1545989127.450 * [misc]progress: [Phase 1 of 3] Setting up. 1545989127.450 * * * [misc]progress: [1/2] Preparing points 1545989127.450 * * * * [misc]points: Sampling 256 additional inputs, on iter 0 have 0 / 256 1545989127.544 * * * * [misc]points: Filtering points with unrepresentable outputs 1545989127.544 * * * * [misc]points: Sampling 194 additional inputs, on iter 1 have 62 / 256 1545989127.628 * * * * [misc]points: Filtering points with unrepresentable outputs 1545989127.628 * * * * [misc]points: Sampling 160 additional inputs, on iter 2 have 96 / 256 1545989127.671 * * * * [misc]points: Filtering points with unrepresentable outputs 1545989127.672 * * * * [misc]points: Sampling 121 additional inputs, on iter 3 have 135 / 256 1545989127.706 * * * * [misc]points: Filtering points with unrepresentable outputs 1545989127.707 * * * * [misc]points: Sampling 85 additional inputs, on iter 4 have 171 / 256 1545989127.740 * * * * [misc]points: Filtering points with unrepresentable outputs 1545989127.740 * * * * [misc]points: Sampling 65 additional inputs, on iter 5 have 191 / 256 1545989127.766 * * * * [misc]points: Filtering points with unrepresentable outputs 1545989127.766 * * * * [misc]points: Sampling 46 additional inputs, on iter 6 have 210 / 256 1545989127.818 * * * * [misc]points: Filtering points with unrepresentable outputs 1545989127.818 * * * * [misc]points: Sampling 40 additional inputs, on iter 7 have 216 / 256 1545989127.828 * * * * [misc]points: Filtering points with unrepresentable outputs 1545989127.828 * * * * [misc]points: Sampling 36 additional inputs, on iter 8 have 220 / 256 1545989127.836 * * * * [misc]points: Filtering points with unrepresentable outputs 1545989127.836 * * * * [misc]points: Sampling 24 additional inputs, on iter 9 have 232 / 256 1545989127.843 * * * * [misc]points: Filtering points with unrepresentable outputs 1545989127.843 * * * * [misc]points: Sampling 17 additional inputs, on iter 10 have 239 / 256 1545989127.848 * * * * [misc]points: Filtering points with unrepresentable outputs 1545989127.848 * * * * [misc]points: Sampling 12 additional inputs, on iter 11 have 244 / 256 1545989127.854 * * * * [misc]points: Filtering points with unrepresentable outputs 1545989127.855 * * * * [misc]points: Sampling 9 additional inputs, on iter 12 have 247 / 256 1545989127.861 * * * * [misc]points: Filtering points with unrepresentable outputs 1545989127.862 * * * * [misc]points: Sampling 6 additional inputs, on iter 13 have 250 / 256 1545989127.867 * * * * [misc]points: Filtering points with unrepresentable outputs 1545989127.867 * * * * [misc]points: Sampling 4 additional inputs, on iter 14 have 252 / 256 1545989127.872 * * * * [misc]points: Filtering points with unrepresentable outputs 1545989127.873 * * * * [misc]points: Sampling 4 additional inputs, on iter 15 have 252 / 256 1545989127.878 * * * * [misc]points: Filtering points with unrepresentable outputs 1545989127.878 * * * * [misc]points: Sampling 4 additional inputs, on iter 16 have 252 / 256 1545989127.883 * * * * [misc]points: Filtering points with unrepresentable outputs 1545989127.883 * * * * [misc]points: Sampling 4 additional inputs, on iter 17 have 255 / 256 1545989127.888 * * * * [misc]points: Filtering points with unrepresentable outputs 1545989127.888 * * * * [exit]points: Sampled 257 points with exact outputs 1545989127.888 * * * [misc]progress: [2/2] Setting up program. 1545989127.896 * [misc]progress: [Phase 2 of 3] Improving. 1545989127.896 * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) 1545989127.896 * * [misc]simplify: iters left: 6 (13 enodes) 1545989127.902 * * [misc]simplify: iters left: 5 (28 enodes) 1545989127.909 * * [misc]simplify: iters left: 4 (44 enodes) 1545989127.921 * * [misc]simplify: iters left: 3 (54 enodes) 1545989127.932 * * [misc]simplify: iters left: 2 (57 enodes) 1545989127.943 * * [misc]simplify: iters left: 1 (65 enodes) 1545989127.979 * [exit]simplify: Simplified to (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)) 1545989127.988 * * [misc]progress: iteration 1 / 4 1545989127.988 * * * [misc]progress: picking best candidate 1545989127.994 * * * * [misc]pick: Picked # 1545989127.994 * * * [misc]progress: localizing error 1545989128.016 * * * [misc]progress: generating rewritten candidates 1545989128.016 * * * * [misc]progress: [ 1 / 3 ] rewriting at (2 1) 1545989128.018 * * * * [misc]progress: [ 2 / 3 ] rewriting at (2 1 1) 1545989128.019 * * * * [misc]progress: [ 3 / 3 ] rewriting at (2) 1545989128.024 * * * [misc]progress: generating series expansions 1545989128.024 * * * * [misc]progress: [ 1 / 3 ] generating series at (2 1) 1545989128.024 * [misc]backup-simplify: Simplify (pow (* PI (* n 2)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 1545989128.024 * [misc]approximate: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 1545989128.024 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1545989128.025 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1545989128.025 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1545989128.025 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1545989128.025 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989128.025 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989128.025 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1545989128.025 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989128.025 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989128.025 * [misc]taylor: Taking taylor expansion of k in k 1545989128.025 * [misc]backup-simplify: Simplify 0 into 0 1545989128.025 * [misc]backup-simplify: Simplify 1 into 1 1545989128.025 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1545989128.025 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1545989128.025 * [misc]taylor: Taking taylor expansion of 2 in k 1545989128.025 * [misc]backup-simplify: Simplify 2 into 2 1545989128.025 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1545989128.025 * [misc]taylor: Taking taylor expansion of n in k 1545989128.025 * [misc]backup-simplify: Simplify n into n 1545989128.025 * [misc]taylor: Taking taylor expansion of PI in k 1545989128.025 * [misc]backup-simplify: Simplify PI into PI 1545989128.025 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1545989128.025 