1547113853.506 * [misc]progress: [Phase 1 of 3] Setting up. 1547113853.506 * * * [misc]progress: [1/2] Preparing points 1547113853.506 * * * * [misc]points: Sampling 256 additional inputs, on iter 0 have 0 / 256 1547113853.541 * * * * [misc]points: Filtering points with unrepresentable outputs 1547113853.542 * * * * [misc]points: Sampling 192 additional inputs, on iter 1 have 64 / 256 1547113853.572 * * * * [misc]points: Filtering points with unrepresentable outputs 1547113853.572 * * * * [misc]points: Sampling 135 additional inputs, on iter 2 have 121 / 256 1547113853.599 * * * * [misc]points: Filtering points with unrepresentable outputs 1547113853.599 * * * * [misc]points: Sampling 106 additional inputs, on iter 3 have 150 / 256 1547113853.656 * * * * [misc]points: Filtering points with unrepresentable outputs 1547113853.656 * * * * [misc]points: Sampling 74 additional inputs, on iter 4 have 182 / 256 1547113853.672 * * * * [misc]points: Filtering points with unrepresentable outputs 1547113853.672 * * * * [misc]points: Sampling 57 additional inputs, on iter 5 have 199 / 256 1547113853.683 * * * * [misc]points: Filtering points with unrepresentable outputs 1547113853.683 * * * * [misc]points: Sampling 48 additional inputs, on iter 6 have 208 / 256 1547113853.696 * * * * [misc]points: Filtering points with unrepresentable outputs 1547113853.696 * * * * [misc]points: Sampling 34 additional inputs, on iter 7 have 222 / 256 1547113853.703 * * * * [misc]points: Filtering points with unrepresentable outputs 1547113853.704 * * * * [misc]points: Sampling 27 additional inputs, on iter 8 have 229 / 256 1547113853.710 * * * * [misc]points: Filtering points with unrepresentable outputs 1547113853.710 * * * * [misc]points: Sampling 21 additional inputs, on iter 9 have 235 / 256 1547113853.720 * * * * [misc]points: Filtering points with unrepresentable outputs 1547113853.720 * * * * [misc]points: Sampling 16 additional inputs, on iter 10 have 240 / 256 1547113853.729 * * * * [misc]points: Filtering points with unrepresentable outputs 1547113853.729 * * * * [misc]points: Sampling 14 additional inputs, on iter 11 have 242 / 256 1547113853.738 * * * * [misc]points: Filtering points with unrepresentable outputs 1547113853.738 * * * * [misc]points: Sampling 12 additional inputs, on iter 12 have 244 / 256 1547113853.746 * * * * [misc]points: Filtering points with unrepresentable outputs 1547113853.747 * * * * [misc]points: Sampling 11 additional inputs, on iter 13 have 245 / 256 1547113853.753 * * * * [misc]points: Filtering points with unrepresentable outputs 1547113853.753 * * * * [misc]points: Sampling 9 additional inputs, on iter 14 have 247 / 256 1547113853.758 * * * * [misc]points: Filtering points with unrepresentable outputs 1547113853.758 * * * * [misc]points: Sampling 7 additional inputs, on iter 15 have 249 / 256 1547113853.762 * * * * [misc]points: Filtering points with unrepresentable outputs 1547113853.762 * * * * [misc]points: Sampling 6 additional inputs, on iter 16 have 250 / 256 1547113853.765 * * * * [misc]points: Filtering points with unrepresentable outputs 1547113853.766 * * * * [misc]points: Sampling 6 additional inputs, on iter 17 have 250 / 256 1547113853.787 * * * * [misc]points: Filtering points with unrepresentable outputs 1547113853.787 * * * * [misc]points: Sampling 5 additional inputs, on iter 18 have 251 / 256 1547113853.793 * * * * [misc]points: Filtering points with unrepresentable outputs 1547113853.793 * * * * [misc]points: Sampling 4 additional inputs, on iter 19 have 252 / 256 1547113853.797 * * * * [misc]points: Filtering points with unrepresentable outputs 1547113853.797 * * * * [misc]points: Sampling 4 additional inputs, on iter 20 have 252 / 256 1547113853.801 * * * * [misc]points: Filtering points with unrepresentable outputs 1547113853.801 * * * * [misc]points: Sampling 4 additional inputs, on iter 21 have 252 / 256 1547113853.804 * * * * [misc]points: Filtering points with unrepresentable outputs 1547113853.804 * * * * [misc]points: Sampling 4 additional inputs, on iter 22 have 253 / 256 1547113853.808 * * * * [misc]points: Filtering points with unrepresentable outputs 1547113853.808 * * * * [misc]points: Sampling 4 additional inputs, on iter 23 have 254 / 256 1547113853.812 * * * * [misc]points: Filtering points with unrepresentable outputs 1547113853.812 * * * * [misc]points: Sampling 4 additional inputs, on iter 24 have 254 / 256 1547113853.819 * * * * [misc]points: Filtering points with unrepresentable outputs 1547113853.819 * * * * [exit]points: Sampled 256 points with exact outputs 1547113853.819 * * * [misc]progress: [2/2] Setting up program. 1547113853.825 * [misc]progress: [Phase 2 of 3] Improving. 1547113853.825 * * * * [misc]progress: [ 1 / 1 ] simplifiying candidate # 1547113853.825 * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) 1547113853.825 * * [misc]simplify: iters left: 6 (13 enodes) 1547113853.831 * * [misc]simplify: iters left: 5 (28 enodes) 1547113853.840 * * [misc]simplify: iters left: 4 (44 enodes) 1547113853.854 * * [misc]simplify: iters left: 3 (54 enodes) 1547113853.867 * * [misc]simplify: iters left: 2 (57 enodes) 1547113853.880 * * [misc]simplify: iters left: 1 (65 enodes) 1547113853.897 * [exit]simplify: Simplified to (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)) 1547113853.897 * [misc]simplify: Simplified (2) to (λ (k n) (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) 1547113853.911 * * [misc]progress: iteration 1 / 4 1547113853.911 * * * [misc]progress: picking best candidate 1547113853.936 * * * * [misc]pick: Picked # 1547113853.936 * * * [misc]progress: localizing error 1547113853.983 * * * [misc]progress: generating rewritten candidates 1547113853.983 * * * * [misc]progress: [ 1 / 3 ] rewriting at (2 1) 1547113853.987 * * * * [misc]progress: [ 2 / 3 ] rewriting at (2 1 1) 1547113853.989 * * * * [misc]progress: [ 3 / 3 ] rewriting at (2) 1547113854.001 * * * [misc]progress: generating series expansions 1547113854.001 * * * * [misc]progress: [ 1 / 3 ] generating series at (2 1) 1547113854.001 * [misc]backup-simplify: Simplify (pow (* PI (* n 2)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 1547113854.001 * [misc]approximate: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 1547113854.001 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1547113854.001 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1547113854.001 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1547113854.001 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1547113854.001 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113854.001 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113854.001 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1547113854.001 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113854.001 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113854.001 * [misc]taylor: Taking taylor expansion of k in k 1547113854.001 * [misc]backup-simplify: Simplify 0 into 0 1547113854.001 * [misc]backup-simplify: Simplify 1 into 1 1547113854.001 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1547113854.001 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1547113854.001 * [misc]taylor: Taking taylor expansion of 2 in k 1547113854.001 * [misc]backup-simplify: Simplify 2 into 2 1547113854.001 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1547113854.002 * [misc]taylor: Taking taylor expansion of n in k 1547113854.002 * [misc]backup-simplify: Simplify n into n 1547113854.002 * [misc]taylor: Taking taylor expansion of PI in k 1547113854.002 * [misc]backup-simplify: Simplify PI into PI 1547113854.002 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1547113854.002 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1547113854.002 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1547113854.002 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1547113854.002 * [misc]backup-simplify: Simplify (- 0) into 0 1547113854.003 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1547113854.003 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1547113854.003 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1547113854.003 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1547113854.003 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1547113854.003 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1547113854.003 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1547113854.003 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113854.003 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113854.003 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1547113854.003 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113854.003 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113854.003 * [misc]taylor: Taking taylor expansion of k in n 1547113854.003 * [misc]backup-simplify: Simplify k into k 1547113854.003 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1547113854.003 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1547113854.003 * [misc]taylor: Taking taylor expansion of 2 in n 1547113854.003 * [misc]backup-simplify: Simplify 2 into 2 1547113854.003 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547113854.004 * [misc]taylor: Taking taylor expansion of n in n 1547113854.004 * [misc]backup-simplify: Simplify 0 into 0 1547113854.004 * [misc]backup-simplify: Simplify 1 into 1 1547113854.004 * [misc]taylor: Taking taylor expansion of PI in n 1547113854.004 * [misc]backup-simplify: Simplify PI into PI 1547113854.004 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547113854.004 * [misc]backup-simplify: Simplify (* 2 0) into 0 1547113854.005 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547113854.006 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1547113854.006 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547113854.006 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1547113854.006 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1547113854.006 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1547113854.007 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547113854.008 * [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)))) 1547113854.008 * [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))))) 1547113854.008 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1547113854.008 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1547113854.008 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1547113854.009 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1547113854.009 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113854.009 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113854.009 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1547113854.009 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113854.009 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113854.009 * [misc]taylor: Taking taylor expansion of k in n 1547113854.009 * [misc]backup-simplify: Simplify k into k 1547113854.009 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1547113854.009 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1547113854.009 * [misc]taylor: Taking taylor expansion of 2 in n 1547113854.009 * [misc]backup-simplify: Simplify 2 into 2 1547113854.009 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547113854.009 * [misc]taylor: Taking taylor expansion of n in n 1547113854.009 * [misc]backup-simplify: Simplify 0 into 0 1547113854.009 * [misc]backup-simplify: Simplify 1 into 1 1547113854.009 * [misc]taylor: Taking taylor expansion of PI in n 1547113854.009 * [misc]backup-simplify: Simplify PI into PI 1547113854.009 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547113854.009 * [misc]backup-simplify: Simplify (* 2 0) into 0 1547113854.010 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547113854.011 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1547113854.011 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547113854.011 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1547113854.011 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1547113854.012 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1547113854.012 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547113854.013 * [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)))) 1547113854.013 * [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))))) 1547113854.013 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1547113854.014 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1547113854.014 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1547113854.014 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113854.014 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113854.014 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1547113854.014 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113854.014 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113854.014 * [misc]taylor: Taking taylor expansion of k in k 1547113854.014 * [misc]backup-simplify: Simplify 0 into 0 1547113854.014 * [misc]backup-simplify: Simplify 1 into 1 1547113854.014 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1547113854.014 * [misc]taylor: Taking taylor expansion of (log n) in k 1547113854.014 * [misc]taylor: Taking taylor expansion of n in k 1547113854.014 * [misc]backup-simplify: Simplify n into n 1547113854.014 * [misc]backup-simplify: Simplify (log n) into (log n) 1547113854.014 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1547113854.014 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1547113854.014 * [misc]taylor: Taking taylor expansion of 2 in k 1547113854.014 * [misc]backup-simplify: Simplify 2 into 2 1547113854.014 * [misc]taylor: Taking taylor expansion of PI in k 1547113854.014 * [misc]backup-simplify: Simplify PI into PI 1547113854.014 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547113854.015 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547113854.015 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1547113854.015 * [misc]backup-simplify: Simplify (- 0) into 0 1547113854.015 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1547113854.016 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547113854.016 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1547113854.017 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1547113854.018 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1547113854.019 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1547113854.020 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1547113854.023 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1547113854.023 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1547113854.024 * [misc]backup-simplify: Simplify (- 0) into 0 1547113854.024 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113854.024 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547113854.025 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1547113854.027 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1547113854.027 * [misc]taylor: Taking taylor expansion of 0 in k 1547113854.027 * [misc]backup-simplify: Simplify 0 into 0 1547113854.027 * [misc]backup-simplify: Simplify 0 into 0 1547113854.028 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1547113854.028 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1547113854.031 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1547113854.031 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113854.031 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1547113854.032 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1547113854.032 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1547113854.032 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1547113854.034 * [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))))))) 1547113854.035 * [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))))))) 1547113854.037 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1547113854.039 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1547113854.044 * [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 1547113854.044 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1547113854.044 * [misc]backup-simplify: Simplify (- 0) into 0 1547113854.044 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113854.045 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547113854.046 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1547113854.048 * [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 1547113854.048 * [misc]taylor: Taking taylor expansion of 0 in k 1547113854.048 * [misc]backup-simplify: Simplify 0 into 0 1547113854.048 * [misc]backup-simplify: Simplify 0 into 0 1547113854.048 * [misc]backup-simplify: Simplify 0 into 0 1547113854.050 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1547113854.051 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1547113854.056 * [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 1547113854.056 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113854.056 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1547113854.056 * [misc]backup-simplify: Simplify (- 0) into 0 1547113854.057 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113854.057 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1547113854.060 * [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))))) 1547113854.062 * [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))))) 1547113854.067 * [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))))) 1547113854.068 * [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)))) 1547113854.068 * [misc]approximate: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 1547113854.068 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1547113854.068 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1547113854.068 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1547113854.068 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1547113854.068 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113854.068 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113854.068 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1547113854.068 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113854.068 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113854.068 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547113854.068 * [misc]taylor: Taking taylor expansion of k in k 1547113854.068 * [misc]backup-simplify: Simplify 0 into 0 1547113854.068 * [misc]backup-simplify: Simplify 1 into 1 1547113854.069 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547113854.069 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1547113854.069 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1547113854.069 * [misc]taylor: Taking taylor expansion of 2 in k 1547113854.069 * [misc]backup-simplify: Simplify 2 into 2 1547113854.069 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1547113854.069 * [misc]taylor: Taking taylor expansion of PI in k 1547113854.069 * [misc]backup-simplify: Simplify PI into PI 1547113854.069 * [misc]taylor: Taking taylor expansion of n in k 1547113854.069 * [misc]backup-simplify: Simplify n into n 1547113854.069 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1547113854.069 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1547113854.069 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1547113854.069 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1547113854.069 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1547113854.070 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1547113854.070 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1547113854.070 * [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)))) 1547113854.070 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1547113854.070 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1547113854.070 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1547113854.070 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1547113854.070 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113854.070 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113854.070 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1547113854.070 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113854.070 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113854.070 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547113854.070 * [misc]taylor: Taking taylor expansion of k in n 1547113854.070 * [misc]backup-simplify: Simplify k into k 1547113854.070 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547113854.070 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1547113854.070 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1547113854.070 * [misc]taylor: Taking taylor expansion of 2 in n 1547113854.070 * [misc]backup-simplify: Simplify 2 into 2 1547113854.070 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547113854.070 * [misc]taylor: Taking taylor expansion of PI in n 1547113854.070 * [misc]backup-simplify: Simplify PI into PI 1547113854.070 * [misc]taylor: Taking taylor expansion of n in n 1547113854.071 * [misc]backup-simplify: Simplify 0 into 0 1547113854.071 * [misc]backup-simplify: Simplify 1 into 1 1547113854.071 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547113854.071 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547113854.072 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547113854.072 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1547113854.072 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1547113854.072 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1547113854.073 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547113854.073 * [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))) 1547113854.074 * [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)))) 1547113854.074 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1547113854.074 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1547113854.074 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1547113854.074 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1547113854.074 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113854.074 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113854.074 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1547113854.074 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113854.074 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113854.074 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547113854.074 * [misc]taylor: Taking taylor expansion of k in n 1547113854.074 * [misc]backup-simplify: Simplify k into k 1547113854.074 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547113854.074 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1547113854.074 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1547113854.075 * [misc]taylor: Taking taylor expansion of 2 in n 1547113854.075 * [misc]backup-simplify: Simplify 2 into 2 1547113854.075 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547113854.075 * [misc]taylor: Taking taylor expansion of PI in n 1547113854.075 * [misc]backup-simplify: Simplify PI into PI 1547113854.075 * [misc]taylor: Taking taylor expansion of n in n 1547113854.075 * [misc]backup-simplify: Simplify 0 into 0 1547113854.075 * [misc]backup-simplify: Simplify 1 into 1 1547113854.075 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547113854.075 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547113854.076 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547113854.076 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1547113854.076 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1547113854.076 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1547113854.077 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547113854.077 * [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))) 1547113854.078 * [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)))) 1547113854.078 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1547113854.078 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1547113854.078 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1547113854.078 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113854.078 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113854.078 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1547113854.078 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113854.078 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113854.078 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547113854.078 * [misc]taylor: Taking taylor expansion of k in k 1547113854.078 * [misc]backup-simplify: Simplify 0 into 0 1547113854.078 * [misc]backup-simplify: Simplify 1 into 1 1547113854.079 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547113854.079 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1547113854.079 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1547113854.079 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1547113854.079 * [misc]taylor: Taking taylor expansion of 2 in k 1547113854.079 * [misc]backup-simplify: Simplify 2 into 2 1547113854.079 * [misc]taylor: Taking taylor expansion of PI in k 1547113854.079 * [misc]backup-simplify: Simplify PI into PI 1547113854.079 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547113854.079 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547113854.079 * [misc]taylor: Taking taylor expansion of (log n) in k 1547113854.080 * [misc]taylor: Taking taylor expansion of n in k 1547113854.080 * [misc]backup-simplify: Simplify n into n 1547113854.080 * [misc]backup-simplify: Simplify (log n) into (log n) 1547113854.080 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1547113854.080 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1547113854.080 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1547113854.080 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1547113854.081 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1547113854.082 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1547113854.082 * [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)))) 1547113854.083 * [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)))) 1547113854.084 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1547113854.085 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1547113854.088 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1547113854.088 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1547113854.088 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1547113854.088 * [misc]backup-simplify: Simplify (- 0) into 0 1547113854.088 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113854.089 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547113854.090 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1547113854.091 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1547113854.091 * [misc]taylor: Taking taylor expansion of 0 in k 1547113854.091 * [misc]backup-simplify: Simplify 0 into 0 1547113854.091 * [misc]backup-simplify: Simplify 0 into 0 1547113854.091 * [misc]backup-simplify: Simplify 0 into 0 1547113854.100 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113854.101 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1547113854.107 * [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 1547113854.108 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1547113854.108 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1547113854.108 * [misc]backup-simplify: Simplify (- 0) into 0 1547113854.108 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113854.109 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547113854.110 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1547113854.112 * [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 1547113854.112 * [misc]taylor: Taking taylor expansion of 0 in k 1547113854.112 * [misc]backup-simplify: Simplify 0 into 0 1547113854.112 * [misc]backup-simplify: Simplify 0 into 0 1547113854.113 * [misc]backup-simplify: Simplify 0 into 0 1547113854.113 * [misc]backup-simplify: Simplify 0 into 0 1547113854.115 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113854.116 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1547113854.124 * [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 1547113854.124 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1547113854.125 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1547113854.125 * [misc]backup-simplify: Simplify (- 0) into 0 1547113854.125 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113854.126 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547113854.127 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1547113854.130 * [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 1547113854.130 * [misc]taylor: Taking taylor expansion of 0 in k 1547113854.130 * [misc]backup-simplify: Simplify 0 into 0 1547113854.131 * [misc]backup-simplify: Simplify 0 into 0 1547113854.132 * [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))))) 1547113854.132 * [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)) 1547113854.132 * [misc]approximate: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 1547113854.132 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1547113854.132 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1547113854.132 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1547113854.132 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1547113854.132 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1547113854.132 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113854.132 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113854.132 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547113854.132 * [misc]taylor: Taking taylor expansion of k in k 1547113854.132 * [misc]backup-simplify: Simplify 0 into 0 1547113854.132 * [misc]backup-simplify: Simplify 1 into 1 1547113854.133 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547113854.133 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113854.133 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113854.133 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1547113854.133 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1547113854.133 * [misc]taylor: Taking taylor expansion of -2 in k 1547113854.133 * [misc]backup-simplify: Simplify -2 into -2 1547113854.133 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1547113854.133 * [misc]taylor: Taking taylor expansion of PI in k 1547113854.133 * [misc]backup-simplify: Simplify PI into PI 1547113854.133 * [misc]taylor: Taking taylor expansion of n in k 1547113854.133 * [misc]backup-simplify: Simplify n into n 1547113854.133 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1547113854.133 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1547113854.133 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1547113854.133 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1547113854.133 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1547113854.134 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1547113854.134 * [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))) 1547113854.134 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1547113854.134 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1547113854.134 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1547113854.134 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1547113854.134 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1547113854.134 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113854.134 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113854.134 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547113854.134 * [misc]taylor: Taking taylor expansion of k in n 1547113854.134 * [misc]backup-simplify: Simplify k into k 1547113854.134 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547113854.134 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113854.134 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113854.134 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1547113854.134 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1547113854.134 * [misc]taylor: Taking taylor expansion of -2 in n 1547113854.134 * [misc]backup-simplify: Simplify -2 into -2 1547113854.134 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547113854.134 * [misc]taylor: Taking taylor expansion of PI in n 1547113854.134 * [misc]backup-simplify: Simplify PI into PI 1547113854.134 * [misc]taylor: Taking taylor expansion of n in n 1547113854.134 * [misc]backup-simplify: Simplify 0 into 0 1547113854.134 * [misc]backup-simplify: Simplify 1 into 1 1547113854.135 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547113854.135 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547113854.136 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1547113854.136 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1547113854.136 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1547113854.136 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547113854.137 * [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))) 1547113854.138 * [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)))) 1547113854.138 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1547113854.138 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1547113854.138 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1547113854.138 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1547113854.138 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1547113854.138 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113854.138 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113854.138 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547113854.138 * [misc]taylor: Taking taylor expansion of k in n 1547113854.138 * [misc]backup-simplify: Simplify k into k 1547113854.138 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547113854.138 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113854.138 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113854.138 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1547113854.138 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1547113854.138 * [misc]taylor: Taking taylor expansion of -2 in n 1547113854.138 * [misc]backup-simplify: Simplify -2 into -2 1547113854.138 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547113854.138 * [misc]taylor: Taking taylor expansion of PI in n 1547113854.138 * [misc]backup-simplify: Simplify PI into PI 1547113854.138 * [misc]taylor: Taking taylor expansion of n in n 1547113854.138 * [misc]backup-simplify: Simplify 0 into 0 1547113854.138 * [misc]backup-simplify: Simplify 1 into 1 1547113854.139 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547113854.139 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547113854.139 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1547113854.139 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1547113854.139 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1547113854.140 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547113854.141 * [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))) 1547113854.141 * [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)))) 1547113854.142 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1547113854.142 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1547113854.142 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1547113854.142 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1547113854.142 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113854.142 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113854.142 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547113854.142 * [misc]taylor: Taking taylor expansion of k in k 1547113854.142 * [misc]backup-simplify: Simplify 0 into 0 1547113854.142 * [misc]backup-simplify: Simplify 1 into 1 1547113854.142 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547113854.142 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113854.142 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113854.142 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1547113854.142 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1547113854.142 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1547113854.142 * [misc]taylor: Taking taylor expansion of -2 in k 1547113854.142 * [misc]backup-simplify: Simplify -2 into -2 1547113854.142 * [misc]taylor: Taking taylor expansion of PI in k 1547113854.142 * [misc]backup-simplify: Simplify PI into PI 1547113854.142 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547113854.143 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1547113854.143 * [misc]taylor: Taking taylor expansion of (log n) in k 1547113854.143 * [misc]taylor: Taking taylor expansion of n in k 1547113854.143 * [misc]backup-simplify: Simplify n into n 1547113854.143 * [misc]backup-simplify: Simplify (log n) into (log n) 1547113854.143 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1547113854.143 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1547113854.143 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1547113854.144 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1547113854.144 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1547113854.144 * [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)))) 1547113854.145 * [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)))) 1547113854.145 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1547113854.146 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1547113854.147 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1547113854.148 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1547113854.148 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1547113854.148 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113854.148 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547113854.149 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1547113854.150 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1547113854.150 * [misc]taylor: Taking taylor expansion of 0 in k 1547113854.150 * [misc]backup-simplify: Simplify 0 into 0 1547113854.150 * [misc]backup-simplify: Simplify 0 into 0 1547113854.150 * [misc]backup-simplify: Simplify 0 into 0 1547113854.151 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113854.151 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1547113854.154 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 1547113854.154 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1547113854.154 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1547113854.154 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113854.155 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547113854.155 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1547113854.157 * [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 1547113854.157 * [misc]taylor: Taking taylor expansion of 0 in k 1547113854.157 * [misc]backup-simplify: Simplify 0 into 0 1547113854.157 * [misc]backup-simplify: Simplify 0 into 0 1547113854.157 * [misc]backup-simplify: Simplify 0 into 0 1547113854.157 * [misc]backup-simplify: Simplify 0 into 0 1547113854.158 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113854.159 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1547113854.163 * [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 1547113854.163 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1547113854.164 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1547113854.164 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113854.164 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547113854.165 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 1547113854.167 * [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 1547113854.167 * [misc]taylor: Taking taylor expansion of 0 in k 1547113854.167 * [misc]backup-simplify: Simplify 0 into 0 1547113854.167 * [misc]backup-simplify: Simplify 0 into 0 1547113854.168 * [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))))) 1547113854.168 * * * * [misc]progress: [ 2 / 3 ] generating series at (2 1 1) 1547113854.168 * [misc]backup-simplify: Simplify (* PI (* n 2)) into (* 2 (* n PI)) 1547113854.168 * [misc]approximate: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1547113854.168 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1547113854.168 * [misc]taylor: Taking taylor expansion of 2 in n 1547113854.168 * [misc]backup-simplify: Simplify 2 into 2 1547113854.168 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547113854.168 * [misc]taylor: Taking taylor expansion of n in n 1547113854.168 * [misc]backup-simplify: Simplify 0 into 0 1547113854.168 * [misc]backup-simplify: Simplify 1 into 1 1547113854.168 * [misc]taylor: Taking taylor expansion of PI in n 1547113854.168 * [misc]backup-simplify: Simplify PI into PI 1547113854.168 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1547113854.168 * [misc]taylor: Taking taylor expansion of 2 in n 1547113854.168 * [misc]backup-simplify: Simplify 2 into 2 1547113854.168 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547113854.168 * [misc]taylor: Taking taylor expansion of n in n 1547113854.168 * [misc]backup-simplify: Simplify 0 into 0 1547113854.168 * [misc]backup-simplify: Simplify 1 into 1 1547113854.168 * [misc]taylor: Taking taylor expansion of PI in n 1547113854.168 * [misc]backup-simplify: Simplify PI into PI 1547113854.169 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547113854.169 * [misc]backup-simplify: Simplify (* 2 0) into 0 1547113854.169 * [misc]backup-simplify: Simplify 0 into 0 1547113854.170 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547113854.170 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1547113854.171 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547113854.172 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1547113854.173 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1547113854.173 * [misc]backup-simplify: Simplify 0 into 0 1547113854.174 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1547113854.176 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1547113854.176 * [misc]backup-simplify: Simplify 0 into 0 1547113854.178 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1547113854.180 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1547113854.180 * [misc]backup-simplify: Simplify 0 into 0 1547113854.184 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1547113854.187 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1547113854.187 * [misc]backup-simplify: Simplify 0 into 0 1547113854.189 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1547113854.191 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1547113854.191 * [misc]backup-simplify: Simplify 0 into 0 1547113854.193 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1547113854.196 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1547113854.196 * [misc]backup-simplify: Simplify 0 into 0 1547113854.196 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1547113854.196 * [misc]backup-simplify: Simplify (* PI (* (/ 1 n) 2)) into (* 2 (/ PI n)) 1547113854.196 * [misc]approximate: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1547113854.196 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1547113854.196 * [misc]taylor: Taking taylor expansion of 2 in n 1547113854.196 * [misc]backup-simplify: Simplify 2 into 2 1547113854.196 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547113854.196 * [misc]taylor: Taking taylor expansion of PI in n 1547113854.196 * [misc]backup-simplify: Simplify PI into PI 1547113854.196 * [misc]taylor: Taking taylor expansion of n in n 1547113854.196 * [misc]backup-simplify: Simplify 0 into 0 1547113854.196 * [misc]backup-simplify: Simplify 1 into 1 1547113854.197 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547113854.197 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1547113854.197 * [misc]taylor: Taking taylor expansion of 2 in n 1547113854.197 * [misc]backup-simplify: Simplify 2 into 2 1547113854.197 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547113854.197 * [misc]taylor: Taking taylor expansion of PI in n 1547113854.197 * [misc]backup-simplify: Simplify PI into PI 1547113854.197 * [misc]taylor: Taking taylor expansion of n in n 1547113854.197 * [misc]backup-simplify: Simplify 0 into 0 1547113854.197 * [misc]backup-simplify: Simplify 1 into 1 1547113854.197 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547113854.197 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547113854.197 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547113854.198 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1547113854.198 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1547113854.198 * [misc]backup-simplify: Simplify 0 into 0 1547113854.199 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113854.200 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1547113854.200 * [misc]backup-simplify: Simplify 0 into 0 1547113854.201 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113854.202 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1547113854.202 * [misc]backup-simplify: Simplify 0 into 0 1547113854.203 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113854.204 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1547113854.204 * [misc]backup-simplify: Simplify 0 into 0 1547113854.205 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113854.207 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1547113854.207 * [misc]backup-simplify: Simplify 0 into 0 1547113854.208 * [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 1547113854.210 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1547113854.210 * [misc]backup-simplify: Simplify 0 into 0 1547113854.210 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 1547113854.210 * [misc]backup-simplify: Simplify (* PI (* (/ 1 (- n)) 2)) into (* -2 (/ PI n)) 1547113854.210 * [misc]approximate: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1547113854.210 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1547113854.210 * [misc]taylor: Taking taylor expansion of -2 in n 1547113854.211 * [misc]backup-simplify: Simplify -2 into -2 1547113854.211 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547113854.211 * [misc]taylor: Taking taylor expansion of PI in n 1547113854.211 * [misc]backup-simplify: Simplify PI into PI 1547113854.211 * [misc]taylor: Taking taylor expansion of n in n 1547113854.211 * [misc]backup-simplify: Simplify 0 into 0 1547113854.211 * [misc]backup-simplify: Simplify 1 into 1 1547113854.211 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547113854.211 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1547113854.211 * [misc]taylor: Taking taylor expansion of -2 in n 1547113854.211 * [misc]backup-simplify: Simplify -2 into -2 1547113854.211 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547113854.211 * [misc]taylor: Taking taylor expansion of PI in n 1547113854.211 * [misc]backup-simplify: Simplify PI into PI 1547113854.211 * [misc]taylor: Taking taylor expansion of n in n 1547113854.211 * [misc]backup-simplify: Simplify 0 into 0 1547113854.211 * [misc]backup-simplify: Simplify 1 into 1 1547113854.211 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547113854.211 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547113854.211 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547113854.212 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1547113854.212 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1547113854.213 * [misc]backup-simplify: Simplify 0 into 0 1547113854.213 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113854.214 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1547113854.214 * [misc]backup-simplify: Simplify 0 into 0 1547113854.215 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113854.216 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1547113854.216 * [misc]backup-simplify: Simplify 0 into 0 1547113854.218 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113854.220 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1547113854.220 * [misc]backup-simplify: Simplify 0 into 0 1547113854.222 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113854.226 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1547113854.226 * [misc]backup-simplify: Simplify 0 into 0 1547113854.229 * [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 1547113854.232 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1547113854.232 * [misc]backup-simplify: Simplify 0 into 0 1547113854.232 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 1547113854.233 * * * * [misc]progress: [ 3 / 3 ] generating series at (2) 1547113854.233 * [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)))) 1547113854.233 * [misc]approximate: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (n k) around 0 1547113854.233 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 1547113854.233 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1547113854.233 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547113854.233 * [misc]taylor: Taking taylor expansion of k in k 1547113854.233 * [misc]backup-simplify: Simplify 0 into 0 1547113854.233 * [misc]backup-simplify: Simplify 1 into 1 1547113854.233 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547113854.234 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547113854.234 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1547113854.234 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1547113854.234 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1547113854.234 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1547113854.234 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1547113854.234 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113854.234 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113854.235 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1547113854.235 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113854.235 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113854.235 * [misc]taylor: Taking taylor expansion of k in k 1547113854.235 * [misc]backup-simplify: Simplify 0 into 0 1547113854.235 * [misc]backup-simplify: Simplify 1 into 1 1547113854.235 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1547113854.235 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1547113854.235 * [misc]taylor: Taking taylor expansion of 2 in k 1547113854.235 * [misc]backup-simplify: Simplify 2 into 2 1547113854.235 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1547113854.235 * [misc]taylor: Taking taylor expansion of n in k 1547113854.235 * [misc]backup-simplify: Simplify n into n 1547113854.235 * [misc]taylor: Taking taylor expansion of PI in k 1547113854.235 * [misc]backup-simplify: Simplify PI into PI 1547113854.235 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1547113854.235 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1547113854.235 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1547113854.235 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1547113854.235 * [misc]backup-simplify: Simplify (- 0) into 0 1547113854.236 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1547113854.236 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1547113854.236 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1547113854.236 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 1547113854.236 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1547113854.236 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547113854.236 * [misc]taylor: Taking taylor expansion of k in n 1547113854.236 * [misc]backup-simplify: Simplify k into k 1547113854.236 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547113854.236 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1547113854.236 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1547113854.236 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1547113854.236 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1547113854.236 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1547113854.236 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1547113854.236 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1547113854.236 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113854.236 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113854.236 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1547113854.236 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113854.237 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113854.237 * [misc]taylor: Taking taylor expansion of k in n 1547113854.237 * [misc]backup-simplify: Simplify k into k 1547113854.237 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1547113854.237 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1547113854.237 * [misc]taylor: Taking taylor expansion of 2 in n 1547113854.237 * [misc]backup-simplify: Simplify 2 into 2 1547113854.237 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547113854.237 * [misc]taylor: Taking taylor expansion of n in n 1547113854.237 * [misc]backup-simplify: Simplify 0 into 0 1547113854.237 * [misc]backup-simplify: Simplify 1 into 1 1547113854.237 * [misc]taylor: Taking taylor expansion of PI in n 1547113854.237 * [misc]backup-simplify: Simplify PI into PI 1547113854.237 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547113854.237 * [misc]backup-simplify: Simplify (* 2 0) into 0 1547113854.238 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547113854.238 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1547113854.239 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547113854.239 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1547113854.239 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1547113854.239 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1547113854.240 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547113854.240 * [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)))) 1547113854.241 * [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))))) 1547113854.241 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 1547113854.241 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1547113854.241 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547113854.241 * [misc]taylor: Taking taylor expansion of k in n 1547113854.241 * [misc]backup-simplify: Simplify k into k 1547113854.241 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547113854.241 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1547113854.241 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1547113854.241 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1547113854.241 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1547113854.241 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1547113854.242 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1547113854.242 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1547113854.242 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113854.242 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113854.242 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1547113854.242 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113854.242 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113854.242 * [misc]taylor: Taking taylor expansion of k in n 1547113854.242 * [misc]backup-simplify: Simplify k into k 1547113854.242 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1547113854.242 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1547113854.242 * [misc]taylor: Taking taylor expansion of 2 in n 1547113854.242 * [misc]backup-simplify: Simplify 2 into 2 1547113854.242 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547113854.242 * [misc]taylor: Taking taylor expansion of n in n 1547113854.242 * [misc]backup-simplify: Simplify 0 into 0 1547113854.242 * [misc]backup-simplify: Simplify 1 into 1 1547113854.242 * [misc]taylor: Taking taylor expansion of PI in n 1547113854.242 * [misc]backup-simplify: Simplify PI into PI 1547113854.242 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547113854.242 * [misc]backup-simplify: Simplify (* 2 0) into 0 1547113854.243 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547113854.244 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1547113854.244 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547113854.244 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1547113854.244 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1547113854.244 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1547113854.245 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547113854.246 * [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)))) 1547113854.246 * [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))))) 1547113854.247 * [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))) 1547113854.247 * [misc]taylor: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k))) in k 1547113854.247 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1547113854.247 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1547113854.247 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1547113854.247 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113854.247 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113854.247 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1547113854.247 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113854.247 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113854.247 * [misc]taylor: Taking taylor expansion of k in k 1547113854.247 * [misc]backup-simplify: Simplify 0 into 0 1547113854.247 * [misc]backup-simplify: Simplify 1 into 1 1547113854.247 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1547113854.247 * [misc]taylor: Taking taylor expansion of (log n) in k 1547113854.247 * [misc]taylor: Taking taylor expansion of n in k 1547113854.247 * [misc]backup-simplify: Simplify n into n 1547113854.247 * [misc]backup-simplify: Simplify (log n) into (log n) 1547113854.248 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1547113854.248 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1547113854.248 * [misc]taylor: Taking taylor expansion of 2 in k 1547113854.248 * [misc]backup-simplify: Simplify 2 into 2 1547113854.248 * [misc]taylor: Taking taylor expansion of PI in k 1547113854.248 * [misc]backup-simplify: Simplify PI into PI 1547113854.248 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547113854.248 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547113854.249 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1547113854.249 * [misc]backup-simplify: Simplify (- 0) into 0 1547113854.249 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1547113854.249 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547113854.250 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1547113854.250 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1547113854.250 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1547113854.250 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547113854.251 * [misc]taylor: Taking taylor expansion of k in k 1547113854.251 * [misc]backup-simplify: Simplify 0 into 0 1547113854.251 * [misc]backup-simplify: Simplify 1 into 1 1547113854.251 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547113854.251 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547113854.251 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1547113854.252 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) into 0 1547113854.252 * [misc]backup-simplify: Simplify 0 into 0 1547113854.253 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1547113854.254 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1547113854.257 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1547113854.257 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1547113854.257 * [misc]backup-simplify: Simplify (- 0) into 0 1547113854.257 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113854.258 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547113854.259 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1547113854.260 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1547113854.261 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 k)) 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))) into 0 1547113854.261 * [misc]taylor: Taking taylor expansion of 0 in k 1547113854.261 * [misc]backup-simplify: Simplify 0 into 0 1547113854.262 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1547113854.262 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1547113854.265 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1547113854.265 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113854.265 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1547113854.266 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1547113854.266 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1547113854.266 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1547113854.268 * [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))))))) 1547113854.270 * [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))))))) 1547113854.271 * [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))))))) 1547113854.273 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1547113854.274 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1547113854.279 * [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 1547113854.280 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1547113854.280 * [misc]backup-simplify: Simplify (- 0) into 0 1547113854.280 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113854.281 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547113854.282 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1547113854.284 * [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 1547113854.284 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1547113854.285 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 1547113854.286 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))))) into 0 1547113854.286 * [misc]taylor: Taking taylor expansion of 0 in k 1547113854.286 * [misc]backup-simplify: Simplify 0 into 0 1547113854.286 * [misc]backup-simplify: Simplify 0 into 0 1547113854.287 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1547113854.288 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1547113854.289 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1547113854.290 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1547113854.295 * [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 1547113854.296 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113854.296 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1547113854.296 * [misc]backup-simplify: Simplify (- 0) into 0 1547113854.296 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113854.297 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1547113854.300 * [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))))) 1547113854.304 * [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)))))))) 1547113854.307 * [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)))))))) 1547113854.309 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1547113854.311 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1547113854.319 * [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 1547113854.320 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 1547113854.320 * [misc]backup-simplify: Simplify (- 0) into 0 1547113854.320 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113854.321 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547113854.322 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 1547113854.325 * [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 1547113854.326 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1547113854.326 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 1547113854.327 * [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 1547113854.327 * [misc]taylor: Taking taylor expansion of 0 in k 1547113854.327 * [misc]backup-simplify: Simplify 0 into 0 1547113854.327 * [misc]backup-simplify: Simplify 0 into 0 1547113854.327 * [misc]backup-simplify: Simplify 0 into 0 1547113854.328 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113854.329 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1547113854.331 * [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 1547113854.333 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1547113854.341 * [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 1547113854.341 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113854.342 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1547113854.342 * [misc]backup-simplify: Simplify (- 0) into 0 1547113854.342 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113854.343 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 1547113854.347 * [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))))))) 1547113854.355 * [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)))))))))))))) 1547113854.362 * [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)))))))))))))) 1547113854.373 * [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)))))))))))))))))))))) 1547113854.373 * [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))))) 1547113854.373 * [misc]approximate: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0 1547113854.373 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 1547113854.373 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1547113854.373 * [misc]taylor: Taking taylor expansion of k in k 1547113854.374 * [misc]backup-simplify: Simplify 0 into 0 1547113854.374 * [misc]backup-simplify: Simplify 1 into 1 1547113854.374 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547113854.374 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1547113854.374 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1547113854.374 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1547113854.374 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1547113854.374 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1547113854.374 