610 * [misc]backup-simplify: Simplify (+ (* 2 1) (* 0 0)) into 2 1540976155.610 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1540976155.610 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1540976155.610 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1540976155.610 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1540976155.610 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 1540976155.610 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (+ (log 2) (log n))) into (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) 1540976155.611 * [misc]backup-simplify: Simplify (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) into (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) 1540976155.611 * [misc]taylor: Taking taylor expansion of (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) in k 1540976155.611 * [misc]taylor: Taking taylor expansion of (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) in k 1540976155.611 * [misc]taylor: Taking taylor expansion of (+ (log 2) (log n)) in k 1540976155.611 * [misc]taylor: Taking taylor expansion of (log 2) in k 1540976155.611 * [misc]taylor: Taking taylor expansion of 2 in k 1540976155.611 * [misc]backup-simplify: Simplify 2 into 2 1540976155.611 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1540976155.611 * [misc]taylor: Taking taylor expansion of (log n) in k 1540976155.611 * [misc]taylor: Taking taylor expansion of n in k 1540976155.611 * [misc]backup-simplify: Simplify n into n 1540976155.611 * [misc]backup-simplify: Simplify (log n) into (log n) 1540976155.611 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1540976155.611 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976155.611 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976155.611 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1540976155.611 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976155.611 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976155.611 * [misc]taylor: Taking taylor expansion of k in k 1540976155.611 * [misc]backup-simplify: Simplify 0 into 0 1540976155.611 * [misc]backup-simplify: Simplify 1 into 1 1540976155.611 * [misc]backup-simplify: Simplify (+ (log 2) (log n)) into (+ (log 2) (log n)) 1540976155.611 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1540976155.611 * [misc]backup-simplify: Simplify (- 0) into 0 1540976155.612 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1540976155.612 * [misc]backup-simplify: Simplify (* (+ (log 2) (log n)) 1/2) into (* 1/2 (+ (log 2) (log n))) 1540976155.612 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log 2) (log n)))) into (exp (* 1/2 (+ (log 2) (log n)))) 1540976155.612 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log 2) (log n)))) into (exp (* 1/2 (+ (log 2) (log n)))) 1540976155.612 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 1) (* 0 0))) into 0 1540976155.614 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 1540976155.614 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1540976155.614 * [misc]backup-simplify: Simplify (- 0) into 0 1540976155.614 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976155.614 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 1540976155.614 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log 2) (log n)))) into 0 1540976155.615 * [misc]backup-simplify: Simplify (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (+ (* (/ (pow 0 1) 1)))) into 0 1540976155.615 * [misc]taylor: Taking taylor expansion of 0 in k 1540976155.615 * [misc]backup-simplify: Simplify 0 into 0 1540976155.615 * [misc]backup-simplify: Simplify 0 into 0 1540976155.615 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1540976155.616 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1540976155.616 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1540976155.617 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 1540976155.618 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1540976155.618 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976155.618 * [misc]backup-simplify: Simplify (+ (* (+ (log 2) (log n)) -1/2) (* 0 1/2)) into (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 1540976155.619 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) 1540976155.619 * [misc]backup-simplify: Simplify (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) into (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) 1540976155.619 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1540976155.622 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 1540976155.622 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1540976155.622 * [misc]backup-simplify: Simplify (- 0) into 0 1540976155.622 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976155.623 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 1540976155.623 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log 2) (log n))))) into 0 1540976155.624 * [misc]backup-simplify: Simplify (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1540976155.624 * [misc]taylor: Taking taylor expansion of 0 in k 1540976155.624 * [misc]backup-simplify: Simplify 0 into 0 1540976155.624 * [misc]backup-simplify: Simplify 0 into 0 1540976155.624 * [misc]backup-simplify: Simplify 0 into 0 1540976155.624 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1540976155.624 * [misc]backup-simplify: Simplify (- 0) into 0 1540976155.625 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976155.628 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 1540976155.630 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1540976155.630 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976155.630 * [misc]backup-simplify: Simplify (+ (* (+ (log 2) (log n)) 0) (+ (* 0 -1/2) (* 0 1/2))) into 0 1540976155.632 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))) 1540976155.633 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))) into (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))) 1540976155.638 * [misc]backup-simplify: Simplify (+ (* (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) (* k 1)) (exp (* 1/2 (+ (log 2) (log n)))))) into (- (+ (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (* (pow (log 2) 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (pow k 2)))) (+ (* 1/4 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) (pow k 2))))) (* 1/8 (* (exp (* 1/2 (+ (log 2) (log n)))) (* (pow (log n) 2) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) k))) (* 1/2 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) k))))) 1540976155.638 * [misc]backup-simplify: Simplify (pow (* (/ 1 n) 2) (- 1/2 (/ (/ 1 k) 2))) into (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) 1540976155.638 * [misc]approximate: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 1540976155.638 * [misc]taylor: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in k 1540976155.638 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in k 1540976155.638 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in k 1540976155.638 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1540976155.638 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976155.638 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976155.638 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1540976155.638 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976155.638 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976155.638 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1540976155.638 * [misc]taylor: Taking taylor expansion of k in k 1540976155.639 * [misc]backup-simplify: Simplify 0 into 0 1540976155.639 * [misc]backup-simplify: Simplify 1 into 1 1540976155.639 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1540976155.639 * [misc]taylor: Taking taylor expansion of (log (/ 2 n)) in k 1540976155.639 * [misc]taylor: Taking taylor expansion of (/ 2 n) in k 1540976155.639 * [misc]taylor: Taking taylor expansion of 2 in k 1540976155.639 * [misc]backup-simplify: Simplify 2 into 2 1540976155.639 * [misc]taylor: Taking taylor expansion of n in k 1540976155.639 * [misc]backup-simplify: Simplify n into n 1540976155.639 * [misc]backup-simplify: Simplify (/ 2 n) into (/ 2 n) 1540976155.639 * [misc]backup-simplify: Simplify (log (/ 2 n)) into (log (/ 2 n)) 1540976155.639 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1540976155.639 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1540976155.640 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1540976155.640 * [misc]backup-simplify: Simplify (* -1/2 (log (/ 2 n))) into (* -1/2 (log (/ 2 n))) 1540976155.640 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) into (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) 1540976155.640 * [misc]taylor: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 1540976155.640 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 1540976155.640 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 1540976155.640 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1540976155.640 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976155.640 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976155.640 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1540976155.640 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976155.640 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976155.640 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1540976155.640 * [misc]taylor: Taking taylor expansion of k in n 1540976155.640 * [misc]backup-simplify: Simplify k into k 1540976155.640 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1540976155.641 * [misc]taylor: Taking taylor expansion of (log (/ 2 n)) in n 1540976155.641 * [misc]taylor: Taking taylor expansion of (/ 2 n) in n 1540976155.641 * [misc]taylor: Taking taylor expansion of 2 in n 1540976155.641 * [misc]backup-simplify: Simplify 2 into 2 1540976155.641 * [misc]taylor: Taking taylor expansion of n in n 1540976155.641 * [misc]backup-simplify: Simplify 0 into 0 1540976155.641 * [misc]backup-simplify: Simplify 1 into 1 1540976155.641 * [misc]backup-simplify: Simplify (/ 2 1) into 2 1540976155.641 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1540976155.641 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1540976155.641 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1540976155.641 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1540976155.642 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 1540976155.642 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 1540976155.642 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 1540976155.642 * [misc]taylor: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 1540976155.643 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 1540976155.643 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 1540976155.643 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1540976155.643 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976155.643 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976155.643 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1540976155.643 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976155.643 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976155.643 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1540976155.643 * [misc]taylor: Taking taylor expansion of k in n 1540976155.643 * [misc]backup-simplify: Simplify k into k 1540976155.643 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1540976155.643 * [misc]taylor: Taking taylor expansion of (log (/ 2 n)) in n 1540976155.643 * [misc]taylor: Taking taylor expansion of (/ 2 n) in n 1540976155.643 * [misc]taylor: Taking taylor expansion of 2 in n 1540976155.643 * [misc]backup-simplify: Simplify 2 into 2 1540976155.643 * [misc]taylor: Taking taylor expansion of n in n 1540976155.643 * [misc]backup-simplify: Simplify 0 into 0 1540976155.643 * [misc]backup-simplify: Simplify 1 into 1 1540976155.643 * [misc]backup-simplify: Simplify (/ 2 1) into 2 1540976155.643 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1540976155.644 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1540976155.644 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1540976155.644 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1540976155.644 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 1540976155.644 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 1540976155.645 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 1540976155.645 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) in k 1540976155.645 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) in k 1540976155.645 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1540976155.645 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976155.645 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976155.645 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1540976155.645 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976155.645 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976155.645 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1540976155.645 * [misc]taylor: Taking taylor expansion of k in k 1540976155.645 * [misc]backup-simplify: Simplify 0 into 0 1540976155.645 * [misc]backup-simplify: Simplify 1 into 1 1540976155.645 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1540976155.645 * [misc]taylor: Taking taylor expansion of (- (log 2) (log n)) in k 1540976155.646 * [misc]taylor: Taking taylor expansion of (log 2) in k 1540976155.646 * [misc]taylor: Taking taylor expansion of 2 in k 1540976155.646 * [misc]backup-simplify: Simplify 2 into 2 1540976155.646 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1540976155.646 * [misc]taylor: Taking taylor expansion of (log n) in k 1540976155.646 * [misc]taylor: Taking taylor expansion of n in k 1540976155.646 * [misc]backup-simplify: Simplify n into n 1540976155.646 * [misc]backup-simplify: Simplify (log n) into (log n) 1540976155.646 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1540976155.646 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1540976155.646 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1540976155.646 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1540976155.647 * [misc]backup-simplify: Simplify (+ (log 2) (- (log n))) into (- (log 2) (log n)) 1540976155.647 * [misc]backup-simplify: Simplify (* -1/2 (- (log 2) (log n))) into (* -1/2 (- (log 2) (log n))) 1540976155.647 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 1540976155.648 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 1540976155.648 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)))) into 0 1540976155.651 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 1540976155.651 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1540976155.651 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1540976155.652 * [misc]backup-simplify: Simplify (- 0) into 0 1540976155.652 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976155.652 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 1540976155.653 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log 2) (log n)))) into 0 1540976155.654 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1540976155.654 * [misc]taylor: Taking taylor expansion of 0 in k 1540976155.654 * [misc]backup-simplify: Simplify 0 into 0 1540976155.654 * [misc]backup-simplify: Simplify 0 into 0 1540976155.654 * [misc]backup-simplify: Simplify 0 into 0 1540976155.654 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976155.659 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 1540976155.659 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1540976155.660 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1540976155.660 * [misc]backup-simplify: Simplify (- 0) into 0 1540976155.660 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976155.660 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 1540976155.661 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log 2) (log n))))) into 0 1540976155.663 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1540976155.663 * [misc]taylor: Taking taylor expansion of 0 in k 1540976155.663 * [misc]backup-simplify: Simplify 0 into 0 1540976155.663 * [misc]backup-simplify: Simplify 0 into 0 1540976155.663 * [misc]backup-simplify: Simplify 0 into 0 1540976155.663 * [misc]backup-simplify: Simplify 0 into 0 1540976155.664 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976155.671 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 1540976155.671 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1540976155.672 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1540976155.672 * [misc]backup-simplify: Simplify (- 0) into 0 1540976155.672 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976155.672 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 1540976155.673 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log 2) (log n)))))) into 0 1540976155.676 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1540976155.676 * [misc]taylor: Taking taylor expansion of 0 in k 1540976155.676 * [misc]backup-simplify: Simplify 0 into 0 1540976155.676 * [misc]backup-simplify: Simplify 0 into 0 1540976155.676 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log 2) (log (/ 1 n))))) into (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) 1540976155.677 * [misc]backup-simplify: Simplify (pow (* (/ 1 (- n)) 2) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) 1540976155.677 * [misc]approximate: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 1540976155.677 * [misc]taylor: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1540976155.677 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in k 1540976155.677 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in k 1540976155.677 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1540976155.677 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1540976155.677 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976155.677 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976155.677 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1540976155.677 * [misc]taylor: Taking taylor expansion of k in k 1540976155.677 * [misc]backup-simplify: Simplify 0 into 0 1540976155.677 * [misc]backup-simplify: Simplify 1 into 1 1540976155.677 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1540976155.677 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976155.677 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976155.677 * [misc]taylor: Taking taylor expansion of (log (/ -2 n)) in k 1540976155.677 * [misc]taylor: Taking taylor expansion of (/ -2 n) in k 1540976155.677 * [misc]taylor: Taking taylor expansion of -2 in k 1540976155.677 * [misc]backup-simplify: Simplify -2 into -2 1540976155.677 * [misc]taylor: Taking taylor expansion of n in k 1540976155.677 * [misc]backup-simplify: Simplify n into n 1540976155.677 * [misc]backup-simplify: Simplify (/ -2 n) into (/ -2 n) 1540976155.677 * [misc]backup-simplify: Simplify (log (/ -2 n)) into (log (/ -2 n)) 1540976155.677 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1540976155.677 