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113854.374 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113854.375 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1547113854.375 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113854.375 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113854.375 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547113854.375 * [misc]taylor: Taking taylor expansion of k in k 1547113854.375 * [misc]backup-simplify: Simplify 0 into 0 1547113854.375 * [misc]backup-simplify: Simplify 1 into 1 1547113854.375 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547113854.375 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1547113854.375 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1547113854.375 * [misc]taylor: Taking taylor expansion of 2 in k 1547113854.375 * [misc]backup-simplify: Simplify 2 into 2 1547113854.375 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1547113854.375 * [misc]taylor: Taking taylor expansion of PI in k 1547113854.375 * [misc]backup-simplify: Simplify PI into PI 1547113854.375 * [misc]taylor: Taking taylor expansion of n in k 1547113854.375 * [misc]backup-simplify: Simplify n into n 1547113854.375 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1547113854.375 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1547113854.375 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1547113854.375 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1547113854.376 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1547113854.376 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1547113854.376 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1547113854.376 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 1547113854.376 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1547113854.376 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1547113854.376 * [misc]taylor: Taking taylor expansion of k in n 1547113854.376 * [misc]backup-simplify: Simplify k into k 1547113854.376 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1547113854.376 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1547113854.376 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1547113854.376 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1547113854.376 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1547113854.376 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1547113854.377 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113854.377 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113854.377 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1547113854.377 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113854.377 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113854.377 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547113854.377 * [misc]taylor: Taking taylor expansion of k in n 1547113854.377 * [misc]backup-simplify: Simplify k into k 1547113854.377 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547113854.377 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1547113854.377 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1547113854.377 * [misc]taylor: Taking taylor expansion of 2 in n 1547113854.377 * [misc]backup-simplify: Simplify 2 into 2 1547113854.377 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547113854.377 * [misc]taylor: Taking taylor expansion of PI in n 1547113854.377 * [misc]backup-simplify: Simplify PI into PI 1547113854.377 * [misc]taylor: Taking taylor expansion of n in n 1547113854.377 * [misc]backup-simplify: Simplify 0 into 0 1547113854.377 * [misc]backup-simplify: Simplify 1 into 1 1547113854.377 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547113854.377 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547113854.378 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547113854.378 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1547113854.378 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1547113854.378 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1547113854.379 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547113854.380 * [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))) 1547113854.380 * [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)))) 1547113854.380 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1547113854.380 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1547113854.380 * [misc]taylor: Taking taylor expansion of k in n 1547113854.380 * [misc]backup-simplify: Simplify k into k 1547113854.380 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1547113854.380 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1547113854.380 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1547113854.380 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1547113854.381 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1547113854.381 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1547113854.381 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113854.381 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113854.381 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1547113854.381 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113854.381 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113854.381 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547113854.381 * [misc]taylor: Taking taylor expansion of k in n 1547113854.381 * [misc]backup-simplify: Simplify k into k 1547113854.381 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547113854.381 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1547113854.381 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1547113854.381 * [misc]taylor: Taking taylor expansion of 2 in n 1547113854.381 * [misc]backup-simplify: Simplify 2 into 2 1547113854.381 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547113854.381 * [misc]taylor: Taking taylor expansion of PI in n 1547113854.381 * [misc]backup-simplify: Simplify PI into PI 1547113854.381 * [misc]taylor: Taking taylor expansion of n in n 1547113854.381 * [misc]backup-simplify: Simplify 0 into 0 1547113854.381 * [misc]backup-simplify: Simplify 1 into 1 1547113854.381 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547113854.382 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547113854.382 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547113854.382 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1547113854.382 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1547113854.382 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1547113854.383 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547113854.384 * [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))) 1547113854.385 * [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)))) 1547113854.386 * [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)) 1547113854.386 * [misc]taylor: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) in k 1547113854.386 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1547113854.386 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1547113854.386 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1547113854.386 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113854.386 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113854.386 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1547113854.386 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113854.386 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113854.386 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547113854.386 * [misc]taylor: Taking taylor expansion of k in k 1547113854.387 * [misc]backup-simplify: Simplify 0 into 0 1547113854.387 * [misc]backup-simplify: Simplify 1 into 1 1547113854.387 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547113854.387 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1547113854.387 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1547113854.387 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1547113854.387 * [misc]taylor: Taking taylor expansion of 2 in k 1547113854.387 * [misc]backup-simplify: Simplify 2 into 2 1547113854.387 * [misc]taylor: Taking taylor expansion of PI in k 1547113854.387 * [misc]backup-simplify: Simplify PI into PI 1547113854.387 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547113854.388 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547113854.388 * [misc]taylor: Taking taylor expansion of (log n) in k 1547113854.388 * [misc]taylor: Taking taylor expansion of n in k 1547113854.388 * [misc]backup-simplify: Simplify n into n 1547113854.388 * [misc]backup-simplify: Simplify (log n) into (log n) 1547113854.388 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1547113854.388 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1547113854.388 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1547113854.388 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1547113854.389 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1547113854.389 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1547113854.390 * [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)))) 1547113854.390 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1547113854.390 * [misc]taylor: Taking taylor expansion of k in k 1547113854.390 * [misc]backup-simplify: Simplify 0 into 0 1547113854.390 * [misc]backup-simplify: Simplify 1 into 1 1547113854.390 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547113854.391 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1547113854.391 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) into 0 1547113854.392 * [misc]backup-simplify: Simplify 0 into 0 1547113854.393 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1547113854.394 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1547113854.396 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1547113854.397 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1547113854.397 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1547113854.397 * [misc]backup-simplify: Simplify (- 0) into 0 1547113854.397 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113854.398 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547113854.398 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1547113854.400 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1547113854.401 * [misc]backup-simplify: Simplify (+ (* (sqrt k) 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0 1547113854.401 * [misc]taylor: Taking taylor expansion of 0 in k 1547113854.401 * [misc]backup-simplify: Simplify 0 into 0 1547113854.401 * [misc]backup-simplify: Simplify 0 into 0 1547113854.402 * [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)))))) 1547113854.403 * [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)))))) 1547113854.404 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113854.405 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1547113854.410 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1547113854.410 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1547113854.411 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1547113854.411 * [misc]backup-simplify: Simplify (- 0) into 0 1547113854.411 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113854.412 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547113854.412 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1547113854.415 * [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 1547113854.416 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 1547113854.416 * [misc]backup-simplify: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0 1547113854.417 * [misc]taylor: Taking taylor expansion of 0 in k 1547113854.417 * [misc]backup-simplify: Simplify 0 into 0 1547113854.417 * [misc]backup-simplify: Simplify 0 into 0 1547113854.417 * [misc]backup-simplify: Simplify 0 into 0 1547113854.418 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1547113854.419 * [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)))))) 1547113854.419 * [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)))))) 1547113854.421 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113854.423 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1547113854.430 * [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 1547113854.431 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1547113854.431 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1547113854.431 * [misc]backup-simplify: Simplify (- 0) into 0 1547113854.432 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113854.432 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547113854.433 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1547113854.437 * [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 1547113854.437 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 1547113854.438 * [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 1547113854.438 * [misc]taylor: Taking taylor expansion of 0 in k 1547113854.438 * [misc]backup-simplify: Simplify 0 into 0 1547113854.438 * [misc]backup-simplify: Simplify 0 into 0 1547113854.438 * [misc]backup-simplify: Simplify 0 into 0 1547113854.438 * [misc]backup-simplify: Simplify 0 into 0 1547113854.439 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1547113854.440 * [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)))))) 1547113854.441 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 1547113854.444 * [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)))))))) 1547113854.444 * [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))) 1547113854.444 * [misc]approximate: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (n k) around 0 1547113854.444 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 1547113854.444 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1547113854.444 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1547113854.444 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1547113854.444 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1547113854.444 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1547113854.444 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113854.444 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113854.444 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547113854.444 * [misc]taylor: Taking taylor expansion of k in k 1547113854.445 * [misc]backup-simplify: Simplify 0 into 0 1547113854.445 * [misc]backup-simplify: Simplify 1 into 1 1547113854.445 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547113854.445 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113854.445 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113854.445 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1547113854.445 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1547113854.445 * [misc]taylor: Taking taylor expansion of -2 in k 1547113854.445 * [misc]backup-simplify: Simplify -2 into -2 1547113854.445 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1547113854.445 * [misc]taylor: Taking taylor expansion of PI in k 1547113854.445 * [misc]backup-simplify: Simplify PI into PI 1547113854.445 * [misc]taylor: Taking taylor expansion of n in k 1547113854.445 * [misc]backup-simplify: Simplify n into n 1547113854.445 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1547113854.445 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1547113854.445 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1547113854.445 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1547113854.446 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1547113854.446 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1547113854.446 * [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))) 1547113854.446 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1547113854.446 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1547113854.446 * [misc]taylor: Taking taylor expansion of -1 in k 1547113854.446 * [misc]backup-simplify: Simplify -1 into -1 1547113854.446 * [misc]taylor: Taking taylor expansion of k in k 1547113854.446 * [misc]backup-simplify: Simplify 0 into 0 1547113854.446 * [misc]backup-simplify: Simplify 1 into 1 1547113854.446 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1547113854.446 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547113854.447 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1547113854.447 * [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)))) 1547113854.447 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 1547113854.447 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1547113854.447 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1547113854.447 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1547113854.447 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1547113854.447 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1547113854.447 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113854.447 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113854.447 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547113854.447 * [misc]taylor: Taking taylor expansion of k in n 1547113854.448 * [misc]backup-simplify: Simplify k into k 1547113854.448 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547113854.448 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113854.448 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113854.448 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1547113854.448 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1547113854.448 * [misc]taylor: Taking taylor expansion of -2 in n 1547113854.448 * [misc]backup-simplify: Simplify -2 into -2 1547113854.448 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547113854.448 * [misc]taylor: Taking taylor expansion of PI in n 1547113854.448 * [misc]backup-simplify: Simplify PI into PI 1547113854.448 * [misc]taylor: Taking taylor expansion of n in n 1547113854.448 * [misc]backup-simplify: Simplify 0 into 0 1547113854.448 * [misc]backup-simplify: Simplify 1 into 1 1547113854.448 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547113854.448 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547113854.449 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1547113854.449 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1547113854.449 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1547113854.450 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547113854.450 * [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))) 1547113854.451 * [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)))) 1547113854.451 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1547113854.451 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1547113854.451 * [misc]taylor: Taking taylor expansion of -1 in n 1547113854.451 * [misc]backup-simplify: Simplify -1 into -1 1547113854.451 * [misc]taylor: Taking taylor expansion of k in n 1547113854.451 * [misc]backup-simplify: Simplify k into k 1547113854.451 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1547113854.451 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1547113854.451 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1547113854.451 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1547113854.452 * [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))) 1547113854.452 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 1547113854.452 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1547113854.452 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1547113854.452 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1547113854.452 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1547113854.452 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1547113854.452 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113854.452 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113854.452 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547113854.452 * [misc]taylor: Taking taylor expansion of k in n 1547113854.452 * [misc]backup-simplify: Simplify k into k 1547113854.453 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547113854.453 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113854.453 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113854.453 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1547113854.453 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1547113854.453 * [misc]taylor: Taking taylor expansion of -2 in n 1547113854.453 * [misc]backup-simplify: Simplify -2 into -2 1547113854.453 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547113854.453 * [misc]taylor: Taking taylor expansion of PI in n 1547113854.453 * [misc]backup-simplify: Simplify PI into PI 1547113854.453 * [misc]taylor: Taking taylor expansion of n in n 1547113854.453 * [misc]backup-simplify: Simplify 0 into 0 1547113854.453 * [misc]backup-simplify: Simplify 1 into 1 1547113854.453 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547113854.453 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547113854.454 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1547113854.454 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1547113854.454 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1547113854.455 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547113854.455 * [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))) 1547113854.456 * [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)))) 1547113854.456 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1547113854.456 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1547113854.456 * [misc]taylor: Taking taylor expansion of -1 in n 1547113854.456 * [misc]backup-simplify: Simplify -1 into -1 1547113854.456 * [misc]taylor: Taking taylor expansion of k in n 1547113854.456 * [misc]backup-simplify: Simplify k into k 1547113854.456 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1547113854.456 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1547113854.456 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1547113854.456 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1547113854.457 * [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))) 1547113854.457 * [misc]taylor: Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) in k 1547113854.457 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1547113854.457 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1547113854.457 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1547113854.457 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1547113854.457 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113854.457 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113854.457 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547113854.457 * [misc]taylor: Taking taylor expansion of k in k 1547113854.457 * [misc]backup-simplify: Simplify 0 into 0 1547113854.457 * [misc]backup-simplify: Simplify 1 into 1 1547113854.458 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547113854.458 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113854.458 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113854.458 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1547113854.458 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1547113854.458 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1547113854.458 * [misc]taylor: Taking taylor expansion of -2 in k 1547113854.458 * [misc]backup-simplify: Simplify -2 into -2 1547113854.458 * [misc]taylor: Taking taylor expansion of PI in k 1547113854.458 * [misc]backup-simplify: Simplify PI into PI 1547113854.458 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547113854.459 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1547113854.459 * [misc]taylor: Taking taylor expansion of (log n) in k 1547113854.459 * [misc]taylor: Taking taylor expansion of n in k 1547113854.459 * [misc]backup-simplify: Simplify n into n 1547113854.459 * [misc]backup-simplify: Simplify (log n) into (log n) 1547113854.459 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1547113854.459 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1547113854.459 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1547113854.460 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1547113854.460 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1547113854.461 * [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)))) 1547113854.461 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1547113854.461 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1547113854.461 * [misc]taylor: Taking taylor expansion of -1 in k 1547113854.461 * [misc]backup-simplify: Simplify -1 into -1 1547113854.461 * [misc]taylor: Taking taylor expansion of k in k 1547113854.461 * [misc]backup-simplify: Simplify 0 into 0 1547113854.461 * [misc]backup-simplify: Simplify 1 into 1 1547113854.461 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1547113854.461 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547113854.462 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1547113854.462 * [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))))) 1547113854.463 * [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))))) 1547113854.464 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1547113854.465 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1547113854.467 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1547113854.467 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1547113854.468 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1547113854.468 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113854.468 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547113854.469 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1547113854.470 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1547113854.471 * [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 1547113854.471 * [misc]taylor: Taking taylor expansion of 0 in k 1547113854.471 * [misc]backup-simplify: Simplify 0 into 0 1547113854.471 * [misc]backup-simplify: Simplify 0 into 0 1547113854.472 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1547113854.473 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1547113854.474 * [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)))))) 1547113854.474 * [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)))))) 1547113854.476 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113854.477 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1547113854.482 * [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 1547113854.482 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1547113854.482 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1547113854.482 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113854.483 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547113854.484 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1547113854.486 * [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 1547113854.487 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1547113854.487 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 1547113854.488 * [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 1547113854.488 * [misc]taylor: Taking taylor expansion of 0 in k 1547113854.488 * [misc]backup-simplify: Simplify 0 into 0 1547113854.488 * [misc]backup-simplify: Simplify 0 into 0 1547113854.488 * [misc]backup-simplify: Simplify 0 into 0 1547113854.489 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113854.490 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1547113854.492 * [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)))))) 1547113854.492 * [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)))))) 1547113854.495 * [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))))))))))) 1547113854.495 * * * [misc]progress: simplifying candidates 1547113854.495 * * * * [misc]progress: [ 1 / 83 ] simplifiying candidate # 1547113854.495 * * * * [misc]progress: [ 2 / 83 ] simplifiying candidate # 1547113854.496 * * * * [misc]progress: [ 3 / 83 ] simplifiying candidate # 1547113854.496 * [enter]simplify: Simplifying (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) 1547113854.496 * * [misc]simplify: iters left: 6 (11 enodes) 1547113854.500 * * [misc]simplify: iters left: 5 (21 enodes) 1547113854.508 * * [misc]simplify: iters left: 4 (47 enodes) 1547113854.526 * * [misc]simplify: iters left: 3 (113 enodes) 1547113854.589 * * [misc]simplify: iters left: 2 (328 enodes) 1547113854.870 * [exit]simplify: Simplified to (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) 1547113854.870 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (exp (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI)))) (sqrt k))) 1547113854.870 * * * * [misc]progress: [ 4 / 83 ] simplifiying candidate # 1547113854.871 * * * * [misc]progress: [ 5 / 83 ] simplifiying candidate # 1547113854.871 * [enter]simplify: Simplifying (* PI (* n 2)) 1547113854.871 * * [misc]simplify: iters left: 4 (5 enodes) 1547113854.872 * * [misc]simplify: iters left: 3 (9 enodes) 1547113854.873 * * [misc]simplify: iters left: 2 (15 enodes) 1547113854.876 * * [misc]simplify: iters left: 1 (17 enodes) 1547113854.878 * [exit]simplify: Simplified to (* (* 2 n) PI) 1547113854.878 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* 2 n) PI) (* 1 (- 1/2 (/ k 2)))) (sqrt k))) 1547113854.878 * * * * [misc]progress: [ 6 / 83 ] simplifiying candidate # 1547113854.878 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (/ k 2)) 1547113854.878 * * [misc]simplify: iters left: 5 (8 enodes) 1547113854.880 * * [misc]simplify: iters left: 4 (12 enodes) 1547113854.882 * * [misc]simplify: iters left: 3 (18 enodes) 1547113854.885 * * [misc]simplify: iters left: 2 (20 enodes) 1547113854.888 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ k 2)) 1547113854.888 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (/ (pow (* PI (* n 2)) 1/2) (pow (* (* 2 n) PI) (/ k 2))) (sqrt k))) 1547113854.888 * * * * [misc]progress: [ 7 / 83 ] simplifiying candidate # 1547113854.888 * [enter]simplify: Simplifying (cbrt (- 1/2 (/ k 2))) 1547113854.888 * * [misc]simplify: iters left: 5 (6 enodes) 1547113854.889 * * [misc]simplify: iters left: 4 (8 enodes) 1547113854.891 * * [misc]simplify: iters left: 3 (11 enodes) 1547113854.893 * [exit]simplify: Simplified to (cbrt (- 1/2 (/ k 2))) 1547113854.893 * [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))) 1547113854.893 * * * * [misc]progress: [ 8 / 83 ] simplifiying candidate # 1547113854.893 * [enter]simplify: Simplifying (sqrt (- 1/2 (/ k 2))) 1547113854.893 * * [misc]simplify: iters left: 5 (6 enodes) 1547113854.894 * * [misc]simplify: iters left: 4 (8 enodes) 1547113854.895 * * [misc]simplify: iters left: 3 (11 enodes) 1547113854.897 * [exit]simplify: Simplified to (sqrt (- 1/2 (/ k 2))) 1547113854.897 * [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))) 1547113854.897 * * * * [misc]progress: [ 9 / 83 ] simplifiying candidate # 1547113854.897 * [enter]simplify: Simplifying (- 1/2 (/ k 2)) 1547113854.897 * * [misc]simplify: iters left: 4 (5 enodes) 1547113854.898 * * [misc]simplify: iters left: 3 (7 enodes) 1547113854.900 * * [misc]simplify: iters left: 2 (10 enodes) 1547113854.901 * [exit]simplify: Simplified to (- 1/2 (/ k 2)) 1547113854.901 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (pow (pow (* PI (* n 2)) 1) (- 1/2 (/ k 2))) (sqrt k))) 1547113854.901 * * * * [misc]progress: [ 10 / 83 ] simplifiying candidate # 1547113854.902 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1547113854.902 * * [misc]simplify: iters left: 5 (9 enodes) 1547113854.904 * * [misc]simplify: iters left: 4 (15 enodes) 1547113854.908 * * [misc]simplify: iters left: 3 (21 enodes) 1547113854.915 * * [misc]simplify: iters left: 2 (22 enodes) 1547113854.921 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1547113854.921 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2)))) (sqrt k))) 1547113854.921 * * * * [misc]progress: [ 11 / 83 ] simplifiying candidate # 1547113854.921 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1547113854.921 * * [misc]simplify: iters left: 5 (9 enodes) 1547113854.924 * * [misc]simplify: iters left: 4 (15 enodes) 1547113854.929 * * [misc]simplify: iters left: 3 (21 enodes) 1547113854.935 * * [misc]simplify: iters left: 2 (22 enodes) 1547113854.941 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1547113854.941 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2)))) (sqrt k))) 1547113854.941 * * * * [misc]progress: [ 12 / 83 ] simplifiying candidate # 1547113854.941 * [enter]simplify: Simplifying (pow PI (- 1/2 (/ k 2))) 1547113854.942 * * [misc]simplify: iters left: 5 (7 enodes) 1547113854.944 * * [misc]simplify: iters left: 4 (9 enodes) 1547113854.950 * * [misc]simplify: iters left: 3 (12 enodes) 1547113854.953 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1547113854.953 * [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))) 1547113854.953 * * * * [misc]progress: [ 13 / 83 ] simplifiying candidate # 1547113854.954 * * * * [misc]progress: [ 14 / 83 ] simplifiying candidate # 1547113854.954 * * * * [misc]progress: [ 15 / 83 ] simplifiying candidate # 1547113854.954 * * * * [misc]progress: [ 16 / 83 ] simplifiying candidate # 1547113854.954 * * * * [misc]progress: [ 17 / 83 ] simplifiying candidate # 1547113854.954 * * * * [misc]progress: [ 18 / 83 ] simplifiying candidate # 1547113854.954 * * * * [misc]progress: [ 19 / 83 ] simplifiying candidate # 1547113854.954 * * * * [misc]progress: [ 20 / 83 ] simplifiying candidate # 1547113854.954 * * * * [misc]progress: [ 21 / 83 ] simplifiying candidate # 1547113854.954 * * * * [misc]progress: [ 22 / 83 ] simplifiying candidate # 1547113854.954 * * * * [misc]progress: [ 23 / 83 ] simplifiying candidate # 1547113854.954 * * * * [misc]progress: [ 24 / 83 ] simplifiying candidate # 1547113854.954 * * * * [misc]progress: [ 25 / 83 ] simplifiying candidate # 1547113854.954 * * * * [misc]progress: [ 26 / 83 ] simplifiying candidate # 1547113854.954 * * * * [misc]progress: [ 27 / 83 ] simplifiying candidate # 1547113854.954 * * * * [misc]progress: [ 28 / 83 ] simplifiying candidate # 1547113854.954 * * * * [misc]progress: [ 29 / 83 ] simplifiying candidate # 1547113854.955 * * * * [misc]progress: [ 30 / 83 ] simplifiying candidate # 1547113854.955 * * * * [misc]progress: [ 31 / 83 ] simplifiying candidate # 1547113854.955 * * * * [misc]progress: [ 32 / 83 ] simplifiying candidate # 1547113854.955 * * * * [misc]progress: [ 33 / 83 ] simplifiying candidate # 1547113854.955 * * * * [misc]progress: [ 34 / 83 ] simplifiying candidate # 1547113854.955 * [enter]simplify: Simplifying (- (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) (log (sqrt k))) 1547113854.955 * * [misc]simplify: iters left: 6 (14 enodes) 1547113854.960 * * [misc]simplify: iters left: 5 (27 enodes) 1547113854.970 * * [misc]simplify: iters left: 4 (55 enodes) 1547113854.987 * * [misc]simplify: iters left: 3 (144 enodes) 1547113855.066 * [exit]simplify: Simplified to (fma (- 1/2 (/ k 2)) (log (* (* 2 n) PI)) (- (log (sqrt k)))) 1547113855.066 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (- 1/2 (/ k 2)) (log (* (* 2 n) PI)) (- (log (sqrt k)))))) 1547113855.066 * * * * [misc]progress: [ 35 / 83 ] simplifiying candidate # 1547113855.066 * [enter]simplify: Simplifying (- (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) (log (sqrt k))) 1547113855.066 * * [misc]simplify: iters left: 6 (14 enodes) 1547113855.069 * * [misc]simplify: iters left: 5 (27 enodes) 1547113855.075 * * [misc]simplify: iters left: 4 (55 enodes) 1547113855.091 * * [misc]simplify: iters left: 3 (144 enodes) 1547113855.170 * [exit]simplify: Simplified to (fma (- 1/2 (/ k 2)) (log (* (* 2 n) PI)) (- (log (sqrt k)))) 1547113855.170 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (- 1/2 (/ k 2)) (log (* (* 2 n) PI)) (- (log (sqrt k)))))) 1547113855.171 * * * * [misc]progress: [ 36 / 83 ] simplifiying candidate # 1547113855.171 * [enter]simplify: Simplifying (- (log (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (log (sqrt k))) 1547113855.171 * * [misc]simplify: iters left: 6 (14 enodes) 1547113855.176 * * [misc]simplify: iters left: 5 (24 enodes) 1547113855.184 * * [misc]simplify: iters left: 4 (43 enodes) 1547113855.198 * * [misc]simplify: iters left: 3 (73 enodes) 1547113855.234 * * [misc]simplify: iters left: 2 (220 enodes) 1547113855.432 * [exit]simplify: Simplified to (fma (log (* (* PI 2) n)) (- 1/2 (/ k 2)) (- (log (sqrt k)))) 1547113855.432 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (log (* (* PI 2) n)) (- 1/2 (/ k 2)) (- (log (sqrt k)))))) 1547113855.432 * * * * [misc]progress: [ 37 / 83 ] simplifiying candidate # 1547113855.432 * * * * [misc]progress: [ 38 / 83 ] simplifiying candidate # 1547113855.432 * * * * [misc]progress: [ 39 / 83 ] simplifiying candidate # 1547113855.432 * [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))) 1547113855.433 * * [misc]simplify: iters left: 6 (16 enodes) 1547113855.439 * * [misc]simplify: iters left: 5 (31 enodes) 1547113855.451 * * [misc]simplify: iters left: 4 (67 enodes) 1547113855.478 * * [misc]simplify: iters left: 3 (124 enodes) 1547113855.519 * * [misc]simplify: iters left: 2 (195 enodes) 1547113855.567 * * [misc]simplify: iters left: 1 (309 enodes) 1547113855.693 * [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)))) 1547113855.694 * [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)))))) 1547113855.694 * * * * [misc]progress: [ 40 / 83 ] simplifiying candidate # 1547113855.694 * * * * [misc]progress: [ 41 / 83 ] simplifiying candidate # 1547113855.694 * * * * [misc]progress: [ 42 / 83 ] simplifiying candidate # 1547113855.694 * * * * [misc]progress: [ 43 / 83 ] simplifiying candidate # 1547113855.694 * * * * [misc]progress: [ 44 / 83 ] simplifiying candidate # 1547113855.694 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1547113855.694 * * [misc]simplify: iters left: 6 (12 enodes) 1547113855.696 * * [misc]simplify: iters left: 5 (19 enodes) 1547113855.699 * * [misc]simplify: iters left: 4 (25 enodes) 1547113855.704 * * [misc]simplify: iters left: 3 (26 enodes) 1547113855.707 * [exit]simplify: Simplified to (/ (sqrt (* (* 2 n) PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1547113855.707 * [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))))) 1547113855.708 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (sqrt k))) 1547113855.708 * * [misc]simplify: iters left: 6 (12 enodes) 1547113855.710 * * [misc]simplify: iters left: 5 (18 enodes) 1547113855.716 * * [misc]simplify: iters left: 4 (24 enodes) 1547113855.723 * * [misc]simplify: iters left: 3 (25 enodes) 1547113855.730 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt k))) 1547113855.730 * [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))))) 1547113855.730 * * * * [misc]progress: [ 45 / 83 ] simplifiying candidate # 1547113855.731 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (sqrt (sqrt k))) 1547113855.731 * * [misc]simplify: iters left: 6 (11 enodes) 1547113855.734 * * [misc]simplify: iters left: 5 (16 enodes) 1547113855.739 * * [misc]simplify: iters left: 4 (22 enodes) 1547113855.746 * * [misc]simplify: iters left: 3 (24 enodes) 1547113855.753 * [exit]simplify: Simplified to (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) 1547113855.753 * [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))))) 1547113855.753 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k))) 1547113855.754 * * [misc]simplify: iters left: 6 (12 enodes) 1547113855.758 * * [misc]simplify: iters left: 5 (18 enodes) 1547113855.764 * * [misc]simplify: iters left: 4 (24 enodes) 1547113855.771 * * [misc]simplify: iters left: 3 (25 enodes) 1547113855.778 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k))) 1547113855.778 * [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))))) 1547113855.778 * * * * [misc]progress: [ 46 / 83 ] simplifiying candidate # 1547113855.778 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) 1) 1547113855.778 * * [misc]simplify: iters left: 6 (9 enodes) 1547113855.782 * * [misc]simplify: iters left: 5 (16 enodes) 1547113855.787 * * [misc]simplify: iters left: 4 (24 enodes) 1547113855.793 * * [misc]simplify: iters left: 3 (26 enodes) 1547113855.799 * [exit]simplify: Simplified to (sqrt (* (* PI 2) n)) 1547113855.799 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) 1547113855.799 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)) 1547113855.800 * * [misc]simplify: iters left: 6 (11 enodes) 1547113855.803 * * [misc]simplify: iters left: 5 (17 enodes) 1547113855.809 * * [misc]simplify: iters left: 4 (23 enodes) 1547113855.816 * * [misc]simplify: iters left: 3 (24 enodes) 1547113855.823 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)) 1547113855.823 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)))) 1547113855.823 * * * * [misc]progress: [ 47 / 83 ] simplifiying candidate # 1547113855.823 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1547113855.823 * * [misc]simplify: iters left: 6 (12 enodes) 1547113855.827 * * [misc]simplify: iters left: 5 (19 enodes) 1547113855.834 * * [misc]simplify: iters left: 4 (25 enodes) 1547113855.838 * * [misc]simplify: iters left: 3 (26 enodes) 1547113855.842 * [exit]simplify: Simplified to (/ (sqrt (* (* 2 n) PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1547113855.842 * [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))))) 1547113855.843 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (sqrt k))) 1547113855.843 * * [misc]simplify: iters left: 6 (12 enodes) 1547113855.845 * * [misc]simplify: iters left: 5 (18 enodes) 1547113855.848 * * [misc]simplify: iters left: 4 (24 enodes) 1547113855.852 * * [misc]simplify: iters left: 3 (25 enodes) 1547113855.856 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt k))) 1547113855.856 * [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))))) 1547113855.856 * * * * [misc]progress: [ 48 / 83 ] simplifiying candidate # 1547113855.856 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (sqrt (sqrt k))) 1547113855.856 * * [misc]simplify: iters left: 6 (11 enodes) 1547113855.859 * * [misc]simplify: iters left: 5 (16 enodes) 1547113855.862 * * [misc]simplify: iters left: 4 (22 enodes) 1547113855.865 * * [misc]simplify: iters left: 3 (24 enodes) 1547113855.869 * [exit]simplify: Simplified to (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) 1547113855.869 * [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))))) 1547113855.869 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k))) 1547113855.869 * * [misc]simplify: iters left: 6 (12 enodes) 1547113855.871 * * [misc]simplify: iters left: 5 (18 enodes) 1547113855.874 * * [misc]simplify: iters left: 4 (24 enodes) 1547113855.878 * * [misc]simplify: iters left: 3 (25 enodes) 1547113855.882 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k))) 1547113855.882 * [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))))) 1547113855.882 * * * * [misc]progress: [ 49 / 83 ] simplifiying candidate # 1547113855.882 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) 1) 1547113855.882 * * [misc]simplify: iters left: 6 (9 enodes) 1547113855.884 * * [misc]simplify: iters left: 5 (16 enodes) 1547113855.887 * * [misc]simplify: iters left: 4 (24 enodes) 1547113855.892 * * [misc]simplify: iters left: 3 (26 enodes) 1547113855.898 * [exit]simplify: Simplified to (sqrt (* (* PI 2) n)) 1547113855.898 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) 1547113855.899 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)) 1547113855.899 * * [misc]simplify: iters left: 6 (11 enodes) 1547113855.902 * * [misc]simplify: iters left: 5 (17 enodes) 1547113855.908 * * [misc]simplify: iters left: 4 (23 enodes) 1547113855.915 * * [misc]simplify: iters left: 3 (24 enodes) 1547113855.922 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)) 1547113855.922 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)))) 1547113855.922 * * * * [misc]progress: [ 50 / 83 ] simplifiying candidate # 1547113855.922 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1547113855.922 * * [misc]simplify: iters left: 6 (11 enodes) 1547113855.926 * * [misc]simplify: iters left: 5 (15 enodes) 1547113855.931 * * [misc]simplify: iters left: 4 (18 enodes) 1547113855.937 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1547113855.937 * [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))))) 1547113855.937 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1547113855.937 * * [misc]simplify: iters left: 6 (11 enodes) 1547113855.940 * * [misc]simplify: iters left: 5 (14 enodes) 1547113855.943 * * [misc]simplify: iters left: 4 (17 enodes) 1547113855.945 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1547113855.946 * [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))))) 1547113855.946 * * * * [misc]progress: [ 51 / 83 ] simplifiying candidate # 1547113855.946 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1547113855.946 * * [misc]simplify: iters left: 6 (10 enodes) 1547113855.948 * * [misc]simplify: iters left: 5 (12 enodes) 1547113855.950 * * [misc]simplify: iters left: 4 (15 enodes) 1547113855.952 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1547113855.952 * [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))))) 1547113855.952 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1547113855.952 * * [misc]simplify: iters left: 6 (11 enodes) 1547113855.954 * * [misc]simplify: iters left: 5 (14 enodes) 1547113855.957 * * [misc]simplify: iters left: 4 (17 enodes) 1547113855.960 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1547113855.960 * [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))))) 1547113855.960 * * * * [misc]progress: [ 52 / 83 ] simplifiying candidate # 1547113855.960 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) 1) 1547113855.960 * * [misc]simplify: iters left: 6 (9 enodes) 1547113855.962 * * [misc]simplify: iters left: 5 (13 enodes) 1547113855.964 * * [misc]simplify: iters left: 4 (18 enodes) 1547113855.967 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1547113855.967 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1547113855.967 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)) 1547113855.967 * * [misc]simplify: iters left: 6 (10 enodes) 1547113855.970 * * [misc]simplify: iters left: 5 (13 enodes) 1547113855.976 * * [misc]simplify: iters left: 4 (16 enodes) 1547113855.981 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)) 1547113855.981 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1547113855.981 * * * * [misc]progress: [ 53 / 83 ] simplifiying candidate # 1547113855.982 * [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)))) 1547113855.982 * * [misc]simplify: iters left: 6 (16 enodes) 1547113855.986 * * [misc]simplify: iters left: 5 (28 enodes) 1547113855.991 * * [misc]simplify: iters left: 4 (46 enodes) 1547113855.998 * * [misc]simplify: iters left: 3 (50 enodes) 1547113856.006 * * [misc]simplify: iters left: 2 (53 enodes) 1547113856.015 * [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)))) 1547113856.016 * [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))))) 1547113856.016 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1547113856.016 * * [misc]simplify: iters left: 6 (14 enodes) 1547113856.021 * * [misc]simplify: iters left: 5 (20 enodes) 1547113856.028 * * [misc]simplify: iters left: 4 (29 enodes) 1547113856.036 * * [misc]simplify: iters left: 3 (30 enodes) 1547113856.044 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1547113856.044 * [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))))) 1547113856.044 * * * * [misc]progress: [ 54 / 83 ] simplifiying candidate # 1547113856.045 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) 1547113856.045 * * [misc]simplify: iters left: 6 (15 enodes) 1547113856.050 * * [misc]simplify: iters left: 5 (23 enodes) 1547113856.058 * * [misc]simplify: iters left: 4 (34 enodes) 1547113856.068 * * [misc]simplify: iters left: 3 (37 enodes) 1547113856.077 * [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)))))) 1547113856.077 * [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))))) 1547113856.077 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1547113856.077 * * [misc]simplify: iters left: 6 (14 enodes) 1547113856.080 * * [misc]simplify: iters left: 5 (20 enodes) 1547113856.083 * * [misc]simplify: iters left: 4 (29 enodes) 1547113856.088 * * [misc]simplify: iters left: 3 (30 enodes) 1547113856.092 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1547113856.092 * [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))))) 1547113856.092 * * * * [misc]progress: [ 55 / 83 ] simplifiying candidate # 1547113856.093 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1) 1547113856.093 * * [misc]simplify: iters left: 6 (14 enodes) 1547113856.096 * * [misc]simplify: iters left: 5 (24 enodes) 1547113856.101 * * [misc]simplify: iters left: 4 (39 enodes) 1547113856.107 * * [misc]simplify: iters left: 3 (54 enodes) 1547113856.115 * * [misc]simplify: iters left: 2 (80 enodes) 1547113856.130 * [exit]simplify: Simplified to (* (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))) 1547113856.130 * [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)))) 1547113856.130 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt k)) 1547113856.130 * * [misc]simplify: iters left: 6 (13 enodes) 1547113856.133 * * [misc]simplify: iters left: 5 (19 enodes) 1547113856.137 * * [misc]simplify: iters left: 4 (28 enodes) 1547113856.141 * * [misc]simplify: iters left: 3 (30 enodes) 1547113856.146 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt k)) 1547113856.146 * [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)))) 1547113856.146 * * * * [misc]progress: [ 56 / 83 ] simplifiying candidate # 1547113856.146 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1547113856.146 * * [misc]simplify: iters left: 6 (15 enodes) 1547113856.149 * * [misc]simplify: iters left: 5 (23 enodes) 1547113856.153 * * [misc]simplify: iters left: 4 (32 enodes) 1547113856.159 * * [misc]simplify: iters left: 3 (34 enodes) 1547113856.168 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1547113856.168 * [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))))) 1547113856.168 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1547113856.168 * * [misc]simplify: iters left: 6 (14 enodes) 1547113856.173 * * [misc]simplify: iters left: 5 (20 enodes) 1547113856.180 * * [misc]simplify: iters left: 4 (29 enodes) 1547113856.189 * * [misc]simplify: iters left: 3 (30 enodes) 1547113856.198 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1547113856.198 * [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))))) 1547113856.198 * * * * [misc]progress: [ 57 / 83 ] simplifiying candidate # 1547113856.198 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1547113856.198 * * [misc]simplify: iters left: 6 (14 enodes) 1547113856.203 * * [misc]simplify: iters left: 5 (20 enodes) 1547113856.210 * * [misc]simplify: iters left: 4 (29 enodes) 1547113856.219 * * [misc]simplify: iters left: 3 (30 enodes) 1547113856.227 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1547113856.228 * [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))))) 1547113856.228 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1547113856.228 * * [misc]simplify: iters left: 6 (14 enodes) 1547113856.233 * * [misc]simplify: iters left: 5 (20 enodes) 1547113856.240 * * [misc]simplify: iters left: 4 (29 enodes) 1547113856.248 * * [misc]simplify: iters left: 3 (30 enodes) 1547113856.257 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1547113856.257 * [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))))) 1547113856.257 * * * * [misc]progress: [ 58 / 83 ] simplifiying candidate # 1547113856.258 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1) 1547113856.258 * * [misc]simplify: iters left: 6 (13 enodes) 1547113856.262 * * [misc]simplify: iters left: 5 (21 enodes) 1547113856.270 * * [misc]simplify: iters left: 4 (32 enodes) 1547113856.278 * * [misc]simplify: iters left: 3 (33 enodes) 1547113856.286 * [exit]simplify: Simplified to (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) 1547113856.286 * [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)))) 1547113856.287 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt k)) 1547113856.287 * * [misc]simplify: iters left: 6 (13 enodes) 1547113856.292 * * [misc]simplify: iters left: 5 (19 enodes) 1547113856.298 * * [misc]simplify: iters left: 4 (28 enodes) 1547113856.307 * * [misc]simplify: iters left: 3 (30 enodes) 1547113856.315 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt k)) 1547113856.315 * [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)))) 1547113856.316 * * * * [misc]progress: [ 59 / 83 ] simplifiying candidate # 1547113856.316 * [enter]simplify: Simplifying (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1547113856.316 * * [misc]simplify: iters left: 6 (6 enodes) 1547113856.318 * * [misc]simplify: iters left: 5 (10 enodes) 1547113856.321 * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) 1547113856.321 * [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))))) 1547113856.322 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1547113856.322 * * [misc]simplify: iters left: 6 (13 enodes) 1547113856.326 * * [misc]simplify: iters left: 5 (19 enodes) 1547113856.333 * * [misc]simplify: iters left: 4 (28 enodes) 1547113856.341 * * [misc]simplify: iters left: 3 (30 enodes) 1547113856.350 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1547113856.350 * [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))))) 1547113856.350 * * * * [misc]progress: [ 60 / 83 ] simplifiying candidate # 1547113856.351 * [enter]simplify: Simplifying (/ 1 (sqrt (sqrt k))) 1547113856.351 * * [misc]simplify: iters left: 4 (5 enodes) 1547113856.352 * * [misc]simplify: iters left: 3 (7 enodes) 1547113856.354 * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt k))) 1547113856.354 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) 1547113856.355 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1547113856.355 * * [misc]simplify: iters left: 6 (13 enodes) 1547113856.359 * * [misc]simplify: iters left: 5 (19 enodes) 1547113856.366 * * [misc]simplify: iters left: 4 (28 enodes) 1547113856.374 * * [misc]simplify: iters left: 3 (30 enodes) 1547113856.384 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1547113856.384 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) 1547113856.384 * * * * [misc]progress: [ 61 / 83 ] simplifiying candidate # 1547113856.385 * [enter]simplify: Simplifying (/ 1 1) 1547113856.385 * * [misc]simplify: iters left: 2 (2 enodes) 1547113856.385 * * [misc]simplify: iters left: 1 (4 enodes) 1547113856.386 * [exit]simplify: Simplified to 1 1547113856.386 * [misc]simplify: Simplified (2 1) to (λ (k n) (* 1 (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))) 1547113856.386 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)) 1547113856.387 * * [misc]simplify: iters left: 6 (12 enodes) 1547113856.391 * * [misc]simplify: iters left: 5 (18 enodes) 1547113856.397 * * [misc]simplify: iters left: 4 (27 enodes) 1547113856.405 * * [misc]simplify: iters left: 3 (29 enodes) 1547113856.413 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k)) 1547113856.413 * [misc]simplify: Simplified (2 2) to (λ (k n) (* 1 (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k)))) 1547113856.414 * * * * [misc]progress: [ 62 / 83 ] simplifiying candidate # 1547113856.414 * * * * [misc]progress: [ 63 / 83 ] simplifiying candidate # 1547113856.414 * * * * [misc]progress: [ 64 / 83 ] simplifiying candidate # 1547113856.414 * * * * [misc]progress: [ 65 / 83 ] simplifiying candidate # 1547113856.414 * [enter]simplify: Simplifying (cbrt (sqrt k)) 1547113856.414 * * [misc]simplify: iters left: 2 (3 enodes) 1547113856.415 * [exit]simplify: Simplified to (cbrt (sqrt k)) 1547113856.415 * [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)))) 1547113856.415 * * * * [misc]progress: [ 66 / 83 ] simplifiying candidate # 1547113856.415 * [enter]simplify: Simplifying (sqrt (sqrt k)) 1547113856.415 * * [misc]simplify: iters left: 2 (3 enodes) 1547113856.416 * [exit]simplify: Simplified to (sqrt (sqrt k)) 1547113856.417 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k)))) 1547113856.417 * * * * [misc]progress: [ 67 / 83 ] simplifiying candidate # 1547113856.417 * [enter]simplify: Simplifying (sqrt k) 1547113856.417 * * [misc]simplify: iters left: 1 (2 enodes) 1547113856.418 * [exit]simplify: Simplified to (sqrt k) 1547113856.418 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) 1) (sqrt k))) 1547113856.418 * * * * [misc]progress: [ 68 / 83 ] simplifiying candidate # 1547113856.418 * [enter]simplify: Simplifying (pow (* PI (* n 2)) 1/2) 1547113856.418 * * [misc]simplify: iters left: 5 (7 enodes) 1547113856.421 * * [misc]simplify: iters left: 4 (12 enodes) 1547113856.424 * * [misc]simplify: iters left: 3 (18 enodes) 1547113856.430 * * [misc]simplify: iters left: 2 (20 enodes) 1547113856.435 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1547113856.435 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2)))))) 1547113856.435 * * * * [misc]progress: [ 69 / 83 ] simplifiying candidate # 1547113856.436 * [enter]simplify: Simplifying (pow (* PI (* n 2)) 1/2) 1547113856.436 * * [misc]simplify: iters left: 5 (7 enodes) 1547113856.438 * * [misc]simplify: iters left: 4 (12 enodes) 1547113856.442 * * [misc]simplify: iters left: 3 (18 enodes) 1547113856.447 * * [misc]simplify: iters left: 2 (20 enodes) 1547113856.452 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1547113856.452 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2)))))) 1547113856.452 * * * * [misc]progress: [ 70 / 83 ] simplifiying candidate # 1547113856.453 * [enter]simplify: Simplifying (pow PI (- 1/2 (/ k 2))) 1547113856.453 * * [misc]simplify: iters left: 5 (7 enodes) 1547113856.456 * * [misc]simplify: iters left: 4 (9 enodes) 1547113856.459 * * [misc]simplify: iters left: 3 (12 enodes) 1547113856.462 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1547113856.462 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (pow PI (- 1/2 (/ k 2))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2)))))) 1547113856.463 * * * * [misc]progress: [ 71 / 83 ] simplifiying candidate # 1547113856.463 * [enter]simplify: Simplifying (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1547113856.463 * * [misc]simplify: iters left: 6 (12 enodes) 1547113856.467 * * [misc]simplify: iters left: 5 (18 enodes) 1547113856.473 * * [misc]simplify: iters left: 4 (27 enodes) 1547113856.478 * * [misc]simplify: iters left: 3 (29 enodes) 1547113856.483 * [exit]simplify: Simplified to (* (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) 1547113856.483 * [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))))))) 1547113856.483 * * * * [misc]progress: [ 72 / 83 ] simplifiying candidate # 1547113856.483 * [enter]simplify: Simplifying (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1547113856.483 * * [misc]simplify: iters left: 6 (11 enodes) 1547113856.485 * * [misc]simplify: iters left: 5 (17 enodes) 1547113856.488 * * [misc]simplify: iters left: 4 (26 enodes) 1547113856.492 * * [misc]simplify: iters left: 3 (27 enodes) 1547113856.496 * [exit]simplify: Simplified to (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) 1547113856.496 * [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))))))) 1547113856.496 * * * * [misc]progress: [ 73 / 83 ] simplifiying candidate # 1547113856.497 * * * * [misc]progress: [ 74 / 83 ] simplifiying candidate # 1547113856.497 * [enter]simplify: Simplifying (pow (* PI (* n 2)) 1/2) 1547113856.497 * * [misc]simplify: iters left: 5 (7 enodes) 1547113856.498 * * [misc]simplify: iters left: 4 (12 enodes) 1547113856.500 * * [misc]simplify: iters left: 3 (18 enodes) 1547113856.503 * * [misc]simplify: iters left: 2 (20 enodes) 1547113856.506 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1547113856.506 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2))))) 1547113856.506 * * * * [misc]progress: [ 75 / 83 ] simplifiying candidate # 1547113856.506 * [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))))) 1547113856.507 * * [misc]simplify: iters left: 6 (37 enodes) 1547113856.517 * * [misc]simplify: iters left: 5 (108 enodes) 1547113856.552 * * [misc]simplify: iters left: 4 (368 enodes) 1547113856.822 * [exit]simplify: Simplified to (fma -1/2 (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) (fma (* (* (* k k) (log n)) (* (log (* PI 2)) 1/4)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (fma (* (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (log (* PI 2)) (log (* PI 2)))) (* (* k k) 1/8) (fma (* (* (* k k) (log n)) (* (log n) 1/8)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (pow n 1/2) (pow (* PI 2) 1/2)))))) 1547113856.822 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (fma -1/2 (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) (fma (* (* (* k k) (log n)) (* (log (* PI 2)) 1/4)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (fma (* (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (log (* PI 2)) (log (* PI 2)))) (* (* k k) 1/8) (fma (* (* (* k k) (log n)) (* (log n) 1/8)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (pow n 1/2) (pow (* PI 2) 1/2)))))) (sqrt k))) 1547113856.822 * * * * [misc]progress: [ 76 / 83 ] simplifiying candidate # 1547113856.822 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 1547113856.823 * * [misc]simplify: iters left: 6 (15 enodes) 1547113856.826 * * [misc]simplify: iters left: 5 (33 enodes) 1547113856.833 * * [misc]simplify: iters left: 4 (64 enodes) 1547113856.850 * * [misc]simplify: iters left: 3 (179 enodes) 1547113856.928 * [exit]simplify: Simplified to (* (pow (* 2 PI) (fma -1/2 k 1/2)) (pow n (fma -1/2 k 1/2))) 1547113856.929 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (* (pow (* 2 PI) (fma -1/2 k 1/2)) (pow n (fma -1/2 k 1/2))) (sqrt k))) 1547113856.929 * * * * [misc]progress: [ 77 / 83 ] simplifiying candidate # 1547113856.929 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 1547113856.929 * * [misc]simplify: iters left: 6 (15 enodes) 1547113856.935 * * [misc]simplify: iters left: 5 (30 enodes) 1547113856.943 * * [misc]simplify: iters left: 4 (65 enodes) 1547113856.960 * * [misc]simplify: iters left: 3 (208 enodes) 1547113857.069 * [exit]simplify: Simplified to (pow (exp (fma -1/2 k 1/2)) (- (log (* -2 PI)) (log (/ -1 n)))) 1547113857.069 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (pow (exp (fma -1/2 k 1/2)) (- (log (* -2 PI)) (log (/ -1 n)))) (sqrt k))) 1547113857.069 * * * * [misc]progress: [ 78 / 83 ] simplifiying candidate # 1547113857.069 * [enter]simplify: Simplifying (* 2 (* n PI)) 1547113857.070 * * [misc]simplify: iters left: 4 (5 enodes) 1547113857.071 * * [misc]simplify: iters left: 3 (9 enodes) 1547113857.072 * * [misc]simplify: iters left: 2 (15 enodes) 1547113857.075 * * [misc]simplify: iters left: 1 (17 enodes) 1547113857.080 * [exit]simplify: Simplified to (* (* PI n) 2) 1547113857.080 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt k))) 1547113857.080 * * * * [misc]progress: [ 79 / 83 ] simplifiying candidate # 1547113857.080 * [enter]simplify: Simplifying (* 2 (* n PI)) 1547113857.080 * * [misc]simplify: iters left: 4 (5 enodes) 1547113857.081 * * [misc]simplify: iters left: 3 (9 enodes) 1547113857.083 * * [misc]simplify: iters left: 2 (15 enodes) 1547113857.085 * * [misc]simplify: iters left: 1 (17 enodes) 1547113857.087 * [exit]simplify: Simplified to (* (* PI n) 2) 1547113857.087 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt k))) 1547113857.087 * * * * [misc]progress: [ 80 / 83 ] simplifiying candidate # 1547113857.087 * [enter]simplify: Simplifying (* 2 (* n PI)) 1547113857.087 * * [misc]simplify: iters left: 4 (5 enodes) 1547113857.088 * * [misc]simplify: iters left: 3 (9 enodes) 1547113857.090 * * [misc]simplify: iters left: 2 (15 enodes) 1547113857.092 * * [misc]simplify: iters left: 1 (17 enodes) 1547113857.095 * [exit]simplify: Simplified to (* (* PI n) 2) 1547113857.095 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt k))) 1547113857.095 * * * * [misc]progress: [ 81 / 83 ] simplifiying candidate # 1547113857.095 * [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)))))))))))))))))))))) 1547113857.095 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1547113857.095 * * * * [misc]progress: [ 82 / 83 ] simplifiying candidate # 1547113857.095 * [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)))))))) 1547113857.095 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1547113857.095 * * * * [misc]progress: [ 83 / 83 ] simplifiying candidate # 1547113857.096 * [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))))))))))) 1547113857.096 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1547113857.096 * * * [misc]progress: adding candidates to table 1547113858.064 * * [misc]progress: iteration 2 / 4 1547113858.064 * * * [misc]progress: picking best candidate 1547113858.104 * * * * [misc]pick: Picked # 1547113858.104 * * * [misc]progress: localizing error 1547113858.126 * * * [misc]progress: generating rewritten candidates 1547113858.126 * * * * [misc]progress: [ 1 / 4 ] rewriting at (2 2) 1547113858.132 * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 1) 1547113858.134 * * * * [misc]progress: [ 3 / 4 ] rewriting at (2 2 1) 1547113858.138 * * * * [misc]progress: [ 4 / 4 ] rewriting at (2) 1547113858.162 * * * [misc]progress: generating series expansions 1547113858.162 * * * * [misc]progress: [ 1 / 4 ] generating series at (2 2) 1547113858.163 * [misc]backup-simplify: Simplify (pow (* (* 2 PI) n) (/ (- 1 k) 2)) into (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) 1547113858.163 * [misc]approximate: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in (n k) around 0 1547113858.163 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k 1547113858.163 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k 1547113858.163 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k 1547113858.163 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 k)) in k 1547113858.163 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113858.163 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113858.163 * [misc]taylor: Taking taylor expansion of (- 1 k) in k 1547113858.163 * [misc]taylor: Taking taylor expansion of 1 in k 1547113858.163 * [misc]backup-simplify: Simplify 1 into 1 1547113858.163 * [misc]taylor: Taking taylor expansion of k in k 1547113858.163 * [misc]backup-simplify: Simplify 0 into 0 1547113858.163 * [misc]backup-simplify: Simplify 1 into 1 1547113858.163 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1547113858.163 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1547113858.163 * [misc]taylor: Taking taylor expansion of 2 in k 1547113858.163 * [misc]backup-simplify: Simplify 2 into 2 1547113858.163 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1547113858.164 * [misc]taylor: Taking taylor expansion of n in k 1547113858.164 * [misc]backup-simplify: Simplify n into n 1547113858.164 * [misc]taylor: Taking taylor expansion of PI in k 1547113858.164 * [misc]backup-simplify: Simplify PI into PI 1547113858.164 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1547113858.164 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1547113858.164 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1547113858.164 * [misc]backup-simplify: Simplify (- 0) into 0 1547113858.164 * [misc]backup-simplify: Simplify (+ 1 0) into 1 1547113858.164 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1547113858.165 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1547113858.165 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1547113858.165 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n 1547113858.165 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n 1547113858.165 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n 1547113858.165 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 k)) in n 1547113858.165 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113858.165 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113858.165 * [misc]taylor: Taking taylor expansion of (- 1 k) in n 1547113858.165 * [misc]taylor: Taking taylor expansion of 1 in n 1547113858.165 * [misc]backup-simplify: Simplify 1 into 1 1547113858.165 * [misc]taylor: Taking taylor expansion of k in n 1547113858.165 * [misc]backup-simplify: Simplify k into k 1547113858.165 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1547113858.165 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1547113858.165 * [misc]taylor: Taking taylor expansion of 2 in n 1547113858.165 * [misc]backup-simplify: Simplify 2 into 2 1547113858.165 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547113858.165 * [misc]taylor: Taking taylor expansion of n in n 1547113858.165 * [misc]backup-simplify: Simplify 0 into 0 1547113858.165 * [misc]backup-simplify: Simplify 1 into 1 1547113858.165 * [misc]taylor: Taking taylor expansion of PI in n 1547113858.165 * [misc]backup-simplify: Simplify PI into PI 1547113858.165 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547113858.166 * [misc]backup-simplify: Simplify (* 2 0) into 0 1547113858.166 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547113858.167 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1547113858.167 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547113858.167 * [misc]backup-simplify: Simplify (- k) into (- k) 1547113858.168 * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) 1547113858.168 * [misc]backup-simplify: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k)) 1547113858.168 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547113858.169 * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) 1547113858.170 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 1547113858.170 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n 1547113858.170 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n 1547113858.170 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n 1547113858.170 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 k)) in n 1547113858.170 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113858.170 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113858.170 * [misc]taylor: Taking taylor expansion of (- 1 k) in n 1547113858.170 * [misc]taylor: Taking taylor expansion of 1 in n 1547113858.170 * [misc]backup-simplify: Simplify 1 into 1 1547113858.170 * [misc]taylor: Taking taylor expansion of k in n 1547113858.170 * [misc]backup-simplify: Simplify k into k 1547113858.170 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1547113858.170 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1547113858.170 * [misc]taylor: Taking taylor expansion of 2 in n 1547113858.170 * [misc]backup-simplify: Simplify 2 into 2 1547113858.170 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547113858.170 * [misc]taylor: Taking taylor expansion of n in n 1547113858.170 * [misc]backup-simplify: Simplify 0 into 0 1547113858.170 * [misc]backup-simplify: Simplify 1 into 1 1547113858.170 * [misc]taylor: Taking taylor expansion of PI in n 1547113858.170 * [misc]backup-simplify: Simplify PI into PI 1547113858.171 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547113858.171 * [misc]backup-simplify: Simplify (* 2 0) into 0 1547113858.171 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547113858.172 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1547113858.172 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547113858.172 * [misc]backup-simplify: Simplify (- k) into (- k) 1547113858.173 * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) 1547113858.173 * [misc]backup-simplify: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k)) 1547113858.173 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547113858.174 * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) 1547113858.174 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 1547113858.174 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) in k 1547113858.175 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) in k 1547113858.175 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113858.175 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113858.175 * [misc]taylor: Taking taylor expansion of (* (- 1 k) (+ (log n) (log (* 2 PI)))) in k 1547113858.175 * [misc]taylor: Taking taylor expansion of (- 1 k) in k 1547113858.175 * [misc]taylor: Taking taylor expansion of 1 in k 1547113858.175 * [misc]backup-simplify: Simplify 1 into 1 1547113858.175 * [misc]taylor: Taking taylor expansion of k in k 1547113858.175 * [misc]backup-simplify: Simplify 0 into 0 1547113858.175 * [misc]backup-simplify: Simplify 1 into 1 1547113858.175 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1547113858.175 * [misc]taylor: Taking taylor expansion of (log n) in k 1547113858.175 * [misc]taylor: Taking taylor expansion of n in k 1547113858.175 * [misc]backup-simplify: Simplify n into n 1547113858.175 * [misc]backup-simplify: Simplify (log n) into (log n) 1547113858.175 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1547113858.175 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1547113858.175 * [misc]taylor: Taking taylor expansion of 2 in k 1547113858.175 * [misc]backup-simplify: Simplify 2 into 2 1547113858.175 * [misc]taylor: Taking taylor expansion of PI in k 1547113858.175 * [misc]backup-simplify: Simplify PI into PI 1547113858.175 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547113858.176 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547113858.176 * [misc]backup-simplify: Simplify (- 0) into 0 1547113858.176 * [misc]backup-simplify: Simplify (+ 1 0) into 1 1547113858.177 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547113858.177 * [misc]backup-simplify: Simplify (* 1 (+ (log n) (log (* 2 PI)))) into (+ (log n) (log (* 2 PI))) 1547113858.178 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1547113858.178 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1547113858.179 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1547113858.180 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1547113858.181 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1547113858.183 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1547113858.183 * [misc]backup-simplify: Simplify (- 0) into 0 1547113858.183 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113858.184 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- 1 k))) into 0 1547113858.184 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547113858.184 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1547113858.185 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0 1547113858.185 * [misc]taylor: Taking taylor expansion of 0 in k 1547113858.185 * [misc]backup-simplify: Simplify 0 into 0 1547113858.185 * [misc]backup-simplify: Simplify 0 into 0 1547113858.186 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1547113858.186 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1547113858.188 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1547113858.188 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113858.188 * [misc]backup-simplify: Simplify (- 1) into -1 1547113858.188 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 1547113858.189 * [misc]backup-simplify: Simplify (+ (* 1 0) (* -1 (+ (log n) (log (* 2 PI))))) into (- (+ (log (* 2 PI)) (log n))) 1547113858.189 * [misc]backup-simplify: Simplify (+ (* 1/2 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1547113858.190 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 1547113858.191 * [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))))))) 1547113858.192 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1547113858.193 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1547113858.196 * [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 1547113858.196 * [misc]backup-simplify: Simplify (- 0) into 0 1547113858.196 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113858.196 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0 1547113858.197 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547113858.197 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1547113858.198 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1547113858.199 * [misc]taylor: Taking taylor expansion of 0 in k 1547113858.199 * [misc]backup-simplify: Simplify 0 into 0 1547113858.199 * [misc]backup-simplify: Simplify 0 into 0 1547113858.199 * [misc]backup-simplify: Simplify 0 into 0 1547113858.200 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1547113858.200 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1547113858.203 * [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 1547113858.203 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113858.203 * [misc]backup-simplify: Simplify (- 0) into 0 1547113858.204 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113858.204 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1547113858.205 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1547113858.206 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 1547113858.208 * [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))))) 1547113858.210 * [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))))) 1547113858.211 * [misc]backup-simplify: Simplify (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) into (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) 1547113858.211 * [misc]approximate: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in (n k) around 0 1547113858.211 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k 1547113858.211 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1547113858.211 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1547113858.211 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k 1547113858.211 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113858.211 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113858.211 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k 1547113858.211 * [misc]taylor: Taking taylor expansion of 1 in k 1547113858.211 * [misc]backup-simplify: Simplify 1 into 1 1547113858.211 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547113858.211 * [misc]taylor: Taking taylor expansion of k in k 1547113858.211 * [misc]backup-simplify: Simplify 0 into 0 1547113858.211 * [misc]backup-simplify: Simplify 1 into 1 1547113858.211 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547113858.211 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1547113858.211 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1547113858.211 * [misc]taylor: Taking taylor expansion of 2 in k 1547113858.211 * [misc]backup-simplify: Simplify 2 into 2 1547113858.211 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1547113858.211 * [misc]taylor: Taking taylor expansion of PI in k 1547113858.211 * [misc]backup-simplify: Simplify PI into PI 1547113858.211 * [misc]taylor: Taking taylor expansion of n in k 1547113858.211 * [misc]backup-simplify: Simplify n into n 1547113858.212 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1547113858.212 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1547113858.212 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1547113858.212 * [misc]backup-simplify: Simplify (- 1) into -1 1547113858.212 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 1547113858.212 * [misc]backup-simplify: Simplify (* 1/2 -1) into -1/2 1547113858.212 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1547113858.212 * [misc]backup-simplify: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 1547113858.212 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n 1547113858.212 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1547113858.212 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1547113858.212 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n 1547113858.212 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113858.212 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113858.212 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n 1547113858.212 * [misc]taylor: Taking taylor expansion of 1 in n 1547113858.212 * [misc]backup-simplify: Simplify 1 into 1 1547113858.212 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547113858.212 * [misc]taylor: Taking taylor expansion of k in n 1547113858.212 * [misc]backup-simplify: Simplify k into k 1547113858.212 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547113858.212 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1547113858.212 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1547113858.212 * [misc]taylor: Taking taylor expansion of 2 in n 1547113858.212 * [misc]backup-simplify: Simplify 2 into 2 1547113858.212 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547113858.212 * [misc]taylor: Taking taylor expansion of PI in n 1547113858.213 * [misc]backup-simplify: Simplify PI into PI 1547113858.213 * [misc]taylor: Taking taylor expansion of n in n 1547113858.213 * [misc]backup-simplify: Simplify 0 into 0 1547113858.213 * [misc]backup-simplify: Simplify 1 into 1 1547113858.213 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547113858.213 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547113858.213 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547113858.213 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1547113858.213 * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 1547113858.213 * [misc]backup-simplify: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k))) 1547113858.214 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547113858.214 * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 1547113858.215 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 1547113858.215 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n 1547113858.215 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1547113858.215 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1547113858.215 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n 1547113858.215 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113858.215 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113858.215 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n 1547113858.215 * [misc]taylor: Taking taylor expansion of 1 in n 1547113858.215 * [misc]backup-simplify: Simplify 1 into 1 1547113858.215 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547113858.215 * [misc]taylor: Taking taylor expansion of k in n 1547113858.215 * [misc]backup-simplify: Simplify k into k 1547113858.215 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547113858.215 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1547113858.215 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1547113858.215 * [misc]taylor: Taking taylor expansion of 2 in n 1547113858.215 * [misc]backup-simplify: Simplify 2 into 2 1547113858.215 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547113858.215 * [misc]taylor: Taking taylor expansion of PI in n 1547113858.215 * [misc]backup-simplify: Simplify PI into PI 1547113858.215 * [misc]taylor: Taking taylor expansion of n in n 1547113858.215 * [misc]backup-simplify: Simplify 0 into 0 1547113858.215 * [misc]backup-simplify: Simplify 1 into 1 1547113858.215 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547113858.215 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547113858.216 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547113858.216 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1547113858.216 * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 1547113858.216 * [misc]backup-simplify: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k))) 1547113858.216 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547113858.216 * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 1547113858.217 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 1547113858.217 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k 1547113858.217 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k 1547113858.217 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113858.217 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113858.217 * [misc]taylor: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k 1547113858.217 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k 1547113858.217 * [misc]taylor: Taking taylor expansion of 1 in k 1547113858.217 * [misc]backup-simplify: Simplify 1 into 1 1547113858.217 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547113858.217 * [misc]taylor: Taking taylor expansion of k in k 1547113858.217 * [misc]backup-simplify: Simplify 0 into 0 1547113858.217 * [misc]backup-simplify: Simplify 1 into 1 1547113858.217 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547113858.217 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1547113858.217 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1547113858.217 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1547113858.217 * [misc]taylor: Taking taylor expansion of 2 in k 1547113858.217 * [misc]backup-simplify: Simplify 2 into 2 1547113858.217 * [misc]taylor: Taking taylor expansion of PI in k 1547113858.217 * [misc]backup-simplify: Simplify PI into PI 1547113858.218 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547113858.218 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547113858.218 * [misc]taylor: Taking taylor expansion of (log n) in k 1547113858.218 * [misc]taylor: Taking taylor expansion of n in k 1547113858.218 * [misc]backup-simplify: Simplify n into n 1547113858.218 * [misc]backup-simplify: Simplify (log n) into (log n) 1547113858.218 * [misc]backup-simplify: Simplify (- 1) into -1 1547113858.218 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 1547113858.218 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1547113858.218 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1547113858.219 * [misc]backup-simplify: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n))) 1547113858.219 * [misc]backup-simplify: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1547113858.220 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 1547113858.220 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 1547113858.221 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1547113858.221 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1547113858.223 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1547113858.223 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1547113858.223 * [misc]backup-simplify: Simplify (- 0) into 0 1547113858.223 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113858.223 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- 1 (/ 1 k)))) into 0 1547113858.224 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547113858.224 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1547113858.225 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1547113858.225 * [misc]taylor: Taking taylor expansion of 0 in k 1547113858.225 * [misc]backup-simplify: Simplify 0 into 0 1547113858.225 * [misc]backup-simplify: Simplify 0 into 0 1547113858.225 * [misc]backup-simplify: Simplify 0 into 0 1547113858.226 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113858.227 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1547113858.230 * [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 1547113858.230 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1547113858.230 * [misc]backup-simplify: Simplify (- 0) into 0 1547113858.230 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113858.230 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0 1547113858.231 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547113858.231 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1547113858.233 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1547113858.233 * [misc]taylor: Taking taylor expansion of 0 in k 1547113858.233 * [misc]backup-simplify: Simplify 0 into 0 1547113858.233 * [misc]backup-simplify: Simplify 0 into 0 1547113858.233 * [misc]backup-simplify: Simplify 0 into 0 1547113858.233 * [misc]backup-simplify: Simplify 0 into 0 1547113858.234 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113858.235 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1547113858.239 * [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 1547113858.239 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1547113858.239 * [misc]backup-simplify: Simplify (- 0) into 0 1547113858.240 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113858.240 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0 1547113858.241 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547113858.242 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1547113858.245 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1547113858.246 * [misc]taylor: Taking taylor expansion of 0 in k 1547113858.246 * [misc]backup-simplify: Simplify 0 into 0 1547113858.246 * [misc]backup-simplify: Simplify 0 into 0 1547113858.246 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) 1547113858.247 * [misc]backup-simplify: Simplify (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) into (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) 1547113858.247 * [misc]approximate: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in (n k) around 0 1547113858.247 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k 1547113858.247 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k 1547113858.247 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k 1547113858.247 * [misc]taylor: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k 1547113858.247 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113858.247 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113858.247 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in k 1547113858.247 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547113858.247 * [misc]taylor: Taking taylor expansion of k in k 1547113858.247 * [misc]backup-simplify: Simplify 0 into 0 1547113858.247 * [misc]backup-simplify: Simplify 1 into 1 1547113858.248 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547113858.248 * [misc]taylor: Taking taylor expansion of 1 in k 1547113858.248 * [misc]backup-simplify: Simplify 1 into 1 1547113858.248 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1547113858.248 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1547113858.248 * [misc]taylor: Taking taylor expansion of -2 in k 1547113858.248 * [misc]backup-simplify: Simplify -2 into -2 1547113858.248 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1547113858.248 * [misc]taylor: Taking taylor expansion of PI in k 1547113858.248 * [misc]backup-simplify: Simplify PI into PI 1547113858.248 * [misc]taylor: Taking taylor expansion of n in k 1547113858.248 * [misc]backup-simplify: Simplify n into n 1547113858.248 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1547113858.248 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1547113858.248 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1547113858.248 * [misc]backup-simplify: Simplify (+ 1 0) into 1 1547113858.248 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1547113858.249 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1547113858.249 * [misc]backup-simplify: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) 1547113858.249 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n 1547113858.249 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n 1547113858.249 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n 1547113858.249 * [misc]taylor: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n 1547113858.249 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113858.249 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113858.249 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in n 1547113858.249 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547113858.249 * [misc]taylor: Taking taylor expansion of k in n 1547113858.249 * [misc]backup-simplify: Simplify k into k 1547113858.249 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547113858.249 * [misc]taylor: Taking taylor expansion of 1 in n 1547113858.249 * [misc]backup-simplify: Simplify 1 into 1 1547113858.249 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1547113858.249 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1547113858.249 * [misc]taylor: Taking taylor expansion of -2 in n 1547113858.249 * [misc]backup-simplify: Simplify -2 into -2 1547113858.249 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547113858.249 * [misc]taylor: Taking taylor expansion of PI in n 1547113858.249 * [misc]backup-simplify: Simplify PI into PI 1547113858.249 * [misc]taylor: Taking taylor expansion of n in n 1547113858.249 * [misc]backup-simplify: Simplify 0 into 0 1547113858.249 * [misc]backup-simplify: Simplify 1 into 1 1547113858.250 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547113858.250 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547113858.250 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1547113858.251 * [misc]backup-simplify: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 1547113858.251 * [misc]backup-simplify: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1)) 1547113858.251 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547113858.252 * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 1547113858.253 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 1547113858.253 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n 1547113858.253 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n 1547113858.253 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n 1547113858.253 * [misc]taylor: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n 1547113858.253 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113858.253 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113858.253 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in n 1547113858.253 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547113858.253 * [misc]taylor: Taking taylor expansion of k in n 1547113858.253 * [misc]backup-simplify: Simplify k into k 1547113858.253 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547113858.253 * [misc]taylor: Taking taylor expansion of 1 in n 1547113858.253 * [misc]backup-simplify: Simplify 1 into 1 1547113858.253 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1547113858.253 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1547113858.253 * [misc]taylor: Taking taylor expansion of -2 in n 1547113858.253 * [misc]backup-simplify: Simplify -2 into -2 1547113858.253 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547113858.253 * [misc]taylor: Taking taylor expansion of PI in n 1547113858.253 * [misc]backup-simplify: Simplify PI into PI 1547113858.253 * [misc]taylor: Taking taylor expansion of n in n 1547113858.253 * [misc]backup-simplify: Simplify 0 into 0 1547113858.253 * [misc]backup-simplify: Simplify 1 into 1 1547113858.254 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547113858.254 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547113858.254 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1547113858.254 * [misc]backup-simplify: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 1547113858.254 * [misc]backup-simplify: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1)) 1547113858.255 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547113858.256 * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 1547113858.256 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 1547113858.257 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k 1547113858.257 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) in k 1547113858.257 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113858.257 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113858.257 * [misc]taylor: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) in k 1547113858.257 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in k 1547113858.257 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547113858.257 * [misc]taylor: Taking taylor expansion of k in k 1547113858.257 * [misc]backup-simplify: Simplify 0 into 0 1547113858.257 * [misc]backup-simplify: Simplify 1 into 1 1547113858.257 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547113858.257 * [misc]taylor: Taking taylor expansion of 1 in k 1547113858.257 * [misc]backup-simplify: Simplify 1 into 1 1547113858.257 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1547113858.257 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1547113858.257 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1547113858.257 * [misc]taylor: Taking taylor expansion of -2 in k 1547113858.257 * [misc]backup-simplify: Simplify -2 into -2 1547113858.257 * [misc]taylor: Taking taylor expansion of PI in k 1547113858.257 * [misc]backup-simplify: Simplify PI into PI 1547113858.257 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547113858.258 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1547113858.258 * [misc]taylor: Taking taylor expansion of (log n) in k 1547113858.258 * [misc]taylor: Taking taylor expansion of n in k 1547113858.258 * [misc]backup-simplify: Simplify n into n 1547113858.258 * [misc]backup-simplify: Simplify (log n) into (log n) 1547113858.258 * [misc]backup-simplify: Simplify (+ 1 0) into 1 1547113858.258 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1547113858.259 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1547113858.259 * [misc]backup-simplify: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n)) 1547113858.260 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1547113858.261 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 1547113858.261 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 1547113858.262 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1547113858.263 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1547113858.266 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1547113858.266 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1547113858.266 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113858.266 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (+ (/ 1 k) 1))) into 0 1547113858.267 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547113858.267 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1547113858.269 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1547113858.269 * [misc]taylor: Taking taylor expansion of 0 in k 1547113858.269 * [misc]backup-simplify: Simplify 0 into 0 1547113858.269 * [misc]backup-simplify: Simplify 0 into 0 1547113858.269 * [misc]backup-simplify: Simplify 0 into 0 1547113858.271 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113858.272 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1547113858.279 * [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 1547113858.279 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1547113858.280 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113858.280 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0 1547113858.281 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547113858.281 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1547113858.284 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1547113858.284 * [misc]taylor: Taking taylor expansion of 0 in k 1547113858.284 * [misc]backup-simplify: Simplify 0 into 0 1547113858.284 * [misc]backup-simplify: Simplify 0 into 0 1547113858.284 * [misc]backup-simplify: Simplify 0 into 0 1547113858.284 * [misc]backup-simplify: Simplify 0 into 0 1547113858.286 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113858.287 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1547113858.295 * [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 1547113858.296 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1547113858.296 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113858.296 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1))))) into 0 1547113858.297 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547113858.298 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 1547113858.302 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1547113858.302 * [misc]taylor: Taking taylor expansion of 0 in k 1547113858.302 * [misc]backup-simplify: Simplify 0 into 0 1547113858.302 * [misc]backup-simplify: Simplify 0 into 0 1547113858.303 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) 1547113858.303 * * * * [misc]progress: [ 2 / 4 ] generating series at (2 1) 1547113858.303 * [misc]backup-simplify: Simplify (/ 1 (sqrt k)) into (sqrt (/ 1 k)) 1547113858.303 * [misc]approximate: Taking taylor expansion of (sqrt (/ 1 k)) in (k) around 0 1547113858.303 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1547113858.303 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547113858.303 * [misc]taylor: Taking taylor expansion of k in k 1547113858.303 * [misc]backup-simplify: Simplify 0 into 0 1547113858.303 * [misc]backup-simplify: Simplify 1 into 1 1547113858.303 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547113858.303 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547113858.304 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1547113858.304 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1547113858.304 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547113858.304 * [misc]taylor: Taking taylor expansion of k in k 1547113858.304 * [misc]backup-simplify: Simplify 0 into 0 1547113858.304 * [misc]backup-simplify: Simplify 1 into 1 1547113858.304 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547113858.304 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547113858.305 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1547113858.305 * [misc]backup-simplify: Simplify 0 into 0 1547113858.305 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547113858.305 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1547113858.306 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1547113858.306 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547113858.307 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113858.308 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1547113858.308 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547113858.308 * [misc]backup-simplify: Simplify (+ (* +nan.0 (pow k 2)) (+ (* +nan.0 k) +nan.0)) into (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) 1547113858.308 * [misc]backup-simplify: Simplify (/ 1 (sqrt (/ 1 k))) into (sqrt k) 1547113858.308 * [misc]approximate: Taking taylor expansion of (sqrt k) in (k) around 0 1547113858.308 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1547113858.308 * [misc]taylor: Taking taylor expansion of k in k 1547113858.308 * [misc]backup-simplify: Simplify 0 into 0 1547113858.308 * [misc]backup-simplify: Simplify 1 into 1 1547113858.308 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547113858.308 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1547113858.308 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1547113858.308 * [misc]taylor: Taking taylor expansion of k in k 1547113858.308 * [misc]backup-simplify: Simplify 0 into 0 1547113858.308 * [misc]backup-simplify: Simplify 1 into 1 1547113858.308 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547113858.309 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1547113858.309 * [misc]backup-simplify: Simplify 0 into 0 1547113858.309 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547113858.310 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1547113858.310 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547113858.310 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1547113858.310 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547113858.310 * [misc]backup-simplify: Simplify (+ (* +nan.0 (pow (/ 1 k) 3)) (+ (* +nan.0 (pow (/ 1 k) 2)) (* +nan.0 (/ 1 k)))) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) 1547113858.311 * [misc]backup-simplify: Simplify (/ 1 (sqrt (/ 1 (- k)))) into (/ 1 (sqrt (/ -1 k))) 1547113858.311 * [misc]approximate: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in (k) around 0 1547113858.311 * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 1547113858.311 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1547113858.311 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1547113858.311 * [misc]taylor: Taking taylor expansion of -1 in k 1547113858.311 * [misc]backup-simplify: Simplify -1 into -1 1547113858.311 * [misc]taylor: Taking taylor expansion of k in k 1547113858.311 * [misc]backup-simplify: Simplify 0 into 0 1547113858.311 * [misc]backup-simplify: Simplify 1 into 1 1547113858.311 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1547113858.311 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547113858.311 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1547113858.311 * [misc]backup-simplify: Simplify (/ 1 +nan.0) into +nan.0 1547113858.311 * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 1547113858.311 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1547113858.311 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1547113858.311 * [misc]taylor: Taking taylor expansion of -1 in k 1547113858.311 * [misc]backup-simplify: Simplify -1 into -1 1547113858.311 * [misc]taylor: Taking taylor expansion of k in k 1547113858.311 * [misc]backup-simplify: Simplify 0 into 0 1547113858.311 * [misc]backup-simplify: Simplify 1 into 1 1547113858.312 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1547113858.312 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547113858.312 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1547113858.312 * [misc]backup-simplify: Simplify (/ 1 +nan.0) into +nan.0 1547113858.312 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547113858.312 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1547113858.313 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1547113858.313 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 1547113858.313 * [misc]backup-simplify: Simplify (- +nan.0) into (- +nan.0) 1547113858.314 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113858.314 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1547113858.315 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 1547113858.315 * [misc]backup-simplify: Simplify (- +nan.0) into (- +nan.0) 1547113858.316 * [misc]backup-simplify: Simplify (+ (* (- +nan.0) (pow (/ 1 (- k)) 2)) (+ (* (- +nan.0) (/ 1 (- k))) +nan.0)) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) 1547113858.316 * * * * [misc]progress: [ 3 / 4 ] generating series at (2 2 1) 1547113858.316 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1547113858.316 * [misc]approximate: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1547113858.316 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1547113858.316 * [misc]taylor: Taking taylor expansion of 2 in n 1547113858.316 * [misc]backup-simplify: Simplify 2 into 2 1547113858.316 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547113858.316 * [misc]taylor: Taking taylor expansion of n in n 1547113858.316 * [misc]backup-simplify: Simplify 0 into 0 1547113858.316 * [misc]backup-simplify: Simplify 1 into 1 1547113858.316 * [misc]taylor: Taking taylor expansion of PI in n 1547113858.316 * [misc]backup-simplify: Simplify PI into PI 1547113858.316 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1547113858.316 * [misc]taylor: Taking taylor expansion of 2 in n 1547113858.316 * [misc]backup-simplify: Simplify 2 into 2 1547113858.316 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547113858.316 * [misc]taylor: Taking taylor expansion of n in n 1547113858.316 * [misc]backup-simplify: Simplify 0 into 0 1547113858.316 * [misc]backup-simplify: Simplify 1 into 1 1547113858.316 * [misc]taylor: Taking taylor expansion of PI in n 1547113858.316 * [misc]backup-simplify: Simplify PI into PI 1547113858.316 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547113858.317 * [misc]backup-simplify: Simplify (* 2 0) into 0 1547113858.317 * [misc]backup-simplify: Simplify 0 into 0 1547113858.317 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547113858.317 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1547113858.317 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547113858.318 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1547113858.319 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1547113858.319 * [misc]backup-simplify: Simplify 0 into 0 1547113858.320 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1547113858.321 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1547113858.321 * [misc]backup-simplify: Simplify 0 into 0 1547113858.322 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1547113858.324 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1547113858.324 * [misc]backup-simplify: Simplify 0 into 0 1547113858.325 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1547113858.327 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1547113858.327 * [misc]backup-simplify: Simplify 0 into 0 1547113858.329 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1547113858.330 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1547113858.330 * [misc]backup-simplify: Simplify 0 into 0 1547113858.333 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1547113858.335 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1547113858.335 * [misc]backup-simplify: Simplify 0 into 0 1547113858.335 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1547113858.336 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 n)) into (* 2 (/ PI n)) 1547113858.336 * [misc]approximate: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1547113858.336 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1547113858.336 * [misc]taylor: Taking taylor expansion of 2 in n 1547113858.336 * [misc]backup-simplify: Simplify 2 into 2 1547113858.336 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547113858.336 * [misc]taylor: Taking taylor expansion of PI in n 1547113858.336 * [misc]backup-simplify: Simplify PI into PI 1547113858.336 * [misc]taylor: Taking taylor expansion of n in n 1547113858.336 * [misc]backup-simplify: Simplify 0 into 0 1547113858.336 * [misc]backup-simplify: Simplify 1 into 1 1547113858.336 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547113858.336 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1547113858.336 * [misc]taylor: Taking taylor expansion of 2 in n 1547113858.336 * [misc]backup-simplify: Simplify 2 into 2 1547113858.336 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547113858.336 * [misc]taylor: Taking taylor expansion of PI in n 1547113858.336 * [misc]backup-simplify: Simplify PI into PI 1547113858.336 * [misc]taylor: Taking taylor expansion of n in n 1547113858.336 * [misc]backup-simplify: Simplify 0 into 0 1547113858.336 * [misc]backup-simplify: Simplify 1 into 1 1547113858.336 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547113858.337 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547113858.337 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547113858.337 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1547113858.338 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1547113858.338 * [misc]backup-simplify: Simplify 0 into 0 1547113858.339 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113858.339 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1547113858.339 * [misc]backup-simplify: Simplify 0 into 0 1547113858.341 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113858.342 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1547113858.342 * [misc]backup-simplify: Simplify 0 into 0 1547113858.344 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113858.346 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1547113858.346 * [misc]backup-simplify: Simplify 0 into 0 1547113858.349 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113858.351 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1547113858.351 * [misc]backup-simplify: Simplify 0 into 0 1547113858.354 * [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 1547113858.357 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1547113858.357 * [misc]backup-simplify: Simplify 0 into 0 1547113858.357 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 1547113858.358 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (- n))) into (* -2 (/ PI n)) 1547113858.358 * [misc]approximate: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1547113858.358 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1547113858.358 * [misc]taylor: Taking taylor expansion of -2 in n 1547113858.358 * [misc]backup-simplify: Simplify -2 into -2 1547113858.358 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547113858.358 * [misc]taylor: Taking taylor expansion of PI in n 1547113858.358 * [misc]backup-simplify: Simplify PI into PI 1547113858.358 * [misc]taylor: Taking taylor expansion of n in n 1547113858.358 * [misc]backup-simplify: Simplify 0 into 0 1547113858.358 * [misc]backup-simplify: Simplify 1 into 1 1547113858.358 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547113858.358 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1547113858.358 * [misc]taylor: Taking taylor expansion of -2 in n 1547113858.358 * [misc]backup-simplify: Simplify -2 into -2 1547113858.358 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547113858.358 * [misc]taylor: Taking taylor expansion of PI in n 1547113858.358 * [misc]backup-simplify: Simplify PI into PI 1547113858.358 * [misc]taylor: Taking taylor expansion of n in n 1547113858.358 * [misc]backup-simplify: Simplify 0 into 0 1547113858.358 * [misc]backup-simplify: Simplify 1 into 1 1547113858.359 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547113858.359 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547113858.359 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547113858.360 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1547113858.361 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1547113858.361 * [misc]backup-simplify: Simplify 0 into 0 1547113858.362 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113858.363 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1547113858.363 * [misc]backup-simplify: Simplify 0 into 0 1547113858.365 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113858.366 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1547113858.366 * [misc]backup-simplify: Simplify 0 into 0 1547113858.368 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113858.369 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1547113858.369 * [misc]backup-simplify: Simplify 0 into 0 1547113858.370 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113858.372 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1547113858.372 * [misc]backup-simplify: Simplify 0 into 0 1547113858.373 * [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 1547113858.375 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1547113858.375 * [misc]backup-simplify: Simplify 0 into 0 1547113858.375 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 1547113858.375 * * * * [misc]progress: [ 4 / 4 ] generating series at (2) 1547113858.376 * [misc]backup-simplify: Simplify (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) into (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) 1547113858.376 * [misc]approximate: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in (k n) around 0 1547113858.376 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in n 1547113858.376 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n 1547113858.376 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n 1547113858.376 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n 1547113858.376 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 k)) in n 1547113858.376 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113858.376 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113858.376 * [misc]taylor: Taking taylor expansion of (- 1 k) in n 1547113858.376 * [misc]taylor: Taking taylor expansion of 1 in n 1547113858.376 * [misc]backup-simplify: Simplify 1 into 1 1547113858.376 * [misc]taylor: Taking taylor expansion of k in n 1547113858.376 * [misc]backup-simplify: Simplify k into k 1547113858.376 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1547113858.376 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1547113858.376 * [misc]taylor: Taking taylor expansion of 2 in n 1547113858.376 * [misc]backup-simplify: Simplify 2 into 2 1547113858.376 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547113858.376 * [misc]taylor: Taking taylor expansion of n in n 1547113858.376 * [misc]backup-simplify: Simplify 0 into 0 1547113858.376 * [misc]backup-simplify: Simplify 1 into 1 1547113858.376 * [misc]taylor: Taking taylor expansion of PI in n 1547113858.376 * [misc]backup-simplify: Simplify PI into PI 1547113858.376 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547113858.376 * [misc]backup-simplify: Simplify (* 2 0) into 0 1547113858.377 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547113858.377 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1547113858.378 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547113858.378 * [misc]backup-simplify: Simplify (- k) into (- k) 1547113858.378 * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) 1547113858.378 * [misc]backup-simplify: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k)) 1547113858.378 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547113858.379 * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) 1547113858.379 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 1547113858.379 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1547113858.379 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547113858.379 * [misc]taylor: Taking taylor expansion of k in n 1547113858.379 * [misc]backup-simplify: Simplify k into k 1547113858.379 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547113858.379 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1547113858.379 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1547113858.379 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1547113858.379 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k 1547113858.379 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k 1547113858.379 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k 1547113858.380 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k 1547113858.380 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 k)) in k 1547113858.380 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113858.380 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113858.380 * [misc]taylor: Taking taylor expansion of (- 1 k) in k 1547113858.380 * [misc]taylor: Taking taylor expansion of 1 in k 1547113858.380 * [misc]backup-simplify: Simplify 1 into 1 1547113858.380 * [misc]taylor: Taking taylor expansion of k in k 1547113858.380 * [misc]backup-simplify: Simplify 0 into 0 1547113858.380 * [misc]backup-simplify: Simplify 1 into 1 1547113858.380 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1547113858.380 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1547113858.380 * [misc]taylor: Taking taylor expansion of 2 in k 1547113858.380 * [misc]backup-simplify: Simplify 2 into 2 1547113858.380 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1547113858.380 * [misc]taylor: Taking taylor expansion of n in k 1547113858.380 * [misc]backup-simplify: Simplify n into n 1547113858.380 * [misc]taylor: Taking taylor expansion of PI in k 1547113858.380 * [misc]backup-simplify: Simplify PI into PI 1547113858.380 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1547113858.380 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1547113858.380 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1547113858.380 * [misc]backup-simplify: Simplify (- 0) into 0 1547113858.380 * [misc]backup-simplify: Simplify (+ 1 0) into 1 1547113858.380 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1547113858.380 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1547113858.380 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1547113858.380 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1547113858.380 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547113858.380 * [misc]taylor: Taking taylor expansion of k in k 1547113858.380 * [misc]backup-simplify: Simplify 0 into 0 1547113858.380 * [misc]backup-simplify: Simplify 1 into 1 1547113858.381 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547113858.381 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547113858.381 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1547113858.381 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k 1547113858.381 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k 1547113858.381 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k 1547113858.381 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k 1547113858.381 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 k)) in k 1547113858.381 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113858.381 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113858.381 * [misc]taylor: Taking taylor expansion of (- 1 k) in k 1547113858.381 * [misc]taylor: Taking taylor expansion of 1 in k 1547113858.381 * [misc]backup-simplify: Simplify 1 into 1 1547113858.381 * [misc]taylor: Taking taylor expansion of k in k 1547113858.381 * [misc]backup-simplify: Simplify 0 into 0 1547113858.381 * [misc]backup-simplify: Simplify 1 into 1 1547113858.381 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1547113858.381 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1547113858.381 * [misc]taylor: Taking taylor expansion of 2 in k 1547113858.381 * [misc]backup-simplify: Simplify 2 into 2 1547113858.381 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1547113858.381 * [misc]taylor: Taking taylor expansion of n in k 1547113858.381 * [misc]backup-simplify: Simplify n into n 1547113858.381 * [misc]taylor: Taking taylor expansion of PI in k 1547113858.381 * [misc]backup-simplify: Simplify PI into PI 1547113858.381 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1547113858.381 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1547113858.381 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1547113858.382 * [misc]backup-simplify: Simplify (- 0) into 0 1547113858.382 * [misc]backup-simplify: Simplify (+ 1 0) into 1 1547113858.382 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1547113858.382 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1547113858.382 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1547113858.382 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1547113858.382 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547113858.382 * [misc]taylor: Taking taylor expansion of k in k 1547113858.382 * [misc]backup-simplify: Simplify 0 into 0 1547113858.382 * [misc]backup-simplify: Simplify 1 into 1 1547113858.382 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547113858.382 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547113858.382 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1547113858.383 * [misc]backup-simplify: Simplify (* (pow (* 2 (* n PI)) 1/2) 0) into 0 1547113858.383 * [misc]taylor: Taking taylor expansion of 0 in n 1547113858.383 * [misc]backup-simplify: Simplify 0 into 0 1547113858.383 * [misc]backup-simplify: Simplify 0 into 0 1547113858.383 * [misc]backup-simplify: Simplify (+ (* n 0) (* 0 PI)) into 0 1547113858.383 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0 1547113858.384 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 1547113858.384 * [misc]backup-simplify: Simplify (- 1) into -1 1547113858.384 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 1547113858.384 * [misc]backup-simplify: Simplify (+ (* 1/2 -1) (* 0 1)) into -1/2 1547113858.384 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI))))) 1547113858.384 * [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))))) 1547113858.384 * [misc]backup-simplify: Simplify (+ (* (pow (* 2 (* n PI)) 1/2) +nan.0) (* (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) 0)) into (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) 1547113858.384 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 1547113858.384 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 1547113858.384 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1547113858.385 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547113858.385 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1547113858.385 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1547113858.385 * [misc]taylor: Taking taylor expansion of 2 in n 1547113858.385 * [misc]backup-simplify: Simplify 2 into 2 1547113858.385 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1547113858.385 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1547113858.385 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1547113858.385 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547113858.385 * [misc]taylor: Taking taylor expansion of n in n 1547113858.385 * [misc]backup-simplify: Simplify 0 into 0 1547113858.385 * [misc]backup-simplify: Simplify 1 into 1 1547113858.385 * [misc]taylor: Taking taylor expansion of PI in n 1547113858.385 * [misc]backup-simplify: Simplify PI into PI 1547113858.385 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547113858.385 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547113858.386 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547113858.386 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1547113858.386 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1547113858.386 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1547113858.386 * [misc]backup-simplify: Simplify (- 0) into 0 1547113858.386 * [misc]backup-simplify: Simplify 0 into 0 1547113858.386 * [misc]backup-simplify: Simplify 0 into 0 1547113858.386 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1547113858.387 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1547113858.388 * [misc]backup-simplify: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 1547113858.388 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 1547113858.389 * [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 1547113858.389 * [misc]backup-simplify: Simplify (- 0) into 0 1547113858.389 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113858.389 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 -1) (* 0 1))) into 0 1547113858.389 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0 1547113858.390 * [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))) 1547113858.390 * [misc]backup-simplify: Simplify (+ (* (pow (* 2 (* n PI)) 1/2) +nan.0) (+ (* (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) +nan.0) (* (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) 0))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) 1547113858.390 * [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 1547113858.390 * [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 1547113858.390 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n 1547113858.391 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1547113858.391 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547113858.391 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n 1547113858.391 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n 1547113858.391 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1547113858.391 * [misc]taylor: Taking taylor expansion of 2 in n 1547113858.391 * [misc]backup-simplify: Simplify 2 into 2 1547113858.391 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1547113858.391 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1547113858.391 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1547113858.391 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1547113858.391 * [misc]taylor: Taking taylor expansion of 2 in n 1547113858.391 * [misc]backup-simplify: Simplify 2 into 2 1547113858.391 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547113858.391 * [misc]taylor: Taking taylor expansion of n in n 1547113858.391 * [misc]backup-simplify: Simplify 0 into 0 1547113858.391 * [misc]backup-simplify: Simplify 1 into 1 1547113858.391 * [misc]taylor: Taking taylor expansion of PI in n 1547113858.391 * [misc]backup-simplify: Simplify PI into PI 1547113858.391 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547113858.391 * [misc]backup-simplify: Simplify (* 2 0) into 0 1547113858.392 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547113858.393 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1547113858.394 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547113858.394 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1547113858.394 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547113858.394 * [misc]taylor: Taking taylor expansion of n in n 1547113858.394 * [misc]backup-simplify: Simplify 0 into 0 1547113858.394 * [misc]backup-simplify: Simplify 1 into 1 1547113858.394 * [misc]taylor: Taking taylor expansion of PI in n 1547113858.394 * [misc]backup-simplify: Simplify PI into PI 1547113858.395 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547113858.395 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547113858.395 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547113858.396 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1547113858.396 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 1547113858.396 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 1547113858.396 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1547113858.396 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547113858.396 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1547113858.396 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1547113858.396 * [misc]taylor: Taking taylor expansion of 2 in n 1547113858.396 * [misc]backup-simplify: Simplify 2 into 2 1547113858.396 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1547113858.397 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1547113858.397 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1547113858.397 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547113858.397 * [misc]taylor: Taking taylor expansion of n in n 1547113858.397 * [misc]backup-simplify: Simplify 0 into 0 1547113858.397 * [misc]backup-simplify: Simplify 1 into 1 1547113858.397 * [misc]taylor: Taking taylor expansion of PI in n 1547113858.397 * [misc]backup-simplify: Simplify PI into PI 1547113858.397 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547113858.398 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547113858.398 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547113858.398 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1547113858.399 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547113858.400 * [misc]backup-simplify: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 1547113858.400 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0 1547113858.400 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1547113858.401 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1547113858.401 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1547113858.401 * [misc]backup-simplify: Simplify (- 0) into 0 1547113858.401 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113858.401 * [misc]backup-simplify: Simplify (- 0) into 0 1547113858.401 * [misc]backup-simplify: Simplify 0 into 0 1547113858.402 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1547113858.404 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1547113858.405 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 1547113858.406 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI))) 1547113858.406 * [misc]backup-simplify: Simplify 0 into 0 1547113858.407 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113858.408 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1547113858.409 * [misc]backup-simplify: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1547113858.409 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 1547113858.412 * [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 