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1540976155.677 * [misc]backup-simplify: Simplify (* 1/2 (log (/ -2 n))) into (* 1/2 (log (/ -2 n))) 1540976155.677 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) into (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) 1540976155.677 * [misc]taylor: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1540976155.677 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 1540976155.678 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 1540976155.678 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1540976155.678 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1540976155.678 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976155.678 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976155.678 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1540976155.678 * [misc]taylor: Taking taylor expansion of k in n 1540976155.678 * [misc]backup-simplify: Simplify k into k 1540976155.678 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1540976155.678 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976155.678 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976155.678 * [misc]taylor: Taking taylor expansion of (log (/ -2 n)) in n 1540976155.678 * [misc]taylor: Taking taylor expansion of (/ -2 n) in n 1540976155.678 * [misc]taylor: Taking taylor expansion of -2 in n 1540976155.678 * [misc]backup-simplify: Simplify -2 into -2 1540976155.678 * [misc]taylor: Taking taylor expansion of n in n 1540976155.678 * [misc]backup-simplify: Simplify 0 into 0 1540976155.678 * [misc]backup-simplify: Simplify 1 into 1 1540976155.678 * [misc]backup-simplify: Simplify (/ -2 1) into -2 1540976155.678 * [misc]backup-simplify: Simplify (log -2) into (log -2) 1540976155.678 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1540976155.678 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1540976155.678 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 1540976155.679 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 1540976155.679 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 1540976155.679 * [misc]taylor: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1540976155.679 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 1540976155.679 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 1540976155.679 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1540976155.679 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1540976155.679 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976155.679 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976155.679 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1540976155.679 * [misc]taylor: Taking taylor expansion of k in n 1540976155.679 * [misc]backup-simplify: Simplify k into k 1540976155.679 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1540976155.679 * [misc]taylor: Taking taylor expansion of 1/2 in n 1540976155.679 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976155.679 * [misc]taylor: Taking taylor expansion of (log (/ -2 n)) in n 1540976155.679 * [misc]taylor: Taking taylor expansion of (/ -2 n) in n 1540976155.679 * [misc]taylor: Taking taylor expansion of -2 in n 1540976155.679 * [misc]backup-simplify: Simplify -2 into -2 1540976155.679 * [misc]taylor: Taking taylor expansion of n in n 1540976155.679 * [misc]backup-simplify: Simplify 0 into 0 1540976155.679 * [misc]backup-simplify: Simplify 1 into 1 1540976155.679 * [misc]backup-simplify: Simplify (/ -2 1) into -2 1540976155.679 * [misc]backup-simplify: Simplify (log -2) into (log -2) 1540976155.679 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1540976155.679 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1540976155.680 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 1540976155.680 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 1540976155.680 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 1540976155.680 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) in k 1540976155.680 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) in k 1540976155.680 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1540976155.680 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1540976155.680 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976155.680 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976155.680 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1540976155.680 * [misc]taylor: Taking taylor expansion of k in k 1540976155.680 * [misc]backup-simplify: Simplify 0 into 0 1540976155.680 * [misc]backup-simplify: Simplify 1 into 1 1540976155.680 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1540976155.680 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976155.680 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976155.680 * [misc]taylor: Taking taylor expansion of (- (log -2) (log n)) in k 1540976155.680 * [misc]taylor: Taking taylor expansion of (log -2) in k 1540976155.680 * [misc]taylor: Taking taylor expansion of -2 in k 1540976155.680 * [misc]backup-simplify: Simplify -2 into -2 1540976155.681 * [misc]backup-simplify: Simplify (log -2) into (log -2) 1540976155.681 * [misc]taylor: Taking taylor expansion of (log n) in k 1540976155.681 * [misc]taylor: Taking taylor expansion of n in k 1540976155.681 * [misc]backup-simplify: Simplify n into n 1540976155.681 * [misc]backup-simplify: Simplify (log n) into (log n) 1540976155.681 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1540976155.681 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1540976155.681 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1540976155.681 * [misc]backup-simplify: Simplify (+ (log -2) (- (log n))) into (- (log -2) (log n)) 1540976155.681 * [misc]backup-simplify: Simplify (* 1/2 (- (log -2) (log n))) into (* 1/2 (- (log -2) (log n))) 1540976155.681 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 1540976155.682 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 1540976155.682 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -2 (/ 0 1)))) into 0 1540976155.683 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -2 1)))) 1) into 0 1540976155.684 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1540976155.684 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1540976155.684 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976155.684 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 1540976155.684 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log -2) (log n)))) into 0 1540976155.685 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1540976155.685 * [misc]taylor: Taking taylor expansion of 0 in k 1540976155.685 * [misc]backup-simplify: Simplify 0 into 0 1540976155.685 * [misc]backup-simplify: Simplify 0 into 0 1540976155.685 * [misc]backup-simplify: Simplify 0 into 0 1540976155.685 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -2 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976155.688 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -2 1)))) 2) into 0 1540976155.688 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1540976155.688 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1540976155.688 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976155.689 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 1540976155.689 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log -2) (log n))))) into 0 1540976155.690 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1540976155.690 * [misc]taylor: Taking taylor expansion of 0 in k 1540976155.690 * [misc]backup-simplify: Simplify 0 into 0 1540976155.690 * [misc]backup-simplify: Simplify 0 into 0 1540976155.690 * [misc]backup-simplify: Simplify 0 into 0 1540976155.690 * [misc]backup-simplify: Simplify 0 into 0 1540976155.690 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -2 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976155.695 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow -2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow -2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow -2 1)))) 6) into 0 1540976155.695 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1540976155.695 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1540976155.696 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976155.696 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 1540976155.696 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log -2) (log n)))))) into 0 1540976155.698 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1540976155.698 * [misc]taylor: Taking taylor expansion of 0 in k 1540976155.698 * [misc]backup-simplify: Simplify 0 into 0 1540976155.698 * [misc]backup-simplify: Simplify 0 into 0 1540976155.698 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -2) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) 1540976155.698 * * * * [misc]progress: [ 3 / 4 ] generating series at (2 1 1 1 1) 1540976155.699 * [misc]backup-simplify: Simplify (pow PI (- 1/2 (/ k 2))) into (pow PI (- 1/2 (* 1/2 k))) 1540976155.699 * [misc]approximate: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in (k) around 0 1540976155.699 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 1540976155.699 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 1540976155.699 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 1540976155.699 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1540976155.699 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976155.699 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976155.699 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1540976155.699 