1547113858.412 * [misc]backup-simplify: Simplify (- 0) into 0 1547113858.412 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113858.413 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1)))) into 0 1547113858.413 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log (* 2 (* n PI))))))) into 0 1547113858.415 * [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))) 1547113858.416 * [misc]backup-simplify: Simplify (+ (* (pow (* 2 (* n PI)) 1/2) +nan.0) (+ (* (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) +nan.0) (+ (* (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) +nan.0) (* (* -1/48 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 3))) 0)))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))))))) 1547113858.416 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))))))) in n 1547113858.416 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))))))) in n 1547113858.416 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n 1547113858.416 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1547113858.416 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547113858.416 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n 1547113858.416 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n 1547113858.416 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1547113858.416 * [misc]taylor: Taking taylor expansion of 2 in n 1547113858.416 * [misc]backup-simplify: Simplify 2 into 2 1547113858.416 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1547113858.416 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1547113858.416 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1547113858.416 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1547113858.416 * [misc]taylor: Taking taylor expansion of 2 in n 1547113858.416 * [misc]backup-simplify: Simplify 2 into 2 1547113858.416 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547113858.416 * [misc]taylor: Taking taylor expansion of n in n 1547113858.416 * [misc]backup-simplify: Simplify 0 into 0 1547113858.416 * [misc]backup-simplify: Simplify 1 into 1 1547113858.416 * [misc]taylor: Taking taylor expansion of PI in n 1547113858.416 * [misc]backup-simplify: Simplify PI into PI 1547113858.417 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547113858.417 * [misc]backup-simplify: Simplify (* 2 0) into 0 1547113858.417 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547113858.417 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1547113858.418 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547113858.418 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1547113858.418 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547113858.418 * [misc]taylor: Taking taylor expansion of n in n 1547113858.418 * [misc]backup-simplify: Simplify 0 into 0 1547113858.418 * [misc]backup-simplify: Simplify 1 into 1 1547113858.418 * [misc]taylor: Taking taylor expansion of PI in n 1547113858.418 * [misc]backup-simplify: Simplify PI into PI 1547113858.418 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547113858.418 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547113858.418 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547113858.419 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1547113858.419 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))))) in n 1547113858.419 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))))) in n 1547113858.419 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 1547113858.419 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1547113858.419 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547113858.419 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1547113858.419 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1547113858.419 * [misc]taylor: Taking taylor expansion of 2 in n 1547113858.419 * [misc]backup-simplify: Simplify 2 into 2 1547113858.419 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1547113858.419 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1547113858.419 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1547113858.419 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547113858.419 * [misc]taylor: Taking taylor expansion of n in n 1547113858.419 * [misc]backup-simplify: Simplify 0 into 0 1547113858.419 * [misc]backup-simplify: Simplify 1 into 1 1547113858.419 * [misc]taylor: Taking taylor expansion of PI in n 1547113858.419 * [misc]backup-simplify: Simplify PI into PI 1547113858.419 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547113858.420 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547113858.420 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547113858.420 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1547113858.420 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))) in n 1547113858.420 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) in n 1547113858.420 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1547113858.420 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547113858.420 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))) in n 1547113858.420 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) in n 1547113858.420 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1547113858.420 * [misc]taylor: Taking taylor expansion of 2 in n 1547113858.420 * [misc]backup-simplify: Simplify 2 into 2 1547113858.420 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1547113858.421 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1547113858.421 * [misc]taylor: Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n 1547113858.421 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1547113858.421 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1547113858.421 * [misc]taylor: Taking taylor expansion of 2 in n 1547113858.421 * [misc]backup-simplify: Simplify 2 into 2 1547113858.421 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547113858.421 * [misc]taylor: Taking taylor expansion of n in n 1547113858.421 * [misc]backup-simplify: Simplify 0 into 0 1547113858.421 * [misc]backup-simplify: Simplify 1 into 1 1547113858.421 * [misc]taylor: Taking taylor expansion of PI in n 1547113858.421 * [misc]backup-simplify: Simplify PI into PI 1547113858.421 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547113858.421 * [misc]backup-simplify: Simplify (* 2 0) into 0 1547113858.421 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547113858.422 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1547113858.422 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547113858.423 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547113858.423 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1547113858.423 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547113858.423 * [misc]taylor: Taking taylor expansion of n in n 1547113858.423 * [misc]backup-simplify: Simplify 0 into 0 1547113858.423 * [misc]backup-simplify: Simplify 1 into 1 1547113858.423 * [misc]taylor: Taking taylor expansion of PI in n 1547113858.423 * [misc]backup-simplify: Simplify PI into PI 1547113858.423 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547113858.423 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547113858.423 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547113858.424 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1547113858.424 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547113858.424 * [misc]backup-simplify: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 1547113858.425 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0 1547113858.425 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1547113858.425 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1547113858.425 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1547113858.426 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547113858.426 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547113858.427 * [misc]backup-simplify: Simplify (* (+ (log n) (log (* 2 PI))) (+ (log n) (log (* 2 PI)))) into (pow (+ (log n) (log (* 2 PI))) 2) 1547113858.427 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) into (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 1547113858.427 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 0) into 0 1547113858.428 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1547113858.428 * [misc]backup-simplify: Simplify (- 0) into 0 1547113858.428 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113858.428 * [misc]backup-simplify: Simplify (- 0) into 0 1547113858.428 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113858.428 * [misc]backup-simplify: Simplify (- 0) into 0 1547113858.428 * [misc]backup-simplify: Simplify 0 into 0 1547113858.429 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1547113858.430 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1547113858.431 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1547113858.432 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547113858.432 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1547113858.433 * [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)))))))) 1547113858.435 * [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)))))))) 1547113858.435 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1547113858.436 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1547113858.437 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 1547113858.439 * [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)))))))))) 1547113858.441 * [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))))))) 1547113858.443 * [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))))))) 1547113858.444 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1547113858.444 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 1547113858.445 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1547113858.447 * [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)))) 1547113858.449 * [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)))) 1547113858.450 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 1547113858.451 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 1547113858.457 * [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))))))))))))) 1547113858.458 * [misc]backup-simplify: Simplify (* (/ 1 (sqrt (/ 1 k))) (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2))) into (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) 1547113858.458 * [misc]approximate: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in (k n) around 0 1547113858.458 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in n 1547113858.458 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n 1547113858.458 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1547113858.458 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1547113858.458 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n 1547113858.458 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113858.458 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113858.458 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n 1547113858.458 * [misc]taylor: Taking taylor expansion of 1 in n 1547113858.458 * [misc]backup-simplify: Simplify 1 into 1 1547113858.458 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547113858.458 * [misc]taylor: Taking taylor expansion of k in n 1547113858.458 * [misc]backup-simplify: Simplify k into k 1547113858.458 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547113858.458 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1547113858.458 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1547113858.458 * [misc]taylor: Taking taylor expansion of 2 in n 1547113858.459 * [misc]backup-simplify: Simplify 2 into 2 1547113858.459 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547113858.459 * [misc]taylor: Taking taylor expansion of PI in n 1547113858.459 * [misc]backup-simplify: Simplify PI into PI 1547113858.459 * [misc]taylor: Taking taylor expansion of n in n 1547113858.459 * [misc]backup-simplify: Simplify 0 into 0 1547113858.459 * [misc]backup-simplify: Simplify 1 into 1 1547113858.459 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547113858.459 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547113858.460 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547113858.460 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1547113858.460 * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 1547113858.460 * [misc]backup-simplify: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k))) 1547113858.461 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547113858.461 * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 1547113858.462 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 1547113858.462 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1547113858.462 * [misc]taylor: Taking taylor expansion of k in n 1547113858.462 * [misc]backup-simplify: Simplify k into k 1547113858.462 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1547113858.462 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1547113858.462 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k 1547113858.462 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k 1547113858.462 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1547113858.462 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1547113858.462 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k 1547113858.462 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113858.462 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113858.462 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k 1547113858.462 * [misc]taylor: Taking taylor expansion of 1 in k 1547113858.462 * [misc]backup-simplify: Simplify 1 into 1 1547113858.462 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547113858.462 * [misc]taylor: Taking taylor expansion of k in k 1547113858.463 * [misc]backup-simplify: Simplify 0 into 0 1547113858.463 * [misc]backup-simplify: Simplify 1 into 1 1547113858.463 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547113858.463 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1547113858.463 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1547113858.463 * [misc]taylor: Taking taylor expansion of 2 in k 1547113858.463 * [misc]backup-simplify: Simplify 2 into 2 1547113858.463 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1547113858.463 * [misc]taylor: Taking taylor expansion of PI in k 1547113858.463 * [misc]backup-simplify: Simplify PI into PI 1547113858.463 * [misc]taylor: Taking taylor expansion of n in k 1547113858.463 * [misc]backup-simplify: Simplify n into n 1547113858.463 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1547113858.463 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1547113858.463 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1547113858.463 * [misc]backup-simplify: Simplify (- 1) into -1 1547113858.464 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 1547113858.464 * [misc]backup-simplify: Simplify (* 1/2 -1) into -1/2 1547113858.464 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1547113858.464 * [misc]backup-simplify: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 1547113858.464 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1547113858.464 * [misc]taylor: Taking taylor expansion of k in k 1547113858.464 * [misc]backup-simplify: Simplify 0 into 0 1547113858.464 * [misc]backup-simplify: Simplify 1 into 1 1547113858.464 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547113858.465 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1547113858.465 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k 1547113858.465 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k 1547113858.465 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1547113858.465 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1547113858.465 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k 1547113858.465 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113858.465 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113858.465 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k 1547113858.465 * [misc]taylor: Taking taylor expansion of 1 in k 1547113858.465 * [misc]backup-simplify: Simplify 1 into 1 1547113858.465 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547113858.465 * [misc]taylor: Taking taylor expansion of k in k 1547113858.465 * [misc]backup-simplify: Simplify 0 into 0 1547113858.465 * [misc]backup-simplify: Simplify 1 into 1 1547113858.465 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547113858.465 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1547113858.465 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1547113858.465 * [misc]taylor: Taking taylor expansion of 2 in k 1547113858.465 * [misc]backup-simplify: Simplify 2 into 2 1547113858.465 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1547113858.466 * [misc]taylor: Taking taylor expansion of PI in k 1547113858.466 * [misc]backup-simplify: Simplify PI into PI 1547113858.466 * [misc]taylor: Taking taylor expansion of n in k 1547113858.466 * [misc]backup-simplify: Simplify n into n 1547113858.466 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1547113858.466 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1547113858.466 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1547113858.466 * [misc]backup-simplify: Simplify (- 1) into -1 1547113858.466 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 1547113858.466 * [misc]backup-simplify: Simplify (* 1/2 -1) into -1/2 1547113858.466 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1547113858.467 * [misc]backup-simplify: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 1547113858.467 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1547113858.467 * [misc]taylor: Taking taylor expansion of k in k 1547113858.467 * [misc]backup-simplify: Simplify 0 into 0 1547113858.467 * [misc]backup-simplify: Simplify 1 into 1 1547113858.467 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547113858.467 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1547113858.468 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 0) into 0 1547113858.468 * [misc]taylor: Taking taylor expansion of 0 in n 1547113858.468 * [misc]backup-simplify: Simplify 0 into 0 1547113858.468 * [misc]backup-simplify: Simplify 0 into 0 1547113858.468 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) 1547113858.468 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n 1547113858.468 * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n 1547113858.468 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1547113858.468 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547113858.468 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n 1547113858.468 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n 1547113858.468 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113858.468 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113858.468 * [misc]taylor: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n 1547113858.469 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n 1547113858.469 * [misc]taylor: Taking taylor expansion of 1 in n 1547113858.469 * [misc]backup-simplify: Simplify 1 into 1 1547113858.469 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547113858.469 * [misc]taylor: Taking taylor expansion of k in n 1547113858.469 * [misc]backup-simplify: Simplify k into k 1547113858.469 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547113858.469 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1547113858.469 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1547113858.469 * [misc]taylor: Taking taylor expansion of 2 in n 1547113858.469 * [misc]backup-simplify: Simplify 2 into 2 1547113858.469 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547113858.469 * [misc]taylor: Taking taylor expansion of PI in n 1547113858.469 * [misc]backup-simplify: Simplify PI into PI 1547113858.469 * [misc]taylor: Taking taylor expansion of n in n 1547113858.469 * [misc]backup-simplify: Simplify 0 into 0 1547113858.469 * [misc]backup-simplify: Simplify 1 into 1 1547113858.469 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547113858.470 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547113858.470 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547113858.470 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1547113858.470 * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 1547113858.471 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547113858.472 * [misc]backup-simplify: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) 1547113858.472 * [misc]backup-simplify: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 1547113858.473 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 1547113858.473 * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) 1547113858.474 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 1547113858.475 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 1547113858.475 * [misc]backup-simplify: Simplify 0 into 0 1547113858.476 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1547113858.477 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) 1547113858.477 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n 1547113858.477 * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n 1547113858.477 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1547113858.477 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547113858.477 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n 1547113858.477 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n 1547113858.477 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113858.477 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113858.477 * [misc]taylor: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n 1547113858.477 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n 1547113858.477 * [misc]taylor: Taking taylor expansion of 1 in n 1547113858.477 * [misc]backup-simplify: Simplify 1 into 1 1547113858.477 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547113858.477 * [misc]taylor: Taking taylor expansion of k in n 1547113858.477 * [misc]backup-simplify: Simplify k into k 1547113858.477 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547113858.477 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1547113858.477 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1547113858.477 * [misc]taylor: Taking taylor expansion of 2 in n 1547113858.477 * [misc]backup-simplify: Simplify 2 into 2 1547113858.477 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547113858.477 * [misc]taylor: Taking taylor expansion of PI in n 1547113858.477 * [misc]backup-simplify: Simplify PI into PI 1547113858.477 * [misc]taylor: Taking taylor expansion of n in n 1547113858.477 * [misc]backup-simplify: Simplify 0 into 0 1547113858.477 * [misc]backup-simplify: Simplify 1 into 1 1547113858.478 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547113858.478 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547113858.478 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547113858.478 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1547113858.479 * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 1547113858.479 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547113858.480 * [misc]backup-simplify: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) 1547113858.480 * [misc]backup-simplify: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 1547113858.481 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 1547113858.482 * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) 1547113858.483 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 1547113858.484 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 1547113858.485 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1547113858.486 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1547113858.488 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1547113858.488 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1547113858.489 * [misc]backup-simplify: Simplify (- 0) into 0 1547113858.489 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113858.489 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547113858.490 * [misc]backup-simplify: Simplify (+ (* (- 1 (/ 1 k)) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1547113858.491 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into 0 1547113858.492 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1547113858.493 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into 0 1547113858.493 * [misc]backup-simplify: Simplify (- 0) into 0 1547113858.493 * [misc]backup-simplify: Simplify 0 into 0 1547113858.493 * [misc]backup-simplify: Simplify 0 into 0 1547113858.495 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1547113858.495 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) 1547113858.495 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n 1547113858.495 * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n 1547113858.495 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1547113858.496 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547113858.496 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n 1547113858.496 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n 1547113858.496 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113858.496 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113858.496 * [misc]taylor: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n 1547113858.496 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n 1547113858.496 * [misc]taylor: Taking taylor expansion of 1 in n 1547113858.496 * [misc]backup-simplify: Simplify 1 into 1 1547113858.496 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547113858.496 * [misc]taylor: Taking taylor expansion of k in n 1547113858.496 * [misc]backup-simplify: Simplify k into k 1547113858.496 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547113858.496 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1547113858.496 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1547113858.496 * [misc]taylor: Taking taylor expansion of 2 in n 1547113858.496 * [misc]backup-simplify: Simplify 2 into 2 1547113858.496 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547113858.496 * [misc]taylor: Taking taylor expansion of PI in n 1547113858.496 * [misc]backup-simplify: Simplify PI into PI 1547113858.496 * [misc]taylor: Taking taylor expansion of n in n 1547113858.496 * [misc]backup-simplify: Simplify 0 into 0 1547113858.496 * [misc]backup-simplify: Simplify 1 into 1 1547113858.496 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547113858.497 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547113858.497 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547113858.497 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1547113858.497 * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 1547113858.498 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547113858.498 * [misc]backup-simplify: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) 1547113858.499 * [misc]backup-simplify: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 1547113858.500 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 1547113858.500 * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) 1547113858.501 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 1547113858.502 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 1547113858.504 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3)))))))) 1547113858.505 * [misc]backup-simplify: Simplify (* (/ 1 (sqrt (/ 1 (- k)))) (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2))) into (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) 1547113858.505 * [misc]approximate: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in (k n) around 0 1547113858.505 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in n 1547113858.505 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n 1547113858.505 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n 1547113858.505 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n 1547113858.505 * [misc]taylor: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n 1547113858.505 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113858.505 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113858.505 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in n 1547113858.505 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547113858.505 * [misc]taylor: Taking taylor expansion of k in n 1547113858.505 * [misc]backup-simplify: Simplify k into k 1547113858.505 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547113858.505 * [misc]taylor: Taking taylor expansion of 1 in n 1547113858.506 * [misc]backup-simplify: Simplify 1 into 1 1547113858.506 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1547113858.506 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1547113858.506 * [misc]taylor: Taking taylor expansion of -2 in n 1547113858.506 * [misc]backup-simplify: Simplify -2 into -2 1547113858.506 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547113858.506 * [misc]taylor: Taking taylor expansion of PI in n 1547113858.506 * [misc]backup-simplify: Simplify PI into PI 1547113858.506 * [misc]taylor: Taking taylor expansion of n in n 1547113858.506 * [misc]backup-simplify: Simplify 0 into 0 1547113858.506 * [misc]backup-simplify: Simplify 1 into 1 1547113858.506 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547113858.506 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547113858.507 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1547113858.507 * [misc]backup-simplify: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 1547113858.507 * [misc]backup-simplify: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1)) 1547113858.508 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547113858.508 * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 1547113858.509 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 1547113858.509 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1547113858.509 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1547113858.509 * [misc]taylor: Taking taylor expansion of -1 in n 1547113858.509 * [misc]backup-simplify: Simplify -1 into -1 1547113858.509 * [misc]taylor: Taking taylor expansion of k in n 1547113858.509 * [misc]backup-simplify: Simplify k into k 1547113858.509 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1547113858.509 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1547113858.509 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1547113858.509 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1547113858.510 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) 1547113858.510 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in k 1547113858.510 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k 1547113858.510 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k 1547113858.510 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k 1547113858.510 * [misc]taylor: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k 1547113858.510 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113858.510 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113858.510 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in k 1547113858.510 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547113858.510 * [misc]taylor: Taking taylor expansion of k in k 1547113858.510 * [misc]backup-simplify: Simplify 0 into 0 1547113858.510 * [misc]backup-simplify: Simplify 1 into 1 1547113858.511 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547113858.511 * [misc]taylor: Taking taylor expansion of 1 in k 1547113858.511 * [misc]backup-simplify: Simplify 1 into 1 1547113858.511 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1547113858.511 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1547113858.511 * [misc]taylor: Taking taylor expansion of -2 in k 1547113858.511 * [misc]backup-simplify: Simplify -2 into -2 1547113858.511 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1547113858.511 * [misc]taylor: Taking taylor expansion of PI in k 1547113858.511 * [misc]backup-simplify: Simplify PI into PI 1547113858.511 * [misc]taylor: Taking taylor expansion of n in k 1547113858.511 * [misc]backup-simplify: Simplify n into n 1547113858.511 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1547113858.511 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1547113858.511 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1547113858.511 * [misc]backup-simplify: Simplify (+ 1 0) into 1 1547113858.512 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1547113858.512 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1547113858.512 * [misc]backup-simplify: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) 1547113858.512 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1547113858.512 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1547113858.512 * [misc]taylor: Taking taylor expansion of -1 in k 1547113858.512 * [misc]backup-simplify: Simplify -1 into -1 1547113858.512 * [misc]taylor: Taking taylor expansion of k in k 1547113858.512 * [misc]backup-simplify: Simplify 0 into 0 1547113858.512 * [misc]backup-simplify: Simplify 1 into 1 1547113858.512 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1547113858.512 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547113858.513 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1547113858.513 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) 1547113858.513 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in k 1547113858.513 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k 1547113858.513 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k 1547113858.513 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k 1547113858.513 * [misc]taylor: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k 1547113858.513 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113858.513 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113858.513 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in k 1547113858.513 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547113858.513 * [misc]taylor: Taking taylor expansion of k in k 1547113858.513 * [misc]backup-simplify: Simplify 0 into 0 1547113858.513 * [misc]backup-simplify: Simplify 1 into 1 1547113858.514 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547113858.514 * [misc]taylor: Taking taylor expansion of 1 in k 1547113858.514 * [misc]backup-simplify: Simplify 1 into 1 1547113858.514 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1547113858.514 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1547113858.514 * [misc]taylor: Taking taylor expansion of -2 in k 1547113858.514 * [misc]backup-simplify: Simplify -2 into -2 1547113858.514 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1547113858.514 * [misc]taylor: Taking taylor expansion of PI in k 1547113858.514 * [misc]backup-simplify: Simplify PI into PI 1547113858.514 * [misc]taylor: Taking taylor expansion of n in k 1547113858.514 * [misc]backup-simplify: Simplify n into n 1547113858.514 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1547113858.514 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1547113858.514 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1547113858.514 * [misc]backup-simplify: Simplify (+ 1 0) into 1 1547113858.515 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1547113858.515 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1547113858.515 * [misc]backup-simplify: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) 1547113858.515 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1547113858.515 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1547113858.515 * [misc]taylor: Taking taylor expansion of -1 in k 1547113858.515 * [misc]backup-simplify: Simplify -1 into -1 1547113858.515 * [misc]taylor: Taking taylor expansion of k in k 1547113858.515 * [misc]backup-simplify: Simplify 0 into 0 1547113858.515 * [misc]backup-simplify: Simplify 1 into 1 1547113858.515 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1547113858.515 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547113858.516 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1547113858.516 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) 1547113858.516 * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n 1547113858.516 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1547113858.516 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547113858.516 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n 1547113858.516 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n 1547113858.516 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113858.516 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113858.516 * [misc]taylor: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n 1547113858.516 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1547113858.516 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1547113858.516 * [misc]taylor: Taking taylor expansion of -2 in n 1547113858.516 * [misc]backup-simplify: Simplify -2 into -2 1547113858.516 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547113858.516 * [misc]taylor: Taking taylor expansion of PI in n 1547113858.516 * [misc]backup-simplify: Simplify PI into PI 1547113858.516 * [misc]taylor: Taking taylor expansion of n in n 1547113858.516 * [misc]backup-simplify: Simplify 0 into 0 1547113858.516 * [misc]backup-simplify: Simplify 1 into 1 1547113858.516 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547113858.516 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547113858.517 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1547113858.517 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in n 1547113858.517 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547113858.517 * [misc]taylor: Taking taylor expansion of k in n 1547113858.517 * [misc]backup-simplify: Simplify k into k 1547113858.517 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547113858.517 * [misc]taylor: Taking taylor expansion of 1 in n 1547113858.517 * [misc]backup-simplify: Simplify 1 into 1 1547113858.517 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547113858.517 * [misc]backup-simplify: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 1547113858.518 * [misc]backup-simplify: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) 1547113858.518 * [misc]backup-simplify: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 1547113858.519 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 1547113858.519 * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) 1547113858.519 * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) 1547113858.520 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1547113858.520 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1547113858.521 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) 1547113858.521 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n 1547113858.521 * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n 1547113858.521 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1547113858.521 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547113858.521 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n 1547113858.521 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n 1547113858.521 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113858.521 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113858.521 * [misc]taylor: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n 1547113858.521 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1547113858.521 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1547113858.521 * [misc]taylor: Taking taylor expansion of -2 in n 1547113858.521 * [misc]backup-simplify: Simplify -2 into -2 1547113858.521 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547113858.521 * [misc]taylor: Taking taylor expansion of PI in n 1547113858.521 * [misc]backup-simplify: Simplify PI into PI 1547113858.521 * [misc]taylor: Taking taylor expansion of n in n 1547113858.521 * [misc]backup-simplify: Simplify 0 into 0 1547113858.521 * [misc]backup-simplify: Simplify 1 into 1 1547113858.521 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547113858.521 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547113858.522 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1547113858.522 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in n 1547113858.522 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547113858.522 * [misc]taylor: Taking taylor expansion of k in n 1547113858.522 * [misc]backup-simplify: Simplify k into k 1547113858.522 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547113858.522 * [misc]taylor: Taking taylor expansion of 1 in n 1547113858.522 * [misc]backup-simplify: Simplify 1 into 1 1547113858.522 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547113858.522 * [misc]backup-simplify: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 1547113858.523 * [misc]backup-simplify: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) 1547113858.523 * [misc]backup-simplify: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 1547113858.523 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 1547113858.524 * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) 1547113858.524 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) 1547113858.525 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) 1547113858.525 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547113858.525 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1547113858.525 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113858.526 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1547113858.526 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1547113858.529 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1547113858.529 * [misc]backup-simplify: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (/ 1 k) 1))) into 0 1547113858.530 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into 0 1547113858.531 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1547113858.532 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into 0 1547113858.532 * [misc]backup-simplify: Simplify 0 into 0 1547113858.532 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113858.533 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1547113858.533 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) 1547113858.533 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n 1547113858.533 * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n 1547113858.533 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1547113858.533 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547113858.533 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n 1547113858.533 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n 1547113858.533 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113858.533 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113858.533 * [misc]taylor: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n 1547113858.533 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1547113858.533 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1547113858.533 * [misc]taylor: Taking taylor expansion of -2 in n 1547113858.533 * [misc]backup-simplify: Simplify -2 into -2 1547113858.533 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547113858.533 * [misc]taylor: Taking taylor expansion of PI in n 1547113858.533 * [misc]backup-simplify: Simplify PI into PI 1547113858.533 * [misc]taylor: Taking taylor expansion of n in n 1547113858.534 * [misc]backup-simplify: Simplify 0 into 0 1547113858.534 * [misc]backup-simplify: Simplify 1 into 1 1547113858.534 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547113858.534 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547113858.534 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1547113858.534 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in n 1547113858.534 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547113858.534 * [misc]taylor: Taking taylor expansion of k in n 1547113858.534 * [misc]backup-simplify: Simplify k into k 1547113858.534 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547113858.534 * [misc]taylor: Taking taylor expansion of 1 in n 1547113858.534 * [misc]backup-simplify: Simplify 1 into 1 1547113858.535 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547113858.535 * [misc]backup-simplify: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 1547113858.535 * [misc]backup-simplify: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) 1547113858.536 * [misc]backup-simplify: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 1547113858.536 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 1547113858.536 * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) 1547113858.537 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) 1547113858.537 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) 1547113858.539 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (* 1 (/ 1 (- k)))) (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))))))))) 1547113858.539 * * * [misc]progress: simplifying candidates 1547113858.539 * * * * [misc]progress: [ 1 / 88 ] simplifiying candidate # 1547113858.539 * * * * [misc]progress: [ 2 / 88 ] simplifiying candidate # 1547113858.539 * * * * [misc]progress: [ 3 / 88 ] simplifiying candidate # 1547113858.539 * [enter]simplify: Simplifying (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)) 1547113858.539 * * [misc]simplify: iters left: 6 (11 enodes) 1547113858.542 * * [misc]simplify: iters left: 5 (29 enodes) 1547113858.551 * * [misc]simplify: iters left: 4 (59 enodes) 1547113858.567 * * [misc]simplify: iters left: 3 (146 enodes) 1547113858.637 * [exit]simplify: Simplified to (* (- 1/2 (/ k 2)) (log (* (* 2 PI) n))) 1547113858.637 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ 1 (sqrt k)) (exp (* (- 1/2 (/ k 2)) (log (* (* 2 PI) n)))))) 1547113858.637 * * * * [misc]progress: [ 4 / 88 ] simplifiying candidate # 1547113858.637 * * * * [misc]progress: [ 5 / 88 ] simplifiying candidate # 1547113858.637 * [enter]simplify: Simplifying (* (* 2 PI) n) 1547113858.637 * * [misc]simplify: iters left: 4 (5 enodes) 1547113858.638 * * [misc]simplify: iters left: 3 (9 enodes) 1547113858.640 * * [misc]simplify: iters left: 2 (15 enodes) 1547113858.642 * * [misc]simplify: iters left: 1 (17 enodes) 1547113858.645 * [exit]simplify: Simplified to (* (* 2 PI) n) 1547113858.645 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (* 1 (/ (- 1 k) 2))))) 1547113858.645 * * * * [misc]progress: [ 6 / 88 ] simplifiying candidate # 1547113858.645 * [enter]simplify: Simplifying (pow (* (* 2 PI) n) (/ k 2)) 1547113858.645 * * [misc]simplify: iters left: 5 (8 enodes) 1547113858.646 * * [misc]simplify: iters left: 4 (12 enodes) 1547113858.650 * * [misc]simplify: iters left: 3 (18 enodes) 1547113858.655 * * [misc]simplify: iters left: 2 (20 enodes) 1547113858.661 * [exit]simplify: Simplified to (pow (* 2 (* n PI)) (/ k 2)) 1547113858.661 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ 1 (sqrt k)) (/ (pow (* (* 2 PI) n) (/ 1 2)) (pow (* 2 (* n PI)) (/ k 2))))) 1547113858.661 * * * * [misc]progress: [ 7 / 88 ] simplifiying candidate # 1547113858.661 * [enter]simplify: Simplifying (cbrt (/ (- 1 k) 2)) 1547113858.661 * * [misc]simplify: iters left: 5 (6 enodes) 1547113858.664 * * [misc]simplify: iters left: 4 (14 enodes) 1547113858.668 * * [misc]simplify: iters left: 3 (17 enodes) 1547113858.670 * * [misc]simplify: iters left: 2 (19 enodes) 1547113858.673 * [exit]simplify: Simplified to (cbrt (/ (- 1 k) 2)) 1547113858.673 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) (cbrt (/ (- 1 k) 2))))) 1547113858.673 * * * * [misc]progress: [ 8 / 88 ] simplifiying candidate # 1547113858.673 * [enter]simplify: Simplifying (sqrt (/ (- 1 k) 2)) 1547113858.673 * * [misc]simplify: iters left: 5 (6 enodes) 1547113858.675 * * [misc]simplify: iters left: 4 (14 enodes) 1547113858.677 * * [misc]simplify: iters left: 3 (17 enodes) 1547113858.680 * * [misc]simplify: iters left: 2 (19 enodes) 1547113858.683 * [exit]simplify: Simplified to (sqrt (/ (- 1 k) 2)) 1547113858.683 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (sqrt (/ (- 1 k) 2))) (sqrt (/ (- 1 k) 2))))) 1547113858.683 * * * * [misc]progress: [ 9 / 88 ] simplifiying candidate # 1547113858.683 * [enter]simplify: Simplifying (/ (- 1 k) 2) 1547113858.683 * * [misc]simplify: iters left: 4 (5 enodes) 1547113858.684 * * [misc]simplify: iters left: 3 (13 enodes) 1547113858.686 * * [misc]simplify: iters left: 2 (16 enodes) 1547113858.689 * * [misc]simplify: iters left: 1 (18 enodes) 1547113858.691 * [exit]simplify: Simplified to (/ (- 1 k) 2) 1547113858.691 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) 1) (/ (- 1 k) 2)))) 1547113858.691 * * * * [misc]progress: [ 10 / 88 ] simplifiying candidate # 1547113858.691 * [enter]simplify: Simplifying (/ 1 2) 1547113858.691 * * [misc]simplify: iters left: 2 (3 enodes) 1547113858.692 * * [misc]simplify: iters left: 1 (6 enodes) 1547113858.693 * [exit]simplify: Simplified to 1/2 1547113858.693 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (- 1 k)) 1/2))) 1547113858.693 * * * * [misc]progress: [ 11 / 88 ] simplifiying candidate # 1547113858.693 * [enter]simplify: Simplifying (pow (* 2 PI) (/ (- 1 k) 2)) 1547113858.693 * * [misc]simplify: iters left: 5 (8 enodes) 1547113858.695 * * [misc]simplify: iters left: 4 (17 enodes) 1547113858.700 * * [misc]simplify: iters left: 3 (20 enodes) 1547113858.706 * * [misc]simplify: iters left: 2 (22 enodes) 1547113858.712 * [exit]simplify: Simplified to (pow (* 2 PI) (- 1/2 (/ k 2))) 1547113858.712 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* 2 PI) (- 1/2 (/ k 2))) (pow n (/ (- 1 k) 2))))) 1547113858.712 * * * * [misc]progress: [ 12 / 88 ] simplifiying candidate # 1547113858.712 * * * * [misc]progress: [ 13 / 88 ] simplifiying candidate # 1547113858.712 * * * * [misc]progress: [ 14 / 88 ] simplifiying candidate # 1547113858.713 * * * * [misc]progress: [ 15 / 88 ] simplifiying candidate # 1547113858.713 * * * * [misc]progress: [ 16 / 88 ] simplifiying candidate # 1547113858.713 * * * * [misc]progress: [ 17 / 88 ] simplifiying candidate # 1547113858.713 * * * * [misc]progress: [ 18 / 88 ] simplifiying candidate # 1547113858.713 * * * * [misc]progress: [ 19 / 88 ] simplifiying candidate # 1547113858.713 * * * * [misc]progress: [ 20 / 88 ] simplifiying candidate # 1547113858.713 * * * * [misc]progress: [ 21 / 88 ] simplifiying candidate # 1547113858.713 * * * * [misc]progress: [ 22 / 88 ] simplifiying candidate # 1547113858.713 * [enter]simplify: Simplifying (- 1/2) 1547113858.713 * * [misc]simplify: iters left: 2 (2 enodes) 1547113858.715 * * [misc]simplify: iters left: 1 (3 enodes) 1547113858.715 * [exit]simplify: Simplified to -1/2 1547113858.715 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) 1547113858.715 * * * * [misc]progress: [ 23 / 88 ] simplifiying candidate # 1547113858.716 * [enter]simplify: Simplifying (- 1) 1547113858.716 * * [misc]simplify: iters left: 2 (2 enodes) 1547113858.717 * * [misc]simplify: iters left: 1 (5 enodes) 1547113858.718 * [exit]simplify: Simplified to -1 1547113858.718 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (pow (sqrt k) -1) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) 1547113858.718 * * * * [misc]progress: [ 24 / 88 ] simplifiying candidate # 1547113858.718 * * * * [misc]progress: [ 25 / 88 ] simplifiying candidate # 1547113858.718 * * * * [misc]progress: [ 26 / 88 ] simplifiying candidate # 1547113858.718 * * * * [misc]progress: [ 27 / 88 ] simplifiying candidate # 1547113858.718 * * * * [misc]progress: [ 28 / 88 ] simplifiying candidate # 1547113858.718 * * * * [misc]progress: [ 29 / 88 ] simplifiying candidate # 1547113858.718 * * * * [misc]progress: [ 30 / 88 ] simplifiying candidate # 1547113858.718 * * * * [misc]progress: [ 31 / 88 ] simplifiying candidate # 1547113858.718 * * * * [misc]progress: [ 32 / 88 ] simplifiying candidate # 1547113858.718 * * * * [misc]progress: [ 33 / 88 ] simplifiying candidate # 1547113858.719 * * * * [misc]progress: [ 34 / 88 ] simplifiying candidate # 1547113858.719 * * * * [misc]progress: [ 35 / 88 ] simplifiying candidate # 1547113858.719 * [enter]simplify: Simplifying (cbrt (sqrt k)) 1547113858.719 * * [misc]simplify: iters left: 2 (3 enodes) 1547113858.720 * [exit]simplify: Simplified to (cbrt (sqrt k)) 1547113858.720 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (/ (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) 1547113858.720 * * * * [misc]progress: [ 36 / 88 ] simplifiying candidate # 1547113858.720 * [enter]simplify: Simplifying (sqrt (sqrt k)) 1547113858.720 * * [misc]simplify: iters left: 2 (3 enodes) 1547113858.721 * [exit]simplify: Simplified to (sqrt (sqrt k)) 1547113858.721 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) 1547113858.721 * * * * [misc]progress: [ 37 / 88 ] simplifiying candidate # 1547113858.722 * [enter]simplify: Simplifying (sqrt k) 1547113858.722 * * [misc]simplify: iters left: 1 (2 enodes) 1547113858.722 * [exit]simplify: Simplified to (sqrt k) 1547113858.722 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (/ (/ 1 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) 1547113858.722 * * * * [misc]progress: [ 38 / 88 ] simplifiying candidate # 1547113858.722 * * * * [misc]progress: [ 39 / 88 ] simplifiying candidate # 1547113858.723 * * * * [misc]progress: [ 40 / 88 ] simplifiying candidate # 1547113858.723 * * * * [misc]progress: [ 41 / 88 ] simplifiying candidate # 1547113858.723 * * * * [misc]progress: [ 42 / 88 ] simplifiying candidate # 1547113858.723 * * * * [misc]progress: [ 43 / 88 ] simplifiying candidate # 1547113858.723 * * * * [misc]progress: [ 44 / 88 ] simplifiying candidate # 1547113858.723 * * * * [misc]progress: [ 45 / 88 ] simplifiying candidate # 1547113858.723 * * * * [misc]progress: [ 46 / 88 ] simplifiying candidate # 1547113858.723 * * * * [misc]progress: [ 47 / 88 ] simplifiying candidate # 1547113858.723 * * * * [misc]progress: [ 48 / 88 ] simplifiying candidate # 1547113858.723 * * * * [misc]progress: [ 49 / 88 ] simplifiying candidate # 1547113858.723 * * * * [misc]progress: [ 50 / 88 ] simplifiying candidate # 1547113858.723 * * * * [misc]progress: [ 51 / 88 ] simplifiying candidate # 1547113858.723 * * * * [misc]progress: [ 52 / 88 ] simplifiying candidate # 1547113858.724 * [enter]simplify: Simplifying (+ (- (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))) 1547113858.724 * * [misc]simplify: iters left: 6 (15 enodes) 1547113858.729 * * [misc]simplify: iters left: 5 (34 enodes) 1547113858.736 * * [misc]simplify: iters left: 4 (67 enodes) 1547113858.752 * * [misc]simplify: iters left: 3 (165 enodes) 1547113858.835 * [exit]simplify: Simplified to (fma (log (* (* n PI) 2)) (- 1/2 (/ k 2)) (- (log (sqrt k)))) 1547113858.835 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (log (* (* n PI) 2)) (- 1/2 (/ k 2)) (- (log (sqrt k)))))) 1547113858.835 * * * * [misc]progress: [ 53 / 88 ] simplifiying candidate # 1547113858.835 * [enter]simplify: Simplifying (+ (- (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))) 1547113858.835 * * [misc]simplify: iters left: 6 (15 enodes) 1547113858.839 * * [misc]simplify: iters left: 5 (34 enodes) 1547113858.847 * * [misc]simplify: iters left: 4 (67 enodes) 1547113858.874 * * [misc]simplify: iters left: 3 (165 enodes) 1547113858.995 * [exit]simplify: Simplified to (fma (log (* (* n PI) 2)) (- 1/2 (/ k 2)) (- (log (sqrt k)))) 1547113858.995 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (log (* (* n PI) 2)) (- 1/2 (/ k 2)) (- (log (sqrt k)))))) 1547113858.995 * * * * [misc]progress: [ 54 / 88 ] simplifiying candidate # 1547113858.995 * [enter]simplify: Simplifying (+ (- (log (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) 1547113858.995 * * [misc]simplify: iters left: 6 (15 enodes) 1547113858.998 * * [misc]simplify: iters left: 5 (30 enodes) 1547113859.004 * * [misc]simplify: iters left: 4 (51 enodes) 1547113859.015 * * [misc]simplify: iters left: 3 (99 enodes) 1547113859.053 * * [misc]simplify: iters left: 2 (301 enodes) 1547113859.294 * [exit]simplify: Simplified to (fma (log (* 2 (* n PI))) (/ (- 1 k) 2) (- (log (sqrt k)))) 1547113859.294 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (log (* 2 (* n PI))) (/ (- 1 k) 2) (- (log (sqrt k)))))) 1547113859.294 * * * * [misc]progress: [ 55 / 88 ] simplifiying candidate # 1547113859.294 * [enter]simplify: Simplifying (+ (log (/ 1 (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))) 1547113859.295 * * [misc]simplify: iters left: 6 (15 enodes) 1547113859.299 * * [misc]simplify: iters left: 5 (38 enodes) 1547113859.306 * * [misc]simplify: iters left: 4 (71 enodes) 1547113859.321 * * [misc]simplify: iters left: 3 (173 enodes) 1547113859.409 * [exit]simplify: Simplified to (fma (/ (- 1 k) 2) (log (* (* n 2) PI)) (- (log (sqrt k)))) 1547113859.409 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (/ (- 1 k) 2) (log (* (* n 2) PI)) (- (log (sqrt k)))))) 1547113859.409 * * * * [misc]progress: [ 56 / 88 ] simplifiying candidate # 1547113859.409 * [enter]simplify: Simplifying (+ (log (/ 1 (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))) 1547113859.410 * * [misc]simplify: iters left: 6 (15 enodes) 1547113859.417 * * [misc]simplify: iters left: 5 (38 enodes) 1547113859.429 * * [misc]simplify: iters left: 4 (71 enodes) 1547113859.450 * * [misc]simplify: iters left: 3 (173 enodes) 1547113859.534 * [exit]simplify: Simplified to (fma (/ (- 1 k) 2) (log (* (* n 2) PI)) (- (log (sqrt k)))) 1547113859.535 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (/ (- 1 k) 2) (log (* (* n 2) PI)) (- (log (sqrt k)))))) 1547113859.535 * * * * [misc]progress: [ 57 / 88 ] simplifiying candidate # 1547113859.535 * [enter]simplify: Simplifying (+ (log (/ 1 (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) 1547113859.535 * * [misc]simplify: iters left: 6 (15 enodes) 1547113859.539 * * [misc]simplify: iters left: 5 (34 enodes) 1547113859.545 * * [misc]simplify: iters left: 4 (55 enodes) 1547113859.561 * * [misc]simplify: iters left: 3 (107 enodes) 1547113859.622 * * [misc]simplify: iters left: 2 (347 enodes) 1547113859.882 * [exit]simplify: Simplified to (fma (- 1/2 (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k)))) 1547113859.882 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (- 1/2 (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k)))))) 1547113859.882 * * * * [misc]progress: [ 58 / 88 ] simplifiying candidate # 1547113859.882 * * * * [misc]progress: [ 59 / 88 ] simplifiying candidate # 1547113859.882 * * * * [misc]progress: [ 60 / 88 ] simplifiying candidate # 1547113859.882 * [enter]simplify: Simplifying (* (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k))) (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) 1547113859.882 * * [misc]simplify: iters left: 6 (17 enodes) 1547113859.890 * * [misc]simplify: iters left: 5 (42 enodes) 1547113859.911 * * [misc]simplify: iters left: 4 (98 enodes) 1547113859.957 * * [misc]simplify: iters left: 3 (175 enodes) 1547113860.020 * * [misc]simplify: iters left: 2 (325 enodes) 1547113860.205 * * [misc]simplify: iters left: 1 (454 enodes) 1547113860.465 * [exit]simplify: Simplified to (* (* (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (* (sqrt k) k))) 1547113860.465 * [misc]simplify: Simplified (2 1) to (λ (k n) (cbrt (* (* (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (* (sqrt k) k))))) 1547113860.465 * * * * [misc]progress: [ 61 / 88 ] simplifiying candidate # 1547113860.465 * * * * [misc]progress: [ 62 / 88 ] simplifiying candidate # 1547113860.465 * * * * [misc]progress: [ 63 / 88 ] simplifiying candidate # 1547113860.466 * * * * [misc]progress: [ 64 / 88 ] simplifiying candidate # 1547113860.466 * [enter]simplify: Simplifying (* 1 (pow (* (* 2 PI) n) (/ 1 2))) 1547113860.466 * * [misc]simplify: iters left: 6 (9 enodes) 1547113860.471 * * [misc]simplify: iters left: 5 (17 enodes) 1547113860.476 * * [misc]simplify: iters left: 4 (26 enodes) 1547113860.483 * * [misc]simplify: iters left: 3 (27 enodes) 1547113860.489 * [exit]simplify: Simplified to (sqrt (* PI (* 2 n))) 1547113860.489 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* PI (* 2 n))) (* (sqrt k) (pow (* (* 2 PI) n) (/ k 2))))) 1547113860.489 * [enter]simplify: Simplifying (* (sqrt k) (pow (* (* 2 PI) n) (/ k 2))) 1547113860.489 * * [misc]simplify: iters left: 6 (10 enodes) 1547113860.493 * * [misc]simplify: iters left: 5 (15 enodes) 1547113860.498 * * [misc]simplify: iters left: 4 (21 enodes) 1547113860.504 * * [misc]simplify: iters left: 3 (22 enodes) 1547113860.510 * [exit]simplify: Simplified to (* (pow (* (* 2 PI) n) (/ k 2)) (sqrt k)) 1547113860.511 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (sqrt (* PI (* 2 n))) (* (pow (* (* 2 PI) n) (/ k 2)) (sqrt k)))) 1547113860.511 * * * * [misc]progress: [ 65 / 88 ] simplifiying candidate # 1547113860.511 * * * * [misc]progress: [ 66 / 88 ] simplifiying candidate # 1547113860.511 * [enter]simplify: Simplifying (pow n (/ (- 1 k) 2)) 1547113860.511 * * [misc]simplify: iters left: 5 (7 enodes) 1547113860.515 * * [misc]simplify: iters left: 4 (15 enodes) 1547113860.519 * * [misc]simplify: iters left: 3 (18 enodes) 1547113860.524 * * [misc]simplify: iters left: 2 (20 enodes) 1547113860.530 * [exit]simplify: Simplified to (pow n (- 1/2 (/ k 2))) 1547113860.530 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ 1 (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2))) (pow n (- 1/2 (/ k 2))))) 1547113860.530 * * * * [misc]progress: [ 67 / 88 ] simplifiying candidate # 1547113860.530 * [enter]simplify: Simplifying (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) 1547113860.530 * * [misc]simplify: iters left: 6 (11 enodes) 1547113860.535 * * [misc]simplify: iters left: 5 (23 enodes) 1547113860.542 * * [misc]simplify: iters left: 4 (32 enodes) 1547113860.551 * * [misc]simplify: iters left: 3 (35 enodes) 1547113860.561 * [exit]simplify: Simplified to (cbrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) 1547113860.561 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ 1 (sqrt k)) (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) (cbrt (pow (* PI (* n 2)) (/ (- 1 k) 2))))) 1547113860.561 * * * * [misc]progress: [ 68 / 88 ] simplifiying candidate # 1547113860.561 * [enter]simplify: Simplifying (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) 1547113860.562 * * [misc]simplify: iters left: 6 (11 enodes) 1547113860.566 * * [misc]simplify: iters left: 5 (23 enodes) 1547113860.573 * * [misc]simplify: iters left: 4 (32 enodes) 1547113860.583 * * [misc]simplify: iters left: 3 (35 enodes) 1547113860.592 * [exit]simplify: Simplified to (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) 1547113860.592 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ 1 (sqrt k)) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))))) 1547113860.592 * * * * [misc]progress: [ 69 / 88 ] simplifiying candidate # 1547113860.592 * [enter]simplify: Simplifying (pow (* (* 2 PI) n) (/ (- 1 k) 2)) 1547113860.593 * * [misc]simplify: iters left: 5 (10 enodes) 1547113860.597 * * [misc]simplify: iters left: 4 (22 enodes) 1547113860.604 * * [misc]simplify: iters left: 3 (31 enodes) 1547113860.613 * * [misc]simplify: iters left: 2 (34 enodes) 1547113860.621 * [exit]simplify: Simplified to (pow (* (* n 2) PI) (/ (- 1 k) 2)) 1547113860.622 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ 1 (sqrt k)) 1) (pow (* (* n 2) PI) (/ (- 1 k) 2)))) 1547113860.622 * * * * [misc]progress: [ 70 / 88 ] simplifiying candidate # 1547113860.622 * [enter]simplify: Simplifying (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k)))) 1547113860.622 * * [misc]simplify: iters left: 6 (6 enodes) 1547113860.624 * * [misc]simplify: iters left: 5 (8 enodes) 1547113860.626 * [exit]simplify: Simplified to (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k)))) 1547113860.627 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k)))) (* (cbrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) 1547113860.627 * * * * [misc]progress: [ 71 / 88 ] simplifiying candidate # 1547113860.627 * [enter]simplify: Simplifying (sqrt (/ 1 (sqrt k))) 1547113860.627 * * [misc]simplify: iters left: 4 (5 enodes) 1547113860.629 * * [misc]simplify: iters left: 3 (7 enodes) 1547113860.631 * [exit]simplify: Simplified to (sqrt (/ 1 (sqrt k))) 1547113860.631 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (/ 1 (sqrt k))) (* (sqrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) 1547113860.631 * * * * [misc]progress: [ 72 / 88 ] simplifiying candidate # 1547113860.631 * * * * [misc]progress: [ 73 / 88 ] simplifiying candidate # 1547113860.631 * * * * [misc]progress: [ 74 / 88 ] simplifiying candidate # 1547113860.631 * [enter]simplify: Simplifying (pow (* (* 2 PI) n) (/ k 2)) 1547113860.632 * * [misc]simplify: iters left: 5 (8 enodes) 1547113860.636 * * [misc]simplify: iters left: 4 (12 enodes) 1547113860.640 * * [misc]simplify: iters left: 3 (18 enodes) 1547113860.646 * * [misc]simplify: iters left: 2 (20 enodes) 1547113860.651 * [exit]simplify: Simplified to (pow (* 2 (* n PI)) (/ k 2)) 1547113860.651 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ 1 2))) (pow (* 2 (* n PI)) (/ k 2)))) 1547113860.651 * * * * [misc]progress: [ 75 / 88 ] simplifiying candidate # 1547113860.652 * [enter]simplify: Simplifying (* 1 (pow (* (* 2 PI) n) (/ (- 1 k) 2))) 1547113860.652 * * [misc]simplify: iters left: 6 (11 enodes) 1547113860.657 * * [misc]simplify: iters left: 5 (24 enodes) 1547113860.666 * * [misc]simplify: iters left: 4 (35 enodes) 1547113860.676 * * [misc]simplify: iters left: 3 (38 enodes) 1547113860.685 * [exit]simplify: Simplified to (pow (* (* n PI) 2) (- 1/2 (/ k 2))) 1547113860.685 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (pow (* (* n PI) 2) (- 1/2 (/ k 2))) (sqrt k))) 1547113860.685 * * * * [misc]progress: [ 76 / 88 ] simplifiying candidate # 1547113860.685 * * * * [misc]progress: [ 77 / 88 ] simplifiying candidate # 1547113860.685 * [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))))) 1547113860.686 * * [misc]simplify: iters left: 6 (37 enodes) 1547113860.703 * * [misc]simplify: iters left: 5 (108 enodes) 1547113860.754 * * [misc]simplify: iters left: 4 (368 enodes) 1547113861.020 * [exit]simplify: Simplified to (fma -1/2 (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) (fma (* (* (* k k) (log n)) (* (log (* PI 2)) 1/4)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (fma (* (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (log (* PI 2)) (log (* PI 2)))) (* (* k k) 1/8) (fma (* (* (* k k) (log n)) (* (log n) 1/8)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (pow n 1/2) (pow (* PI 2) 1/2)))))) 1547113861.020 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ 1 (sqrt k)) (fma -1/2 (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) (fma (* (* (* k k) (log n)) (* (log (* PI 2)) 1/4)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (fma (* (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (log (* PI 2)) (log (* PI 2)))) (* (* k k) 1/8) (fma (* (* (* k k) (log n)) (* (log n) 1/8)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (pow n 1/2) (pow (* PI 2) 1/2)))))))) 1547113861.020 * * * * [misc]progress: [ 78 / 88 ] simplifiying candidate # 1547113861.020 * [enter]simplify: Simplifying (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) 1547113861.021 * * [misc]simplify: iters left: 6 (15 enodes) 1547113861.028 * * [misc]simplify: iters left: 5 (35 enodes) 1547113861.036 * * [misc]simplify: iters left: 4 (72 enodes) 1547113861.056 * * [misc]simplify: iters left: 3 (240 enodes) 1547113861.203 * [exit]simplify: Simplified to (pow (exp (- 1/2 (* 1/2 k))) (+ (log (* 2 PI)) (log n))) 1547113861.203 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ 1 (sqrt k)) (pow (exp (- 1/2 (* 1/2 k))) (+ (log (* 2 PI)) (log n))))) 1547113861.203 * * * * [misc]progress: [ 79 / 88 ] simplifiying candidate # 1547113861.203 * [enter]simplify: Simplifying (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) 1547113861.203 * * [misc]simplify: iters left: 6 (16 enodes) 1547113861.210 * * [misc]simplify: iters left: 5 (35 enodes) 1547113861.223 * * [misc]simplify: iters left: 4 (76 enodes) 1547113861.259 * * [misc]simplify: iters left: 3 (278 enodes) 1547113861.861 * [exit]simplify: Simplified to (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))) 1547113861.861 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ 1 (sqrt k)) (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))))) 1547113861.861 * * * * [misc]progress: [ 80 / 88 ] simplifiying candidate # 1547113861.861 * [enter]simplify: Simplifying (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) 1547113861.861 * [misc]simplify: Simplified (2 1) to (λ (k n) (* +nan.0 (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) 1547113861.861 * * * * [misc]progress: [ 81 / 88 ] simplifiying candidate # 1547113861.861 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) 1547113861.861 * [misc]simplify: Simplified (2 1) to (λ (k n) (* +nan.0 (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) 1547113861.861 * * * * [misc]progress: [ 82 / 88 ] simplifiying candidate # 1547113861.862 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) 1547113861.862 * [misc]simplify: Simplified (2 1) to (λ (k n) (* +nan.0 (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) 1547113861.862 * * * * [misc]progress: [ 83 / 88 ] simplifiying candidate # 1547113861.862 * [enter]simplify: Simplifying (* 2 (* n PI)) 1547113861.862 * * [misc]simplify: iters left: 4 (5 enodes) 1547113861.864 * * [misc]simplify: iters left: 3 (9 enodes) 1547113861.867 * * [misc]simplify: iters left: 2 (15 enodes) 1547113861.871 * * [misc]simplify: iters left: 1 (17 enodes) 1547113861.875 * [exit]simplify: Simplified to (* (* PI n) 2) 1547113861.876 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* PI n) 2) (/ (- 1 k) 2)))) 1547113861.876 * * * * [misc]progress: [ 84 / 88 ] simplifiying candidate # 1547113861.876 * [enter]simplify: Simplifying (* 2 (* n PI)) 1547113861.876 * * [misc]simplify: iters left: 4 (5 enodes) 1547113861.878 * * [misc]simplify: iters left: 3 (9 enodes) 1547113861.881 * * [misc]simplify: iters left: 2 (15 enodes) 1547113861.886 * * [misc]simplify: iters left: 1 (17 enodes) 1547113861.890 * [exit]simplify: Simplified to (* (* PI n) 2) 1547113861.890 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* PI n) 2) (/ (- 1 k) 2)))) 1547113861.890 * * * * [misc]progress: [ 85 / 88 ] simplifiying candidate # 1547113861.890 * [enter]simplify: Simplifying (* 2 (* n PI)) 1547113861.891 * * [misc]simplify: iters left: 4 (5 enodes) 1547113861.892 * * [misc]simplify: iters left: 3 (9 enodes) 1547113861.895 * * [misc]simplify: iters left: 2 (15 enodes) 1547113861.900 * * [misc]simplify: iters left: 1 (17 enodes) 1547113861.904 * [exit]simplify: Simplified to (* (* PI n) 2) 1547113861.904 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* PI n) 2) (/ (- 1 k) 2)))) 1547113861.904 * * * * [misc]progress: [ 86 / 88 ] simplifiying candidate # 1547113861.905 * [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))))))))))))) 1547113861.905 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1547113861.905 * * * * [misc]progress: [ 87 / 88 ] simplifiying candidate # 1547113861.905 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3)))))))) 1547113861.905 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1547113861.905 * * * * [misc]progress: [ 88 / 88 ] simplifiying candidate # 1547113861.905 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))))))))) 1547113861.905 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1547113861.905 * * * [misc]progress: adding candidates to table 1547113862.869 * * [misc]progress: iteration 3 / 4 1547113862.869 * * * [misc]progress: picking best candidate 1547113862.908 * * * * [misc]pick: Picked # 1547113862.908 * * * [misc]progress: localizing error 1547113862.928 * * * [misc]progress: generating rewritten candidates 1547113862.929 * * * * [misc]progress: [ 1 / 3 ] rewriting at (2 2) 1547113862.935 * * * * [misc]progress: [ 2 / 3 ] rewriting at (2 2 1) 1547113862.939 * * * * [misc]progress: [ 3 / 3 ] rewriting at (2) 1547113862.955 * * * [misc]progress: generating series expansions 1547113862.955 * * * * [misc]progress: [ 1 / 3 ] generating series at (2 2) 1547113862.956 * [misc]backup-simplify: Simplify (pow (* (* 2 PI) n) (/ (- 1 k) 2)) into (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) 1547113862.956 * [misc]approximate: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in (n k) around 0 1547113862.956 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k 1547113862.956 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k 1547113862.956 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k 1547113862.956 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 k)) in k 1547113862.956 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113862.956 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113862.956 * [misc]taylor: Taking taylor expansion of (- 1 k) in k 1547113862.956 * [misc]taylor: Taking taylor expansion of 1 in k 1547113862.956 * [misc]backup-simplify: Simplify 1 into 1 1547113862.956 * [misc]taylor: Taking taylor expansion of k in k 1547113862.956 * [misc]backup-simplify: Simplify 0 into 0 1547113862.956 * [misc]backup-simplify: Simplify 1 into 1 1547113862.956 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1547113862.956 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1547113862.956 * [misc]taylor: Taking taylor expansion of 2 in k 1547113862.956 * [misc]backup-simplify: Simplify 2 into 2 1547113862.956 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1547113862.956 * [misc]taylor: Taking taylor expansion of n in k 1547113862.956 * [misc]backup-simplify: Simplify n into n 1547113862.956 * [misc]taylor: Taking taylor expansion of PI in k 1547113862.956 * [misc]backup-simplify: Simplify PI into PI 1547113862.956 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1547113862.956 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1547113862.957 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1547113862.957 * [misc]backup-simplify: Simplify (- 0) into 0 1547113862.957 * [misc]backup-simplify: Simplify (+ 1 0) into 1 1547113862.957 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1547113862.957 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1547113862.957 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1547113862.957 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n 1547113862.957 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n 1547113862.957 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n 1547113862.958 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 k)) in n 1547113862.958 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113862.958 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113862.958 * [misc]taylor: Taking taylor expansion of (- 1 k) in n 1547113862.958 * [misc]taylor: Taking taylor expansion of 1 in n 1547113862.958 * [misc]backup-simplify: Simplify 1 into 1 1547113862.958 * [misc]taylor: Taking taylor expansion of k in n 1547113862.958 * [misc]backup-simplify: Simplify k into k 1547113862.958 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1547113862.958 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1547113862.958 * [misc]taylor: Taking taylor expansion of 2 in n 1547113862.958 * [misc]backup-simplify: Simplify 2 into 2 1547113862.958 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547113862.958 * [misc]taylor: Taking taylor expansion of n in n 1547113862.958 * [misc]backup-simplify: Simplify 0 into 0 1547113862.958 * [misc]backup-simplify: Simplify 1 into 1 1547113862.958 * [misc]taylor: Taking taylor expansion of PI in n 1547113862.958 * [misc]backup-simplify: Simplify PI into PI 1547113862.958 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547113862.958 * [misc]backup-simplify: Simplify (* 2 0) into 0 1547113862.959 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547113862.960 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1547113862.960 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547113862.960 * [misc]backup-simplify: Simplify (- k) into (- k) 1547113862.961 * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) 1547113862.961 * [misc]backup-simplify: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k)) 1547113862.961 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547113862.962 * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) 1547113862.962 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 1547113862.962 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n 1547113862.963 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n 1547113862.963 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n 1547113862.963 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 k)) in n 1547113862.963 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113862.963 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113862.963 * [misc]taylor: Taking taylor expansion of (- 1 k) in n 1547113862.963 * [misc]taylor: Taking taylor expansion of 1 in n 1547113862.963 * [misc]backup-simplify: Simplify 1 into 1 1547113862.963 * [misc]taylor: Taking taylor expansion of k in n 1547113862.963 * [misc]backup-simplify: Simplify k into k 1547113862.963 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1547113862.963 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1547113862.963 * [misc]taylor: Taking taylor expansion of 2 in n 1547113862.963 * [misc]backup-simplify: Simplify 2 into 2 1547113862.963 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547113862.963 * [misc]taylor: Taking taylor expansion of n in n 1547113862.963 * [misc]backup-simplify: Simplify 0 into 0 1547113862.963 * [misc]backup-simplify: Simplify 1 into 1 1547113862.963 * [misc]taylor: Taking taylor expansion of PI in n 1547113862.963 * [misc]backup-simplify: Simplify PI into PI 1547113862.963 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547113862.963 * [misc]backup-simplify: Simplify (* 2 0) into 0 1547113862.964 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547113862.965 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1547113862.965 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547113862.965 * [misc]backup-simplify: Simplify (- k) into (- k) 1547113862.965 * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) 1547113862.965 * [misc]backup-simplify: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k)) 1547113862.966 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547113862.967 * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) 1547113862.967 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 1547113862.967 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) in k 1547113862.967 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) in k 1547113862.967 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113862.967 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113862.967 * [misc]taylor: Taking taylor expansion of (* (- 1 k) (+ (log n) (log (* 2 PI)))) in k 1547113862.968 * [misc]taylor: Taking taylor expansion of (- 1 k) in k 1547113862.968 * [misc]taylor: Taking taylor expansion of 1 in k 1547113862.968 * [misc]backup-simplify: Simplify 1 into 1 1547113862.968 * [misc]taylor: Taking taylor expansion of k in k 1547113862.968 * [misc]backup-simplify: Simplify 0 into 0 1547113862.968 * [misc]backup-simplify: Simplify 1 into 1 1547113862.968 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1547113862.968 * [misc]taylor: Taking taylor expansion of (log n) in k 1547113862.968 * [misc]taylor: Taking taylor expansion of n in k 1547113862.968 * [misc]backup-simplify: Simplify n into n 1547113862.968 * [misc]backup-simplify: Simplify (log n) into (log n) 1547113862.968 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1547113862.968 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1547113862.968 * [misc]taylor: Taking taylor expansion of 2 in k 1547113862.968 * [misc]backup-simplify: Simplify 2 into 2 1547113862.968 * [misc]taylor: Taking taylor expansion of PI in k 1547113862.968 * [misc]backup-simplify: Simplify PI into PI 1547113862.968 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547113862.969 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547113862.969 * [misc]backup-simplify: Simplify (- 0) into 0 1547113862.969 * [misc]backup-simplify: Simplify (+ 1 0) into 1 1547113862.970 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547113862.970 * [misc]backup-simplify: Simplify (* 1 (+ (log n) (log (* 2 PI)))) into (+ (log n) (log (* 2 PI))) 1547113862.971 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1547113862.971 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1547113862.972 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1547113862.973 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1547113862.974 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1547113862.976 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1547113862.976 * [misc]backup-simplify: Simplify (- 0) into 0 1547113862.976 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113862.977 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- 1 k))) into 0 1547113862.977 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547113862.977 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1547113862.978 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0 1547113862.978 * [misc]taylor: Taking taylor expansion of 0 in k 1547113862.978 * [misc]backup-simplify: Simplify 0 into 0 1547113862.978 * [misc]backup-simplify: Simplify 0 into 0 1547113862.979 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1547113862.979 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1547113862.981 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1547113862.981 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113862.981 * [misc]backup-simplify: Simplify (- 1) into -1 1547113862.981 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 1547113862.982 * [misc]backup-simplify: Simplify (+ (* 1 0) (* -1 (+ (log n) (log (* 2 PI))))) into (- (+ (log (* 2 PI)) (log n))) 1547113862.982 * [misc]backup-simplify: Simplify (+ (* 1/2 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1547113862.983 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 1547113862.984 * [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))))))) 1547113862.985 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1547113862.986 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1547113862.989 * [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 1547113862.989 * [misc]backup-simplify: Simplify (- 0) into 0 1547113862.989 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113862.990 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0 1547113862.990 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547113862.990 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1547113862.992 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1547113862.992 * [misc]taylor: Taking taylor expansion of 0 in k 1547113862.992 * [misc]backup-simplify: Simplify 0 into 0 1547113862.992 * [misc]backup-simplify: Simplify 0 into 0 1547113862.992 * [misc]backup-simplify: Simplify 0 into 0 1547113862.993 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1547113862.994 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1547113862.997 * [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 1547113862.997 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113862.997 * [misc]backup-simplify: Simplify (- 0) into 0 1547113862.997 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113862.998 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1547113862.998 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1547113863.000 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 1547113863.001 * [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))))) 1547113863.009 * [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))))) 1547113863.010 * [misc]backup-simplify: Simplify (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) into (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) 1547113863.010 * [misc]approximate: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in (n k) around 0 1547113863.010 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k 1547113863.010 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1547113863.010 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1547113863.010 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k 1547113863.010 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113863.011 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113863.011 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k 1547113863.011 * [misc]taylor: Taking taylor expansion of 1 in k 1547113863.011 * [misc]backup-simplify: Simplify 1 into 1 1547113863.011 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547113863.011 * [misc]taylor: Taking taylor expansion of k in k 1547113863.011 * [misc]backup-simplify: Simplify 0 into 0 1547113863.011 * [misc]backup-simplify: Simplify 1 into 1 1547113863.011 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547113863.011 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1547113863.011 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1547113863.011 * [misc]taylor: Taking taylor expansion of 2 in k 1547113863.011 * [misc]backup-simplify: Simplify 2 into 2 1547113863.011 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1547113863.011 * [misc]taylor: Taking taylor expansion of PI in k 1547113863.011 * [misc]backup-simplify: Simplify PI into PI 1547113863.011 * [misc]taylor: Taking taylor expansion of n in k 1547113863.011 * [misc]backup-simplify: Simplify n into n 1547113863.011 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1547113863.011 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1547113863.011 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1547113863.012 * [misc]backup-simplify: Simplify (- 1) into -1 1547113863.012 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 1547113863.012 * [misc]backup-simplify: Simplify (* 1/2 -1) into -1/2 1547113863.012 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1547113863.012 * [misc]backup-simplify: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 1547113863.012 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n 1547113863.012 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1547113863.012 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1547113863.012 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n 1547113863.012 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113863.013 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113863.013 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n 1547113863.013 * [misc]taylor: Taking taylor expansion of 1 in n 1547113863.013 * [misc]backup-simplify: Simplify 1 into 1 1547113863.013 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547113863.013 * [misc]taylor: Taking taylor expansion of k in n 1547113863.013 * [misc]backup-simplify: Simplify k into k 1547113863.013 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547113863.013 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1547113863.013 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1547113863.013 * [misc]taylor: Taking taylor expansion of 2 in n 1547113863.013 * [misc]backup-simplify: Simplify 2 into 2 1547113863.013 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547113863.013 * [misc]taylor: Taking taylor expansion of PI in n 1547113863.013 * [misc]backup-simplify: Simplify PI into PI 1547113863.013 * [misc]taylor: Taking taylor expansion of n in n 1547113863.013 * [misc]backup-simplify: Simplify 0 into 0 1547113863.013 * [misc]backup-simplify: Simplify 1 into 1 1547113863.013 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547113863.014 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547113863.014 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547113863.014 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1547113863.015 * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 1547113863.015 * [misc]backup-simplify: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k))) 1547113863.015 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547113863.016 * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 1547113863.017 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 1547113863.017 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n 1547113863.017 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1547113863.017 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1547113863.017 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n 1547113863.017 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113863.017 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113863.017 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n 1547113863.017 * [misc]taylor: Taking taylor expansion of 1 in n 1547113863.017 * [misc]backup-simplify: Simplify 1 into 1 1547113863.017 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547113863.017 * [misc]taylor: Taking taylor expansion of k in n 1547113863.017 * [misc]backup-simplify: Simplify k into k 1547113863.017 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547113863.017 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1547113863.017 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1547113863.017 * [misc]taylor: Taking taylor expansion of 2 in n 1547113863.017 * [misc]backup-simplify: Simplify 2 into 2 1547113863.017 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547113863.017 * [misc]taylor: Taking taylor expansion of PI in n 1547113863.017 * [misc]backup-simplify: Simplify PI into PI 1547113863.017 * [misc]taylor: Taking taylor expansion of n in n 1547113863.017 * [misc]backup-simplify: Simplify 0 into 0 1547113863.017 * [misc]backup-simplify: Simplify 1 into 1 1547113863.018 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547113863.018 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547113863.018 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547113863.018 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1547113863.018 * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 1547113863.019 * [misc]backup-simplify: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k))) 1547113863.019 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547113863.020 * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 1547113863.020 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 1547113863.021 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k 1547113863.021 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k 1547113863.021 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113863.021 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113863.021 * [misc]taylor: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k 1547113863.021 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k 1547113863.021 * [misc]taylor: Taking taylor expansion of 1 in k 1547113863.021 * [misc]backup-simplify: Simplify 1 into 1 1547113863.021 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547113863.021 * [misc]taylor: Taking taylor expansion of k in k 1547113863.021 * [misc]backup-simplify: Simplify 0 into 0 1547113863.021 * [misc]backup-simplify: Simplify 1 into 1 1547113863.021 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547113863.021 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1547113863.021 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1547113863.021 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1547113863.021 * [misc]taylor: Taking taylor expansion of 2 in k 1547113863.021 * [misc]backup-simplify: Simplify 2 into 2 1547113863.021 * [misc]taylor: Taking taylor expansion of PI in k 1547113863.021 * [misc]backup-simplify: Simplify PI into PI 1547113863.022 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547113863.022 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547113863.022 * [misc]taylor: Taking taylor expansion of (log n) in k 1547113863.022 * [misc]taylor: Taking taylor expansion of n in k 1547113863.022 * [misc]backup-simplify: Simplify n into n 1547113863.022 * [misc]backup-simplify: Simplify (log n) into (log n) 1547113863.022 * [misc]backup-simplify: Simplify (- 1) into -1 1547113863.022 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 1547113863.023 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1547113863.023 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1547113863.024 * [misc]backup-simplify: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n))) 1547113863.024 * [misc]backup-simplify: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1547113863.025 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 1547113863.025 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 1547113863.026 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1547113863.027 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1547113863.030 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1547113863.030 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1547113863.030 * [misc]backup-simplify: Simplify (- 0) into 0 1547113863.030 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113863.030 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- 1 (/ 1 k)))) into 0 1547113863.031 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547113863.032 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1547113863.033 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1547113863.033 * [misc]taylor: Taking taylor expansion of 0 in k 1547113863.033 * [misc]backup-simplify: Simplify 0 into 0 1547113863.033 * [misc]backup-simplify: Simplify 0 into 0 1547113863.034 * [misc]backup-simplify: Simplify 0 into 0 1547113863.035 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113863.036 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1547113863.039 * [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 1547113863.039 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1547113863.039 * [misc]backup-simplify: Simplify (- 0) into 0 1547113863.039 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113863.039 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0 1547113863.040 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547113863.040 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1547113863.041 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1547113863.042 * [misc]taylor: Taking taylor expansion of 0 in k 1547113863.042 * [misc]backup-simplify: Simplify 0 into 0 1547113863.042 * [misc]backup-simplify: Simplify 0 into 0 1547113863.042 * [misc]backup-simplify: Simplify 0 into 0 1547113863.042 * [misc]backup-simplify: Simplify 0 into 0 1547113863.043 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113863.044 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1547113863.048 * [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 1547113863.049 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1547113863.049 * [misc]backup-simplify: Simplify (- 0) into 0 1547113863.049 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113863.049 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0 1547113863.050 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547113863.050 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1547113863.052 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1547113863.052 * [misc]taylor: Taking taylor expansion of 0 in k 1547113863.052 * [misc]backup-simplify: Simplify 0 into 0 1547113863.052 * [misc]backup-simplify: Simplify 0 into 0 1547113863.053 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) 1547113863.053 * [misc]backup-simplify: Simplify (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) into (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) 1547113863.053 * [misc]approximate: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in (n k) around 0 1547113863.053 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k 1547113863.053 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k 1547113863.053 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k 1547113863.053 * [misc]taylor: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k 1547113863.053 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113863.053 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113863.053 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in k 1547113863.053 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547113863.053 * [misc]taylor: Taking taylor expansion of k in k 1547113863.053 * [misc]backup-simplify: Simplify 0 into 0 1547113863.053 * [misc]backup-simplify: Simplify 1 into 1 1547113863.053 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547113863.054 * [misc]taylor: Taking taylor expansion of 1 in k 1547113863.054 * [misc]backup-simplify: Simplify 1 into 1 1547113863.054 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1547113863.054 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1547113863.054 * [misc]taylor: Taking taylor expansion of -2 in k 1547113863.054 * [misc]backup-simplify: Simplify -2 into -2 1547113863.054 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1547113863.054 * [misc]taylor: Taking taylor expansion of PI in k 1547113863.054 * [misc]backup-simplify: Simplify PI into PI 1547113863.054 * [misc]taylor: Taking taylor expansion of n in k 1547113863.054 * [misc]backup-simplify: Simplify n into n 1547113863.054 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1547113863.054 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1547113863.054 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1547113863.054 * [misc]backup-simplify: Simplify (+ 1 0) into 1 1547113863.054 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1547113863.054 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1547113863.054 * [misc]backup-simplify: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) 1547113863.054 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n 1547113863.054 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n 1547113863.054 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n 1547113863.054 * [misc]taylor: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n 1547113863.054 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113863.054 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113863.054 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in n 1547113863.054 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547113863.054 * [misc]taylor: Taking taylor expansion of k in n 1547113863.054 * [misc]backup-simplify: Simplify k into k 1547113863.054 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547113863.054 * [misc]taylor: Taking taylor expansion of 1 in n 1547113863.054 * [misc]backup-simplify: Simplify 1 into 1 1547113863.054 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1547113863.055 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1547113863.055 * [misc]taylor: Taking taylor expansion of -2 in n 1547113863.055 * [misc]backup-simplify: Simplify -2 into -2 1547113863.055 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547113863.055 * [misc]taylor: Taking taylor expansion of PI in n 1547113863.055 * [misc]backup-simplify: Simplify PI into PI 1547113863.055 * [misc]taylor: Taking taylor expansion of n in n 1547113863.055 * [misc]backup-simplify: Simplify 0 into 0 1547113863.055 * [misc]backup-simplify: Simplify 1 into 1 1547113863.055 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547113863.055 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547113863.055 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1547113863.055 * [misc]backup-simplify: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 1547113863.055 * [misc]backup-simplify: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1)) 1547113863.056 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547113863.056 * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 1547113863.057 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 1547113863.057 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n 1547113863.057 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n 1547113863.057 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n 1547113863.057 * [misc]taylor: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n 1547113863.057 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113863.057 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113863.057 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in n 1547113863.057 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547113863.057 * [misc]taylor: Taking taylor expansion of k in n 1547113863.057 * [misc]backup-simplify: Simplify k into k 1547113863.057 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547113863.057 * [misc]taylor: Taking taylor expansion of 1 in n 1547113863.057 * [misc]backup-simplify: Simplify 1 into 1 1547113863.057 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1547113863.057 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1547113863.057 * [misc]taylor: Taking taylor expansion of -2 in n 1547113863.057 * [misc]backup-simplify: Simplify -2 into -2 1547113863.057 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547113863.057 * [misc]taylor: Taking taylor expansion of PI in n 1547113863.057 * [misc]backup-simplify: Simplify PI into PI 1547113863.057 * [misc]taylor: Taking taylor expansion of n in n 1547113863.057 * [misc]backup-simplify: Simplify 0 into 0 1547113863.057 * [misc]backup-simplify: Simplify 1 into 1 1547113863.057 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547113863.058 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547113863.058 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1547113863.058 * [misc]backup-simplify: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 1547113863.058 * [misc]backup-simplify: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1)) 1547113863.058 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547113863.059 * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 1547113863.059 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 1547113863.059 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k 1547113863.059 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) in k 1547113863.059 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113863.059 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113863.059 * [misc]taylor: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) in k 1547113863.059 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in k 1547113863.059 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547113863.059 * [misc]taylor: Taking taylor expansion of k in k 1547113863.060 * [misc]backup-simplify: Simplify 0 into 0 1547113863.060 * [misc]backup-simplify: Simplify 1 into 1 1547113863.060 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547113863.060 * [misc]taylor: Taking taylor expansion of 1 in k 1547113863.060 * [misc]backup-simplify: Simplify 1 into 1 1547113863.060 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1547113863.060 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1547113863.060 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1547113863.060 * [misc]taylor: Taking taylor expansion of -2 in k 1547113863.060 * [misc]backup-simplify: Simplify -2 into -2 1547113863.060 * [misc]taylor: Taking taylor expansion of PI in k 1547113863.060 * [misc]backup-simplify: Simplify PI into PI 1547113863.060 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547113863.060 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1547113863.060 * [misc]taylor: Taking taylor expansion of (log n) in k 1547113863.060 * [misc]taylor: Taking taylor expansion of n in k 1547113863.060 * [misc]backup-simplify: Simplify n into n 1547113863.060 * [misc]backup-simplify: Simplify (log n) into (log n) 1547113863.060 * [misc]backup-simplify: Simplify (+ 1 0) into 1 1547113863.060 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1547113863.061 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1547113863.061 * [misc]backup-simplify: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n)) 1547113863.061 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1547113863.062 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 1547113863.062 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 1547113863.063 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1547113863.063 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1547113863.065 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1547113863.065 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1547113863.065 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113863.065 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (+ (/ 1 k) 1))) into 0 1547113863.066 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547113863.066 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1547113863.067 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1547113863.067 * [misc]taylor: Taking taylor expansion of 0 in k 1547113863.067 * [misc]backup-simplify: Simplify 0 into 0 1547113863.067 * [misc]backup-simplify: Simplify 0 into 0 1547113863.067 * [misc]backup-simplify: Simplify 0 into 0 1547113863.068 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113863.069 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1547113863.072 * [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 1547113863.072 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1547113863.072 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113863.073 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0 1547113863.073 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547113863.074 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1547113863.077 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1547113863.077 * [misc]taylor: Taking taylor expansion of 0 in k 1547113863.077 * [misc]backup-simplify: Simplify 0 into 0 1547113863.077 * [misc]backup-simplify: Simplify 0 into 0 1547113863.077 * [misc]backup-simplify: Simplify 0 into 0 1547113863.077 * [misc]backup-simplify: Simplify 0 into 0 1547113863.078 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113863.080 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1547113863.088 * [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 1547113863.088 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1547113863.088 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113863.089 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1))))) into 0 1547113863.089 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547113863.090 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 1547113863.094 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1547113863.094 * [misc]taylor: Taking taylor expansion of 0 in k 1547113863.094 * [misc]backup-simplify: Simplify 0 into 0 1547113863.094 * [misc]backup-simplify: Simplify 0 into 0 1547113863.095 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) 1547113863.095 * * * * [misc]progress: [ 2 / 3 ] generating series at (2 2 1) 1547113863.095 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1547113863.095 * [misc]approximate: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1547113863.095 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1547113863.095 * [misc]taylor: Taking taylor expansion of 2 in n 1547113863.095 * [misc]backup-simplify: Simplify 2 into 2 1547113863.095 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547113863.095 * [misc]taylor: Taking taylor expansion of n in n 1547113863.095 * [misc]backup-simplify: Simplify 0 into 0 1547113863.095 * [misc]backup-simplify: Simplify 1 into 1 1547113863.095 * [misc]taylor: Taking taylor expansion of PI in n 1547113863.095 * [misc]backup-simplify: Simplify PI into PI 1547113863.095 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1547113863.095 * [misc]taylor: Taking taylor expansion of 2 in n 1547113863.095 * [misc]backup-simplify: Simplify 2 into 2 1547113863.095 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547113863.095 * [misc]taylor: Taking taylor expansion of n in n 1547113863.095 * [misc]backup-simplify: Simplify 0 into 0 1547113863.095 * [misc]backup-simplify: Simplify 1 into 1 1547113863.095 * [misc]taylor: Taking taylor expansion of PI in n 1547113863.096 * [misc]backup-simplify: Simplify PI into PI 1547113863.096 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547113863.096 * [misc]backup-simplify: Simplify (* 2 0) into 0 1547113863.096 * [misc]backup-simplify: Simplify 0 into 0 1547113863.096 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547113863.097 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1547113863.097 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547113863.098 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1547113863.098 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1547113863.098 * [misc]backup-simplify: Simplify 0 into 0 1547113863.099 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1547113863.100 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1547113863.100 * [misc]backup-simplify: Simplify 0 into 0 1547113863.101 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1547113863.103 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1547113863.103 * [misc]backup-simplify: Simplify 0 into 0 1547113863.104 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1547113863.106 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1547113863.106 * [misc]backup-simplify: Simplify 0 into 0 1547113863.108 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1547113863.110 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1547113863.110 * [misc]backup-simplify: Simplify 0 into 0 1547113863.112 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1547113863.115 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1547113863.115 * [misc]backup-simplify: Simplify 0 into 0 1547113863.115 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1547113863.115 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 n)) into (* 2 (/ PI n)) 1547113863.115 * [misc]approximate: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1547113863.115 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1547113863.115 * [misc]taylor: Taking taylor expansion of 2 in n 1547113863.115 * [misc]backup-simplify: Simplify 2 into 2 1547113863.115 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547113863.115 * [misc]taylor: Taking taylor expansion of PI in n 1547113863.116 * [misc]backup-simplify: Simplify PI into PI 1547113863.116 * [misc]taylor: Taking taylor expansion of n in n 1547113863.116 * [misc]backup-simplify: Simplify 0 into 0 1547113863.116 * [misc]backup-simplify: Simplify 1 into 1 1547113863.116 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547113863.116 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1547113863.116 * [misc]taylor: Taking taylor expansion of 2 in n 1547113863.116 * [misc]backup-simplify: Simplify 2 into 2 1547113863.116 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547113863.116 * [misc]taylor: Taking taylor expansion of PI in n 1547113863.116 * [misc]backup-simplify: Simplify PI into PI 1547113863.116 * [misc]taylor: Taking taylor expansion of n in n 1547113863.116 * [misc]backup-simplify: Simplify 0 into 0 1547113863.116 * [misc]backup-simplify: Simplify 1 into 1 1547113863.116 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547113863.116 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547113863.116 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547113863.117 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1547113863.117 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1547113863.118 * [misc]backup-simplify: Simplify 0 into 0 1547113863.118 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113863.119 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1547113863.119 * [misc]backup-simplify: Simplify 0 into 0 1547113863.120 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113863.121 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1547113863.121 * [misc]backup-simplify: Simplify 0 into 0 1547113863.122 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113863.123 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1547113863.123 * [misc]backup-simplify: Simplify 0 into 0 1547113863.125 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113863.128 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1547113863.128 * [misc]backup-simplify: Simplify 0 into 0 1547113863.129 * [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 1547113863.131 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1547113863.131 * [misc]backup-simplify: Simplify 0 into 0 1547113863.131 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 1547113863.131 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (- n))) into (* -2 (/ PI n)) 1547113863.132 * [misc]approximate: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1547113863.132 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1547113863.132 * [misc]taylor: Taking taylor expansion of -2 in n 1547113863.132 * [misc]backup-simplify: Simplify -2 into -2 1547113863.132 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547113863.132 * [misc]taylor: Taking taylor expansion of PI in n 1547113863.132 * [misc]backup-simplify: Simplify PI into PI 1547113863.132 * [misc]taylor: Taking taylor expansion of n in n 1547113863.132 * [misc]backup-simplify: Simplify 0 into 0 1547113863.132 * [misc]backup-simplify: Simplify 1 into 1 1547113863.132 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547113863.132 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1547113863.132 * [misc]taylor: Taking taylor expansion of -2 in n 1547113863.132 * [misc]backup-simplify: Simplify -2 into -2 1547113863.132 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547113863.132 * [misc]taylor: Taking taylor expansion of PI in n 1547113863.132 * [misc]backup-simplify: Simplify PI into PI 1547113863.132 * [misc]taylor: Taking taylor expansion of n in n 1547113863.132 * [misc]backup-simplify: Simplify 0 into 0 1547113863.132 * [misc]backup-simplify: Simplify 1 into 1 1547113863.132 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547113863.132 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547113863.133 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547113863.133 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1547113863.134 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1547113863.134 * [misc]backup-simplify: Simplify 0 into 0 1547113863.134 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113863.135 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1547113863.135 * [misc]backup-simplify: Simplify 0 into 0 1547113863.137 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113863.138 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1547113863.138 * [misc]backup-simplify: Simplify 0 into 0 1547113863.140 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113863.142 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1547113863.142 * [misc]backup-simplify: Simplify 0 into 0 1547113863.144 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113863.147 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1547113863.147 * [misc]backup-simplify: Simplify 0 into 0 1547113863.150 * [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 1547113863.153 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1547113863.153 * [misc]backup-simplify: Simplify 0 into 0 1547113863.154 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 1547113863.154 * * * * [misc]progress: [ 3 / 3 ] generating series at (2) 1547113863.154 * [misc]backup-simplify: Simplify (* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) into (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) 1547113863.154 * [misc]approximate: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in (k n) around 0 1547113863.154 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in n 1547113863.154 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n 1547113863.154 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n 1547113863.155 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n 1547113863.155 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 k)) in n 1547113863.155 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113863.155 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113863.155 * [misc]taylor: Taking taylor expansion of (- 1 k) in n 1547113863.155 * [misc]taylor: Taking taylor expansion of 1 in n 1547113863.155 * [misc]backup-simplify: Simplify 1 into 1 1547113863.155 * [misc]taylor: Taking taylor expansion of k in n 1547113863.155 * [misc]backup-simplify: Simplify k into k 1547113863.155 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1547113863.155 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1547113863.155 * [misc]taylor: Taking taylor expansion of 2 in n 1547113863.155 * [misc]backup-simplify: Simplify 2 into 2 1547113863.155 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547113863.155 * [misc]taylor: Taking taylor expansion of n in n 1547113863.155 * [misc]backup-simplify: Simplify 0 into 0 1547113863.155 * [misc]backup-simplify: Simplify 1 into 1 1547113863.155 * [misc]taylor: Taking taylor expansion of PI in n 1547113863.155 * [misc]backup-simplify: Simplify PI into PI 1547113863.155 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547113863.155 * [misc]backup-simplify: Simplify (* 2 0) into 0 1547113863.156 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547113863.157 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1547113863.157 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547113863.157 * [misc]backup-simplify: Simplify (- k) into (- k) 1547113863.157 * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) 1547113863.157 * [misc]backup-simplify: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k)) 1547113863.159 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547113863.159 * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) 1547113863.160 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 1547113863.160 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1547113863.160 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547113863.160 * [misc]taylor: Taking taylor expansion of k in n 1547113863.160 * [misc]backup-simplify: Simplify k into k 1547113863.160 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547113863.160 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1547113863.160 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1547113863.160 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1547113863.160 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k 1547113863.160 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k 1547113863.160 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k 1547113863.160 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k 1547113863.160 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 k)) in k 1547113863.160 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113863.160 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113863.160 * [misc]taylor: Taking taylor expansion of (- 1 k) in k 1547113863.160 * [misc]taylor: Taking taylor expansion of 1 in k 1547113863.160 * [misc]backup-simplify: Simplify 1 into 1 1547113863.160 * [misc]taylor: Taking taylor expansion of k in k 1547113863.160 * [misc]backup-simplify: Simplify 0 into 0 1547113863.160 * [misc]backup-simplify: Simplify 1 into 1 1547113863.160 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1547113863.160 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1547113863.160 * [misc]taylor: Taking taylor expansion of 2 in k 1547113863.160 * [misc]backup-simplify: Simplify 2 into 2 1547113863.160 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1547113863.160 * [misc]taylor: Taking taylor expansion of n in k 1547113863.160 * [misc]backup-simplify: Simplify n into n 1547113863.160 * [misc]taylor: Taking taylor expansion of PI in k 1547113863.160 * [misc]backup-simplify: Simplify PI into PI 1547113863.160 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1547113863.160 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1547113863.160 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1547113863.161 * [misc]backup-simplify: Simplify (- 0) into 0 1547113863.161 * [misc]backup-simplify: Simplify (+ 1 0) into 1 1547113863.161 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1547113863.161 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1547113863.161 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1547113863.161 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1547113863.161 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547113863.161 * [misc]taylor: Taking taylor expansion of k in k 1547113863.161 * [misc]backup-simplify: Simplify 0 into 0 1547113863.161 * [misc]backup-simplify: Simplify 1 into 1 1547113863.161 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547113863.161 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547113863.161 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1547113863.162 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k 1547113863.162 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k 1547113863.162 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k 1547113863.162 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k 1547113863.162 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 k)) in k 1547113863.162 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113863.162 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113863.162 * [misc]taylor: Taking taylor expansion of (- 1 k) in k 1547113863.162 * [misc]taylor: Taking taylor expansion of 1 in k 1547113863.162 * [misc]backup-simplify: Simplify 1 into 1 1547113863.162 * [misc]taylor: Taking taylor expansion of k in k 1547113863.162 * [misc]backup-simplify: Simplify 0 into 0 1547113863.162 * [misc]backup-simplify: Simplify 1 into 1 1547113863.162 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1547113863.162 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1547113863.162 * [misc]taylor: Taking taylor expansion of 2 in k 1547113863.162 * [misc]backup-simplify: Simplify 2 into 2 1547113863.162 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1547113863.162 * [misc]taylor: Taking taylor expansion of n in k 1547113863.162 * [misc]backup-simplify: Simplify n into n 1547113863.162 * [misc]taylor: Taking taylor expansion of PI in k 1547113863.162 * [misc]backup-simplify: Simplify PI into PI 1547113863.162 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1547113863.162 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1547113863.162 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1547113863.162 * [misc]backup-simplify: Simplify (- 0) into 0 1547113863.162 * [misc]backup-simplify: Simplify (+ 1 0) into 1 1547113863.162 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1547113863.162 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1547113863.162 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1547113863.162 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1547113863.162 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547113863.162 * [misc]taylor: Taking taylor expansion of k in k 1547113863.162 * [misc]backup-simplify: Simplify 0 into 0 1547113863.163 * [misc]backup-simplify: Simplify 1 into 1 1547113863.163 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547113863.163 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547113863.163 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1547113863.163 * [misc]backup-simplify: Simplify (* (pow (* 2 (* n PI)) 1/2) 0) into 0 1547113863.163 * [misc]taylor: Taking taylor expansion of 0 in n 1547113863.163 * [misc]backup-simplify: Simplify 0 into 0 1547113863.163 * [misc]backup-simplify: Simplify 0 into 0 1547113863.163 * [misc]backup-simplify: Simplify (+ (* n 0) (* 0 PI)) into 0 1547113863.164 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0 1547113863.164 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 1547113863.164 * [misc]backup-simplify: Simplify (- 1) into -1 1547113863.164 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 1547113863.164 * [misc]backup-simplify: Simplify (+ (* 1/2 -1) (* 0 1)) into -1/2 1547113863.165 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI))))) 1547113863.165 * [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))))) 1547113863.165 * [misc]backup-simplify: Simplify (+ (* (pow (* 2 (* n PI)) 1/2) +nan.0) (* (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) 0)) into (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) 1547113863.165 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 1547113863.165 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 1547113863.165 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1547113863.165 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547113863.165 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1547113863.165 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1547113863.165 * [misc]taylor: Taking taylor expansion of 2 in n 1547113863.165 * [misc]backup-simplify: Simplify 2 into 2 1547113863.165 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1547113863.165 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1547113863.165 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1547113863.165 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547113863.166 * [misc]taylor: Taking taylor expansion of n in n 1547113863.166 * [misc]backup-simplify: Simplify 0 into 0 1547113863.166 * [misc]backup-simplify: Simplify 1 into 1 1547113863.166 * [misc]taylor: Taking taylor expansion of PI in n 1547113863.166 * [misc]backup-simplify: Simplify PI into PI 1547113863.166 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547113863.166 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547113863.166 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547113863.167 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1547113863.167 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1547113863.167 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1547113863.167 * [misc]backup-simplify: Simplify (- 0) into 0 1547113863.167 * [misc]backup-simplify: Simplify 0 into 0 1547113863.167 * [misc]backup-simplify: Simplify 0 into 0 1547113863.167 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1547113863.168 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1547113863.168 * [misc]backup-simplify: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 1547113863.169 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 1547113863.169 * [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 1547113863.170 * [misc]backup-simplify: Simplify (- 0) into 0 1547113863.170 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113863.170 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 -1) (* 0 1))) into 0 1547113863.170 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0 1547113863.171 * [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))) 1547113863.171 * [misc]backup-simplify: Simplify (+ (* (pow (* 2 (* n PI)) 1/2) +nan.0) (+ (* (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) +nan.0) (* (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) 0))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) 1547113863.171 * [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 1547113863.171 * [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 1547113863.171 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n 1547113863.171 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1547113863.171 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547113863.171 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n 1547113863.171 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n 1547113863.171 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1547113863.171 * [misc]taylor: Taking taylor expansion of 2 in n 1547113863.171 * [misc]backup-simplify: Simplify 2 into 2 1547113863.172 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1547113863.172 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1547113863.172 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1547113863.172 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1547113863.172 * [misc]taylor: Taking taylor expansion of 2 in n 1547113863.172 * [misc]backup-simplify: Simplify 2 into 2 1547113863.172 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547113863.172 * [misc]taylor: Taking taylor expansion of n in n 1547113863.172 * [misc]backup-simplify: Simplify 0 into 0 1547113863.172 * [misc]backup-simplify: Simplify 1 into 1 1547113863.172 * [misc]taylor: Taking taylor expansion of PI in n 1547113863.172 * [misc]backup-simplify: Simplify PI into PI 1547113863.172 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547113863.172 * [misc]backup-simplify: Simplify (* 2 0) into 0 1547113863.172 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547113863.173 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1547113863.173 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547113863.173 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1547113863.173 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547113863.173 * [misc]taylor: Taking taylor expansion of n in n 1547113863.173 * [misc]backup-simplify: Simplify 0 into 0 1547113863.173 * [misc]backup-simplify: Simplify 1 into 1 1547113863.173 * [misc]taylor: Taking taylor expansion of PI in n 1547113863.173 * [misc]backup-simplify: Simplify PI into PI 1547113863.173 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547113863.174 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547113863.174 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547113863.174 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1547113863.174 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 1547113863.174 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 1547113863.174 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1547113863.174 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547113863.174 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1547113863.174 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1547113863.174 * [misc]taylor: Taking taylor expansion of 2 in n 1547113863.174 * [misc]backup-simplify: Simplify 2 into 2 1547113863.174 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1547113863.175 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1547113863.175 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1547113863.175 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547113863.175 * [misc]taylor: Taking taylor expansion of n in n 1547113863.175 * [misc]backup-simplify: Simplify 0 into 0 1547113863.175 * [misc]backup-simplify: Simplify 1 into 1 1547113863.175 * [misc]taylor: Taking taylor expansion of PI in n 1547113863.175 * [misc]backup-simplify: Simplify PI into PI 1547113863.175 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547113863.175 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547113863.175 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547113863.176 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1547113863.176 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547113863.176 * [misc]backup-simplify: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 1547113863.177 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0 1547113863.177 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1547113863.177 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1547113863.177 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1547113863.177 * [misc]backup-simplify: Simplify (- 0) into 