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976155.699 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976155.699 * [misc]taylor: Taking taylor expansion of k in k 1540976155.699 * [misc]backup-simplify: Simplify 0 into 0 1540976155.699 * [misc]backup-simplify: Simplify 1 into 1 1540976155.699 * [misc]taylor: Taking taylor expansion of (log PI) in k 1540976155.699 * [misc]taylor: Taking taylor expansion of PI in k 1540976155.699 * [misc]backup-simplify: Simplify PI into PI 1540976155.699 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1540976155.699 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1540976155.699 * [misc]backup-simplify: Simplify (- 0) into 0 1540976155.700 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1540976155.700 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1540976155.701 * [misc]backup-simplify: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 1540976155.701 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 1540976155.701 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 1540976155.701 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 1540976155.701 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1540976155.701 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976155.701 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976155.701 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1540976155.701 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976155.701 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976155.701 * [misc]taylor: Taking taylor expansion of k in k 1540976155.701 * [misc]backup-simplify: Simplify 0 into 0 1540976155.701 * [misc]backup-simplify: Simplify 1 into 1 1540976155.701 * [misc]taylor: Taking taylor expansion of (log PI) in k 1540976155.701 * [misc]taylor: Taking taylor expansion of PI in k 1540976155.701 * [misc]backup-simplify: Simplify PI into PI 1540976155.701 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1540976155.701 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1540976155.701 * [misc]backup-simplify: Simplify (- 0) into 0 1540976155.701 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1540976155.702 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1540976155.702 * [misc]backup-simplify: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 1540976155.703 * [misc]backup-simplify: Simplify (pow PI 1/2) into (pow PI 1/2) 1540976155.705 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 1540976155.705 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1540976155.705 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1540976155.705 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1540976155.706 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (log PI))) into (- (* 1/2 (log PI))) 1540976155.710 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 1) 1)))) into (* -1/2 (* (log PI) (sqrt PI))) 1540976155.711 * [misc]backup-simplify: Simplify (* -1/2 (* (log PI) (sqrt PI))) into (* -1/2 (* (log PI) (sqrt PI))) 1540976155.716 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 1540976155.716 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1540976155.716 * [misc]backup-simplify: Simplify (- 0) into 0 1540976155.716 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1540976155.717 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log PI)))) into 0 1540976155.720 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI))) 1540976155.722 * [misc]backup-simplify: Simplify (* 1/8 (* (pow (log PI) 2) (sqrt PI))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI))) 1540976155.724 * [misc]backup-simplify: Simplify (+ (* (* 1/8 (* (pow (log PI) 2) (sqrt PI))) (pow k 2)) (+ (* (* -1/2 (* (log PI) (sqrt PI))) k) (pow PI 1/2))) into (- (+ (pow PI 1/2) (* 1/8 (* (* (pow (log PI) 2) (pow k 2)) (sqrt PI)))) (* 1/2 (* (* (log PI) k) (sqrt PI)))) 1540976155.724 * [misc]backup-simplify: Simplify (pow PI (- 1/2 (/ (/ 1 k) 2))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1540976155.725 * [misc]approximate: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in (k) around 0 1540976155.725 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 1540976155.725 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 1540976155.725 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 1540976155.725 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1540976155.725 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976155.725 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976155.725 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1540976155.725 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976155.725 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976155.725 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1540976155.725 * [misc]taylor: Taking taylor expansion of k in k 1540976155.725 * [misc]backup-simplify: Simplify 0 into 0 1540976155.725 * [misc]backup-simplify: Simplify 1 into 1 1540976155.725 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1540976155.725 * [misc]taylor: Taking taylor expansion of (log PI) in k 1540976155.725 * [misc]taylor: Taking taylor expansion of PI in k 1540976155.725 * [misc]backup-simplify: Simplify PI into PI 1540976155.725 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1540976155.725 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1540976155.725 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1540976155.726 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1540976155.726 * [misc]backup-simplify: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 1540976155.726 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1540976155.726 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 1540976155.726 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 1540976155.726 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 1540976155.726 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1540976155.726 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976155.726 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976155.726 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1540976155.726 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976155.726 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976155.726 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1540976155.726 * [misc]taylor: Taking taylor expansion of k in k 1540976155.726 * [misc]backup-simplify: Simplify 0 into 0 1540976155.726 * [misc]backup-simplify: Simplify 1 into 1 1540976155.726 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1540976155.726 * [misc]taylor: Taking taylor expansion of (log PI) in k 1540976155.726 * [misc]taylor: Taking taylor expansion of PI in k 1540976155.727 * [misc]backup-simplify: Simplify PI into PI 1540976155.727 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1540976155.727 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1540976155.727 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1540976155.727 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1540976155.727 * [misc]backup-simplify: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 1540976155.728 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1540976155.728 * [misc]backup-simplify: Simplify (pow PI (- 1/2 (* 1/2 (/ 1 k)))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1540976155.728 * [misc]backup-simplify: Simplify 0 into 0 1540976155.728 * [misc]backup-simplify: Simplify 0 into 0 1540976155.728 * [misc]backup-simplify: Simplify 0 into 0 1540976155.728 * [misc]backup-simplify: Simplify 0 into 0 1540976155.728 * [misc]backup-simplify: Simplify 0 into 0 1540976155.728 * [misc]backup-simplify: Simplify 0 into 0 1540976155.728 * [misc]backup-simplify: Simplify (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k))))) into (pow PI (- 1/2 (* 1/2 k))) 1540976155.728 * [misc]backup-simplify: Simplify (pow PI (- 1/2 (/ (/ 1 (- k)) 2))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1540976155.728 * [misc]approximate: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in (k) around 0 1540976155.728 * [misc]taylor: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 1540976155.728 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 1540976155.728 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 1540976155.728 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1540976155.728 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1540976155.728 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976155.728 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976155.728 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1540976155.728 * [misc]taylor: Taking taylor expansion of k in k 1540976155.728 * [misc]backup-simplify: Simplify 0 into 0 1540976155.728 * [misc]backup-simplify: Simplify 1 into 1 1540976155.728 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1540976155.728 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976155.728 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976155.729 * [misc]taylor: Taking taylor expansion of (log PI) in k 1540976155.729 * [misc]taylor: Taking taylor expansion of PI in k 1540976155.729 * [misc]backup-simplify: Simplify PI into PI 1540976155.729 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1540976155.729 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1540976155.729 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1540976155.729 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1540976155.730 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1540976155.730 * [misc]taylor: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 1540976155.730 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 1540976155.730 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 1540976155.730 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1540976155.730 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1540976155.730 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976155.730 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976155.730 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1540976155.730 * [misc]taylor: Taking taylor expansion of k in k 1540976155.730 * [misc]backup-simplify: Simplify 0 into 0 1540976155.730 * [misc]backup-simplify: Simplify 1 into 1 1540976155.730 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1540976155.730 * [misc]taylor: Taking taylor expansion of 1/2 in k 1540976155.730 * [misc]backup-simplify: Simplify 1/2 into 1/2 1540976155.730 * [misc]taylor: Taking taylor expansion of (log PI) in k 1540976155.730 * [misc]taylor: Taking taylor expansion of PI in k 1540976155.730 * [misc]backup-simplify: Simplify PI into PI 1540976155.730 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1540976155.730 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1540976155.730 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1540976155.731 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1540976155.731 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1540976155.731 * [misc]backup-simplify: Simplify (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1540976155.731 * [misc]backup-simplify: Simplify 0 into 0 1540976155.731 * [misc]backup-simplify: Simplify 0 into 0 1540976155.731 * [misc]backup-simplify: Simplify 0 into 0 1540976155.731 * [misc]backup-simplify: Simplify 0 into 0 1540976155.731 * [misc]backup-simplify: Simplify 0 into 0 1540976155.731 * [misc]backup-simplify: Simplify 0 into 0 1540976155.731 * [misc]backup-simplify: Simplify (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)) into (pow PI (- 1/2 (* 1/2 k))) 1540976155.732 * * * * [misc]progress: [ 4 / 4 ] generating series at (2 1 2 1 1) 1540976155.732 * [misc]backup-simplify: Simplify (* PI (* n 2)) into (* 2 (* n PI)) 1540976155.732 * [misc]approximate: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1540976155.732 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1540976155.732 * [misc]taylor: Taking taylor expansion of 2 in n 1540976155.732 * [misc]backup-simplify: Simplify 2 into 2 1540976155.732 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1540976155.732 * [misc]taylor: Taking taylor expansion of n in n 1540976155.732 * [misc]backup-simplify: Simplify 0 into 0 1540976155.732 * [misc]backup-simplify: Simplify 1 into 1 1540976155.732 * [misc]taylor: Taking taylor expansion of PI in n 1540976155.732 * [misc]backup-simplify: Simplify PI into PI 1540976155.732 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1540976155.732 * [misc]taylor: Taking taylor expansion of 2 in n 1540976155.732 * [misc]backup-simplify: Simplify 2 into 2 1540976155.732 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1540976155.732 * [misc]taylor: Taking taylor expansion of n in n 1540976155.732 * [misc]backup-simplify: Simplify 0 into 0 1540976155.732 * [misc]backup-simplify: Simplify 1 into 1 1540976155.732 * [misc]taylor: Taking taylor expansion of PI in n 1540976155.732 * [misc]backup-simplify: Simplify PI into PI 1540976155.732 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1540976155.732 * [misc]backup-simplify: Simplify (* 2 0) into 0 1540976155.732 * [misc]backup-simplify: Simplify 0 into 0 1540976155.733 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1540976155.733 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1540976155.734 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1540976155.734 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1540976155.735 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1540976155.735 * [misc]backup-simplify: Simplify 0 into 0 1540976155.736 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1540976155.737 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1540976155.737 * [misc]backup-simplify: Simplify 0 into 0 1540976155.738 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1540976155.740 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1540976155.740 * [misc]backup-simplify: Simplify 0 into 0 1540976155.741 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1540976155.743 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1540976155.743 * [misc]backup-simplify: Simplify 0 into 0 1540976155.745 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1540976155.748 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1540976155.749 * [misc]backup-simplify: Simplify 0 into 0 1540976155.751 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1540976155.754 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1540976155.754 * [misc]backup-simplify: Simplify 0 into 0 1540976155.754 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1540976155.754 * [misc]backup-simplify: Simplify (* PI (* (/ 1 n) 2)) into (* 2 (/ PI n)) 1540976155.754 * [misc]approximate: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1540976155.754 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1540976155.754 * [misc]taylor: Taking taylor expansion of 2 in n 1540976155.754 * [misc]backup-simplify: Simplify 2 into 2 1540976155.754 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1540976155.754 * [misc]taylor: Taking taylor expansion of PI in n 1540976155.754 * [misc]backup-simplify: Simplify PI into PI 1540976155.754 * [misc]taylor: Taking taylor expansion of n in n 1540976155.754 * [misc]backup-simplify: Simplify 0 into 0 1540976155.754 * [misc]backup-simplify: Simplify 1 into 1 1540976155.754 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1540976155.755 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1540976155.755 * [misc]taylor: Taking taylor expansion of 2 in n 1540976155.755 * [misc]backup-simplify: Simplify 2 into 2 1540976155.755 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1540976155.755 * [misc]taylor: Taking taylor expansion of PI in n 1540976155.755 * [misc]backup-simplify: Simplify PI into PI 1540976155.755 * [misc]taylor: Taking taylor expansion of n in n 1540976155.755 * [misc]backup-simplify: Simplify 0 into 0 1540976155.755 * [misc]backup-simplify: Simplify 1 into 1 1540976155.755 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1540976155.755 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1540976155.755 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1540976155.756 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1540976155.756 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1540976155.756 * [misc]backup-simplify: Simplify 0 into 0 1540976155.757 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976155.758 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1540976155.758 * [misc]backup-simplify: Simplify 0 into 0 1540976155.759 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976155.760 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1540976155.760 * [misc]backup-simplify: Simplify 0 into 0 1540976155.761 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976155.762 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1540976155.762 * [misc]backup-simplify: Simplify 0 into 0 1540976155.764 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976155.765 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1540976155.765 * [misc]backup-simplify: Simplify 0 into 0 1540976155.767 * [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 1540976155.769 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1540976155.769 * [misc]backup-simplify: Simplify 0 into 0 1540976155.769 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 1540976155.769 * [misc]backup-simplify: Simplify (* PI (* (/ 1 (- n)) 2)) into (* -2 (/ PI n)) 1540976155.769 * [misc]approximate: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1540976155.769 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1540976155.769 * [misc]taylor: Taking taylor expansion of -2 in n 1540976155.769 * [misc]backup-simplify: Simplify -2 into -2 1540976155.769 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1540976155.769 * [misc]taylor: Taking taylor expansion of PI in n 1540976155.769 * [misc]backup-simplify: Simplify PI into PI 1540976155.769 * [misc]taylor: Taking taylor expansion of n in n 1540976155.769 * [misc]backup-simplify: Simplify 0 into 0 1540976155.769 * [misc]backup-simplify: Simplify 1 into 1 1540976155.769 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1540976155.770 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1540976155.770 * [misc]taylor: Taking taylor expansion of -2 in n 1540976155.770 * [misc]backup-simplify: Simplify -2 into -2 1540976155.770 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1540976155.770 * [misc]taylor: Taking taylor expansion of PI in n 1540976155.770 * [misc]backup-simplify: Simplify PI into PI 1540976155.770 * [misc]taylor: Taking taylor expansion of n in n 1540976155.770 * [misc]backup-simplify: Simplify 0 into 0 1540976155.770 * [misc]backup-simplify: Simplify 1 into 1 1540976155.770 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1540976155.770 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1540976155.770 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1540976155.771 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1540976155.771 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1540976155.771 * [misc]backup-simplify: Simplify 0 into 0 1540976155.772 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976155.773 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1540976155.773 * [misc]backup-simplify: Simplify 0 into 0 1540976155.774 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976155.775 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1540976155.775 * [misc]backup-simplify: Simplify 0 into 0 1540976155.776 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976155.777 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1540976155.777 * [misc]backup-simplify: Simplify 0 into 0 1540976155.779 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1540976155.781 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1540976155.781 * [misc]backup-simplify: Simplify 0 into 0 1540976155.783 * [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 1540976155.786 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1540976155.787 * [misc]backup-simplify: Simplify 0 into 0 1540976155.787 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 1540976155.787 * * * [misc]progress: simplifying candidates 1540976155.787 * * * * [misc]progress: [ 1 / 69 ] simplifiying candidate # 1540976155.787 * [enter]simplify: Simplifying (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) 1540976155.788 * * [misc]simplify: iters left: 6 (11 enodes) 1540976155.793 * * [misc]simplify: iters left: 5 (21 enodes) 1540976155.804 * * [misc]simplify: iters left: 4 (47 enodes) 1540976155.821 * * [misc]simplify: iters left: 3 (109 enodes) 1540976155.896 * * [misc]simplify: iters left: 2 (300 enodes) 1540976156.215 * [exit]simplify: Simplified to (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) 1540976156.215 * [misc]simplify: Simplified (2 1 2 1 1) to (λ (k n) (/ (* (sqrt (* (pow PI (- 1/2 (/ k 2))) (pow (* n 2) (- 1/2 (/ k 2))))) (sqrt (exp (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI)))))) (sqrt k))) 1540976156.216 * * * * [misc]progress: [ 2 / 69 ] simplifiying candidate # 1540976156.216 * * * * [misc]progress: [ 3 / 69 ] simplifiying candidate # 1540976156.216 * [enter]simplify: Simplifying (* PI (* n 2)) 1540976156.217 * * [misc]simplify: iters left: 4 (5 enodes) 1540976156.219 * * [misc]simplify: iters left: 3 (9 enodes) 1540976156.223 * * [misc]simplify: iters left: 2 (15 enodes) 1540976156.228 * * [misc]simplify: iters left: 1 (17 enodes) 1540976156.234 * [exit]simplify: Simplified to (* (* 2 n) PI) 1540976156.234 * [misc]simplify: Simplified (2 1 2 1 1) to (λ (k n) (/ (* (sqrt (* (pow PI (- 1/2 (/ k 2))) (pow (* n 2) (- 1/2 (/ k 2))))) (sqrt (pow (* (* 2 n) PI) (* 1 (- 1/2 (/ k 2)))))) (sqrt k))) 1540976156.234 * * * * [misc]progress: [ 4 / 69 ] simplifiying candidate # 1540976156.234 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (/ k 2)) 1540976156.235 * * [misc]simplify: iters left: 5 (8 enodes) 1540976156.239 * * [misc]simplify: iters left: 4 (12 enodes) 1540976156.244 * * [misc]simplify: iters left: 3 (18 enodes) 1540976156.250 * * [misc]simplify: iters left: 2 (20 enodes) 1540976156.257 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ k 2)) 1540976156.257 * [misc]simplify: Simplified (2 1 2 1 2) to (λ (k n) (/ (* (sqrt (* (pow PI (- 1/2 (/ k 2))) (pow (* n 2) (- 1/2 (/ k 2))))) (sqrt (/ (pow (* PI (* n 2)) 1/2) (pow (* (* 2 n) PI) (/ k 2))))) (sqrt k))) 1540976156.257 * * * * [misc]progress: [ 5 / 69 ] simplifiying candidate # 1540976156.257 * [enter]simplify: Simplifying (cbrt (- 1/2 (/ k 2))) 1540976156.258 * * [misc]simplify: iters left: 5 (6 enodes) 1540976156.260 * * [misc]simplify: iters left: 4 (8 enodes) 1540976156.263 * * [misc]simplify: iters left: 3 (11 enodes) 1540976156.267 * [exit]simplify: Simplified to (cbrt (- 1/2 (/ k 2))) 1540976156.267 * [misc]simplify: Simplified (2 1 2 1 2) to (λ (k n) (/ (* (sqrt (* (pow PI (- 1/2 (/ k 2))) (pow (* n 2) (- 1/2 (/ k 2))))) (sqrt (pow (pow (* PI (* n 2)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))))) (sqrt k))) 1540976156.267 * * * * [misc]progress: [ 6 / 69 ] simplifiying candidate # 1540976156.267 * [enter]simplify: Simplifying (sqrt (- 1/2 (/ k 2))) 1540976156.268 * * [misc]simplify: iters left: 5 (6 enodes) 1540976156.269 * * [misc]simplify: iters left: 4 (8 enodes) 1540976156.270 * * [misc]simplify: iters left: 3 (11 enodes) 1540976156.272 * [exit]simplify: Simplified to (sqrt (- 1/2 (/ k 2))) 1540976156.273 * [misc]simplify: Simplified (2 1 2 1 2) to (λ (k n) (/ (* (sqrt (* (pow PI (- 1/2 (/ k 2))) (pow (* n 2) (- 1/2 (/ k 2))))) (sqrt (pow (pow (* PI (* n 2)) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))))) (sqrt k))) 1540976156.273 * * * * [misc]progress: [ 7 / 69 ] simplifiying candidate # 1540976156.273 * [enter]simplify: Simplifying (- 1/2 (/ k 2)) 1540976156.273 * * [misc]simplify: iters left: 4 (5 enodes) 1540976156.274 * * [misc]simplify: iters left: 3 (7 enodes) 1540976156.275 * * [misc]simplify: iters left: 2 (10 enodes) 1540976156.277 * [exit]simplify: Simplified to (- 1/2 (/ k 2)) 1540976156.277 * [misc]simplify: Simplified (2 1 2 1 2) to (λ (k n) (/ (* (sqrt (* (pow PI (- 1/2 (/ k 2))) (pow (* n 2) (- 1/2 (/ k 2))))) (sqrt (pow (pow (* PI (* n 2)) 1) (- 1/2 (/ k 2))))) (sqrt k))) 1540976156.277 * * * * [misc]progress: [ 8 / 69 ] simplifiying candidate # 1540976156.277 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1540976156.278 * * [misc]simplify: iters left: 5 (9 enodes) 1540976156.281 * * [misc]simplify: iters left: 4 (15 enodes) 1540976156.284 * * [misc]simplify: iters left: 3 (21 enodes) 1540976156.287 * * [misc]simplify: iters left: 2 (22 enodes) 1540976156.290 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1540976156.290 * [misc]simplify: Simplified (2 1 2 1 2) to (λ (k n) (/ (* (sqrt (* (pow PI (- 1/2 (/ k 2))) (pow (* n 2) (- 1/2 (/ k 2))))) (sqrt (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2)))))) (sqrt k))) 1540976156.290 * * * * [misc]progress: [ 9 / 69 ] simplifiying candidate # 1540976156.291 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1540976156.291 * * [misc]simplify: iters left: 5 (9 enodes) 1540976156.293 * * [misc]simplify: iters left: 4 (15 enodes) 1540976156.297 * * [misc]simplify: iters left: 3 (21 enodes) 1540976156.303 * * [misc]simplify: iters left: 2 (22 enodes) 1540976156.311 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1540976156.311 * [misc]simplify: Simplified (2 1 2 1 2) to (λ (k n) (/ (* (sqrt (* (pow PI (- 1/2 (/ k 2))) (pow (* n 2) (- 1/2 (/ k 2))))) (sqrt (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2)))))) (sqrt k))) 1540976156.311 * * * * [misc]progress: [ 10 / 69 ] simplifiying candidate # 1540976156.311 * [enter]simplify: Simplifying (pow PI (- 1/2 (/ k 2))) 1540976156.312 * * [misc]simplify: iters left: 5 (7 enodes) 1540976156.315 * * [misc]simplify: iters left: 4 (9 enodes) 1540976156.319 * * [misc]simplify: iters left: 3 (12 enodes) 1540976156.323 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1540976156.323 * [misc]simplify: Simplified (2 1 2 1 1) to (λ (k n) (/ (* (sqrt (* (pow PI (- 1/2 (/ k 2))) (pow (* n 2) (- 1/2 (/ k 2))))) (sqrt (* (pow PI (- 1/2 (/ k 2))) (pow (* n 2) (- 1/2 (/ k 2)))))) (sqrt k))) 1540976156.323 * * * * [misc]progress: [ 11 / 69 ] simplifiying candidate # 1540976156.323 * * * * [misc]progress: [ 12 / 69 ] simplifiying candidate # 1540976156.323 * * * * [misc]progress: [ 13 / 69 ] simplifiying candidate # 1540976156.323 * * * * [misc]progress: [ 14 / 69 ] simplifiying candidate # 1540976156.323 * * * * [misc]progress: [ 15 / 69 ] simplifiying candidate # 1540976156.323 * * * * [misc]progress: [ 16 / 69 ] simplifiying candidate # 1540976156.323 * * * * [misc]progress: [ 17 / 69 ] simplifiying candidate # 1540976156.323 * * * * [misc]progress: [ 18 / 69 ] simplifiying candidate # 1540976156.324 * [enter]simplify: Simplifying (* (log (* n 2)) (- 1/2 (/ k 2))) 1540976156.324 * * [misc]simplify: iters left: 6 (9 enodes) 1540976156.329 * * [misc]simplify: iters left: 5 (16 enodes) 1540976156.337 * * [misc]simplify: iters left: 4 (32 enodes) 1540976156.354 * * [misc]simplify: iters left: 3 (68 enodes) 1540976156.395 * * [misc]simplify: iters left: 2 (171 enodes) 1540976156.469 * * [misc]simplify: iters left: 1 (342 enodes) 1540976156.624 * [exit]simplify: Simplified to (* (log (* n 2)) (- 1/2 (/ k 2))) 1540976156.624 * [misc]simplify: Simplified (2 1 1 1 2 1) to (λ (k n) (/ (* (sqrt (* (pow PI (- 1/2 (/ k 2))) (exp (* (log (* n 2)) (- 1/2 (/ k 2)))))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt k))) 1540976156.624 * * * * [misc]progress: [ 19 / 69 ] simplifiying candidate # 1540976156.624 * * * * [misc]progress: [ 20 / 69 ] simplifiying candidate # 1540976156.624 * [enter]simplify: Simplifying (* n 2) 1540976156.625 * * [misc]simplify: iters left: 2 (3 enodes) 1540976156.625 * * [misc]simplify: iters left: 1 (4 enodes) 1540976156.626 * [exit]simplify: Simplified to (* n 2) 1540976156.626 * [misc]simplify: Simplified (2 1 1 1 2 1) to (λ (k n) (/ (* (sqrt (* (pow PI (- 1/2 (/ k 2))) (pow (* n 2) (* 1 (- 1/2 (/ k 2)))))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt k))) 1540976156.626 * * * * [misc]progress: [ 21 / 69 ] simplifiying candidate # 1540976156.626 * [enter]simplify: Simplifying (pow (* n 2) (/ k 2)) 1540976156.626 * * [misc]simplify: iters left: 3 (6 enodes) 1540976156.628 * * [misc]simplify: iters left: 2 (7 enodes) 1540976156.629 * [exit]simplify: Simplified to (pow (* n 2) (/ k 2)) 1540976156.629 * [misc]simplify: Simplified (2 1 1 1 2 2) to (λ (k n) (/ (* (sqrt (* (pow PI (- 1/2 (/ k 2))) (/ (pow (* n 2) 1/2) (pow (* n 2) (/ k 2))))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt k))) 1540976156.629 * * * * [misc]progress: [ 22 / 69 ] simplifiying candidate # 1540976156.630 * [enter]simplify: Simplifying (cbrt (- 1/2 (/ k 2))) 1540976156.630 * * [misc]simplify: iters left: 5 (6 enodes) 1540976156.631 * * [misc]simplify: iters left: 4 (8 enodes) 1540976156.632 * * [misc]simplify: iters left: 3 (11 enodes) 1540976156.634 * [exit]simplify: Simplified to (cbrt (- 1/2 (/ k 2))) 1540976156.634 * [misc]simplify: Simplified (2 1 1 1 2 2) to (λ (k n) (/ (* (sqrt (* (pow PI (- 1/2 (/ k 2))) (pow (pow (* n 2) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt k))) 1540976156.634 * * * * [misc]progress: [ 23 / 69 ] simplifiying candidate # 1540976156.634 * [enter]simplify: Simplifying (sqrt (- 1/2 (/ k 2))) 1540976156.635 * * [misc]simplify: iters left: 5 (6 enodes) 1540976156.636 * * [misc]simplify: iters left: 4 (8 enodes) 1540976156.637 * * [misc]simplify: iters left: 3 (11 enodes) 1540976156.639 * [exit]simplify: Simplified to (sqrt (- 1/2 (/ k 2))) 1540976156.639 * [misc]simplify: Simplified (2 1 1 1 2 2) to (λ (k n) (/ (* (sqrt (* (pow PI (- 1/2 (/ k 2))) (pow (pow (* n 2) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt k))) 1540976156.639 * * * * [misc]progress: [ 24 / 69 ] simplifiying candidate # 1540976156.639 * [enter]simplify: Simplifying (- 1/2 (/ k 2)) 1540976156.639 * * [misc]simplify: iters left: 4 (5 enodes) 1540976156.640 * * [misc]simplify: iters left: 3 (7 enodes) 1540976156.642 * * [misc]simplify: iters left: 2 (10 enodes) 1540976156.643 * [exit]simplify: Simplified to (- 1/2 (/ k 2)) 1540976156.644 * [misc]simplify: Simplified (2 1 1 1 2 2) to (λ (k n) (/ (* (sqrt (* (pow PI (- 1/2 (/ k 2))) (pow (pow (* n 2) 1) (- 1/2 (/ k 2))))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt k))) 1540976156.644 * * * * [misc]progress: [ 25 / 69 ] simplifiying candidate # 1540976156.644 * [enter]simplify: Simplifying (pow (* n 2) (- (/ k 2))) 1540976156.645 * * [misc]simplify: iters left: 5 (7 enodes) 1540976156.647 * * [misc]simplify: iters left: 4 (10 enodes) 1540976156.651 * [exit]simplify: Simplified to (pow (* n 2) (- (/ k 2))) 1540976156.651 * [misc]simplify: Simplified (2 1 1 1 2 2) to (λ (k n) (/ (* (sqrt (* (pow PI (- 1/2 (/ k 2))) (* (pow (* n 2) 1/2) (pow (* n 2) (- (/ k 2)))))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt k))) 1540976156.651 * * * * [misc]progress: [ 26 / 69 ] simplifiying candidate # 1540976156.651 * [enter]simplify: Simplifying (pow (* n 2) (- (/ k 2))) 1540976156.652 * * [misc]simplify: iters left: 5 (7 enodes) 1540976156.658 * * [misc]simplify: iters left: 4 (10 enodes) 1540976156.661 * [exit]simplify: Simplified to (pow (* n 2) (- (/ k 2))) 1540976156.661 * [misc]simplify: Simplified (2 1 1 1 2 2) to (λ (k n) (/ (* (sqrt (* (pow PI (- 1/2 (/ k 2))) (* (pow (* n 2) 1/2) (pow (* n 2) (- (/ k 2)))))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt k))) 1540976156.662 * * * * [misc]progress: [ 27 / 69 ] simplifiying candidate # 1540976156.662 * [enter]simplify: Simplifying (pow n (- 1/2 (/ k 2))) 1540976156.662 * * [misc]simplify: iters left: 5 (7 enodes) 1540976156.665 * * [misc]simplify: iters left: 4 (9 enodes) 1540976156.669 * * [misc]simplify: iters left: 3 (12 enodes) 1540976156.673 * [exit]simplify: Simplified to (pow n (- 1/2 (/ k 2))) 1540976156.673 * [misc]simplify: Simplified (2 1 1 1 2 1) to (λ (k n) (/ (* (sqrt (* (pow PI (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (pow 2 (- 1/2 (/ k 2)))))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt k))) 1540976156.673 * * * * [misc]progress: [ 28 / 69 ] simplifiying candidate # 1540976156.673 * * * * [misc]progress: [ 29 / 69 ] simplifiying candidate # 1540976156.673 * * * * [misc]progress: [ 30 / 69 ] simplifiying candidate # 1540976156.673 * * * * [misc]progress: [ 31 / 69 ] simplifiying candidate # 1540976156.673 * * * * [misc]progress: [ 32 / 69 ] simplifiying candidate # 1540976156.673 * * * * [misc]progress: [ 33 / 69 ] simplifiying candidate # 1540976156.673 * * * * [misc]progress: [ 34 / 69 ] simplifiying candidate # 1540976156.673 * * * * [misc]progress: [ 35 / 69 ] simplifiying candidate # 1540976156.673 * * * * [misc]progress: [ 36 / 69 ] simplifiying candidate # 1540976156.674 * [enter]simplify: Simplifying (pow PI (/ k 2)) 1540976156.674 * * [misc]simplify: iters left: 3 (5 enodes) 1540976156.676 * [exit]simplify: Simplified to (pow PI (/ k 2)) 1540976156.676 * [misc]simplify: Simplified (2 1 1 1 1 2) to (λ (k n) (/ (* (sqrt (* (/ (pow PI 1/2) (pow PI (/ k 2))) (pow (* n 2) (- 1/2 (/ k 2))))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt k))) 1540976156.676 * * * * [misc]progress: [ 37 / 69 ] simplifiying candidate # 1540976156.676 * [enter]simplify: Simplifying (cbrt (- 1/2 (/ k 2))) 1540976156.677 * * [misc]simplify: iters left: 5 (6 enodes) 1540976156.679 * * [misc]simplify: iters left: 4 (8 enodes) 1540976156.682 * * [misc]simplify: iters left: 3 (11 enodes) 1540976156.686 * [exit]simplify: Simplified to (cbrt (- 1/2 (/ k 2))) 1540976156.686 * [misc]simplify: Simplified (2 1 1 1 1 2) to (λ (k n) (/ (* (sqrt (* (pow (pow PI (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))) (pow (* n 2) (- 1/2 (/ k 2))))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt k))) 1540976156.686 * * * * [misc]progress: [ 38 / 69 ] simplifiying candidate # 1540976156.686 * [enter]simplify: Simplifying (sqrt (- 1/2 (/ k 2))) 1540976156.687 * * [misc]simplify: iters left: 5 (6 enodes) 1540976156.689 * * [misc]simplify: iters left: 4 (8 enodes) 1540976156.692 * * [misc]simplify: iters left: 3 (11 enodes) 1540976156.696 * [exit]simplify: Simplified to (sqrt (- 1/2 (/ k 2))) 1540976156.696 * [misc]simplify: Simplified (2 1 1 1 1 2) to (λ (k n) (/ (* (sqrt (* (pow (pow PI (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))) (pow (* n 2) (- 1/2 (/ k 2))))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt k))) 1540976156.696 * * * * [misc]progress: [ 39 / 69 ] simplifiying candidate # 1540976156.696 * [enter]simplify: Simplifying (- 1/2 (/ k 2)) 1540976156.697 * * [misc]simplify: iters left: 4 (5 enodes) 1540976156.699 * * [misc]simplify: iters left: 3 (7 enodes) 1540976156.701 * * [misc]simplify: iters left: 2 (10 enodes) 1540976156.704 * [exit]simplify: Simplified to (- 1/2 (/ k 2)) 1540976156.704 * [misc]simplify: Simplified (2 1 1 1 1 2) to (λ (k n) (/ (* (sqrt (* (pow (pow PI 1) (- 1/2 (/ k 2))) (pow (* n 2) (- 1/2 (/ k 2))))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt k))) 1540976156.705 * * * * [misc]progress: [ 40 / 69 ] simplifiying candidate # 1540976156.705 * [enter]simplify: Simplifying (pow PI (- (/ k 2))) 1540976156.705 * * [misc]simplify: iters left: 5 (6 enodes) 1540976156.708 * * [misc]simplify: iters left: 4 (8 enodes) 1540976156.711 * [exit]simplify: Simplified to (pow PI (/ (- k) 2)) 1540976156.711 * [misc]simplify: Simplified (2 1 1 1 1 2) to (λ (k n) (/ (* (sqrt (* (* (pow PI 1/2) (pow PI (/ (- k) 2))) (pow (* n 2) (- 1/2 (/ k 2))))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt k))) 1540976156.711 * * * * [misc]progress: [ 41 / 69 ] simplifiying candidate # 1540976156.711 * [enter]simplify: Simplifying (pow PI (- (/ k 2))) 1540976156.712 * * [misc]simplify: iters left: 5 (6 enodes) 1540976156.714 * * [misc]simplify: iters left: 4 (8 enodes) 1540976156.717 * [exit]simplify: Simplified to (pow PI (/ (- k) 2)) 1540976156.717 * [misc]simplify: Simplified (2 1 1 1 1 2) to (λ (k n) (/ (* (sqrt (* (* (pow PI 1/2) (pow PI (/ (- k) 2))) (pow (* n 2) (- 1/2 (/ k 2))))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt k))) 1540976156.717 * * * * [misc]progress: [ 42 / 69 ] simplifiying candidate # 1540976156.717 * * * * [misc]progress: [ 43 / 69 ] simplifiying candidate # 1540976156.717 * * * * [misc]progress: [ 44 / 69 ] simplifiying candidate # 1540976156.717 * * * * [misc]progress: [ 45 / 69 ] simplifiying candidate # 1540976156.718 * * * * [misc]progress: [ 46 / 69 ] simplifiying candidate # 1540976156.718 * * * * [misc]progress: [ 47 / 69 ] simplifiying candidate # 1540976156.718 * * * * [misc]progress: [ 48 / 69 ] simplifiying candidate # 1540976156.718 * * * * [misc]progress: [ 49 / 69 ] simplifiying candidate # 1540976156.718 * * * * [misc]progress: [ 50 / 69 ] simplifiying candidate # 1540976156.718 * * * * [misc]progress: [ 51 / 69 ] simplifiying candidate # 1540976156.718 * * * * [misc]progress: [ 52 / 69 ] simplifiying candidate # 1540976156.718 * * * * [misc]progress: [ 53 / 69 ] simplifiying candidate # 1540976156.718 * * * * [misc]progress: [ 54 / 69 ] simplifiying candidate # 1540976156.718 * * * * [misc]progress: [ 55 / 69 ] simplifiying candidate # 1540976156.718 * * * * [misc]progress: [ 56 / 69 ] simplifiying candidate # 1540976156.718 * * * * [misc]progress: [ 57 / 69 ] simplifiying candidate # 1540976156.718 * * * * [misc]progress: [ 58 / 69 ] simplifiying candidate # 1540976156.719 * [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))))) 1540976156.723 * * [misc]simplify: iters left: 6 (37 enodes) 1540976156.750 * * [misc]simplify: iters left: 5 (105 enodes) 1540976156.830 * * [misc]simplify: iters left: 4 (339 enodes) 1540976157.395 * [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))))) 1540976157.395 * [misc]simplify: Simplified (2 1 2 1) to (λ (k n) (/ (* (sqrt (* (pow PI (- 1/2 (/ k 2))) (pow (* n 2) (- 1/2 (/ k 2))))) (sqrt (+ (+ (* (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) -1/2) (+ (* (* (* k (log n)) (* k (log n))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (pow (* PI 2) 1/2) (pow n 1/2)))) (* (* k k) (+ (* (* (log (* PI 2)) (log (* PI 2))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (* (* (log n) (pow n 1/2)) (pow (* PI 2) 1/2)) (* (log (* PI 2)) 1/4))))))) (sqrt k))) 1540976157.395 * * * * [misc]progress: [ 59 / 69 ] simplifiying candidate # 1540976157.395 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 1540976157.396 * * [misc]simplify: iters left: 6 (15 enodes) 1540976157.401 * * [misc]simplify: iters left: 5 (33 enodes) 1540976157.410 * * [misc]simplify: iters left: 4 (64 enodes) 1540976157.431 * * [misc]simplify: iters left: 3 (171 enodes) 1540976157.629 * [exit]simplify: Simplified to (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow n (- 1/2 (* 1/2 k)))) 1540976157.629 * [misc]simplify: Simplified (2 1 2 1) to (λ (k n) (/ (* (sqrt (* (pow PI (- 1/2 (/ k 2))) (pow (* n 2) (- 1/2 (/ k 2))))) (sqrt (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow n (- 1/2 (* 1/2 k)))))) (sqrt k))) 1540976157.629 * * * * [misc]progress: [ 60 / 69 ] simplifiying candidate # 1540976157.630 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 1540976157.631 * * [misc]simplify: iters left: 6 (15 enodes) 1540976157.640 * * [misc]simplify: iters left: 5 (30 enodes) 1540976157.657 * * [misc]simplify: iters left: 4 (65 enodes) 1540976157.682 * * [misc]simplify: iters left: 3 (200 enodes) 1540976157.949 * [exit]simplify: Simplified to (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))) 1540976157.949 * [misc]simplify: Simplified (2 1 2 1) to (λ (k n) (/ (* (sqrt (* (pow PI (- 1/2 (/ k 2))) (pow (* n 2) (- 1/2 (/ k 2))))) (sqrt (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))))) (sqrt k))) 1540976157.949 * * * * [misc]progress: [ 61 / 69 ] simplifiying candidate # 1540976157.950 * [enter]simplify: Simplifying (- (+ (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (* (pow (log 2) 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (pow k 2)))) (+ (* 1/4 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) (pow k 2))))) (* 1/8 (* (exp (* 1/2 (+ (log 2) (log n)))) (* (pow (log n) 2) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) k))) (* 1/2 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) k))))) 1540976157.953 * * [misc]simplify: iters left: 6 (35 enodes) 1540976157.973 * * [misc]simplify: iters left: 5 (99 enodes) 1540976158.027 * * [misc]simplify: iters left: 4 (298 enodes) 1540976158.427 * [exit]simplify: Simplified to (+ (- (* (pow n 1/2) (pow 2 1/2)) (* (* 1/2 k) (* (* (pow n 1/2) (pow 2 1/2)) (+ (log 2) (log n))))) (+ (* (* (log 2) 1/8) (* (* (pow n 1/2) (pow 2 1/2)) (* (* k k) (log 2)))) (* (* (pow n 1/2) (pow 2 1/2)) (+ (* (* 1/4 (log 2)) (* (* k k) (log n))) (* (* 1/8 (log n)) (* (* k k) (log n))))))) 1540976158.427 * [misc]simplify: Simplified (2 1 1 1 2) to (λ (k n) (/ (* (sqrt (* (pow PI (- 1/2 (/ k 2))) (+ (- (* (pow n 1/2) (pow 2 1/2)) (* (* 1/2 k) (* (* (pow n 1/2) (pow 2 1/2)) (+ (log 2) (log n))))) (+ (* (* (log 2) 1/8) (* (* (pow n 1/2) (pow 2 1/2)) (* (* k k) (log 2)))) (* (* (pow n 1/2) (pow 2 1/2)) (+ (* (* 1/4 (log 2)) (* (* k k) (log n))) (* (* 1/8 (log n)) (* (* k k) (log n))))))))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt k))) 1540976158.427 * * * * [misc]progress: [ 62 / 69 ] simplifiying candidate # 1540976158.428 * [enter]simplify: Simplifying (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) 1540976158.428 * * [misc]simplify: iters left: 6 (13 enodes) 1540976158.433 * * [misc]simplify: iters left: 5 (27 enodes) 1540976158.440 * * [misc]simplify: iters left: 4 (53 enodes) 1540976158.460 * * [misc]simplify: iters left: 3 (116 enodes) 1540976158.560 * * [misc]simplify: iters left: 2 (362 enodes) 1540976158.928 * [exit]simplify: Simplified to (pow (sqrt (* n 2)) (- 1 k)) 1540976158.928 * [misc]simplify: Simplified (2 1 1 1 2) to (λ (k n) (/ (* (sqrt (* (pow PI (- 1/2 (/ k 2))) (pow (sqrt (* n 2)) (- 1 k)))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt k))) 1540976158.928 * * * * [misc]progress: [ 63 / 69 ] simplifiying candidate # 1540976158.928 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) 1540976158.930 * * [misc]simplify: iters left: 6 (13 enodes) 1540976158.937 * * [misc]simplify: iters left: 5 (24 enodes) 1540976158.951 * * [misc]simplify: iters left: 4 (54 enodes) 1540976158.972 * * [misc]simplify: iters left: 3 (143 enodes) 1540976159.110 * [exit]simplify: Simplified to (pow (exp (- 1/2 (* 1/2 k))) (- (log -2) (log (/ -1 n)))) 1540976159.110 * [misc]simplify: Simplified (2 1 1 1 2) to (λ (k n) (/ (* (sqrt (* (pow PI (- 1/2 (/ k 2))) (pow (exp (- 1/2 (* 1/2 k))) (- (log -2) (log (/ -1 n)))))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt k))) 1540976159.110 * * * * [misc]progress: [ 64 / 69 ] simplifiying candidate # 1540976159.111 * [enter]simplify: Simplifying (- (+ (pow PI 1/2) (* 1/8 (* (* (pow (log PI) 2) (pow k 2)) (sqrt PI)))) (* 1/2 (* (* (log PI) k) (sqrt PI)))) 1540976159.113 * * [misc]simplify: iters left: 6 (18 enodes) 1540976159.121 * * [misc]simplify: iters left: 5 (39 enodes) 1540976159.134 * * [misc]simplify: iters left: 4 (104 enodes) 1540976159.181 * * [misc]simplify: iters left: 3 (275 enodes) 1540976159.409 * [exit]simplify: Simplified to (+ (* (* (* k (log PI)) (* k (log PI))) (* (sqrt PI) 1/8)) (+ (* (* k (log PI)) (* (sqrt PI) -1/2)) (sqrt PI))) 1540976159.409 * [misc]simplify: Simplified (2 1 1 1 1) to (λ (k n) (/ (* (sqrt (* (+ (* (* (* k (log PI)) (* k (log PI))) (* (sqrt PI) 1/8)) (+ (* (* k (log PI)) (* (sqrt PI) -1/2)) (sqrt PI))) (pow (* n 2) (- 1/2 (/ k 2))))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt k))) 1540976159.410 * * * * [misc]progress: [ 65 / 69 ] simplifiying candidate # 1540976159.410 * [enter]simplify: Simplifying (pow PI (- 1/2 (* 1/2 k))) 1540976159.411 * * [misc]simplify: iters left: 5 (6 enodes) 1540976159.413 * * [misc]simplify: iters left: 4 (9 enodes) 1540976159.418 * * [misc]simplify: iters left: 3 (17 enodes) 1540976159.423 * * [misc]simplify: iters left: 2 (20 enodes) 1540976159.429 * * [misc]simplify: iters left: 1 (24 enodes) 1540976159.441 * [exit]simplify: Simplified to (pow PI (- 1/2 (* k 1/2))) 1540976159.441 * [misc]simplify: Simplified (2 1 1 1 1) to (λ (k n) (/ (* (sqrt (* (pow PI (- 1/2 (* k 1/2))) (pow (* n 2) (- 1/2 (/ k 2))))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt k))) 1540976159.441 * * * * [misc]progress: [ 66 / 69 ] simplifiying candidate # 1540976159.441 * [enter]simplify: Simplifying (pow PI (- 1/2 (* 1/2 k))) 1540976159.442 * * [misc]simplify: iters left: 5 (6 enodes) 1540976159.445 * * [misc]simplify: iters left: 4 (9 enodes) 1540976159.450 * * [misc]simplify: iters left: 3 (17 enodes) 1540976159.455 * * [misc]simplify: iters left: 2 (20 enodes) 1540976159.461 * * [misc]simplify: iters left: 1 (24 enodes) 1540976159.474 * [exit]simplify: Simplified to (pow PI (- 1/2 (* k 1/2))) 1540976159.474 * [misc]simplify: Simplified (2 1 1 1 1) to (λ (k n) (/ (* (sqrt (* (pow PI (- 1/2 (* k 1/2))) (pow (* n 2) (- 1/2 (/ k 2))))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt k))) 1540976159.474 * * * * [misc]progress: [ 67 / 69 ] simplifiying candidate # 1540976159.474 * [enter]simplify: Simplifying (* 2 (* n PI)) 1540976159.475 * * [misc]simplify: iters left: 4 (5 enodes) 1540976159.477 * * [misc]simplify: iters left: 3 (9 enodes) 1540976159.482 * * [misc]simplify: iters left: 2 (15 enodes) 1540976159.485 * * [misc]simplify: iters left: 1 (17 enodes) 1540976159.488 * [exit]simplify: Simplified to (* (* PI n) 2) 1540976159.488 * [misc]simplify: Simplified (2 1 2 1 1) to (λ (k n) (/ (* (sqrt (* (pow PI (- 1/2 (/ k 2))) (pow (* n 2) (- 1/2 (/ k 2))))) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) (sqrt k))) 1540976159.488 * * * * [misc]progress: [ 68 / 69 ] simplifiying candidate # 1540976159.488 * [enter]simplify: Simplifying (* 2 (* n PI)) 1540976159.488 * * [misc]simplify: iters left: 4 (5 enodes) 1540976159.489 * * [misc]simplify: iters left: 3 (9 enodes) 1540976159.492 * * [misc]simplify: iters left: 2 (15 enodes) 1540976159.494 * * [misc]simplify: iters left: 1 (17 enodes) 1540976159.497 * [exit]simplify: Simplified to (* (* PI n) 2) 1540976159.497 * [misc]simplify: Simplified (2 1 2 1 1) to (λ (k n) (/ (* (sqrt (* (pow PI (- 1/2 (/ k 2))) (pow (* n 2) (- 1/2 (/ k 2))))) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) (sqrt k))) 1540976159.497 * * * * [misc]progress: [ 69 / 69 ] simplifiying candidate # 1540976159.497 * [enter]simplify: Simplifying (* 2 (* n PI)) 1540976159.498 * * [misc]simplify: iters left: 4 (5 enodes) 1540976159.499 * * [misc]simplify: iters left: 3 (9 enodes) 1540976159.501 * * [misc]simplify: iters left: 2 (15 enodes) 1540976159.505 * * [misc]simplify: iters left: 1 (17 enodes) 1540976159.508 * [exit]simplify: Simplified to (* (* PI n) 2) 1540976159.508 * [misc]simplify: Simplified (2 1 2 1 1) to (λ (k n) (/ (* (sqrt (* (pow PI (- 1/2 (/ k 2))) (pow (* n 2) (- 1/2 (/ k 2))))) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) (sqrt k))) 1540976159.508 * * * [misc]progress: adding candidates to table 1540976161.997 * [misc]progress: [Phase 3 of 3] Extracting. 1540976161.997 * * [misc]regime: Finding splitpoints for: (# # # # # # # # #) 1540976162.001 * * * [misc]regime-changes: Trying 2 branch expressions: (n k) 1540976162.001 * * * * [misc]regimes: Trying to branch on n from (# # # # # # # # #) 1540976162.089 * * * * [misc]regimes: Trying to branch on k from (# # # # # # # # #) 1540976162.205 * * * [misc]regime: Found split indices: #