0 1547113863.177 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113863.178 * [misc]backup-simplify: Simplify (- 0) into 0 1547113863.178 * [misc]backup-simplify: Simplify 0 into 0 1547113863.179 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1547113863.181 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1547113863.182 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 1547113863.183 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI))) 1547113863.183 * [misc]backup-simplify: Simplify 0 into 0 1547113863.183 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113863.184 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1547113863.185 * [misc]backup-simplify: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1547113863.186 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 1547113863.189 * [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 1547113863.189 * [misc]backup-simplify: Simplify (- 0) into 0 1547113863.189 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113863.189 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1)))) into 0 1547113863.190 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log (* 2 (* n PI))))))) into 0 1547113863.192 * [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))) 1547113863.193 * [misc]backup-simplify: Simplify (+ (* (pow (* 2 (* n PI)) 1/2) +nan.0) (+ (* (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) +nan.0) (+ (* (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) +nan.0) (* (* -1/48 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 3))) 0)))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))))))) 1547113863.193 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))))))) in n 1547113863.193 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))))))) in n 1547113863.193 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n 1547113863.193 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1547113863.193 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547113863.193 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n 1547113863.193 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n 1547113863.193 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1547113863.193 * [misc]taylor: Taking taylor expansion of 2 in n 1547113863.193 * [misc]backup-simplify: Simplify 2 into 2 1547113863.194 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1547113863.194 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1547113863.194 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1547113863.194 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1547113863.194 * [misc]taylor: Taking taylor expansion of 2 in n 1547113863.194 * [misc]backup-simplify: Simplify 2 into 2 1547113863.194 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547113863.194 * [misc]taylor: Taking taylor expansion of n in n 1547113863.194 * [misc]backup-simplify: Simplify 0 into 0 1547113863.194 * [misc]backup-simplify: Simplify 1 into 1 1547113863.194 * [misc]taylor: Taking taylor expansion of PI in n 1547113863.194 * [misc]backup-simplify: Simplify PI into PI 1547113863.194 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547113863.194 * [misc]backup-simplify: Simplify (* 2 0) into 0 1547113863.195 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547113863.196 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1547113863.196 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547113863.196 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1547113863.196 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547113863.196 * [misc]taylor: Taking taylor expansion of n in n 1547113863.196 * [misc]backup-simplify: Simplify 0 into 0 1547113863.196 * [misc]backup-simplify: Simplify 1 into 1 1547113863.196 * [misc]taylor: Taking taylor expansion of PI in n 1547113863.196 * [misc]backup-simplify: Simplify PI into PI 1547113863.196 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547113863.197 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547113863.197 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547113863.197 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1547113863.197 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))))) in n 1547113863.197 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))))) in n 1547113863.197 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 1547113863.197 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1547113863.197 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547113863.197 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1547113863.197 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1547113863.197 * [misc]taylor: Taking taylor expansion of 2 in n 1547113863.197 * [misc]backup-simplify: Simplify 2 into 2 1547113863.197 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1547113863.197 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1547113863.197 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1547113863.197 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547113863.197 * [misc]taylor: Taking taylor expansion of n in n 1547113863.197 * [misc]backup-simplify: Simplify 0 into 0 1547113863.197 * [misc]backup-simplify: Simplify 1 into 1 1547113863.197 * [misc]taylor: Taking taylor expansion of PI in n 1547113863.198 * [misc]backup-simplify: Simplify PI into PI 1547113863.198 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547113863.198 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547113863.198 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547113863.198 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1547113863.198 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))) in n 1547113863.199 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) in n 1547113863.199 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1547113863.199 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547113863.199 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))) in n 1547113863.199 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) in n 1547113863.199 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1547113863.199 * [misc]taylor: Taking taylor expansion of 2 in n 1547113863.199 * [misc]backup-simplify: Simplify 2 into 2 1547113863.199 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1547113863.199 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1547113863.199 * [misc]taylor: Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n 1547113863.199 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1547113863.199 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1547113863.199 * [misc]taylor: Taking taylor expansion of 2 in n 1547113863.199 * [misc]backup-simplify: Simplify 2 into 2 1547113863.199 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547113863.199 * [misc]taylor: Taking taylor expansion of n in n 1547113863.199 * [misc]backup-simplify: Simplify 0 into 0 1547113863.199 * [misc]backup-simplify: Simplify 1 into 1 1547113863.199 * [misc]taylor: Taking taylor expansion of PI in n 1547113863.199 * [misc]backup-simplify: Simplify PI into PI 1547113863.199 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547113863.199 * [misc]backup-simplify: Simplify (* 2 0) into 0 1547113863.200 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547113863.200 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1547113863.200 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547113863.201 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547113863.201 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1547113863.201 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547113863.201 * [misc]taylor: Taking taylor expansion of n in n 1547113863.201 * [misc]backup-simplify: Simplify 0 into 0 1547113863.201 * [misc]backup-simplify: Simplify 1 into 1 1547113863.201 * [misc]taylor: Taking taylor expansion of PI in n 1547113863.201 * [misc]backup-simplify: Simplify PI into PI 1547113863.201 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547113863.202 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547113863.202 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547113863.202 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1547113863.202 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547113863.203 * [misc]backup-simplify: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 1547113863.203 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0 1547113863.203 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1547113863.203 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1547113863.204 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1547113863.204 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547113863.204 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547113863.205 * [misc]backup-simplify: Simplify (* (+ (log n) (log (* 2 PI))) (+ (log n) (log (* 2 PI)))) into (pow (+ (log n) (log (* 2 PI))) 2) 1547113863.205 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) into (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 1547113863.206 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 0) into 0 1547113863.206 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1547113863.206 * [misc]backup-simplify: Simplify (- 0) into 0 1547113863.206 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113863.206 * [misc]backup-simplify: Simplify (- 0) into 0 1547113863.206 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113863.206 * [misc]backup-simplify: Simplify (- 0) into 0 1547113863.207 * [misc]backup-simplify: Simplify 0 into 0 1547113863.207 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1547113863.208 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1547113863.209 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1547113863.210 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547113863.210 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1547113863.211 * [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)))))))) 1547113863.213 * [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)))))))) 1547113863.213 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1547113863.214 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1547113863.215 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 1547113863.217 * [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)))))))))) 1547113863.219 * [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))))))) 1547113863.221 * [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))))))) 1547113863.222 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1547113863.223 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 1547113863.224 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1547113863.225 * [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)))) 1547113863.228 * [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)))) 1547113863.230 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 1547113863.231 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 1547113863.238 * [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))))))))))))) 1547113863.238 * [misc]backup-simplify: Simplify (* (pow (/ 1 k) -1/2) (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2))) into (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) 1547113863.239 * [misc]approximate: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in (k n) around 0 1547113863.239 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in n 1547113863.239 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n 1547113863.239 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1547113863.239 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1547113863.239 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n 1547113863.239 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113863.239 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113863.239 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n 1547113863.239 * [misc]taylor: Taking taylor expansion of 1 in n 1547113863.239 * [misc]backup-simplify: Simplify 1 into 1 1547113863.239 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547113863.239 * [misc]taylor: Taking taylor expansion of k in n 1547113863.239 * [misc]backup-simplify: Simplify k into k 1547113863.239 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547113863.239 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1547113863.239 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1547113863.239 * [misc]taylor: Taking taylor expansion of 2 in n 1547113863.239 * [misc]backup-simplify: Simplify 2 into 2 1547113863.239 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547113863.239 * [misc]taylor: Taking taylor expansion of PI in n 1547113863.239 * [misc]backup-simplify: Simplify PI into PI 1547113863.239 * [misc]taylor: Taking taylor expansion of n in n 1547113863.239 * [misc]backup-simplify: Simplify 0 into 0 1547113863.239 * [misc]backup-simplify: Simplify 1 into 1 1547113863.240 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547113863.240 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547113863.240 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547113863.240 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1547113863.241 * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 1547113863.241 * [misc]backup-simplify: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k))) 1547113863.241 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547113863.242 * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 1547113863.243 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 1547113863.243 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1547113863.243 * [misc]taylor: Taking taylor expansion of k in n 1547113863.243 * [misc]backup-simplify: Simplify k into k 1547113863.243 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1547113863.243 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1547113863.243 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k 1547113863.243 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k 1547113863.243 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1547113863.243 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1547113863.243 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k 1547113863.243 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113863.243 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113863.243 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k 1547113863.243 * [misc]taylor: Taking taylor expansion of 1 in k 1547113863.243 * [misc]backup-simplify: Simplify 1 into 1 1547113863.243 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547113863.243 * [misc]taylor: Taking taylor expansion of k in k 1547113863.243 * [misc]backup-simplify: Simplify 0 into 0 1547113863.243 * [misc]backup-simplify: Simplify 1 into 1 1547113863.243 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547113863.244 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1547113863.244 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1547113863.244 * [misc]taylor: Taking taylor expansion of 2 in k 1547113863.244 * [misc]backup-simplify: Simplify 2 into 2 1547113863.244 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1547113863.244 * [misc]taylor: Taking taylor expansion of PI in k 1547113863.244 * [misc]backup-simplify: Simplify PI into PI 1547113863.244 * [misc]taylor: Taking taylor expansion of n in k 1547113863.244 * [misc]backup-simplify: Simplify n into n 1547113863.244 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1547113863.244 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1547113863.244 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1547113863.244 * [misc]backup-simplify: Simplify (- 1) into -1 1547113863.244 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 1547113863.244 * [misc]backup-simplify: Simplify (* 1/2 -1) into -1/2 1547113863.245 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1547113863.245 * [misc]backup-simplify: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 1547113863.245 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1547113863.245 * [misc]taylor: Taking taylor expansion of k in k 1547113863.245 * [misc]backup-simplify: Simplify 0 into 0 1547113863.245 * [misc]backup-simplify: Simplify 1 into 1 1547113863.245 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547113863.246 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1547113863.246 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k 1547113863.246 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k 1547113863.246 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1547113863.246 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1547113863.246 * [misc]taylor: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k 1547113863.246 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113863.246 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113863.246 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k 1547113863.246 * [misc]taylor: Taking taylor expansion of 1 in k 1547113863.246 * [misc]backup-simplify: Simplify 1 into 1 1547113863.246 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547113863.246 * [misc]taylor: Taking taylor expansion of k in k 1547113863.246 * [misc]backup-simplify: Simplify 0 into 0 1547113863.246 * [misc]backup-simplify: Simplify 1 into 1 1547113863.246 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547113863.246 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1547113863.246 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1547113863.246 * [misc]taylor: Taking taylor expansion of 2 in k 1547113863.246 * [misc]backup-simplify: Simplify 2 into 2 1547113863.246 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1547113863.246 * [misc]taylor: Taking taylor expansion of PI in k 1547113863.246 * [misc]backup-simplify: Simplify PI into PI 1547113863.246 * [misc]taylor: Taking taylor expansion of n in k 1547113863.246 * [misc]backup-simplify: Simplify n into n 1547113863.246 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1547113863.247 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1547113863.247 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1547113863.247 * [misc]backup-simplify: Simplify (- 1) into -1 1547113863.247 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 1547113863.247 * [misc]backup-simplify: Simplify (* 1/2 -1) into -1/2 1547113863.247 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1547113863.247 * [misc]backup-simplify: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 1547113863.247 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1547113863.248 * [misc]taylor: Taking taylor expansion of k in k 1547113863.248 * [misc]backup-simplify: Simplify 0 into 0 1547113863.248 * [misc]backup-simplify: Simplify 1 into 1 1547113863.248 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547113863.248 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1547113863.248 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 0) into 0 1547113863.249 * [misc]taylor: Taking taylor expansion of 0 in n 1547113863.249 * [misc]backup-simplify: Simplify 0 into 0 1547113863.249 * [misc]backup-simplify: Simplify 0 into 0 1547113863.249 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) 1547113863.249 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n 1547113863.249 * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n 1547113863.249 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1547113863.249 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547113863.249 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n 1547113863.249 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n 1547113863.249 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113863.249 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113863.249 * [misc]taylor: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n 1547113863.249 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n 1547113863.249 * [misc]taylor: Taking taylor expansion of 1 in n 1547113863.249 * [misc]backup-simplify: Simplify 1 into 1 1547113863.249 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547113863.249 * [misc]taylor: Taking taylor expansion of k in n 1547113863.249 * [misc]backup-simplify: Simplify k into k 1547113863.250 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547113863.250 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1547113863.250 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1547113863.250 * [misc]taylor: Taking taylor expansion of 2 in n 1547113863.250 * [misc]backup-simplify: Simplify 2 into 2 1547113863.250 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547113863.250 * [misc]taylor: Taking taylor expansion of PI in n 1547113863.250 * [misc]backup-simplify: Simplify PI into PI 1547113863.250 * [misc]taylor: Taking taylor expansion of n in n 1547113863.250 * [misc]backup-simplify: Simplify 0 into 0 1547113863.250 * [misc]backup-simplify: Simplify 1 into 1 1547113863.250 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547113863.250 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547113863.252 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547113863.252 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1547113863.252 * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 1547113863.253 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547113863.253 * [misc]backup-simplify: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) 1547113863.254 * [misc]backup-simplify: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 1547113863.255 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 1547113863.255 * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) 1547113863.256 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 1547113863.257 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 1547113863.257 * [misc]backup-simplify: Simplify 0 into 0 1547113863.258 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1547113863.258 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) 1547113863.259 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n 1547113863.259 * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n 1547113863.259 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1547113863.259 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547113863.259 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n 1547113863.259 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n 1547113863.259 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113863.259 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113863.259 * [misc]taylor: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n 1547113863.259 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n 1547113863.259 * [misc]taylor: Taking taylor expansion of 1 in n 1547113863.259 * [misc]backup-simplify: Simplify 1 into 1 1547113863.259 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547113863.259 * [misc]taylor: Taking taylor expansion of k in n 1547113863.259 * [misc]backup-simplify: Simplify k into k 1547113863.259 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547113863.259 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1547113863.259 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1547113863.259 * [misc]taylor: Taking taylor expansion of 2 in n 1547113863.259 * [misc]backup-simplify: Simplify 2 into 2 1547113863.259 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547113863.259 * [misc]taylor: Taking taylor expansion of PI in n 1547113863.259 * [misc]backup-simplify: Simplify PI into PI 1547113863.259 * [misc]taylor: Taking taylor expansion of n in n 1547113863.259 * [misc]backup-simplify: Simplify 0 into 0 1547113863.259 * [misc]backup-simplify: Simplify 1 into 1 1547113863.259 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547113863.260 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547113863.260 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547113863.260 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1547113863.260 * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 1547113863.260 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547113863.261 * [misc]backup-simplify: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) 1547113863.261 * [misc]backup-simplify: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 1547113863.262 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 1547113863.262 * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) 1547113863.262 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 1547113863.263 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 1547113863.264 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1547113863.264 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1547113863.266 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1547113863.266 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1547113863.266 * [misc]backup-simplify: Simplify (- 0) into 0 1547113863.266 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113863.266 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547113863.267 * [misc]backup-simplify: Simplify (+ (* (- 1 (/ 1 k)) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1547113863.267 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into 0 1547113863.268 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1547113863.269 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into 0 1547113863.269 * [misc]backup-simplify: Simplify (- 0) into 0 1547113863.269 * [misc]backup-simplify: Simplify 0 into 0 1547113863.269 * [misc]backup-simplify: Simplify 0 into 0 1547113863.270 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1547113863.270 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) 1547113863.270 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n 1547113863.270 * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n 1547113863.270 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1547113863.271 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547113863.271 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n 1547113863.271 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n 1547113863.271 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113863.271 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113863.271 * [misc]taylor: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n 1547113863.271 * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n 1547113863.271 * [misc]taylor: Taking taylor expansion of 1 in n 1547113863.271 * [misc]backup-simplify: Simplify 1 into 1 1547113863.271 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547113863.271 * [misc]taylor: Taking taylor expansion of k in n 1547113863.271 * [misc]backup-simplify: Simplify k into k 1547113863.271 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547113863.271 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1547113863.271 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1547113863.271 * [misc]taylor: Taking taylor expansion of 2 in n 1547113863.271 * [misc]backup-simplify: Simplify 2 into 2 1547113863.271 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547113863.271 * [misc]taylor: Taking taylor expansion of PI in n 1547113863.271 * [misc]backup-simplify: Simplify PI into PI 1547113863.271 * [misc]taylor: Taking taylor expansion of n in n 1547113863.271 * [misc]backup-simplify: Simplify 0 into 0 1547113863.271 * [misc]backup-simplify: Simplify 1 into 1 1547113863.271 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547113863.271 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547113863.272 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547113863.272 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1547113863.272 * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 1547113863.272 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547113863.272 * [misc]backup-simplify: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) 1547113863.273 * [misc]backup-simplify: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 1547113863.273 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 1547113863.274 * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) 1547113863.274 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 1547113863.274 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 1547113863.276 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3)))))))) 1547113863.276 * [misc]backup-simplify: Simplify (* (pow (/ 1 (- k)) -1/2) (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2))) into (* (sqrt (/ k -1)) (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1)))) 1547113863.277 * [misc]approximate: Taking taylor expansion of (* (sqrt (/ k -1)) (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1)))) in (k n) around 0 1547113863.277 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ k -1)) (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1)))) in n 1547113863.277 * [misc]taylor: Taking taylor expansion of (sqrt (/ k -1)) in n 1547113863.277 * [misc]taylor: Taking taylor expansion of (/ k -1) in n 1547113863.277 * [misc]taylor: Taking taylor expansion of k in n 1547113863.277 * [misc]backup-simplify: Simplify k into k 1547113863.277 * [misc]taylor: Taking taylor expansion of -1 in n 1547113863.277 * [misc]backup-simplify: Simplify -1 into -1 1547113863.277 * [misc]backup-simplify: Simplify (/ k -1) into (* -1 k) 1547113863.277 * [misc]backup-simplify: Simplify (sqrt (* -1 k)) into (sqrt (* -1 k)) 1547113863.277 * [misc]backup-simplify: Simplify (- (/ 0 -1) (+ (* (* -1 k) (/ 0 -1)))) into 0 1547113863.277 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (* -1 k)))) into 0 1547113863.277 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n 1547113863.277 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n 1547113863.277 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n 1547113863.277 * [misc]taylor: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n 1547113863.277 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113863.277 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113863.277 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in n 1547113863.277 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547113863.277 * [misc]taylor: Taking taylor expansion of k in n 1547113863.277 * [misc]backup-simplify: Simplify k into k 1547113863.277 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547113863.277 * [misc]taylor: Taking taylor expansion of 1 in n 1547113863.277 * [misc]backup-simplify: Simplify 1 into 1 1547113863.277 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1547113863.277 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1547113863.277 * [misc]taylor: Taking taylor expansion of -2 in n 1547113863.277 * [misc]backup-simplify: Simplify -2 into -2 1547113863.277 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547113863.277 * [misc]taylor: Taking taylor expansion of PI in n 1547113863.277 * [misc]backup-simplify: Simplify PI into PI 1547113863.277 * [misc]taylor: Taking taylor expansion of n in n 1547113863.277 * [misc]backup-simplify: Simplify 0 into 0 1547113863.277 * [misc]backup-simplify: Simplify 1 into 1 1547113863.278 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547113863.278 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547113863.278 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1547113863.278 * [misc]backup-simplify: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 1547113863.278 * [misc]backup-simplify: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1)) 1547113863.279 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547113863.279 * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 1547113863.280 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 1547113863.280 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ k -1)) (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1)))) in k 1547113863.280 * [misc]taylor: Taking taylor expansion of (sqrt (/ k -1)) in k 1547113863.280 * [misc]taylor: Taking taylor expansion of (/ k -1) in k 1547113863.280 * [misc]taylor: Taking taylor expansion of k in k 1547113863.280 * [misc]backup-simplify: Simplify 0 into 0 1547113863.280 * [misc]backup-simplify: Simplify 1 into 1 1547113863.280 * [misc]taylor: Taking taylor expansion of -1 in k 1547113863.280 * [misc]backup-simplify: Simplify -1 into -1 1547113863.280 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 1547113863.280 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547113863.280 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1547113863.280 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k 1547113863.280 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k 1547113863.280 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k 1547113863.280 * [misc]taylor: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k 1547113863.280 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113863.280 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113863.280 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in k 1547113863.280 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547113863.280 * [misc]taylor: Taking taylor expansion of k in k 1547113863.280 * [misc]backup-simplify: Simplify 0 into 0 1547113863.280 * [misc]backup-simplify: Simplify 1 into 1 1547113863.280 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547113863.280 * [misc]taylor: Taking taylor expansion of 1 in k 1547113863.281 * [misc]backup-simplify: Simplify 1 into 1 1547113863.281 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1547113863.281 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1547113863.281 * [misc]taylor: Taking taylor expansion of -2 in k 1547113863.281 * [misc]backup-simplify: Simplify -2 into -2 1547113863.281 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1547113863.281 * [misc]taylor: Taking taylor expansion of PI in k 1547113863.281 * [misc]backup-simplify: Simplify PI into PI 1547113863.281 * [misc]taylor: Taking taylor expansion of n in k 1547113863.281 * [misc]backup-simplify: Simplify n into n 1547113863.281 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1547113863.281 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1547113863.281 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1547113863.281 * [misc]backup-simplify: Simplify (+ 1 0) into 1 1547113863.281 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1547113863.281 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1547113863.281 * [misc]backup-simplify: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) 1547113863.281 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ k -1)) (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1)))) in k 1547113863.281 * [misc]taylor: Taking taylor expansion of (sqrt (/ k -1)) in k 1547113863.281 * [misc]taylor: Taking taylor expansion of (/ k -1) in k 1547113863.281 * [misc]taylor: Taking taylor expansion of k in k 1547113863.281 * [misc]backup-simplify: Simplify 0 into 0 1547113863.281 * [misc]backup-simplify: Simplify 1 into 1 1547113863.281 * [misc]taylor: Taking taylor expansion of -1 in k 1547113863.281 * [misc]backup-simplify: Simplify -1 into -1 1547113863.281 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 1547113863.282 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547113863.282 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1547113863.282 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k 1547113863.282 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k 1547113863.282 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k 1547113863.282 * [misc]taylor: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k 1547113863.282 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113863.282 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113863.282 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in k 1547113863.282 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547113863.282 * [misc]taylor: Taking taylor expansion of k in k 1547113863.282 * [misc]backup-simplify: Simplify 0 into 0 1547113863.282 * [misc]backup-simplify: Simplify 1 into 1 1547113863.282 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547113863.282 * [misc]taylor: Taking taylor expansion of 1 in k 1547113863.282 * [misc]backup-simplify: Simplify 1 into 1 1547113863.282 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1547113863.282 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1547113863.282 * [misc]taylor: Taking taylor expansion of -2 in k 1547113863.282 * [misc]backup-simplify: Simplify -2 into -2 1547113863.282 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1547113863.282 * [misc]taylor: Taking taylor expansion of PI in k 1547113863.282 * [misc]backup-simplify: Simplify PI into PI 1547113863.282 * [misc]taylor: Taking taylor expansion of n in k 1547113863.282 * [misc]backup-simplify: Simplify n into n 1547113863.282 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1547113863.282 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1547113863.282 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1547113863.283 * [misc]backup-simplify: Simplify (+ 1 0) into 1 1547113863.283 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1547113863.283 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1547113863.283 * [misc]backup-simplify: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) 1547113863.283 * [misc]backup-simplify: Simplify (* 0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) into 0 1547113863.283 * [misc]taylor: Taking taylor expansion of 0 in n 1547113863.283 * [misc]backup-simplify: Simplify 0 into 0 1547113863.283 * [misc]backup-simplify: Simplify 0 into 0 1547113863.283 * [misc]backup-simplify: Simplify (+ (* 0 0) (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) into (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) 1547113863.283 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n 1547113863.283 * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n 1547113863.283 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1547113863.283 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547113863.283 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n 1547113863.283 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n 1547113863.283 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113863.284 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113863.284 * [misc]taylor: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n 1547113863.284 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1547113863.284 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1547113863.284 * [misc]taylor: Taking taylor expansion of -2 in n 1547113863.284 * [misc]backup-simplify: Simplify -2 into -2 1547113863.284 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547113863.284 * [misc]taylor: Taking taylor expansion of PI in n 1547113863.284 * [misc]backup-simplify: Simplify PI into PI 1547113863.284 * [misc]taylor: Taking taylor expansion of n in n 1547113863.284 * [misc]backup-simplify: Simplify 0 into 0 1547113863.284 * [misc]backup-simplify: Simplify 1 into 1 1547113863.284 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547113863.284 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547113863.284 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1547113863.284 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in n 1547113863.284 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547113863.284 * [misc]taylor: Taking taylor expansion of k in n 1547113863.284 * [misc]backup-simplify: Simplify k into k 1547113863.284 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547113863.284 * [misc]taylor: Taking taylor expansion of 1 in n 1547113863.284 * [misc]backup-simplify: Simplify 1 into 1 1547113863.285 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547113863.285 * [misc]backup-simplify: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 1547113863.285 * [misc]backup-simplify: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) 1547113863.286 * [misc]backup-simplify: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 1547113863.286 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 1547113863.287 * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) 1547113863.287 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) 1547113863.288 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) 1547113863.288 * [misc]backup-simplify: Simplify 0 into 0 1547113863.288 * [misc]backup-simplify: Simplify (- (/ 0 -1) (+ (* -1 (/ 0 -1)))) into 0 1547113863.289 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1547113863.290 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))))) into (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) 1547113863.290 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n 1547113863.290 * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n 1547113863.290 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1547113863.290 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547113863.290 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n 1547113863.290 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n 1547113863.290 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113863.290 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113863.290 * [misc]taylor: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n 1547113863.290 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1547113863.290 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1547113863.290 * [misc]taylor: Taking taylor expansion of -2 in n 1547113863.290 * [misc]backup-simplify: Simplify -2 into -2 1547113863.290 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547113863.290 * [misc]taylor: Taking taylor expansion of PI in n 1547113863.290 * [misc]backup-simplify: Simplify PI into PI 1547113863.290 * [misc]taylor: Taking taylor expansion of n in n 1547113863.290 * [misc]backup-simplify: Simplify 0 into 0 1547113863.290 * [misc]backup-simplify: Simplify 1 into 1 1547113863.291 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547113863.291 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547113863.291 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1547113863.291 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in n 1547113863.291 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547113863.291 * [misc]taylor: Taking taylor expansion of k in n 1547113863.291 * [misc]backup-simplify: Simplify k into k 1547113863.291 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547113863.292 * [misc]taylor: Taking taylor expansion of 1 in n 1547113863.292 * [misc]backup-simplify: Simplify 1 into 1 1547113863.292 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547113863.292 * [misc]backup-simplify: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 1547113863.293 * [misc]backup-simplify: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) 1547113863.294 * [misc]backup-simplify: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 1547113863.294 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 1547113863.295 * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) 1547113863.296 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) 1547113863.296 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) 1547113863.297 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547113863.297 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1547113863.297 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113863.299 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1547113863.299 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1547113863.302 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1547113863.303 * [misc]backup-simplify: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (/ 1 k) 1))) into 0 1547113863.303 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into 0 1547113863.305 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1547113863.306 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into 0 1547113863.306 * [misc]backup-simplify: Simplify (- 0) into 0 1547113863.306 * [misc]backup-simplify: Simplify 0 into 0 1547113863.306 * [misc]backup-simplify: Simplify 0 into 0 1547113863.307 * [misc]backup-simplify: Simplify (- (/ 0 -1) (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 1547113863.308 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1547113863.309 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* +nan.0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))))) into (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) 1547113863.309 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n 1547113863.309 * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n 1547113863.309 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1547113863.309 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1547113863.309 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n 1547113863.309 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n 1547113863.309 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113863.309 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113863.309 * [misc]taylor: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n 1547113863.309 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1547113863.309 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1547113863.309 * [misc]taylor: Taking taylor expansion of -2 in n 1547113863.309 * [misc]backup-simplify: Simplify -2 into -2 1547113863.309 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547113863.309 * [misc]taylor: Taking taylor expansion of PI in n 1547113863.309 * [misc]backup-simplify: Simplify PI into PI 1547113863.309 * [misc]taylor: Taking taylor expansion of n in n 1547113863.309 * [misc]backup-simplify: Simplify 0 into 0 1547113863.309 * [misc]backup-simplify: Simplify 1 into 1 1547113863.309 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547113863.310 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547113863.310 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1547113863.310 * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in n 1547113863.310 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547113863.310 * [misc]taylor: Taking taylor expansion of k in n 1547113863.310 * [misc]backup-simplify: Simplify k into k 1547113863.310 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547113863.310 * [misc]taylor: Taking taylor expansion of 1 in n 1547113863.310 * [misc]backup-simplify: Simplify 1 into 1 1547113863.311 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547113863.311 * [misc]backup-simplify: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 1547113863.312 * [misc]backup-simplify: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) 1547113863.312 * [misc]backup-simplify: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 1547113863.313 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 1547113863.314 * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) 1547113863.314 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) 1547113863.315 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) 1547113863.318 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 3)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 2)) (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (* 1 (/ 1 (- k)))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k))))))) 1547113863.318 * * * [misc]progress: simplifying candidates 1547113863.318 * * * * [misc]progress: [ 1 / 63 ] simplifiying candidate # 1547113863.318 * * * * [misc]progress: [ 2 / 63 ] simplifiying candidate # 1547113863.318 * * * * [misc]progress: [ 3 / 63 ] simplifiying candidate # 1547113863.319 * [enter]simplify: Simplifying (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)) 1547113863.319 * * [misc]simplify: iters left: 6 (11 enodes) 1547113863.324 * * [misc]simplify: iters left: 5 (29 enodes) 1547113863.329 * * [misc]simplify: iters left: 4 (59 enodes) 1547113863.342 * * [misc]simplify: iters left: 3 (146 enodes) 1547113863.418 * [exit]simplify: Simplified to (* (- 1/2 (/ k 2)) (log (* (* 2 PI) n))) 1547113863.418 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow k -1/2) (exp (* (- 1/2 (/ k 2)) (log (* (* 2 PI) n)))))) 1547113863.418 * * * * [misc]progress: [ 4 / 63 ] simplifiying candidate # 1547113863.419 * * * * [misc]progress: [ 5 / 63 ] simplifiying candidate # 1547113863.419 * [enter]simplify: Simplifying (* (* 2 PI) n) 1547113863.419 * * [misc]simplify: iters left: 4 (5 enodes) 1547113863.420 * * [misc]simplify: iters left: 3 (9 enodes) 1547113863.422 * * [misc]simplify: iters left: 2 (15 enodes) 1547113863.424 * * [misc]simplify: iters left: 1 (17 enodes) 1547113863.426 * [exit]simplify: Simplified to (* (* 2 PI) n) 1547113863.426 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow k -1/2) (pow (* (* 2 PI) n) (* 1 (/ (- 1 k) 2))))) 1547113863.426 * * * * [misc]progress: [ 6 / 63 ] simplifiying candidate # 1547113863.427 * [enter]simplify: Simplifying (pow (* (* 2 PI) n) (/ k 2)) 1547113863.427 * * [misc]simplify: iters left: 5 (8 enodes) 1547113863.428 * * [misc]simplify: iters left: 4 (12 enodes) 1547113863.430 * * [misc]simplify: iters left: 3 (18 enodes) 1547113863.433 * * [misc]simplify: iters left: 2 (20 enodes) 1547113863.436 * [exit]simplify: Simplified to (pow (* 2 (* n PI)) (/ k 2)) 1547113863.436 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow k -1/2) (/ (pow (* (* 2 PI) n) (/ 1 2)) (pow (* 2 (* n PI)) (/ k 2))))) 1547113863.436 * * * * [misc]progress: [ 7 / 63 ] simplifiying candidate # 1547113863.436 * [enter]simplify: Simplifying (cbrt (/ (- 1 k) 2)) 1547113863.437 * * [misc]simplify: iters left: 5 (6 enodes) 1547113863.438 * * [misc]simplify: iters left: 4 (14 enodes) 1547113863.440 * * [misc]simplify: iters left: 3 (17 enodes) 1547113863.443 * * [misc]simplify: iters left: 2 (19 enodes) 1547113863.447 * [exit]simplify: Simplified to (cbrt (/ (- 1 k) 2)) 1547113863.447 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow k -1/2) (pow (pow (* (* 2 PI) n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) (cbrt (/ (- 1 k) 2))))) 1547113863.447 * * * * [misc]progress: [ 8 / 63 ] simplifiying candidate # 1547113863.448 * [enter]simplify: Simplifying (sqrt (/ (- 1 k) 2)) 1547113863.448 * * [misc]simplify: iters left: 5 (6 enodes) 1547113863.451 * * [misc]simplify: iters left: 4 (14 enodes) 1547113863.454 * * [misc]simplify: iters left: 3 (17 enodes) 1547113863.459 * * [misc]simplify: iters left: 2 (19 enodes) 1547113863.464 * [exit]simplify: Simplified to (sqrt (/ (- 1 k) 2)) 1547113863.464 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow k -1/2) (pow (pow (* (* 2 PI) n) (sqrt (/ (- 1 k) 2))) (sqrt (/ (- 1 k) 2))))) 1547113863.464 * * * * [misc]progress: [ 9 / 63 ] simplifiying candidate # 1547113863.465 * [enter]simplify: Simplifying (/ (- 1 k) 2) 1547113863.465 * * [misc]simplify: iters left: 4 (5 enodes) 1547113863.467 * * [misc]simplify: iters left: 3 (13 enodes) 1547113863.474 * * [misc]simplify: iters left: 2 (16 enodes) 1547113863.478 * * [misc]simplify: iters left: 1 (18 enodes) 1547113863.483 * [exit]simplify: Simplified to (/ (- 1 k) 2) 1547113863.483 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow k -1/2) (pow (pow (* (* 2 PI) n) 1) (/ (- 1 k) 2)))) 1547113863.483 * * * * [misc]progress: [ 10 / 63 ] simplifiying candidate # 1547113863.484 * [enter]simplify: Simplifying (/ 1 2) 1547113863.484 * * [misc]simplify: iters left: 2 (3 enodes) 1547113863.485 * * [misc]simplify: iters left: 1 (6 enodes) 1547113863.487 * [exit]simplify: Simplified to 1/2 1547113863.487 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow k -1/2) (pow (pow (* (* 2 PI) n) (- 1 k)) 1/2))) 1547113863.487 * * * * [misc]progress: [ 11 / 63 ] simplifiying candidate # 1547113863.487 * [enter]simplify: Simplifying (pow (* 2 PI) (/ (- 1 k) 2)) 1547113863.487 * * [misc]simplify: iters left: 5 (8 enodes) 1547113863.491 * * [misc]simplify: iters left: 4 (17 enodes) 1547113863.496 * * [misc]simplify: iters left: 3 (20 enodes) 1547113863.502 * * [misc]simplify: iters left: 2 (22 enodes) 1547113863.507 * [exit]simplify: Simplified to (pow (* 2 PI) (- 1/2 (/ k 2))) 1547113863.507 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow k -1/2) (* (pow (* 2 PI) (- 1/2 (/ k 2))) (pow n (/ (- 1 k) 2))))) 1547113863.507 * * * * [misc]progress: [ 12 / 63 ] simplifiying candidate # 1547113863.508 * * * * [misc]progress: [ 13 / 63 ] simplifiying candidate # 1547113863.508 * * * * [misc]progress: [ 14 / 63 ] simplifiying candidate # 1547113863.508 * * * * [misc]progress: [ 15 / 63 ] simplifiying candidate # 1547113863.508 * * * * [misc]progress: [ 16 / 63 ] simplifiying candidate # 1547113863.508 * * * * [misc]progress: [ 17 / 63 ] simplifiying candidate # 1547113863.508 * * * * [misc]progress: [ 18 / 63 ] simplifiying candidate # 1547113863.508 * * * * [misc]progress: [ 19 / 63 ] simplifiying candidate # 1547113863.508 * * * * [misc]progress: [ 20 / 63 ] simplifiying candidate # 1547113863.508 * * * * [misc]progress: [ 21 / 63 ] simplifiying candidate # 1547113863.508 * * * * [misc]progress: [ 22 / 63 ] simplifiying candidate # 1547113863.508 * * * * [misc]progress: [ 23 / 63 ] simplifiying candidate # 1547113863.508 * * * * [misc]progress: [ 24 / 63 ] simplifiying candidate # 1547113863.508 * * * * [misc]progress: [ 25 / 63 ] simplifiying candidate # 1547113863.508 * * * * [misc]progress: [ 26 / 63 ] simplifiying candidate # 1547113863.508 * * * * [misc]progress: [ 27 / 63 ] simplifiying candidate # 1547113863.508 * * * * [misc]progress: [ 28 / 63 ] simplifiying candidate # 1547113863.508 * * * * [misc]progress: [ 29 / 63 ] simplifiying candidate # 1547113863.508 * * * * [misc]progress: [ 30 / 63 ] simplifiying candidate # 1547113863.508 * * * * [misc]progress: [ 31 / 63 ] simplifiying candidate # 1547113863.508 * * * * [misc]progress: [ 32 / 63 ] simplifiying candidate # 1547113863.508 * * * * [misc]progress: [ 33 / 63 ] simplifiying candidate # 1547113863.508 * [enter]simplify: Simplifying (+ (* (log k) -1/2) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))) 1547113863.509 * * [misc]simplify: iters left: 6 (15 enodes) 1547113863.512 * * [misc]simplify: iters left: 5 (36 enodes) 1547113863.519 * * [misc]simplify: iters left: 4 (69 enodes) 1547113863.534 * * [misc]simplify: iters left: 3 (163 enodes) 1547113863.616 * [exit]simplify: Simplified to (fma (log (* 2 (* n PI))) (- 1/2 (/ k 2)) (* -1/2 (log k))) 1547113863.616 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (log (* 2 (* n PI))) (- 1/2 (/ k 2)) (* -1/2 (log k))))) 1547113863.616 * * * * [misc]progress: [ 34 / 63 ] simplifiying candidate # 1547113863.616 * [enter]simplify: Simplifying (+ (* (log k) -1/2) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))) 1547113863.616 * * [misc]simplify: iters left: 6 (15 enodes) 1547113863.620 * * [misc]simplify: iters left: 5 (36 enodes) 1547113863.627 * * [misc]simplify: iters left: 4 (69 enodes) 1547113863.653 * * [misc]simplify: iters left: 3 (163 enodes) 1547113863.754 * [exit]simplify: Simplified to (fma (log (* 2 (* n PI))) (- 1/2 (/ k 2)) (* -1/2 (log k))) 1547113863.754 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (log (* 2 (* n PI))) (- 1/2 (/ k 2)) (* -1/2 (log k))))) 1547113863.754 * * * * [misc]progress: [ 35 / 63 ] simplifiying candidate # 1547113863.755 * [enter]simplify: Simplifying (+ (* (log k) -1/2) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) 1547113863.755 * * [misc]simplify: iters left: 6 (15 enodes) 1547113863.761 * * [misc]simplify: iters left: 5 (32 enodes) 1547113863.772 * * [misc]simplify: iters left: 4 (53 enodes) 1547113863.789 * * [misc]simplify: iters left: 3 (100 enodes) 1547113863.821 * * [misc]simplify: iters left: 2 (286 enodes) 1547113864.050 * [exit]simplify: Simplified to (fma (/ (- 1 k) 2) (log (* (* n PI) 2)) (* -1/2 (log k))) 1547113864.050 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (/ (- 1 k) 2) (log (* (* n PI) 2)) (* -1/2 (log k))))) 1547113864.050 * * * * [misc]progress: [ 36 / 63 ] simplifiying candidate # 1547113864.051 * [enter]simplify: Simplifying (+ (log (pow k -1/2)) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))) 1547113864.051 * * [misc]simplify: iters left: 6 (15 enodes) 1547113864.057 * * [misc]simplify: iters left: 5 (36 enodes) 1547113864.070 * * [misc]simplify: iters left: 4 (70 enodes) 1547113864.091 * * [misc]simplify: iters left: 3 (165 enodes) 1547113864.164 * [exit]simplify: Simplified to (fma (log (* (* n 2) PI)) (- 1/2 (/ k 2)) (* -1/2 (log k))) 1547113864.164 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (log (* (* n 2) PI)) (- 1/2 (/ k 2)) (* -1/2 (log k))))) 1547113864.164 * * * * [misc]progress: [ 37 / 63 ] simplifiying candidate # 1547113864.164 * [enter]simplify: Simplifying (+ (log (pow k -1/2)) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))) 1547113864.164 * * [misc]simplify: iters left: 6 (15 enodes) 1547113864.171 * * [misc]simplify: iters left: 5 (36 enodes) 1547113864.183 * * [misc]simplify: iters left: 4 (70 enodes) 1547113864.210 * * [misc]simplify: iters left: 3 (165 enodes) 1547113864.305 * [exit]simplify: Simplified to (fma (log (* (* n 2) PI)) (- 1/2 (/ k 2)) (* -1/2 (log k))) 1547113864.305 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (log (* (* n 2) PI)) (- 1/2 (/ k 2)) (* -1/2 (log k))))) 1547113864.305 * * * * [misc]progress: [ 38 / 63 ] simplifiying candidate # 1547113864.305 * [enter]simplify: Simplifying (+ (log (pow k -1/2)) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) 1547113864.305 * * [misc]simplify: iters left: 6 (15 enodes) 1547113864.311 * * [misc]simplify: iters left: 5 (32 enodes) 1547113864.323 * * [misc]simplify: iters left: 4 (54 enodes) 1547113864.338 * * [misc]simplify: iters left: 3 (101 enodes) 1547113864.368 * * [misc]simplify: iters left: 2 (287 enodes) 1547113864.567 * [exit]simplify: Simplified to (fma (log (* 2 (* n PI))) (/ (- 1 k) 2) (* (log k) -1/2)) 1547113864.567 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (log (* 2 (* n PI))) (/ (- 1 k) 2) (* (log k) -1/2)))) 1547113864.567 * * * * [misc]progress: [ 39 / 63 ] simplifiying candidate # 1547113864.568 * * * * [misc]progress: [ 40 / 63 ] simplifiying candidate # 1547113864.568 * * * * [misc]progress: [ 41 / 63 ] simplifiying candidate # 1547113864.568 * [enter]simplify: Simplifying (* (* (* (pow k -1/2) (pow k -1/2)) (pow k -1/2)) (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) 1547113864.568 * * [misc]simplify: iters left: 6 (17 enodes) 1547113864.572 * * [misc]simplify: iters left: 5 (36 enodes) 1547113864.579 * * [misc]simplify: iters left: 4 (70 enodes) 1547113864.598 * * [misc]simplify: iters left: 3 (105 enodes) 1547113864.629 * * [misc]simplify: iters left: 2 (126 enodes) 1547113864.656 * * [misc]simplify: iters left: 1 (129 enodes) 1547113864.676 * [exit]simplify: Simplified to (pow (* (pow k -1/2) (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) 3) 1547113864.676 * [misc]simplify: Simplified (2 1) to (λ (k n) (cbrt (pow (* (pow k -1/2) (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) 3))) 1547113864.676 * * * * [misc]progress: [ 42 / 63 ] simplifiying candidate # 1547113864.676 * * * * [misc]progress: [ 43 / 63 ] simplifiying candidate # 1547113864.676 * * * * [misc]progress: [ 44 / 63 ] simplifiying candidate # 1547113864.676 * * * * [misc]progress: [ 45 / 63 ] simplifiying candidate # 1547113864.676 * * * * [misc]progress: [ 46 / 63 ] simplifiying candidate # 1547113864.677 * [enter]simplify: Simplifying (pow n (/ (- 1 k) 2)) 1547113864.677 * * [misc]simplify: iters left: 5 (7 enodes) 1547113864.680 * * [misc]simplify: iters left: 4 (15 enodes) 1547113864.684 * * [misc]simplify: iters left: 3 (18 enodes) 1547113864.689 * * [misc]simplify: iters left: 2 (20 enodes) 1547113864.695 * [exit]simplify: Simplified to (pow n (- 1/2 (/ k 2))) 1547113864.695 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow k -1/2) (pow (* 2 PI) (/ (- 1 k) 2))) (pow n (- 1/2 (/ k 2))))) 1547113864.695 * * * * [misc]progress: [ 47 / 63 ] simplifiying candidate # 1547113864.695 * [enter]simplify: Simplifying (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) 1547113864.695 * * [misc]simplify: iters left: 6 (11 enodes) 1547113864.700 * * [misc]simplify: iters left: 5 (23 enodes) 1547113864.707 * * [misc]simplify: iters left: 4 (32 enodes) 1547113864.716 * * [misc]simplify: iters left: 3 (35 enodes) 1547113864.723 * [exit]simplify: Simplified to (cbrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) 1547113864.723 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow k -1/2) (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) (cbrt (pow (* PI (* n 2)) (/ (- 1 k) 2))))) 1547113864.723 * * * * [misc]progress: [ 48 / 63 ] simplifiying candidate # 1547113864.723 * [enter]simplify: Simplifying (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) 1547113864.723 * * [misc]simplify: iters left: 6 (11 enodes) 1547113864.726 * * [misc]simplify: iters left: 5 (23 enodes) 1547113864.729 * * [misc]simplify: iters left: 4 (32 enodes) 1547113864.734 * * [misc]simplify: iters left: 3 (35 enodes) 1547113864.739 * [exit]simplify: Simplified to (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) 1547113864.739 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow k -1/2) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))))) 1547113864.739 * * * * [misc]progress: [ 49 / 63 ] simplifiying candidate # 1547113864.739 * [enter]simplify: Simplifying (pow (* (* 2 PI) n) (/ (- 1 k) 2)) 1547113864.739 * * [misc]simplify: iters left: 5 (10 enodes) 1547113864.742 * * [misc]simplify: iters left: 4 (22 enodes) 1547113864.745 * * [misc]simplify: iters left: 3 (31 enodes) 1547113864.750 * * [misc]simplify: iters left: 2 (34 enodes) 1547113864.759 * [exit]simplify: Simplified to (pow (* (* n 2) PI) (/ (- 1 k) 2)) 1547113864.759 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow k -1/2) 1) (pow (* (* n 2) PI) (/ (- 1 k) 2)))) 1547113864.759 * * * * [misc]progress: [ 50 / 63 ] simplifiying candidate # 1547113864.759 * [enter]simplify: Simplifying (* (cbrt (pow k -1/2)) (cbrt (pow k -1/2))) 1547113864.760 * * [misc]simplify: iters left: 4 (5 enodes) 1547113864.761 * [exit]simplify: Simplified to (* (cbrt (pow k -1/2)) (cbrt (pow k -1/2))) 1547113864.761 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (* (cbrt (pow k -1/2)) (cbrt (pow k -1/2))) (* (cbrt (pow k -1/2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) 1547113864.761 * * * * [misc]progress: [ 51 / 63 ] simplifiying candidate # 1547113864.762 * [enter]simplify: Simplifying (sqrt (pow k -1/2)) 1547113864.762 * * [misc]simplify: iters left: 2 (4 enodes) 1547113864.763 * [exit]simplify: Simplified to (sqrt (pow k -1/2)) 1547113864.763 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (pow k -1/2)) (* (sqrt (pow k -1/2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) 1547113864.763 * * * * [misc]progress: [ 52 / 63 ] simplifiying candidate # 1547113864.764 * * * * [misc]progress: [ 53 / 63 ] simplifiying candidate # 1547113864.764 * [enter]simplify: Simplifying (pow (* (* 2 PI) n) (/ k 2)) 1547113864.764 * * [misc]simplify: iters left: 5 (8 enodes) 1547113864.767 * * [misc]simplify: iters left: 4 (12 enodes) 1547113864.771 * * [misc]simplify: iters left: 3 (18 enodes) 1547113864.777 * * [misc]simplify: iters left: 2 (20 enodes) 1547113864.782 * [exit]simplify: Simplified to (pow (* 2 (* n PI)) (/ k 2)) 1547113864.782 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (* (pow k -1/2) (pow (* (* 2 PI) n) (/ 1 2))) (pow (* 2 (* n PI)) (/ k 2)))) 1547113864.782 * * * * [misc]progress: [ 54 / 63 ] simplifiying candidate # 1547113864.783 * * * * [misc]progress: [ 55 / 63 ] simplifiying candidate # 1547113864.783 * [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))))) 1547113864.783 * * [misc]simplify: iters left: 6 (37 enodes) 1547113864.795 * * [misc]simplify: iters left: 5 (108 enodes) 1547113864.822 * * [misc]simplify: iters left: 4 (368 enodes) 1547113865.060 * [exit]simplify: Simplified to (fma -1/2 (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) (fma (* (* (* k k) (log n)) (* (log (* PI 2)) 1/4)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (fma (* (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (log (* PI 2)) (log (* PI 2)))) (* (* k k) 1/8) (fma (* (* (* k k) (log n)) (* (log n) 1/8)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (pow n 1/2) (pow (* PI 2) 1/2)))))) 1547113865.060 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (pow k -1/2) (fma -1/2 (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) (fma (* (* (* k k) (log n)) (* (log (* PI 2)) 1/4)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (fma (* (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (log (* PI 2)) (log (* PI 2)))) (* (* k k) 1/8) (fma (* (* (* k k) (log n)) (* (log n) 1/8)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (pow n 1/2) (pow (* PI 2) 1/2)))))))) 1547113865.060 * * * * [misc]progress: [ 56 / 63 ] simplifiying candidate # 1547113865.061 * [enter]simplify: Simplifying (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) 1547113865.061 * * [misc]simplify: iters left: 6 (15 enodes) 1547113865.068 * * [misc]simplify: iters left: 5 (35 enodes) 1547113865.083 * * [misc]simplify: iters left: 4 (72 enodes) 1547113865.104 * * [misc]simplify: iters left: 3 (240 enodes) 1547113865.229 * [exit]simplify: Simplified to (pow (exp (- 1/2 (* 1/2 k))) (+ (log (* 2 PI)) (log n))) 1547113865.229 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (pow k -1/2) (pow (exp (- 1/2 (* 1/2 k))) (+ (log (* 2 PI)) (log n))))) 1547113865.230 * * * * [misc]progress: [ 57 / 63 ] simplifiying candidate # 1547113865.230 * [enter]simplify: Simplifying (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) 1547113865.230 * * [misc]simplify: iters left: 6 (16 enodes) 1547113865.236 * * [misc]simplify: iters left: 5 (35 enodes) 1547113865.252 * * [misc]simplify: iters left: 4 (76 enodes) 1547113865.275 * * [misc]simplify: iters left: 3 (278 enodes) 1547113865.488 * [exit]simplify: Simplified to (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))) 1547113865.488 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (pow k -1/2) (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))))) 1547113865.488 * * * * [misc]progress: [ 58 / 63 ] simplifiying candidate # 1547113865.489 * [enter]simplify: Simplifying (* 2 (* n PI)) 1547113865.489 * * [misc]simplify: iters left: 4 (5 enodes) 1547113865.491 * * [misc]simplify: iters left: 3 (9 enodes) 1547113865.494 * * [misc]simplify: iters left: 2 (15 enodes) 1547113865.498 * * [misc]simplify: iters left: 1 (17 enodes) 1547113865.503 * [exit]simplify: Simplified to (* (* PI n) 2) 1547113865.503 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow k -1/2) (pow (* (* PI n) 2) (/ (- 1 k) 2)))) 1547113865.503 * * * * [misc]progress: [ 59 / 63 ] simplifiying candidate # 1547113865.503 * [enter]simplify: Simplifying (* 2 (* n PI)) 1547113865.503 * * [misc]simplify: iters left: 4 (5 enodes) 1547113865.505 * * [misc]simplify: iters left: 3 (9 enodes) 1547113865.508 * * [misc]simplify: iters left: 2 (15 enodes) 1547113865.512 * * [misc]simplify: iters left: 1 (17 enodes) 1547113865.517 * [exit]simplify: Simplified to (* (* PI n) 2) 1547113865.517 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow k -1/2) (pow (* (* PI n) 2) (/ (- 1 k) 2)))) 1547113865.517 * * * * [misc]progress: [ 60 / 63 ] simplifiying candidate # 1547113865.517 * [enter]simplify: Simplifying (* 2 (* n PI)) 1547113865.517 * * [misc]simplify: iters left: 4 (5 enodes) 1547113865.519 * * [misc]simplify: iters left: 3 (9 enodes) 1547113865.522 * * [misc]simplify: iters left: 2 (15 enodes) 1547113865.526 * * [misc]simplify: iters left: 1 (17 enodes) 1547113865.531 * [exit]simplify: Simplified to (* (* PI n) 2) 1547113865.531 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow k -1/2) (pow (* (* PI n) 2) (/ (- 1 k) 2)))) 1547113865.531 * * * * [misc]progress: [ 61 / 63 ] simplifiying candidate # 1547113865.531 * [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))))))))))))) 1547113865.531 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1547113865.531 * * * * [misc]progress: [ 62 / 63 ] simplifiying candidate # 1547113865.531 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3)))))))) 1547113865.531 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1547113865.531 * * * * [misc]progress: [ 63 / 63 ] simplifiying candidate # 1547113865.532 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k))))))) 1547113865.532 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1547113865.532 * * * [misc]progress: adding candidates to table 1547113866.249 * * [misc]progress: iteration 4 / 4 1547113866.249 * * * [misc]progress: picking best candidate 1547113866.281 * * * * [misc]pick: Picked # 1547113866.281 * * * [misc]progress: localizing error 1547113866.308 * * * [misc]progress: generating rewritten candidates 1547113866.308 * * * * [misc]progress: [ 1 / 3 ] rewriting at (2 1) 1547113866.314 * * * * [misc]progress: [ 2 / 3 ] rewriting at (2 1 1 1) 1547113866.314 * * * * [misc]progress: [ 3 / 3 ] rewriting at (2) 1547113866.327 * * * [misc]progress: generating series expansions 1547113866.327 * * * * [misc]progress: [ 1 / 3 ] generating series at (2 1) 1547113866.327 * [misc]backup-simplify: Simplify (pow (* (* n PI) 2) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 1547113866.327 * [misc]approximate: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 1547113866.327 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1547113866.327 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1547113866.327 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1547113866.327 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1547113866.327 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113866.327 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113866.327 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1547113866.327 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113866.327 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113866.327 * [misc]taylor: Taking taylor expansion of k in k 1547113866.327 * [misc]backup-simplify: Simplify 0 into 0 1547113866.327 * [misc]backup-simplify: Simplify 1 into 1 1547113866.327 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1547113866.327 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1547113866.327 * [misc]taylor: Taking taylor expansion of 2 in k 1547113866.327 * [misc]backup-simplify: Simplify 2 into 2 1547113866.327 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1547113866.327 * [misc]taylor: Taking taylor expansion of n in k 1547113866.328 * [misc]backup-simplify: Simplify n into n 1547113866.328 * [misc]taylor: Taking taylor expansion of PI in k 1547113866.328 * [misc]backup-simplify: Simplify PI into PI 1547113866.328 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1547113866.328 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1547113866.328 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1547113866.328 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1547113866.328 * [misc]backup-simplify: Simplify (- 0) into 0 1547113866.328 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1547113866.329 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1547113866.329 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1547113866.329 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1547113866.329 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1547113866.329 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1547113866.329 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1547113866.329 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113866.329 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113866.329 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1547113866.329 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113866.329 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113866.329 * [misc]taylor: Taking taylor expansion of k in n 1547113866.329 * [misc]backup-simplify: Simplify k into k 1547113866.329 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1547113866.329 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1547113866.329 * [misc]taylor: Taking taylor expansion of 2 in n 1547113866.329 * [misc]backup-simplify: Simplify 2 into 2 1547113866.329 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547113866.329 * [misc]taylor: Taking taylor expansion of n in n 1547113866.329 * [misc]backup-simplify: Simplify 0 into 0 1547113866.329 * [misc]backup-simplify: Simplify 1 into 1 1547113866.329 * [misc]taylor: Taking taylor expansion of PI in n 1547113866.329 * [misc]backup-simplify: Simplify PI into PI 1547113866.330 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547113866.330 * [misc]backup-simplify: Simplify (* 2 0) into 0 1547113866.331 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547113866.331 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1547113866.332 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547113866.332 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1547113866.332 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1547113866.332 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1547113866.332 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547113866.333 * [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)))) 1547113866.333 * [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))))) 1547113866.333 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1547113866.333 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1547113866.333 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1547113866.333 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1547113866.333 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113866.333 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113866.333 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1547113866.333 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113866.333 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113866.333 * [misc]taylor: Taking taylor expansion of k in n 1547113866.333 * [misc]backup-simplify: Simplify k into k 1547113866.333 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1547113866.333 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1547113866.333 * [misc]taylor: Taking taylor expansion of 2 in n 1547113866.333 * [misc]backup-simplify: Simplify 2 into 2 1547113866.333 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547113866.333 * [misc]taylor: Taking taylor expansion of n in n 1547113866.333 * [misc]backup-simplify: Simplify 0 into 0 1547113866.333 * [misc]backup-simplify: Simplify 1 into 1 1547113866.333 * [misc]taylor: Taking taylor expansion of PI in n 1547113866.333 * [misc]backup-simplify: Simplify PI into PI 1547113866.334 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547113866.334 * [misc]backup-simplify: Simplify (* 2 0) into 0 1547113866.334 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547113866.334 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1547113866.335 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547113866.335 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1547113866.335 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1547113866.335 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1547113866.335 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547113866.336 * [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)))) 1547113866.336 * [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))))) 1547113866.336 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1547113866.336 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1547113866.336 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1547113866.336 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113866.336 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113866.336 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1547113866.336 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113866.336 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113866.336 * [misc]taylor: Taking taylor expansion of k in k 1547113866.336 * [misc]backup-simplify: Simplify 0 into 0 1547113866.336 * [misc]backup-simplify: Simplify 1 into 1 1547113866.336 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1547113866.336 * [misc]taylor: Taking taylor expansion of (log n) in k 1547113866.336 * [misc]taylor: Taking taylor expansion of n in k 1547113866.336 * [misc]backup-simplify: Simplify n into n 1547113866.336 * [misc]backup-simplify: Simplify (log n) into (log n) 1547113866.336 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1547113866.337 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1547113866.337 * [misc]taylor: Taking taylor expansion of 2 in k 1547113866.337 * [misc]backup-simplify: Simplify 2 into 2 1547113866.337 * [misc]taylor: Taking taylor expansion of PI in k 1547113866.337 * [misc]backup-simplify: Simplify PI into PI 1547113866.337 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547113866.337 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547113866.337 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1547113866.337 * [misc]backup-simplify: Simplify (- 0) into 0 1547113866.337 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1547113866.338 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547113866.338 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1547113866.338 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1547113866.339 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1547113866.339 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1547113866.340 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1547113866.342 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1547113866.342 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1547113866.342 * [misc]backup-simplify: Simplify (- 0) into 0 1547113866.342 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113866.342 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547113866.343 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1547113866.344 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1547113866.344 * [misc]taylor: Taking taylor expansion of 0 in k 1547113866.344 * [misc]backup-simplify: Simplify 0 into 0 1547113866.344 * [misc]backup-simplify: Simplify 0 into 0 1547113866.344 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1547113866.345 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1547113866.346 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1547113866.346 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113866.346 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1547113866.347 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1547113866.347 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1547113866.347 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1547113866.348 * [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))))))) 1547113866.349 * [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))))))) 1547113866.350 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1547113866.351 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1547113866.354 * [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 1547113866.354 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1547113866.354 * [misc]backup-simplify: Simplify (- 0) into 0 1547113866.354 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113866.355 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547113866.355 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1547113866.357 * [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 1547113866.357 * [misc]taylor: Taking taylor expansion of 0 in k 1547113866.357 * [misc]backup-simplify: Simplify 0 into 0 1547113866.357 * [misc]backup-simplify: Simplify 0 into 0 1547113866.357 * [misc]backup-simplify: Simplify 0 into 0 1547113866.358 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1547113866.358 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1547113866.363 * [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 1547113866.363 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113866.363 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1547113866.363 * [misc]backup-simplify: Simplify (- 0) into 0 1547113866.364 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113866.364 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1547113866.367 * [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))))) 1547113866.369 * [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))))) 1547113866.374 * [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))))) 1547113866.374 * [misc]backup-simplify: Simplify (pow (* (* (/ 1 n) PI) 2) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 1547113866.375 * [misc]approximate: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 1547113866.375 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1547113866.375 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1547113866.375 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1547113866.375 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1547113866.375 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113866.375 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113866.375 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1547113866.375 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113866.375 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113866.375 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547113866.375 * [misc]taylor: Taking taylor expansion of k in k 1547113866.375 * [misc]backup-simplify: Simplify 0 into 0 1547113866.375 * [misc]backup-simplify: Simplify 1 into 1 1547113866.375 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547113866.375 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1547113866.375 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1547113866.375 * [misc]taylor: Taking taylor expansion of 2 in k 1547113866.375 * [misc]backup-simplify: Simplify 2 into 2 1547113866.375 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1547113866.375 * [misc]taylor: Taking taylor expansion of PI in k 1547113866.375 * [misc]backup-simplify: Simplify PI into PI 1547113866.375 * [misc]taylor: Taking taylor expansion of n in k 1547113866.375 * [misc]backup-simplify: Simplify n into n 1547113866.375 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1547113866.376 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1547113866.376 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1547113866.376 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1547113866.376 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1547113866.376 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1547113866.376 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1547113866.376 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 1547113866.376 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1547113866.377 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1547113866.377 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1547113866.377 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1547113866.377 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113866.377 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113866.377 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1547113866.377 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113866.377 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113866.377 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547113866.377 * [misc]taylor: Taking taylor expansion of k in n 1547113866.377 * [misc]backup-simplify: Simplify k into k 1547113866.377 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547113866.377 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1547113866.377 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1547113866.377 * [misc]taylor: Taking taylor expansion of 2 in n 1547113866.377 * [misc]backup-simplify: Simplify 2 into 2 1547113866.377 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547113866.377 * [misc]taylor: Taking taylor expansion of PI in n 1547113866.377 * [misc]backup-simplify: Simplify PI into PI 1547113866.377 * [misc]taylor: Taking taylor expansion of n in n 1547113866.377 * [misc]backup-simplify: Simplify 0 into 0 1547113866.377 * [misc]backup-simplify: Simplify 1 into 1 1547113866.378 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547113866.378 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547113866.379 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547113866.379 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1547113866.379 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1547113866.379 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1547113866.380 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547113866.380 * [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))) 1547113866.381 * [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)))) 1547113866.381 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1547113866.381 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1547113866.381 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1547113866.381 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1547113866.381 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113866.381 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113866.381 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1547113866.381 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113866.381 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113866.381 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547113866.381 * [misc]taylor: Taking taylor expansion of k in n 1547113866.381 * [misc]backup-simplify: Simplify k into k 1547113866.381 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547113866.381 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1547113866.381 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1547113866.381 * [misc]taylor: Taking taylor expansion of 2 in n 1547113866.381 * [misc]backup-simplify: Simplify 2 into 2 1547113866.381 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547113866.381 * [misc]taylor: Taking taylor expansion of PI in n 1547113866.381 * [misc]backup-simplify: Simplify PI into PI 1547113866.382 * [misc]taylor: Taking taylor expansion of n in n 1547113866.382 * [misc]backup-simplify: Simplify 0 into 0 1547113866.382 * [misc]backup-simplify: Simplify 1 into 1 1547113866.382 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547113866.382 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547113866.383 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547113866.383 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1547113866.383 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1547113866.383 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1547113866.387 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547113866.387 * [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))) 1547113866.388 * [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)))) 1547113866.388 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1547113866.388 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1547113866.388 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1547113866.388 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113866.388 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113866.388 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1547113866.388 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113866.388 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113866.388 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547113866.388 * [misc]taylor: Taking taylor expansion of k in k 1547113866.388 * [misc]backup-simplify: Simplify 0 into 0 1547113866.388 * [misc]backup-simplify: Simplify 1 into 1 1547113866.388 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547113866.388 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1547113866.388 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1547113866.388 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1547113866.388 * [misc]taylor: Taking taylor expansion of 2 in k 1547113866.388 * [misc]backup-simplify: Simplify 2 into 2 1547113866.388 * [misc]taylor: Taking taylor expansion of PI in k 1547113866.388 * [misc]backup-simplify: Simplify PI into PI 1547113866.389 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547113866.389 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547113866.389 * [misc]taylor: Taking taylor expansion of (log n) in k 1547113866.389 * [misc]taylor: Taking taylor expansion of n in k 1547113866.389 * [misc]backup-simplify: Simplify n into n 1547113866.389 * [misc]backup-simplify: Simplify (log n) into (log n) 1547113866.389 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1547113866.389 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1547113866.389 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1547113866.389 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1547113866.390 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1547113866.390 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1547113866.390 * [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)))) 1547113866.391 * [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)))) 1547113866.392 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1547113866.392 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1547113866.393 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1547113866.394 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1547113866.394 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1547113866.394 * [misc]backup-simplify: Simplify (- 0) into 0 1547113866.394 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113866.394 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547113866.395 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1547113866.396 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1547113866.396 * [misc]taylor: Taking taylor expansion of 0 in k 1547113866.396 * [misc]backup-simplify: Simplify 0 into 0 1547113866.396 * [misc]backup-simplify: Simplify 0 into 0 1547113866.396 * [misc]backup-simplify: Simplify 0 into 0 1547113866.397 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113866.397 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1547113866.401 * [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 1547113866.401 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1547113866.401 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1547113866.401 * [misc]backup-simplify: Simplify (- 0) into 0 1547113866.401 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113866.402 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547113866.402 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1547113866.403 * [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 1547113866.403 * [misc]taylor: Taking taylor expansion of 0 in k 1547113866.403 * [misc]backup-simplify: Simplify 0 into 0 1547113866.404 * [misc]backup-simplify: Simplify 0 into 0 1547113866.404 * [misc]backup-simplify: Simplify 0 into 0 1547113866.404 * [misc]backup-simplify: Simplify 0 into 0 1547113866.405 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113866.406 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1547113866.410 * [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 1547113866.410 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1547113866.411 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1547113866.411 * [misc]backup-simplify: Simplify (- 0) into 0 1547113866.411 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113866.411 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547113866.412 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1547113866.414 * [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 1547113866.414 * [misc]taylor: Taking taylor expansion of 0 in k 1547113866.414 * [misc]backup-simplify: Simplify 0 into 0 1547113866.414 * [misc]backup-simplify: Simplify 0 into 0 1547113866.415 * [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))))) 1547113866.415 * [misc]backup-simplify: Simplify (pow (* (* (/ 1 (- n)) PI) 2) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 1547113866.415 * [misc]approximate: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 1547113866.415 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1547113866.415 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1547113866.415 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1547113866.415 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1547113866.415 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1547113866.415 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113866.415 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113866.415 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547113866.415 * [misc]taylor: Taking taylor expansion of k in k 1547113866.415 * [misc]backup-simplify: Simplify 0 into 0 1547113866.415 * [misc]backup-simplify: Simplify 1 into 1 1547113866.415 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547113866.415 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113866.415 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113866.415 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1547113866.415 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1547113866.415 * [misc]taylor: Taking taylor expansion of -2 in k 1547113866.415 * [misc]backup-simplify: Simplify -2 into -2 1547113866.415 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1547113866.415 * [misc]taylor: Taking taylor expansion of PI in k 1547113866.415 * [misc]backup-simplify: Simplify PI into PI 1547113866.415 * [misc]taylor: Taking taylor expansion of n in k 1547113866.415 * [misc]backup-simplify: Simplify n into n 1547113866.415 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1547113866.415 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1547113866.415 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1547113866.416 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1547113866.416 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1547113866.416 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1547113866.416 * [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))) 1547113866.416 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1547113866.416 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1547113866.416 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1547113866.416 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1547113866.416 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1547113866.416 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113866.416 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113866.416 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547113866.416 * [misc]taylor: Taking taylor expansion of k in n 1547113866.416 * [misc]backup-simplify: Simplify k into k 1547113866.416 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547113866.416 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113866.416 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113866.416 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1547113866.416 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1547113866.416 * [misc]taylor: Taking taylor expansion of -2 in n 1547113866.416 * [misc]backup-simplify: Simplify -2 into -2 1547113866.416 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547113866.416 * [misc]taylor: Taking taylor expansion of PI in n 1547113866.416 * [misc]backup-simplify: Simplify PI into PI 1547113866.416 * [misc]taylor: Taking taylor expansion of n in n 1547113866.416 * [misc]backup-simplify: Simplify 0 into 0 1547113866.416 * [misc]backup-simplify: Simplify 1 into 1 1547113866.416 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547113866.417 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547113866.417 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1547113866.417 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1547113866.417 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1547113866.418 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547113866.418 * [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))) 1547113866.418 * [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)))) 1547113866.418 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1547113866.418 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1547113866.418 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1547113866.418 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1547113866.418 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1547113866.418 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113866.418 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113866.419 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547113866.419 * [misc]taylor: Taking taylor expansion of k in n 1547113866.419 * [misc]backup-simplify: Simplify k into k 1547113866.419 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547113866.419 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113866.419 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113866.419 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1547113866.419 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1547113866.419 * [misc]taylor: Taking taylor expansion of -2 in n 1547113866.419 * [misc]backup-simplify: Simplify -2 into -2 1547113866.419 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547113866.419 * [misc]taylor: Taking taylor expansion of PI in n 1547113866.419 * [misc]backup-simplify: Simplify PI into PI 1547113866.419 * [misc]taylor: Taking taylor expansion of n in n 1547113866.419 * [misc]backup-simplify: Simplify 0 into 0 1547113866.419 * [misc]backup-simplify: Simplify 1 into 1 1547113866.419 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547113866.419 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547113866.420 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1547113866.420 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1547113866.420 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1547113866.420 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547113866.421 * [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))) 1547113866.422 * [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)))) 1547113866.422 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1547113866.422 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1547113866.422 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1547113866.422 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1547113866.422 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113866.422 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113866.422 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547113866.422 * [misc]taylor: Taking taylor expansion of k in k 1547113866.422 * [misc]backup-simplify: Simplify 0 into 0 1547113866.422 * [misc]backup-simplify: Simplify 1 into 1 1547113866.422 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547113866.422 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113866.422 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113866.422 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1547113866.422 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1547113866.422 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1547113866.422 * [misc]taylor: Taking taylor expansion of -2 in k 1547113866.422 * [misc]backup-simplify: Simplify -2 into -2 1547113866.422 * [misc]taylor: Taking taylor expansion of PI in k 1547113866.422 * [misc]backup-simplify: Simplify PI into PI 1547113866.423 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547113866.423 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1547113866.423 * [misc]taylor: Taking taylor expansion of (log n) in k 1547113866.423 * [misc]taylor: Taking taylor expansion of n in k 1547113866.423 * [misc]backup-simplify: Simplify n into n 1547113866.423 * [misc]backup-simplify: Simplify (log n) into (log n) 1547113866.424 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1547113866.424 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1547113866.424 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1547113866.424 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1547113866.425 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1547113866.425 * [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)))) 1547113866.426 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 1547113866.427 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1547113866.428 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1547113866.430 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1547113866.431 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1547113866.431 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1547113866.431 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113866.432 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547113866.432 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1547113866.434 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1547113866.434 * [misc]taylor: Taking taylor expansion of 0 in k 1547113866.434 * [misc]backup-simplify: Simplify 0 into 0 1547113866.434 * [misc]backup-simplify: Simplify 0 into 0 1547113866.434 * [misc]backup-simplify: Simplify 0 into 0 1547113866.435 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113866.436 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1547113866.441 * [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 1547113866.442 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1547113866.442 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1547113866.442 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113866.443 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547113866.444 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1547113866.446 * [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 1547113866.446 * [misc]taylor: Taking taylor expansion of 0 in k 1547113866.446 * [misc]backup-simplify: Simplify 0 into 0 1547113866.446 * [misc]backup-simplify: Simplify 0 into 0 1547113866.446 * [misc]backup-simplify: Simplify 0 into 0 1547113866.446 * [misc]backup-simplify: Simplify 0 into 0 1547113866.448 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113866.449 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1547113866.458 * [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 1547113866.458 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1547113866.459 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1547113866.459 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113866.459 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547113866.460 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 1547113866.464 * [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 1547113866.464 * [misc]taylor: Taking taylor expansion of 0 in k 1547113866.464 * [misc]backup-simplify: Simplify 0 into 0 1547113866.464 * [misc]backup-simplify: Simplify 0 into 0 1547113866.465 * [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))))) 1547113866.465 * * * * [misc]progress: [ 2 / 3 ] generating series at (2 1 1 1) 1547113866.465 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1547113866.465 * [misc]approximate: Taking taylor expansion of (* n PI) in (n) around 0 1547113866.466 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547113866.466 * [misc]taylor: Taking taylor expansion of n in n 1547113866.466 * [misc]backup-simplify: Simplify 0 into 0 1547113866.466 * [misc]backup-simplify: Simplify 1 into 1 1547113866.466 * [misc]taylor: Taking taylor expansion of PI in n 1547113866.466 * [misc]backup-simplify: Simplify PI into PI 1547113866.466 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547113866.466 * [misc]taylor: Taking taylor expansion of n in n 1547113866.466 * [misc]backup-simplify: Simplify 0 into 0 1547113866.466 * [misc]backup-simplify: Simplify 1 into 1 1547113866.466 * [misc]taylor: Taking taylor expansion of PI in n 1547113866.466 * [misc]backup-simplify: Simplify PI into PI 1547113866.466 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547113866.466 * [misc]backup-simplify: Simplify 0 into 0 1547113866.467 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547113866.467 * [misc]backup-simplify: Simplify PI into PI 1547113866.468 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1547113866.468 * [misc]backup-simplify: Simplify 0 into 0 1547113866.470 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1547113866.470 * [misc]backup-simplify: Simplify 0 into 0 1547113866.472 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1547113866.472 * [misc]backup-simplify: Simplify 0 into 0 1547113866.475 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1547113866.475 * [misc]backup-simplify: Simplify 0 into 0 1547113866.478 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1547113866.478 * [misc]backup-simplify: Simplify 0 into 0 1547113866.481 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1547113866.481 * [misc]backup-simplify: Simplify 0 into 0 1547113866.481 * [misc]backup-simplify: Simplify (* PI n) into (* n PI) 1547113866.481 * [misc]backup-simplify: Simplify (* (/ 1 n) PI) into (/ PI n) 1547113866.481 * [misc]approximate: Taking taylor expansion of (/ PI n) in (n) around 0 1547113866.481 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547113866.481 * [misc]taylor: Taking taylor expansion of PI in n 1547113866.481 * [misc]backup-simplify: Simplify PI into PI 1547113866.481 * [misc]taylor: Taking taylor expansion of n in n 1547113866.481 * [misc]backup-simplify: Simplify 0 into 0 1547113866.481 * [misc]backup-simplify: Simplify 1 into 1 1547113866.482 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547113866.482 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547113866.482 * [misc]taylor: Taking taylor expansion of PI in n 1547113866.482 * [misc]backup-simplify: Simplify PI into PI 1547113866.482 * [misc]taylor: Taking taylor expansion of n in n 1547113866.482 * [misc]backup-simplify: Simplify 0 into 0 1547113866.482 * [misc]backup-simplify: Simplify 1 into 1 1547113866.482 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547113866.482 * [misc]backup-simplify: Simplify PI into PI 1547113866.483 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1547113866.483 * [misc]backup-simplify: Simplify 0 into 0 1547113866.484 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113866.484 * [misc]backup-simplify: Simplify 0 into 0 1547113866.485 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113866.485 * [misc]backup-simplify: Simplify 0 into 0 1547113866.486 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113866.486 * [misc]backup-simplify: Simplify 0 into 0 1547113866.487 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113866.487 * [misc]backup-simplify: Simplify 0 into 0 1547113866.488 * [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 1547113866.488 * [misc]backup-simplify: Simplify 0 into 0 1547113866.488 * [misc]backup-simplify: Simplify (* PI (/ 1 (/ 1 n))) into (* n PI) 1547113866.489 * [misc]backup-simplify: Simplify (* (/ 1 (- n)) PI) into (* -1 (/ PI n)) 1547113866.489 * [misc]approximate: Taking taylor expansion of (* -1 (/ PI n)) in (n) around 0 1547113866.489 * [misc]taylor: Taking taylor expansion of (* -1 (/ PI n)) in n 1547113866.489 * [misc]taylor: Taking taylor expansion of -1 in n 1547113866.489 * [misc]backup-simplify: Simplify -1 into -1 1547113866.489 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547113866.489 * [misc]taylor: Taking taylor expansion of PI in n 1547113866.489 * [misc]backup-simplify: Simplify PI into PI 1547113866.489 * [misc]taylor: Taking taylor expansion of n in n 1547113866.489 * [misc]backup-simplify: Simplify 0 into 0 1547113866.489 * [misc]backup-simplify: Simplify 1 into 1 1547113866.489 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547113866.489 * [misc]taylor: Taking taylor expansion of (* -1 (/ PI n)) in n 1547113866.489 * [misc]taylor: Taking taylor expansion of -1 in n 1547113866.489 * [misc]backup-simplify: Simplify -1 into -1 1547113866.489 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547113866.489 * [misc]taylor: Taking taylor expansion of PI in n 1547113866.489 * [misc]backup-simplify: Simplify PI into PI 1547113866.489 * [misc]taylor: Taking taylor expansion of n in n 1547113866.489 * [misc]backup-simplify: Simplify 0 into 0 1547113866.489 * [misc]backup-simplify: Simplify 1 into 1 1547113866.489 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547113866.489 * [misc]backup-simplify: Simplify (* -1 PI) into (* -1 PI) 1547113866.490 * [misc]backup-simplify: Simplify (* -1 PI) into (* -1 PI) 1547113866.490 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1547113866.491 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 PI)) into 0 1547113866.491 * [misc]backup-simplify: Simplify 0 into 0 1547113866.492 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113866.492 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 PI))) into 0 1547113866.492 * [misc]backup-simplify: Simplify 0 into 0 1547113866.493 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113866.494 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1547113866.494 * [misc]backup-simplify: Simplify 0 into 0 1547113866.495 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113866.496 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1547113866.496 * [misc]backup-simplify: Simplify 0 into 0 1547113866.498 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113866.499 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1547113866.499 * [misc]backup-simplify: Simplify 0 into 0 1547113866.501 * [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 1547113866.503 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1547113866.503 * [misc]backup-simplify: Simplify 0 into 0 1547113866.503 * [misc]backup-simplify: Simplify (* (* -1 PI) (/ 1 (/ 1 (- n)))) into (* n PI) 1547113866.503 * * * * [misc]progress: [ 3 / 3 ] generating series at (2) 1547113866.503 * [misc]backup-simplify: Simplify (/ (pow (* (* n PI) 2) (- 1/2 (/ k 2))) (sqrt k)) into (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) 1547113866.503 * [misc]approximate: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (n k) around 0 1547113866.503 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 1547113866.504 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1547113866.504 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547113866.504 * [misc]taylor: Taking taylor expansion of k in k 1547113866.504 * [misc]backup-simplify: Simplify 0 into 0 1547113866.504 * [misc]backup-simplify: Simplify 1 into 1 1547113866.504 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547113866.504 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547113866.504 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1547113866.504 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1547113866.504 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1547113866.504 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1547113866.504 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1547113866.504 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113866.504 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113866.504 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1547113866.504 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113866.504 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113866.504 * [misc]taylor: Taking taylor expansion of k in k 1547113866.504 * [misc]backup-simplify: Simplify 0 into 0 1547113866.504 * [misc]backup-simplify: Simplify 1 into 1 1547113866.504 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1547113866.504 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1547113866.504 * [misc]taylor: Taking taylor expansion of 2 in k 1547113866.504 * [misc]backup-simplify: Simplify 2 into 2 1547113866.504 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1547113866.504 * [misc]taylor: Taking taylor expansion of n in k 1547113866.504 * [misc]backup-simplify: Simplify n into n 1547113866.504 * [misc]taylor: Taking taylor expansion of PI in k 1547113866.505 * [misc]backup-simplify: Simplify PI into PI 1547113866.505 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1547113866.505 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1547113866.505 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1547113866.505 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1547113866.505 * [misc]backup-simplify: Simplify (- 0) into 0 1547113866.505 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1547113866.505 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1547113866.505 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1547113866.505 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 1547113866.505 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1547113866.505 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547113866.505 * [misc]taylor: Taking taylor expansion of k in n 1547113866.505 * [misc]backup-simplify: Simplify k into k 1547113866.505 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547113866.505 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1547113866.505 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1547113866.505 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1547113866.505 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1547113866.505 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1547113866.505 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1547113866.505 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1547113866.506 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113866.506 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113866.506 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1547113866.506 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113866.506 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113866.506 * [misc]taylor: Taking taylor expansion of k in n 1547113866.506 * [misc]backup-simplify: Simplify k into k 1547113866.506 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1547113866.506 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1547113866.506 * [misc]taylor: Taking taylor expansion of 2 in n 1547113866.506 * [misc]backup-simplify: Simplify 2 into 2 1547113866.506 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547113866.506 * [misc]taylor: Taking taylor expansion of n in n 1547113866.506 * [misc]backup-simplify: Simplify 0 into 0 1547113866.506 * [misc]backup-simplify: Simplify 1 into 1 1547113866.506 * [misc]taylor: Taking taylor expansion of PI in n 1547113866.506 * [misc]backup-simplify: Simplify PI into PI 1547113866.506 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547113866.506 * [misc]backup-simplify: Simplify (* 2 0) into 0 1547113866.506 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547113866.507 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1547113866.507 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547113866.507 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1547113866.507 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1547113866.507 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1547113866.508 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547113866.508 * [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)))) 1547113866.508 * [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))))) 1547113866.508 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 1547113866.508 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1547113866.509 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547113866.509 * [misc]taylor: Taking taylor expansion of k in n 1547113866.509 * [misc]backup-simplify: Simplify k into k 1547113866.509 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547113866.509 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1547113866.509 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1547113866.510 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1547113866.510 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1547113866.510 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1547113866.510 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1547113866.510 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1547113866.510 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113866.510 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113866.510 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1547113866.510 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113866.510 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113866.510 * [misc]taylor: Taking taylor expansion of k in n 1547113866.510 * [misc]backup-simplify: Simplify k into k 1547113866.510 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1547113866.510 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1547113866.510 * [misc]taylor: Taking taylor expansion of 2 in n 1547113866.510 * [misc]backup-simplify: Simplify 2 into 2 1547113866.510 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1547113866.510 * [misc]taylor: Taking taylor expansion of n in n 1547113866.510 * [misc]backup-simplify: Simplify 0 into 0 1547113866.510 * [misc]backup-simplify: Simplify 1 into 1 1547113866.510 * [misc]taylor: Taking taylor expansion of PI in n 1547113866.510 * [misc]backup-simplify: Simplify PI into PI 1547113866.510 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1547113866.510 * [misc]backup-simplify: Simplify (* 2 0) into 0 1547113866.511 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1547113866.511 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1547113866.512 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547113866.512 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1547113866.512 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1547113866.512 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1547113866.513 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547113866.513 * [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)))) 1547113866.514 * [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))))) 1547113866.514 * [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))) 1547113866.514 * [misc]taylor: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k))) in k 1547113866.515 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1547113866.515 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1547113866.515 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1547113866.515 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113866.515 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113866.515 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1547113866.515 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113866.515 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113866.515 * [misc]taylor: Taking taylor expansion of k in k 1547113866.515 * [misc]backup-simplify: Simplify 0 into 0 1547113866.515 * [misc]backup-simplify: Simplify 1 into 1 1547113866.515 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1547113866.515 * [misc]taylor: Taking taylor expansion of (log n) in k 1547113866.515 * [misc]taylor: Taking taylor expansion of n in k 1547113866.515 * [misc]backup-simplify: Simplify n into n 1547113866.515 * [misc]backup-simplify: Simplify (log n) into (log n) 1547113866.515 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1547113866.515 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1547113866.515 * [misc]taylor: Taking taylor expansion of 2 in k 1547113866.515 * [misc]backup-simplify: Simplify 2 into 2 1547113866.515 * [misc]taylor: Taking taylor expansion of PI in k 1547113866.515 * [misc]backup-simplify: Simplify PI into PI 1547113866.515 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547113866.516 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547113866.516 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1547113866.516 * [misc]backup-simplify: Simplify (- 0) into 0 1547113866.516 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1547113866.517 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547113866.517 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1547113866.518 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1547113866.518 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1547113866.518 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547113866.518 * [misc]taylor: Taking taylor expansion of k in k 1547113866.518 * [misc]backup-simplify: Simplify 0 into 0 1547113866.518 * [misc]backup-simplify: Simplify 1 into 1 1547113866.518 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547113866.518 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547113866.519 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1547113866.519 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) into 0 1547113866.519 * [misc]backup-simplify: Simplify 0 into 0 1547113866.520 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1547113866.522 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1547113866.524 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1547113866.524 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1547113866.525 * [misc]backup-simplify: Simplify (- 0) into 0 1547113866.525 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113866.525 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547113866.526 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1547113866.527 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1547113866.528 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 k)) 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))) into 0 1547113866.528 * [misc]taylor: Taking taylor expansion of 0 in k 1547113866.528 * [misc]backup-simplify: Simplify 0 into 0 1547113866.529 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1547113866.529 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1547113866.531 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1547113866.531 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113866.531 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1547113866.531 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1547113866.531 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1547113866.531 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1547113866.532 * [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))))))) 1547113866.533 * [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))))))) 1547113866.534 * [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))))))) 1547113866.535 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1547113866.536 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1547113866.539 * [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 1547113866.539 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1547113866.539 * [misc]backup-simplify: Simplify (- 0) into 0 1547113866.539 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113866.540 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547113866.540 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1547113866.541 * [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 1547113866.542 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1547113866.542 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 1547113866.542 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))))) into 0 1547113866.543 * [misc]taylor: Taking taylor expansion of 0 in k 1547113866.543 * [misc]backup-simplify: Simplify 0 into 0 1547113866.543 * [misc]backup-simplify: Simplify 0 into 0 1547113866.543 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1547113866.543 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1547113866.544 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1547113866.545 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1547113866.548 * [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 1547113866.548 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113866.548 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1547113866.548 * [misc]backup-simplify: Simplify (- 0) into 0 1547113866.548 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113866.549 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1547113866.550 * [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))))) 1547113866.553 * [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)))))))) 1547113866.555 * [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)))))))) 1547113866.557 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1547113866.559 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1547113866.567 * [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 1547113866.568 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 1547113866.568 * [misc]backup-simplify: Simplify (- 0) into 0 1547113866.568 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113866.569 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1547113866.570 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 1547113866.574 * [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 1547113866.574 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1547113866.574 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 1547113866.575 * [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 1547113866.576 * [misc]taylor: Taking taylor expansion of 0 in k 1547113866.576 * [misc]backup-simplify: Simplify 0 into 0 1547113866.576 * [misc]backup-simplify: Simplify 0 into 0 1547113866.576 * [misc]backup-simplify: Simplify 0 into 0 1547113866.576 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113866.577 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1547113866.578 * [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 1547113866.579 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1547113866.586 * [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 1547113866.586 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113866.587 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1547113866.587 * [misc]backup-simplify: Simplify (- 0) into 0 1547113866.588 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113866.589 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 1547113866.592 * [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))))))) 1547113866.601 * [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)))))))))))))) 1547113866.608 * [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)))))))))))))) 1547113866.619 * [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)))))))))))))))))))))) 1547113866.620 * [misc]backup-simplify: Simplify (/ (pow (* (* (/ 1 n) PI) 2) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) into (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 1547113866.620 * [misc]approximate: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0 1547113866.620 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 1547113866.620 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1547113866.620 * [misc]taylor: Taking taylor expansion of k in k 1547113866.620 * [misc]backup-simplify: Simplify 0 into 0 1547113866.620 * [misc]backup-simplify: Simplify 1 into 1 1547113866.620 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547113866.621 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1547113866.621 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1547113866.621 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1547113866.621 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1547113866.621 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1547113866.621 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113866.621 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113866.621 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1547113866.621 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113866.621 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113866.621 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547113866.621 * [misc]taylor: Taking taylor expansion of k in k 1547113866.621 * [misc]backup-simplify: Simplify 0 into 0 1547113866.621 * [misc]backup-simplify: Simplify 1 into 1 1547113866.622 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547113866.622 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1547113866.622 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1547113866.622 * [misc]taylor: Taking taylor expansion of 2 in k 1547113866.622 * [misc]backup-simplify: Simplify 2 into 2 1547113866.622 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1547113866.622 * [misc]taylor: Taking taylor expansion of PI in k 1547113866.622 * [misc]backup-simplify: Simplify PI into PI 1547113866.622 * [misc]taylor: Taking taylor expansion of n in k 1547113866.622 * [misc]backup-simplify: Simplify n into n 1547113866.622 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1547113866.622 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1547113866.622 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1547113866.622 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1547113866.622 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1547113866.623 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1547113866.623 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1547113866.623 * [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)))) 1547113866.623 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1547113866.623 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1547113866.623 * [misc]taylor: Taking taylor expansion of k in n 1547113866.623 * [misc]backup-simplify: Simplify k into k 1547113866.623 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1547113866.623 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1547113866.623 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1547113866.623 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1547113866.623 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1547113866.623 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1547113866.623 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113866.623 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113866.623 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1547113866.624 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113866.624 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113866.624 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547113866.624 * [misc]taylor: Taking taylor expansion of k in n 1547113866.624 * [misc]backup-simplify: Simplify k into k 1547113866.624 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547113866.624 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1547113866.624 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1547113866.624 * [misc]taylor: Taking taylor expansion of 2 in n 1547113866.624 * [misc]backup-simplify: Simplify 2 into 2 1547113866.624 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547113866.624 * [misc]taylor: Taking taylor expansion of PI in n 1547113866.624 * [misc]backup-simplify: Simplify PI into PI 1547113866.624 * [misc]taylor: Taking taylor expansion of n in n 1547113866.624 * [misc]backup-simplify: Simplify 0 into 0 1547113866.624 * [misc]backup-simplify: Simplify 1 into 1 1547113866.624 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547113866.625 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547113866.625 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547113866.625 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1547113866.625 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1547113866.625 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1547113866.626 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547113866.627 * [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))) 1547113866.627 * [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)))) 1547113866.627 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1547113866.627 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1547113866.627 * [misc]taylor: Taking taylor expansion of k in n 1547113866.627 * [misc]backup-simplify: Simplify k into k 1547113866.627 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1547113866.628 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1547113866.628 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1547113866.628 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1547113866.628 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1547113866.628 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1547113866.628 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113866.628 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113866.628 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1547113866.628 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113866.628 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113866.628 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547113866.628 * [misc]taylor: Taking taylor expansion of k in n 1547113866.628 * [misc]backup-simplify: Simplify k into k 1547113866.628 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547113866.628 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1547113866.628 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1547113866.628 * [misc]taylor: Taking taylor expansion of 2 in n 1547113866.628 * [misc]backup-simplify: Simplify 2 into 2 1547113866.628 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547113866.628 * [misc]taylor: Taking taylor expansion of PI in n 1547113866.628 * [misc]backup-simplify: Simplify PI into PI 1547113866.628 * [misc]taylor: Taking taylor expansion of n in n 1547113866.628 * [misc]backup-simplify: Simplify 0 into 0 1547113866.628 * [misc]backup-simplify: Simplify 1 into 1 1547113866.629 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547113866.629 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547113866.629 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547113866.629 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1547113866.629 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1547113866.630 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1547113866.630 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547113866.631 * [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))) 1547113866.631 * [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)))) 1547113866.632 * [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)) 1547113866.632 * [misc]taylor: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) in k 1547113866.632 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1547113866.632 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1547113866.632 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1547113866.632 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113866.632 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113866.632 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1547113866.632 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113866.632 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113866.632 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547113866.632 * [misc]taylor: Taking taylor expansion of k in k 1547113866.632 * [misc]backup-simplify: Simplify 0 into 0 1547113866.632 * [misc]backup-simplify: Simplify 1 into 1 1547113866.632 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547113866.632 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1547113866.632 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1547113866.632 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1547113866.632 * [misc]taylor: Taking taylor expansion of 2 in k 1547113866.632 * [misc]backup-simplify: Simplify 2 into 2 1547113866.632 * [misc]taylor: Taking taylor expansion of PI in k 1547113866.632 * [misc]backup-simplify: Simplify PI into PI 1547113866.632 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1547113866.633 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1547113866.633 * [misc]taylor: Taking taylor expansion of (log n) in k 1547113866.633 * [misc]taylor: Taking taylor expansion of n in k 1547113866.633 * [misc]backup-simplify: Simplify n into n 1547113866.633 * [misc]backup-simplify: Simplify (log n) into (log n) 1547113866.633 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1547113866.633 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1547113866.633 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1547113866.633 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1547113866.634 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1547113866.634 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1547113866.635 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 1547113866.635 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1547113866.635 * [misc]taylor: Taking taylor expansion of k in k 1547113866.635 * [misc]backup-simplify: Simplify 0 into 0 1547113866.635 * [misc]backup-simplify: Simplify 1 into 1 1547113866.635 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547113866.635 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1547113866.636 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) into 0 1547113866.636 * [misc]backup-simplify: Simplify 0 into 0 1547113866.636 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1547113866.637 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1547113866.638 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1547113866.638 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1547113866.639 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1547113866.639 * [misc]backup-simplify: Simplify (- 0) into 0 1547113866.639 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113866.639 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547113866.640 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1547113866.641 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1547113866.641 * [misc]backup-simplify: Simplify (+ (* (sqrt k) 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0 1547113866.641 * [misc]taylor: Taking taylor expansion of 0 in k 1547113866.641 * [misc]backup-simplify: Simplify 0 into 0 1547113866.641 * [misc]backup-simplify: Simplify 0 into 0 1547113866.642 * [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)))))) 1547113866.642 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 1547113866.644 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113866.644 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1547113866.647 * [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 1547113866.647 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1547113866.648 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1547113866.648 * [misc]backup-simplify: Simplify (- 0) into 0 1547113866.648 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113866.648 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547113866.649 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1547113866.650 * [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 1547113866.651 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 1547113866.651 * [misc]backup-simplify: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0 1547113866.651 * [misc]taylor: Taking taylor expansion of 0 in k 1547113866.651 * [misc]backup-simplify: Simplify 0 into 0 1547113866.651 * [misc]backup-simplify: Simplify 0 into 0 1547113866.651 * [misc]backup-simplify: Simplify 0 into 0 1547113866.652 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1547113866.653 * [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)))))) 1547113866.653 * [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)))))) 1547113866.654 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113866.655 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1547113866.660 * [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 1547113866.660 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1547113866.660 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1547113866.660 * [misc]backup-simplify: Simplify (- 0) into 0 1547113866.661 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113866.661 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1547113866.662 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1547113866.664 * [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 1547113866.664 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 1547113866.665 * [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 1547113866.665 * [misc]taylor: Taking taylor expansion of 0 in k 1547113866.665 * [misc]backup-simplify: Simplify 0 into 0 1547113866.665 * [misc]backup-simplify: Simplify 0 into 0 1547113866.665 * [misc]backup-simplify: Simplify 0 into 0 1547113866.665 * [misc]backup-simplify: Simplify 0 into 0 1547113866.666 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1547113866.666 * [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)))))) 1547113866.667 * [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)))))) 1547113866.669 * [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)))))))) 1547113866.669 * [misc]backup-simplify: Simplify (/ (pow (* (* (/ 1 (- n)) PI) 2) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) into (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) 1547113866.669 * [misc]approximate: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (n k) around 0 1547113866.669 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 1547113866.669 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1547113866.669 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1547113866.669 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1547113866.669 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1547113866.669 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1547113866.669 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113866.669 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113866.669 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547113866.669 * [misc]taylor: Taking taylor expansion of k in k 1547113866.669 * [misc]backup-simplify: Simplify 0 into 0 1547113866.670 * [misc]backup-simplify: Simplify 1 into 1 1547113866.670 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547113866.670 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113866.670 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113866.670 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1547113866.670 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1547113866.670 * [misc]taylor: Taking taylor expansion of -2 in k 1547113866.670 * [misc]backup-simplify: Simplify -2 into -2 1547113866.670 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1547113866.670 * [misc]taylor: Taking taylor expansion of PI in k 1547113866.670 * [misc]backup-simplify: Simplify PI into PI 1547113866.670 * [misc]taylor: Taking taylor expansion of n in k 1547113866.670 * [misc]backup-simplify: Simplify n into n 1547113866.670 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1547113866.670 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1547113866.670 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1547113866.670 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1547113866.671 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1547113866.671 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1547113866.671 * [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))) 1547113866.671 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1547113866.671 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1547113866.671 * [misc]taylor: Taking taylor expansion of -1 in k 1547113866.671 * [misc]backup-simplify: Simplify -1 into -1 1547113866.671 * [misc]taylor: Taking taylor expansion of k in k 1547113866.671 * [misc]backup-simplify: Simplify 0 into 0 1547113866.671 * [misc]backup-simplify: Simplify 1 into 1 1547113866.671 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1547113866.671 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547113866.672 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1547113866.672 * [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)))) 1547113866.672 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 1547113866.672 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1547113866.672 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1547113866.672 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1547113866.672 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1547113866.672 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1547113866.672 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113866.673 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113866.673 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547113866.673 * [misc]taylor: Taking taylor expansion of k in n 1547113866.673 * [misc]backup-simplify: Simplify k into k 1547113866.673 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547113866.673 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113866.673 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113866.673 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1547113866.673 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1547113866.673 * [misc]taylor: Taking taylor expansion of -2 in n 1547113866.673 * [misc]backup-simplify: Simplify -2 into -2 1547113866.673 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547113866.673 * [misc]taylor: Taking taylor expansion of PI in n 1547113866.673 * [misc]backup-simplify: Simplify PI into PI 1547113866.673 * [misc]taylor: Taking taylor expansion of n in n 1547113866.673 * [misc]backup-simplify: Simplify 0 into 0 1547113866.673 * [misc]backup-simplify: Simplify 1 into 1 1547113866.673 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547113866.673 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547113866.674 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1547113866.674 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1547113866.674 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1547113866.675 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547113866.675 * [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))) 1547113866.676 * [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)))) 1547113866.676 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1547113866.676 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1547113866.676 * [misc]taylor: Taking taylor expansion of -1 in n 1547113866.676 * [misc]backup-simplify: Simplify -1 into -1 1547113866.676 * [misc]taylor: Taking taylor expansion of k in n 1547113866.676 * [misc]backup-simplify: Simplify k into k 1547113866.676 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1547113866.676 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1547113866.677 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1547113866.677 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1547113866.677 * [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))) 1547113866.677 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 1547113866.677 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1547113866.677 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1547113866.677 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1547113866.677 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1547113866.678 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1547113866.678 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113866.678 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113866.678 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1547113866.678 * [misc]taylor: Taking taylor expansion of k in n 1547113866.678 * [misc]backup-simplify: Simplify k into k 1547113866.678 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1547113866.678 * [misc]taylor: Taking taylor expansion of 1/2 in n 1547113866.678 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113866.678 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1547113866.678 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1547113866.678 * [misc]taylor: Taking taylor expansion of -2 in n 1547113866.678 * [misc]backup-simplify: Simplify -2 into -2 1547113866.678 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1547113866.678 * [misc]taylor: Taking taylor expansion of PI in n 1547113866.678 * [misc]backup-simplify: Simplify PI into PI 1547113866.678 * [misc]taylor: Taking taylor expansion of n in n 1547113866.678 * [misc]backup-simplify: Simplify 0 into 0 1547113866.678 * [misc]backup-simplify: Simplify 1 into 1 1547113866.678 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1547113866.679 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547113866.679 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1547113866.679 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1547113866.679 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1547113866.680 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547113866.680 * [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))) 1547113866.681 * [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)))) 1547113866.681 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1547113866.681 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1547113866.681 * [misc]taylor: Taking taylor expansion of -1 in n 1547113866.681 * [misc]backup-simplify: Simplify -1 into -1 1547113866.681 * [misc]taylor: Taking taylor expansion of k in n 1547113866.681 * [misc]backup-simplify: Simplify k into k 1547113866.681 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1547113866.681 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1547113866.682 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1547113866.682 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1547113866.682 * [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))) 1547113866.683 * [misc]taylor: Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) in k 1547113866.683 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1547113866.683 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1547113866.683 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1547113866.683 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1547113866.683 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113866.683 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113866.683 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1547113866.683 * [misc]taylor: Taking taylor expansion of k in k 1547113866.683 * [misc]backup-simplify: Simplify 0 into 0 1547113866.683 * [misc]backup-simplify: Simplify 1 into 1 1547113866.683 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1547113866.683 * [misc]taylor: Taking taylor expansion of 1/2 in k 1547113866.683 * [misc]backup-simplify: Simplify 1/2 into 1/2 1547113866.683 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1547113866.683 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1547113866.683 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1547113866.683 * [misc]taylor: Taking taylor expansion of -2 in k 1547113866.683 * [misc]backup-simplify: Simplify -2 into -2 1547113866.683 * [misc]taylor: Taking taylor expansion of PI in k 1547113866.683 * [misc]backup-simplify: Simplify PI into PI 1547113866.684 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1547113866.684 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1547113866.684 * [misc]taylor: Taking taylor expansion of (log n) in k 1547113866.684 * [misc]taylor: Taking taylor expansion of n in k 1547113866.684 * [misc]backup-simplify: Simplify n into n 1547113866.684 * [misc]backup-simplify: Simplify (log n) into (log n) 1547113866.684 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1547113866.685 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1547113866.685 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1547113866.685 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1547113866.686 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1547113866.686 * [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)))) 1547113866.686 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1547113866.686 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1547113866.686 * [misc]taylor: Taking taylor expansion of -1 in k 1547113866.686 * [misc]backup-simplify: Simplify -1 into -1 1547113866.686 * [misc]taylor: Taking taylor expansion of k in k 1547113866.686 * [misc]backup-simplify: Simplify 0 into 0 1547113866.687 * [misc]backup-simplify: Simplify 1 into 1 1547113866.687 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1547113866.687 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1547113866.687 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1547113866.688 * [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))))) 1547113866.689 * [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))))) 1547113866.690 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1547113866.690 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1547113866.693 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1547113866.693 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1547113866.694 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1547113866.694 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113866.694 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547113866.695 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1547113866.697 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1547113866.697 * [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 1547113866.697 * [misc]taylor: Taking taylor expansion of 0 in k 1547113866.698 * [misc]backup-simplify: Simplify 0 into 0 1547113866.698 * [misc]backup-simplify: Simplify 0 into 0 1547113866.698 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1547113866.699 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1547113866.700 * [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)))))) 1547113866.701 * [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)))))) 1547113866.702 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113866.703 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1547113866.708 * [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 1547113866.708 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1547113866.708 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1547113866.709 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1547113866.709 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1547113866.709 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1547113866.711 * [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 1547113866.711 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1547113866.711 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 1547113866.712 * [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 1547113866.712 * [misc]taylor: Taking taylor expansion of 0 in k 1547113866.712 * [misc]backup-simplify: Simplify 0 into 0 1547113866.712 * [misc]backup-simplify: Simplify 0 into 0 1547113866.712 * [misc]backup-simplify: Simplify 0 into 0 1547113866.712 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1547113866.713 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1547113866.714 * [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)))))) 1547113866.715 * [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)))))) 1547113866.716 * [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))))))))))) 1547113866.716 * * * [misc]progress: simplifying candidates 1547113866.716 * * * * [misc]progress: [ 1 / 82 ] simplifiying candidate # 1547113866.716 * * * * [misc]progress: [ 2 / 82 ] simplifiying candidate # 1547113866.716 * * * * [misc]progress: [ 3 / 82 ] simplifiying candidate # 1547113866.717 * [enter]simplify: Simplifying (* (log (* (* n PI) 2)) (- 1/2 (/ k 2))) 1547113866.717 * * [misc]simplify: iters left: 6 (11 enodes) 1547113866.719 * * [misc]simplify: iters left: 5 (21 enodes) 1547113866.724 * * [misc]simplify: iters left: 4 (47 enodes) 1547113866.734 * * [misc]simplify: iters left: 3 (111 enodes) 1547113866.785 * * [misc]simplify: iters left: 2 (336 enodes) 1547113867.031 * [exit]simplify: Simplified to (* (- 1/2 (/ k 2)) (log (* n (* 2 PI)))) 1547113867.031 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (exp (* (- 1/2 (/ k 2)) (log (* n (* 2 PI))))) (sqrt k))) 1547113867.031 * * * * [misc]progress: [ 4 / 82 ] simplifiying candidate # 1547113867.031 * * * * [misc]progress: [ 5 / 82 ] simplifiying candidate # 1547113867.031 * [enter]simplify: Simplifying (* (* n PI) 2) 1547113867.031 * * [misc]simplify: iters left: 4 (5 enodes) 1547113867.032 * * [misc]simplify: iters left: 3 (9 enodes) 1547113867.034 * * [misc]simplify: iters left: 2 (15 enodes) 1547113867.037 * * [misc]simplify: iters left: 1 (17 enodes) 1547113867.041 * [exit]simplify: Simplified to (* (* n PI) 2) 1547113867.042 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* n PI) 2) (* 1 (- 1/2 (/ k 2)))) (sqrt k))) 1547113867.042 * * * * [misc]progress: [ 6 / 82 ] simplifiying candidate # 1547113867.042 * [enter]simplify: Simplifying (pow (* (* n PI) 2) (/ k 2)) 1547113867.042 * * [misc]simplify: iters left: 5 (8 enodes) 1547113867.045 * * [misc]simplify: iters left: 4 (12 enodes) 1547113867.049 * * [misc]simplify: iters left: 3 (18 enodes) 1547113867.055 * * [misc]simplify: iters left: 2 (20 enodes) 1547113867.060 * [exit]simplify: Simplified to (pow (* n (* 2 PI)) (/ k 2)) 1547113867.060 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (/ (pow (* (* n PI) 2) 1/2) (pow (* n (* 2 PI)) (/ k 2))) (sqrt k))) 1547113867.060 * * * * [misc]progress: [ 7 / 82 ] simplifiying candidate # 1547113867.061 * [enter]simplify: Simplifying (cbrt (- 1/2 (/ k 2))) 1547113867.061 * * [misc]simplify: iters left: 5 (6 enodes) 1547113867.063 * * [misc]simplify: iters left: 4 (8 enodes) 1547113867.066 * * [misc]simplify: iters left: 3 (11 enodes) 1547113867.069 * [exit]simplify: Simplified to (cbrt (- 1/2 (/ k 2))) 1547113867.069 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (pow (pow (* (* n PI) 2) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))) (sqrt k))) 1547113867.069 * * * * [misc]progress: [ 8 / 82 ] simplifiying candidate # 1547113867.074 * [enter]simplify: Simplifying (sqrt (- 1/2 (/ k 2))) 1547113867.074 * * [misc]simplify: iters left: 5 (6 enodes) 1547113867.076 * * [misc]simplify: iters left: 4 (8 enodes) 1547113867.079 * * [misc]simplify: iters left: 3 (11 enodes) 1547113867.082 * [exit]simplify: Simplified to (sqrt (- 1/2 (/ k 2))) 1547113867.082 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (pow (pow (* (* n PI) 2) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))) (sqrt k))) 1547113867.082 * * * * [misc]progress: [ 9 / 82 ] simplifiying candidate # 1547113867.083 * [enter]simplify: Simplifying (- 1/2 (/ k 2)) 1547113867.083 * * [misc]simplify: iters left: 4 (5 enodes) 1547113867.085 * * [misc]simplify: iters left: 3 (7 enodes) 1547113867.087 * * [misc]simplify: iters left: 2 (10 enodes) 1547113867.090 * [exit]simplify: Simplified to (- 1/2 (/ k 2)) 1547113867.090 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (pow (pow (* (* n PI) 2) 1) (- 1/2 (/ k 2))) (sqrt k))) 1547113867.090 * * * * [misc]progress: [ 10 / 82 ] simplifiying candidate # 1547113867.091 * [enter]simplify: Simplifying (pow (* (* n PI) 2) (- (/ k 2))) 1547113867.091 * * [misc]simplify: iters left: 5 (9 enodes) 1547113867.094 * * [misc]simplify: iters left: 4 (15 enodes) 1547113867.097 * * [misc]simplify: iters left: 3 (21 enodes) 1547113867.100 * * [misc]simplify: iters left: 2 (22 enodes) 1547113867.104 * [exit]simplify: Simplified to (pow (* (* 2 PI) n) (- (/ k 2))) 1547113867.104 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (pow (* (* n PI) 2) 1/2) (pow (* (* 2 PI) n) (- (/ k 2)))) (sqrt k))) 1547113867.104 * * * * [misc]progress: [ 11 / 82 ] simplifiying candidate # 1547113867.104 * [enter]simplify: Simplifying (pow (* (* n PI) 2) (- (/ k 2))) 1547113867.104 * * [misc]simplify: iters left: 5 (9 enodes) 1547113867.106 * * [misc]simplify: iters left: 4 (15 enodes) 1547113867.109 * * [misc]simplify: iters left: 3 (21 enodes) 1547113867.112 * * [misc]simplify: iters left: 2 (22 enodes) 1547113867.115 * [exit]simplify: Simplified to (pow (* (* 2 PI) n) (- (/ k 2))) 1547113867.116 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (pow (* (* n PI) 2) 1/2) (pow (* (* 2 PI) n) (- (/ k 2)))) (sqrt k))) 1547113867.116 * * * * [misc]progress: [ 12 / 82 ] simplifiying candidate # 1547113867.116 * [enter]simplify: Simplifying (pow (* n PI) (- 1/2 (/ k 2))) 1547113867.116 * * [misc]simplify: iters left: 5 (9 enodes) 1547113867.118 * * [misc]simplify: iters left: 4 (12 enodes) 1547113867.120 * * [misc]simplify: iters left: 3 (15 enodes) 1547113867.124 * [exit]simplify: Simplified to (pow (* n PI) (- 1/2 (/ k 2))) 1547113867.125 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (* (pow (* n PI) (- 1/2 (/ k 2))) (pow 2 (- 1/2 (/ k 2)))) (sqrt k))) 1547113867.125 * * * * [misc]progress: [ 13 / 82 ] simplifiying candidate # 1547113867.125 * * * * [misc]progress: [ 14 / 82 ] simplifiying candidate # 1547113867.125 * * * * [misc]progress: [ 15 / 82 ] simplifiying candidate # 1547113867.125 * * * * [misc]progress: [ 16 / 82 ] simplifiying candidate # 1547113867.125 * * * * [misc]progress: [ 17 / 82 ] simplifiying candidate # 1547113867.125 * * * * [misc]progress: [ 18 / 82 ] simplifiying candidate # 1547113867.125 * * * * [misc]progress: [ 19 / 82 ] simplifiying candidate # 1547113867.125 * * * * [misc]progress: [ 20 / 82 ] simplifiying candidate # 1547113867.125 * * * * [misc]progress: [ 21 / 82 ] simplifiying candidate # 1547113867.125 * * * * [misc]progress: [ 22 / 82 ] simplifiying candidate # 1547113867.125 * * * * [misc]progress: [ 23 / 82 ] simplifiying candidate # 1547113867.125 * * * * [misc]progress: [ 24 / 82 ] simplifiying candidate # 1547113867.125 * * * * [misc]progress: [ 25 / 82 ] simplifiying candidate # 1547113867.125 * * * * [misc]progress: [ 26 / 82 ] simplifiying candidate # 1547113867.125 * * * * [misc]progress: [ 27 / 82 ] simplifiying candidate # 1547113867.126 * * * * [misc]progress: [ 28 / 82 ] simplifiying candidate # 1547113867.126 * * * * [misc]progress: [ 29 / 82 ] simplifiying candidate # 1547113867.126 * * * * [misc]progress: [ 30 / 82 ] simplifiying candidate # 1547113867.126 * * * * [misc]progress: [ 31 / 82 ] simplifiying candidate # 1547113867.126 * * * * [misc]progress: [ 32 / 82 ] simplifiying candidate # 1547113867.126 * * * * [misc]progress: [ 33 / 82 ] simplifiying candidate # 1547113867.126 * [enter]simplify: Simplifying (- (* (log (* (* n PI) 2)) (- 1/2 (/ k 2))) (log (sqrt k))) 1547113867.126 * * [misc]simplify: iters left: 6 (14 enodes) 1547113867.132 * * [misc]simplify: iters left: 5 (27 enodes) 1547113867.139 * * [misc]simplify: iters left: 4 (55 enodes) 1547113867.151 * * [misc]simplify: iters left: 3 (144 enodes) 1547113867.211 * * [misc]simplify: iters left: 2 (484 enodes) 1547113867.676 * [exit]simplify: Simplified to (fma (- 1/2 (/ k 2)) (log (* (* n PI) 2)) (- (log (sqrt k)))) 1547113867.676 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (- 1/2 (/ k 2)) (log (* (* n PI) 2)) (- (log (sqrt k)))))) 1547113867.676 * * * * [misc]progress: [ 34 / 82 ] simplifiying candidate # 1547113867.677 * [enter]simplify: Simplifying (- (* (log (* (* n PI) 2)) (- 1/2 (/ k 2))) (log (sqrt k))) 1547113867.677 * * [misc]simplify: iters left: 6 (14 enodes) 1547113867.682 * * [misc]simplify: iters left: 5 (27 enodes) 1547113867.692 * * [misc]simplify: iters left: 4 (55 enodes) 1547113867.705 * * [misc]simplify: iters left: 3 (144 enodes) 1547113867.770 * * [misc]simplify: iters left: 2 (484 enodes) 1547113868.335 * [exit]simplify: Simplified to (fma (- 1/2 (/ k 2)) (log (* (* n PI) 2)) (- (log (sqrt k)))) 1547113868.335 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (- 1/2 (/ k 2)) (log (* (* n PI) 2)) (- (log (sqrt k)))))) 1547113868.335 * * * * [misc]progress: [ 35 / 82 ] simplifiying candidate # 1547113868.335 * [enter]simplify: Simplifying (- (log (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (log (sqrt k))) 1547113868.335 * * [misc]simplify: iters left: 6 (14 enodes) 1547113868.338 * * [misc]simplify: iters left: 5 (24 enodes) 1547113868.343 * * [misc]simplify: iters left: 4 (43 enodes) 1547113868.350 * * [misc]simplify: iters left: 3 (73 enodes) 1547113868.376 * * [misc]simplify: iters left: 2 (220 enodes) 1547113868.567 * [exit]simplify: Simplified to (fma (log (* (* n PI) 2)) (- 1/2 (/ k 2)) (- (log (sqrt k)))) 1547113868.567 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (log (* (* n PI) 2)) (- 1/2 (/ k 2)) (- (log (sqrt k)))))) 1547113868.567 * * * * [misc]progress: [ 36 / 82 ] simplifiying candidate # 1547113868.567 * * * * [misc]progress: [ 37 / 82 ] simplifiying candidate # 1547113868.567 * * * * [misc]progress: [ 38 / 82 ] simplifiying candidate # 1547113868.567 * [enter]simplify: Simplifying (/ (* (* (pow (* (* n PI) 2) (- 1/2 (/ k 2))) (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k))) 1547113868.567 * * [misc]simplify: iters left: 6 (16 enodes) 1547113868.571 * * [misc]simplify: iters left: 5 (31 enodes) 1547113868.577 * * [misc]simplify: iters left: 4 (67 enodes) 1547113868.603 * * [misc]simplify: iters left: 3 (124 enodes) 1547113868.630 * * [misc]simplify: iters left: 2 (195 enodes) 1547113868.697 * * [misc]simplify: iters left: 1 (309 enodes) 1547113868.844 * [exit]simplify: Simplified to (* (* (pow (* (* n PI) 2) (- 1/2 (/ k 2))) (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (/ (pow (* (* n PI) 2) (- 1/2 (/ k 2))) (* k (sqrt k)))) 1547113868.845 * [misc]simplify: Simplified (2 1) to (λ (k n) (cbrt (* (* (pow (* (* n PI) 2) (- 1/2 (/ k 2))) (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (/ (pow (* (* n PI) 2) (- 1/2 (/ k 2))) (* k (sqrt k)))))) 1547113868.845 * * * * [misc]progress: [ 39 / 82 ] simplifiying candidate # 1547113868.845 * * * * [misc]progress: [ 40 / 82 ] simplifiying candidate # 1547113868.845 * * * * [misc]progress: [ 41 / 82 ] simplifiying candidate # 1547113868.845 * * * * [misc]progress: [ 42 / 82 ] simplifiying candidate # 1547113868.845 * * * * [misc]progress: [ 43 / 82 ] simplifiying candidate # 1547113868.845 * [enter]simplify: Simplifying (/ (pow (* (* n PI) 2) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1547113868.845 * * [misc]simplify: iters left: 6 (12 enodes) 1547113868.850 * * [misc]simplify: iters left: 5 (19 enodes) 1547113868.856 * * [misc]simplify: iters left: 4 (25 enodes) 1547113868.863 * * [misc]simplify: iters left: 3 (26 enodes) 1547113868.870 * [exit]simplify: Simplified to (/ (sqrt (* (* n PI) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1547113868.870 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (* (* n PI) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* n PI) 2) (- (/ k 2))) (cbrt (sqrt k))))) 1547113868.870 * [enter]simplify: Simplifying (/ (pow (* (* n PI) 2) (- (/ k 2))) (cbrt (sqrt k))) 1547113868.871 * * [misc]simplify: iters left: 6 (12 enodes) 1547113868.875 * * [misc]simplify: iters left: 5 (18 enodes) 1547113868.882 * * [misc]simplify: iters left: 4 (24 enodes) 1547113868.890 * * [misc]simplify: iters left: 3 (25 enodes) 1547113868.897 * [exit]simplify: Simplified to (/ (pow (* n (* 2 PI)) (- (/ k 2))) (cbrt (sqrt k))) 1547113868.897 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (* (* n PI) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (cbrt (sqrt k))))) 1547113868.897 * * * * [misc]progress: [ 44 / 82 ] simplifiying candidate # 1547113868.897 * [enter]simplify: Simplifying (/ (pow (* (* n PI) 2) 1/2) (sqrt (sqrt k))) 1547113868.897 * * [misc]simplify: iters left: 6 (11 enodes) 1547113868.901 * * [misc]simplify: iters left: 5 (16 enodes) 1547113868.906 * * [misc]simplify: iters left: 4 (22 enodes) 1547113868.913 * * [misc]simplify: iters left: 3 (24 enodes) 1547113868.917 * [exit]simplify: Simplified to (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k))) 1547113868.917 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k))) (/ (pow (* (* n PI) 2) (- (/ k 2))) (sqrt (sqrt k))))) 1547113868.918 * [enter]simplify: Simplifying (/ (pow (* (* n PI) 2) (- (/ k 2))) (sqrt (sqrt k))) 1547113868.918 * * [misc]simplify: iters left: 6 (12 enodes) 1547113868.920 * * [misc]simplify: iters left: 5 (18 enodes) 1547113868.923 * * [misc]simplify: iters left: 4 (24 enodes) 1547113868.927 * * [misc]simplify: iters left: 3 (25 enodes) 1547113868.930 * [exit]simplify: Simplified to (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (sqrt k))) 1547113868.930 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (sqrt k))))) 1547113868.930 * * * * [misc]progress: [ 45 / 82 ] simplifiying candidate # 1547113868.931 * [enter]simplify: Simplifying (/ (pow (* (* n PI) 2) 1/2) 1) 1547113868.931 * * [misc]simplify: iters left: 6 (9 enodes) 1547113868.932 * * [misc]simplify: iters left: 5 (16 enodes) 1547113868.935 * * [misc]simplify: iters left: 4 (24 enodes) 1547113868.939 * * [misc]simplify: iters left: 3 (26 enodes) 1547113868.942 * [exit]simplify: Simplified to (sqrt (* (* 2 PI) n)) 1547113868.942 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (* (* 2 PI) n)) (/ (pow (* (* n PI) 2) (- (/ k 2))) (sqrt k)))) 1547113868.942 * [enter]simplify: Simplifying (/ (pow (* (* n PI) 2) (- (/ k 2))) (sqrt k)) 1547113868.942 * * [misc]simplify: iters left: 6 (11 enodes) 1547113868.945 * * [misc]simplify: iters left: 5 (17 enodes) 1547113868.951 * * [misc]simplify: iters left: 4 (23 enodes) 1547113868.958 * * [misc]simplify: iters left: 3 (24 enodes) 1547113868.964 * [exit]simplify: Simplified to (/ (pow (* (* n PI) 2) (- (/ k 2))) (sqrt k)) 1547113868.964 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (sqrt (* (* 2 PI) n)) (/ (pow (* (* n PI) 2) (- (/ k 2))) (sqrt k)))) 1547113868.964 * * * * [misc]progress: [ 46 / 82 ] simplifiying candidate # 1547113868.964 * [enter]simplify: Simplifying (/ (pow (* (* n PI) 2) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1547113868.965 * * [misc]simplify: iters left: 6 (12 enodes) 1547113868.967 * * [misc]simplify: iters left: 5 (19 enodes) 1547113868.970 * * [misc]simplify: iters left: 4 (25 enodes) 1547113868.974 * * [misc]simplify: iters left: 3 (26 enodes) 1547113868.978 * [exit]simplify: Simplified to (/ (sqrt (* (* n PI) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1547113868.978 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (* (* n PI) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* n PI) 2) (- (/ k 2))) (cbrt (sqrt k))))) 1547113868.978 * [enter]simplify: Simplifying (/ (pow (* (* n PI) 2) (- (/ k 2))) (cbrt (sqrt k))) 1547113868.978 * * [misc]simplify: iters left: 6 (12 enodes) 1547113868.980 * * [misc]simplify: iters left: 5 (18 enodes) 1547113868.983 * * [misc]simplify: iters left: 4 (24 enodes) 1547113868.987 * * [misc]simplify: iters left: 3 (25 enodes) 1547113868.991 * [exit]simplify: Simplified to (/ (pow (* n (* 2 PI)) (- (/ k 2))) (cbrt (sqrt k))) 1547113868.991 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (* (* n PI) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (cbrt (sqrt k))))) 1547113868.992 * * * * [misc]progress: [ 47 / 82 ] simplifiying candidate # 1547113868.992 * [enter]simplify: Simplifying (/ (pow (* (* n PI) 2) 1/2) (sqrt (sqrt k))) 1547113868.992 * * [misc]simplify: iters left: 6 (11 enodes) 1547113868.995 * * [misc]simplify: iters left: 5 (16 enodes) 1547113869.002 * * [misc]simplify: iters left: 4 (22 enodes) 1547113869.008 * * [misc]simplify: iters left: 3 (24 enodes) 1547113869.014 * [exit]simplify: Simplified to (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k))) 1547113869.014 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k))) (/ (pow (* (* n PI) 2) (- (/ k 2))) (sqrt (sqrt k))))) 1547113869.015 * [enter]simplify: Simplifying (/ (pow (* (* n PI) 2) (- (/ k 2))) (sqrt (sqrt k))) 1547113869.015 * * [misc]simplify: iters left: 6 (12 enodes) 1547113869.019 * * [misc]simplify: iters left: 5 (18 enodes) 1547113869.025 * * [misc]simplify: iters left: 4 (24 enodes) 1547113869.032 * * [misc]simplify: iters left: 3 (25 enodes) 1547113869.040 * [exit]simplify: Simplified to (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (sqrt k))) 1547113869.040 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (sqrt k))))) 1547113869.040 * * * * [misc]progress: [ 48 / 82 ] simplifiying candidate # 1547113869.040 * [enter]simplify: Simplifying (/ (pow (* (* n PI) 2) 1/2) 1) 1547113869.040 * * [misc]simplify: iters left: 6 (9 enodes) 1547113869.044 * * [misc]simplify: iters left: 5 (16 enodes) 1547113869.049 * * [misc]simplify: iters left: 4 (24 enodes) 1547113869.055 * * [misc]simplify: iters left: 3 (26 enodes) 1547113869.062 * [exit]simplify: Simplified to (sqrt (* (* 2 PI) n)) 1547113869.062 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (* (* 2 PI) n)) (/ (pow (* (* n PI) 2) (- (/ k 2))) (sqrt k)))) 1547113869.062 * [enter]simplify: Simplifying (/ (pow (* (* n PI) 2) (- (/ k 2))) (sqrt k)) 1547113869.062 * * [misc]simplify: iters left: 6 (11 enodes) 1547113869.066 * * [misc]simplify: iters left: 5 (17 enodes) 1547113869.070 * * [misc]simplify: iters left: 4 (23 enodes) 1547113869.073 * * [misc]simplify: iters left: 3 (24 enodes) 1547113869.077 * [exit]simplify: Simplified to (/ (pow (* (* n PI) 2) (- (/ k 2))) (sqrt k)) 1547113869.077 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (sqrt (* (* 2 PI) n)) (/ (pow (* (* n PI) 2) (- (/ k 2))) (sqrt k)))) 1547113869.077 * * * * [misc]progress: [ 49 / 82 ] simplifiying candidate # 1547113869.077 * [enter]simplify: Simplifying (/ (pow (* n PI) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1547113869.077 * * [misc]simplify: iters left: 6 (13 enodes) 1547113869.080 * * [misc]simplify: iters left: 5 (18 enodes) 1547113869.083 * * [misc]simplify: iters left: 4 (21 enodes) 1547113869.086 * [exit]simplify: Simplified to (/ (pow (* n PI) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1547113869.086 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (pow (* n PI) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow 2 (- 1/2 (/ k 2))) (cbrt (sqrt k))))) 1547113869.086 * [enter]simplify: Simplifying (/ (pow 2 (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1547113869.086 * * [misc]simplify: iters left: 6 (9 enodes) 1547113869.088 * * [misc]simplify: iters left: 5 (11 enodes) 1547113869.090 * * [misc]simplify: iters left: 4 (14 enodes) 1547113869.092 * [exit]simplify: Simplified to (/ (pow 2 (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1547113869.092 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (pow (* n PI) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow 2 (- 1/2 (/ k 2))) (cbrt (sqrt k))))) 1547113869.092 * * * * [misc]progress: [ 50 / 82 ] simplifiying candidate # 1547113869.092 * [enter]simplify: Simplifying (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1547113869.092 * * [misc]simplify: iters left: 6 (12 enodes) 1547113869.095 * * [misc]simplify: iters left: 5 (15 enodes) 1547113869.097 * * [misc]simplify: iters left: 4 (18 enodes) 1547113869.101 * [exit]simplify: Simplified to (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1547113869.101 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow 2 (- 1/2 (/ k 2))) (sqrt (sqrt k))))) 1547113869.102 * [enter]simplify: Simplifying (/ (pow 2 (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1547113869.102 * * [misc]simplify: iters left: 6 (9 enodes) 1547113869.105 * * [misc]simplify: iters left: 5 (11 enodes) 1547113869.109 * * [misc]simplify: iters left: 4 (14 enodes) 1547113869.113 * [exit]simplify: Simplified to (/ (pow 2 (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1547113869.113 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow 2 (- 1/2 (/ k 2))) (sqrt (sqrt k))))) 1547113869.113 * * * * [misc]progress: [ 51 / 82 ] simplifiying candidate # 1547113869.113 * [enter]simplify: Simplifying (/ (pow (* n PI) (- 1/2 (/ k 2))) 1) 1547113869.114 * * [misc]simplify: iters left: 6 (11 enodes) 1547113869.118 * * [misc]simplify: iters left: 5 (16 enodes) 1547113869.123 * * [misc]simplify: iters left: 4 (21 enodes) 1547113869.128 * [exit]simplify: Simplified to (pow (* n PI) (- 1/2 (/ k 2))) 1547113869.128 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (pow (* n PI) (- 1/2 (/ k 2))) (/ (pow 2 (- 1/2 (/ k 2))) (sqrt k)))) 1547113869.128 * [enter]simplify: Simplifying (/ (pow 2 (- 1/2 (/ k 2))) (sqrt k)) 1547113869.128 * * [misc]simplify: iters left: 6 (8 enodes) 1547113869.130 * * [misc]simplify: iters left: 5 (10 enodes) 1547113869.131 * * [misc]simplify: iters left: 4 (13 enodes) 1547113869.135 * [exit]simplify: Simplified to (/ (pow 2 (- 1/2 (/ k 2))) (sqrt k)) 1547113869.135 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (pow (* n PI) (- 1/2 (/ k 2))) (/ (pow 2 (- 1/2 (/ k 2))) (sqrt k)))) 1547113869.135 * * * * [misc]progress: [ 52 / 82 ] simplifiying candidate # 1547113869.135 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1547113869.135 * * [misc]simplify: iters left: 6 (16 enodes) 1547113869.138 * * [misc]simplify: iters left: 5 (28 enodes) 1547113869.143 * * [misc]simplify: iters left: 4 (46 enodes) 1547113869.151 * * [misc]simplify: iters left: 3 (50 enodes) 1547113869.158 * * [misc]simplify: iters left: 2 (53 enodes) 1547113869.173 * [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)))) 1547113869.173 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (* (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))) (/ (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))) 1547113869.173 * [enter]simplify: Simplifying (/ (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1547113869.173 * * [misc]simplify: iters left: 6 (14 enodes) 1547113869.178 * * [misc]simplify: iters left: 5 (20 enodes) 1547113869.185 * * [misc]simplify: iters left: 4 (29 enodes) 1547113869.193 * * [misc]simplify: iters left: 3 (30 enodes) 1547113869.202 * [exit]simplify: Simplified to (/ (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1547113869.202 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (* (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))) 1547113869.202 * * * * [misc]progress: [ 53 / 82 ] simplifiying candidate # 1547113869.202 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) 1547113869.202 * * [misc]simplify: iters left: 6 (15 enodes) 1547113869.208 * * [misc]simplify: iters left: 5 (23 enodes) 1547113869.215 * * [misc]simplify: iters left: 4 (34 enodes) 1547113869.226 * * [misc]simplify: iters left: 3 (36 enodes) 1547113869.236 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (/ (sqrt (sqrt k)) (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))))) 1547113869.237 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (/ (sqrt (sqrt k)) (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))))) (/ (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) 1547113869.237 * [enter]simplify: Simplifying (/ (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1547113869.237 * * [misc]simplify: iters left: 6 (14 enodes) 1547113869.242 * * [misc]simplify: iters left: 5 (20 enodes) 1547113869.249 * * [misc]simplify: iters left: 4 (29 enodes) 1547113869.258 * * [misc]simplify: iters left: 3 (30 enodes) 1547113869.265 * [exit]simplify: Simplified to (/ (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1547113869.266 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (* (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) (/ (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) 1547113869.266 * * * * [misc]progress: [ 54 / 82 ] simplifiying candidate # 1547113869.266 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2))))) 1) 1547113869.266 * * [misc]simplify: iters left: 6 (14 enodes) 1547113869.270 * * [misc]simplify: iters left: 5 (24 enodes) 1547113869.279 * * [misc]simplify: iters left: 4 (39 enodes) 1547113869.288 * * [misc]simplify: iters left: 3 (54 enodes) 1547113869.302 * * [misc]simplify: iters left: 2 (80 enodes) 1547113869.320 * [exit]simplify: Simplified to (* (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2))))) 1547113869.320 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (* (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2))))) (/ (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (sqrt k)))) 1547113869.321 * [enter]simplify: Simplifying (/ (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (sqrt k)) 1547113869.321 * * [misc]simplify: iters left: 6 (13 enodes) 1547113869.325 * * [misc]simplify: iters left: 5 (19 enodes) 1547113869.332 * * [misc]simplify: iters left: 4 (28 enodes) 1547113869.340 * * [misc]simplify: iters left: 3 (29 enodes) 1547113869.346 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (sqrt k)) 1547113869.346 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2))))) (/ (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (sqrt k)))) 1547113869.346 * * * * [misc]progress: [ 55 / 82 ] simplifiying candidate # 1547113869.346 * [enter]simplify: Simplifying (/ (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1547113869.346 * * [misc]simplify: iters left: 6 (15 enodes) 1547113869.349 * * [misc]simplify: iters left: 5 (23 enodes) 1547113869.354 * * [misc]simplify: iters left: 4 (32 enodes) 1547113869.359 * * [misc]simplify: iters left: 3 (33 enodes) 1547113869.364 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1547113869.364 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))) 1547113869.364 * [enter]simplify: Simplifying (/ (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1547113869.364 * * [misc]simplify: iters left: 6 (14 enodes) 1547113869.366 * * [misc]simplify: iters left: 5 (20 enodes) 1547113869.370 * * [misc]simplify: iters left: 4 (29 enodes) 1547113869.375 * * [misc]simplify: iters left: 3 (30 enodes) 1547113869.383 * [exit]simplify: Simplified to (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1547113869.383 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))) 1547113869.383 * * * * [misc]progress: [ 56 / 82 ] simplifiying candidate # 1547113869.383 * [enter]simplify: Simplifying (/ (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1547113869.383 * * [misc]simplify: iters left: 6 (14 enodes) 1547113869.388 * * [misc]simplify: iters left: 5 (20 enodes) 1547113869.395 * * [misc]simplify: iters left: 4 (29 enodes) 1547113869.406 * * [misc]simplify: iters left: 3 (30 enodes) 1547113869.414 * [exit]simplify: Simplified to (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1547113869.414 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) 1547113869.415 * [enter]simplify: Simplifying (/ (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1547113869.415 * * [misc]simplify: iters left: 6 (14 enodes) 1547113869.420 * * [misc]simplify: iters left: 5 (20 enodes) 1547113869.427 * * [misc]simplify: iters left: 4 (29 enodes) 1547113869.434 * * [misc]simplify: iters left: 3 (30 enodes) 1547113869.438 * [exit]simplify: Simplified to (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1547113869.438 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) 1547113869.438 * * * * [misc]progress: [ 57 / 82 ] simplifiying candidate # 1547113869.439 * [enter]simplify: Simplifying (/ (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) 1) 1547113869.439 * * [misc]simplify: iters left: 6 (13 enodes) 1547113869.441 * * [misc]simplify: iters left: 5 (21 enodes) 1547113869.445 * * [misc]simplify: iters left: 4 (32 enodes) 1547113869.450 * * [misc]simplify: iters left: 3 (33 enodes) 1547113869.454 * [exit]simplify: Simplified to (sqrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) 1547113869.454 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (/ (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (sqrt k)))) 1547113869.455 * [enter]simplify: Simplifying (/ (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (sqrt k)) 1547113869.455 * * [misc]simplify: iters left: 6 (13 enodes) 1547113869.457 * * [misc]simplify: iters left: 5 (19 enodes) 1547113869.461 * * [misc]simplify: iters left: 4 (28 enodes) 1547113869.465 * * [misc]simplify: iters left: 3 (29 enodes) 1547113869.471 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (sqrt k)) 1547113869.471 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (sqrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (/ (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (sqrt k)))) 1547113869.471 * * * * [misc]progress: [ 58 / 82 ] simplifiying candidate # 1547113869.471 * [enter]simplify: Simplifying (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1547113869.471 * * [misc]simplify: iters left: 6 (6 enodes) 1547113869.473 * * [misc]simplify: iters left: 5 (10 enodes) 1547113869.477 * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) 1547113869.477 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (pow (* (* n PI) 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))))) 1547113869.477 * [enter]simplify: Simplifying (/ (pow (* (* n PI) 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1547113869.477 * * [misc]simplify: iters left: 6 (13 enodes) 1547113869.482 * * [misc]simplify: iters left: 5 (19 enodes) 1547113869.488 * * [misc]simplify: iters left: 4 (28 enodes) 1547113869.496 * * [misc]simplify: iters left: 3 (29 enodes) 1547113869.504 * [exit]simplify: Simplified to (/ (pow (* (* n PI) 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1547113869.504 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* n PI) 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))))) 1547113869.505 * * * * [misc]progress: [ 59 / 82 ] simplifiying candidate # 1547113869.505 * [enter]simplify: Simplifying (/ 1 (sqrt (sqrt k))) 1547113869.505 * * [misc]simplify: iters left: 4 (5 enodes) 1547113869.507 * * [misc]simplify: iters left: 3 (7 enodes) 1547113869.509 * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt k))) 1547113869.509 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* (* n PI) 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) 1547113869.509 * [enter]simplify: Simplifying (/ (pow (* (* n PI) 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1547113869.509 * * [misc]simplify: iters left: 6 (13 enodes) 1547113869.514 * * [misc]simplify: iters left: 5 (19 enodes) 1547113869.520 * * [misc]simplify: iters left: 4 (28 enodes) 1547113869.528 * * [misc]simplify: iters left: 3 (29 enodes) 1547113869.536 * [exit]simplify: Simplified to (/ (pow (* (* n PI) 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1547113869.536 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* (* n PI) 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) 1547113869.536 * * * * [misc]progress: [ 60 / 82 ] simplifiying candidate # 1547113869.537 * [enter]simplify: Simplifying (/ 1 1) 1547113869.537 * * [misc]simplify: iters left: 2 (2 enodes) 1547113869.538 * * [misc]simplify: iters left: 1 (4 enodes) 1547113869.538 * [exit]simplify: Simplified to 1 1547113869.538 * [misc]simplify: Simplified (2 1) to (λ (k n) (* 1 (/ (pow (* (* n PI) 2) (- 1/2 (/ k 2))) (sqrt k)))) 1547113869.539 * [enter]simplify: Simplifying (/ (pow (* (* n PI) 2) (- 1/2 (/ k 2))) (sqrt k)) 1547113869.539 * * [misc]simplify: iters left: 6 (12 enodes) 1547113869.544 * * [misc]simplify: iters left: 5 (18 enodes) 1547113869.550 * * [misc]simplify: iters left: 4 (27 enodes) 1547113869.558 * * [misc]simplify: iters left: 3 (28 enodes) 1547113869.563 * [exit]simplify: Simplified to (/ (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (sqrt k)) 1547113869.563 * [misc]simplify: Simplified (2 2) to (λ (k n) (* 1 (/ (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (sqrt k)))) 1547113869.563 * * * * [misc]progress: [ 61 / 82 ] simplifiying candidate # 1547113869.563 * * * * [misc]progress: [ 62 / 82 ] simplifiying candidate # 1547113869.563 * * * * [misc]progress: [ 63 / 82 ] simplifiying candidate # 1547113869.563 * * * * [misc]progress: [ 64 / 82 ] simplifiying candidate # 1547113869.563 * [enter]simplify: Simplifying (cbrt (sqrt k)) 1547113869.563 * * [misc]simplify: iters left: 2 (3 enodes) 1547113869.564 * [exit]simplify: Simplified to (cbrt (sqrt k)) 1547113869.564 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (pow (* (* n PI) 2) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k)))) 1547113869.564 * * * * [misc]progress: [ 65 / 82 ] simplifiying candidate # 1547113869.564 * [enter]simplify: Simplifying (sqrt (sqrt k)) 1547113869.564 * * [misc]simplify: iters left: 2 (3 enodes) 1547113869.565 * [exit]simplify: Simplified to (sqrt (sqrt k)) 1547113869.565 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (pow (* (* n PI) 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k)))) 1547113869.565 * * * * [misc]progress: [ 66 / 82 ] simplifiying candidate # 1547113869.565 * [enter]simplify: Simplifying (sqrt k) 1547113869.565 * * [misc]simplify: iters left: 1 (2 enodes) 1547113869.565 * [exit]simplify: Simplified to (sqrt k) 1547113869.565 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (pow (* (* n PI) 2) (- 1/2 (/ k 2))) 1) (sqrt k))) 1547113869.565 * * * * [misc]progress: [ 67 / 82 ] simplifiying candidate # 1547113869.565 * [enter]simplify: Simplifying (pow (* (* n PI) 2) 1/2) 1547113869.565 * * [misc]simplify: iters left: 5 (7 enodes) 1547113869.567 * * [misc]simplify: iters left: 4 (12 enodes) 1547113869.569 * * [misc]simplify: iters left: 3 (18 enodes) 1547113869.571 * * [misc]simplify: iters left: 2 (20 enodes) 1547113869.574 * [exit]simplify: Simplified to (sqrt (* n (* 2 PI))) 1547113869.574 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* n (* 2 PI))) (/ (sqrt k) (pow (* (* n PI) 2) (- (/ k 2)))))) 1547113869.574 * * * * [misc]progress: [ 68 / 82 ] simplifiying candidate # 1547113869.574 * [enter]simplify: Simplifying (pow (* (* n PI) 2) 1/2) 1547113869.575 * * [misc]simplify: iters left: 5 (7 enodes) 1547113869.576 * * [misc]simplify: iters left: 4 (12 enodes) 1547113869.578 * * [misc]simplify: iters left: 3 (18 enodes) 1547113869.581 * * [misc]simplify: iters left: 2 (20 enodes) 1547113869.584 * [exit]simplify: Simplified to (sqrt (* n (* 2 PI))) 1547113869.584 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* n (* 2 PI))) (/ (sqrt k) (pow (* (* n PI) 2) (- (/ k 2)))))) 1547113869.584 * * * * [misc]progress: [ 69 / 82 ] simplifiying candidate # 1547113869.584 * [enter]simplify: Simplifying (pow (* n PI) (- 1/2 (/ k 2))) 1547113869.584 * * [misc]simplify: iters left: 5 (9 enodes) 1547113869.585 * * [misc]simplify: iters left: 4 (12 enodes) 1547113869.587 * * [misc]simplify: iters left: 3 (15 enodes) 1547113869.590 * [exit]simplify: Simplified to (pow (* n PI) (- 1/2 (/ k 2))) 1547113869.590 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (pow (* n PI) (- 1/2 (/ k 2))) (/ (sqrt k) (pow 2 (- 1/2 (/ k 2)))))) 1547113869.590 * * * * [misc]progress: [ 70 / 82 ] simplifiying candidate # 1547113869.590 * [enter]simplify: Simplifying (* (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2))))) 1547113869.590 * * [misc]simplify: iters left: 6 (12 enodes) 1547113869.593 * * [misc]simplify: iters left: 5 (18 enodes) 1547113869.599 * * [misc]simplify: iters left: 4 (27 enodes) 1547113869.608 * * [misc]simplify: iters left: 3 (28 enodes) 1547113869.615 * [exit]simplify: Simplified to (* (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2))))) 1547113869.616 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (* (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2))))) (/ (sqrt k) (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2))))))) 1547113869.616 * * * * [misc]progress: [ 71 / 82 ] simplifiying candidate # 1547113869.616 * [enter]simplify: Simplifying (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) 1547113869.616 * * [misc]simplify: iters left: 6 (11 enodes) 1547113869.620 * * [misc]simplify: iters left: 5 (17 enodes) 1547113869.626 * * [misc]simplify: iters left: 4 (26 enodes) 1547113869.633 * * [misc]simplify: iters left: 3 (27 enodes) 1547113869.640 * [exit]simplify: Simplified to (sqrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) 1547113869.641 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2))))))) 1547113869.641 * * * * [misc]progress: [ 72 / 82 ] simplifiying candidate # 1547113869.641 * * * * [misc]progress: [ 73 / 82 ] simplifiying candidate # 1547113869.641 * [enter]simplify: Simplifying (pow (* (* n PI) 2) 1/2) 1547113869.641 * * [misc]simplify: iters left: 5 (7 enodes) 1547113869.644 * * [misc]simplify: iters left: 4 (12 enodes) 1547113869.647 * * [misc]simplify: iters left: 3 (18 enodes) 1547113869.653 * * [misc]simplify: iters left: 2 (20 enodes) 1547113869.657 * [exit]simplify: Simplified to (sqrt (* n (* 2 PI))) 1547113869.658 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* n (* 2 PI))) (* (sqrt k) (pow (* (* n PI) 2) (/ k 2))))) 1547113869.658 * * * * [misc]progress: [ 74 / 82 ] simplifiying candidate # 1547113869.658 * [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))))) 1547113869.658 * * [misc]simplify: iters left: 6 (37 enodes) 1547113869.676 * * [misc]simplify: iters left: 5 (108 enodes) 1547113869.727 * * [misc]simplify: iters left: 4 (368 enodes) 1547113870.006 * [exit]simplify: Simplified to (fma -1/2 (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) (fma (* (* (* k k) (log n)) (* (log (* PI 2)) 1/4)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (fma (* (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (log (* PI 2)) (log (* PI 2)))) (* (* k k) 1/8) (fma (* (* (* k k) (log n)) (* (log n) 1/8)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (pow n 1/2) (pow (* PI 2) 1/2)))))) 1547113870.006 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (fma -1/2 (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) (fma (* (* (* k k) (log n)) (* (log (* PI 2)) 1/4)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (fma (* (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (log (* PI 2)) (log (* PI 2)))) (* (* k k) 1/8) (fma (* (* (* k k) (log n)) (* (log n) 1/8)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (pow n 1/2) (pow (* PI 2) 1/2)))))) (sqrt k))) 1547113870.007 * * * * [misc]progress: [ 75 / 82 ] simplifiying candidate # 1547113870.007 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 1547113870.007 * * [misc]simplify: iters left: 6 (15 enodes) 1547113870.011 * * [misc]simplify: iters left: 5 (33 enodes) 1547113870.017 * * [misc]simplify: iters left: 4 (64 enodes) 1547113870.036 * * [misc]simplify: iters left: 3 (179 enodes) 1547113870.149 * [exit]simplify: Simplified to (* (pow (* 2 PI) (fma -1/2 k 1/2)) (pow n (fma -1/2 k 1/2))) 1547113870.149 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (* (pow (* 2 PI) (fma -1/2 k 1/2)) (pow n (fma -1/2 k 1/2))) (sqrt k))) 1547113870.149 * * * * [misc]progress: [ 76 / 82 ] simplifiying candidate # 1547113870.149 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 1547113870.149 * * [misc]simplify: iters left: 6 (15 enodes) 1547113870.156 * * [misc]simplify: iters left: 5 (30 enodes) 1547113870.168 * * [misc]simplify: iters left: 4 (65 enodes) 1547113870.198 * * [misc]simplify: iters left: 3 (208 enodes) 1547113870.338 * [exit]simplify: Simplified to (pow (exp (fma -1/2 k 1/2)) (- (log (* -2 PI)) (log (/ -1 n)))) 1547113870.338 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (pow (exp (fma -1/2 k 1/2)) (- (log (* -2 PI)) (log (/ -1 n)))) (sqrt k))) 1547113870.338 * * * * [misc]progress: [ 77 / 82 ] simplifiying candidate # 1547113870.338 * [enter]simplify: Simplifying (* n PI) 1547113870.338 * * [misc]simplify: iters left: 2 (3 enodes) 1547113870.339 * * [misc]simplify: iters left: 1 (4 enodes) 1547113870.339 * [exit]simplify: Simplified to (* n PI) 1547113870.339 * [misc]simplify: Simplified (2 1 1 1) to (λ (k n) (/ (pow (* (* n PI) 2) (- 1/2 (/ k 2))) (sqrt k))) 1547113870.339 * * * * [misc]progress: [ 78 / 82 ] simplifiying candidate # 1547113870.340 * [enter]simplify: Simplifying (* n PI) 1547113870.340 * * [misc]simplify: iters left: 2 (3 enodes) 1547113870.340 * * [misc]simplify: iters left: 1 (4 enodes) 1547113870.341 * [exit]simplify: Simplified to (* n PI) 1547113870.341 * [misc]simplify: Simplified (2 1 1 1) to (λ (k n) (/ (pow (* (* n PI) 2) (- 1/2 (/ k 2))) (sqrt k))) 1547113870.341 * * * * [misc]progress: [ 79 / 82 ] simplifiying candidate # 1547113870.341 * [enter]simplify: Simplifying (* n PI) 1547113870.341 * * [misc]simplify: iters left: 2 (3 enodes) 1547113870.342 * * [misc]simplify: iters left: 1 (4 enodes) 1547113870.342 * [exit]simplify: Simplified to (* n PI) 1547113870.342 * [misc]simplify: Simplified (2 1 1 1) to (λ (k n) (/ (pow (* (* n PI) 2) (- 1/2 (/ k 2))) (sqrt k))) 1547113870.343 * * * * [misc]progress: [ 80 / 82 ] simplifiying candidate # 1547113870.343 * [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)))))))))))))))))))))) 1547113870.343 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1547113870.343 * * * * [misc]progress: [ 81 / 82 ] simplifiying candidate # 1547113870.343 * [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)))))))) 1547113870.343 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1547113870.343 * * * * [misc]progress: [ 82 / 82 ] simplifiying candidate # 1547113870.343 * [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))))))))))) 1547113870.343 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1547113870.343 * * * [misc]progress: adding candidates to table 1547113871.308 * [misc]progress: [Phase 3 of 3] Extracting. 1547113871.308 * * [misc]regime: Finding splitpoints for: (# # # # # #) 1547113871.310 * * * [misc]regime-changes: Trying 3 branch expressions: (n (* (* 2 PI) n) k) 1547113871.310 * * * * [misc]regimes: Trying to branch on n from (# # # # # #) 1547113871.373 * * * * [misc]regimes: Trying to branch on (* (* 2 PI) n) from (# # # # # #) 1547113871.437 * * * * [misc]regimes: Trying to branch on k from (# # # # # #) 1547113871.512 * * * [misc]regime: Found split indices: #