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1545989128.025 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1545989128.025 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1545989128.025 * [misc]backup-simplify: Simplify (- 0) into 0 1545989128.026 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545989128.026 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1545989128.026 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1545989128.026 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1545989128.026 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1545989128.026 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1545989128.026 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1545989128.026 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989128.026 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989128.026 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1545989128.026 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989128.026 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989128.026 * [misc]taylor: Taking taylor expansion of k in n 1545989128.026 * [misc]backup-simplify: Simplify k into k 1545989128.026 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1545989128.026 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1545989128.026 * [misc]taylor: Taking taylor expansion of 2 in n 1545989128.026 * [misc]backup-simplify: Simplify 2 into 2 1545989128.026 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545989128.026 * [misc]taylor: Taking taylor expansion of n in n 1545989128.026 * [misc]backup-simplify: Simplify 0 into 0 1545989128.026 * [misc]backup-simplify: Simplify 1 into 1 1545989128.026 * [misc]taylor: Taking taylor expansion of PI in n 1545989128.026 * [misc]backup-simplify: Simplify PI into PI 1545989128.026 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1545989128.026 * [misc]backup-simplify: Simplify (* 2 0) into 0 1545989128.027 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1545989128.027 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1545989128.028 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545989128.028 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1545989128.028 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1545989128.028 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1545989128.029 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545989128.029 * [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)))) 1545989128.030 * [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))))) 1545989128.030 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1545989128.030 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1545989128.030 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1545989128.030 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1545989128.030 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989128.030 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989128.030 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1545989128.030 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989128.030 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989128.030 * [misc]taylor: Taking taylor expansion of k in n 1545989128.030 * [misc]backup-simplify: Simplify k into k 1545989128.030 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1545989128.030 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1545989128.030 * [misc]taylor: Taking taylor expansion of 2 in n 1545989128.030 * [misc]backup-simplify: Simplify 2 into 2 1545989128.031 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545989128.031 * [misc]taylor: Taking taylor expansion of n in n 1545989128.031 * [misc]backup-simplify: Simplify 0 into 0 1545989128.031 * [misc]backup-simplify: Simplify 1 into 1 1545989128.031 * [misc]taylor: Taking taylor expansion of PI in n 1545989128.031 * [misc]backup-simplify: Simplify PI into PI 1545989128.031 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1545989128.031 * [misc]backup-simplify: Simplify (* 2 0) into 0 1545989128.032 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1545989128.032 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1545989128.033 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545989128.033 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1545989128.033 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1545989128.033 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1545989128.034 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545989128.034 * [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)))) 1545989128.035 * [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))))) 1545989128.035 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1545989128.035 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1545989128.035 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1545989128.035 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989128.035 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989128.035 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1545989128.035 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989128.035 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989128.035 * [misc]taylor: Taking taylor expansion of k in k 1545989128.035 * [misc]backup-simplify: Simplify 0 into 0 1545989128.035 * [misc]backup-simplify: Simplify 1 into 1 1545989128.035 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1545989128.035 * [misc]taylor: Taking taylor expansion of (log n) in k 1545989128.035 * [misc]taylor: Taking taylor expansion of n in k 1545989128.036 * [misc]backup-simplify: Simplify n into n 1545989128.036 * [misc]backup-simplify: Simplify (log n) into (log n) 1545989128.036 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1545989128.036 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1545989128.036 * [misc]taylor: Taking taylor expansion of 2 in k 1545989128.036 * [misc]backup-simplify: Simplify 2 into 2 1545989128.036 * [misc]taylor: Taking taylor expansion of PI in k 1545989128.036 * [misc]backup-simplify: Simplify PI into PI 1545989128.036 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545989128.036 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545989128.037 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1545989128.037 * [misc]backup-simplify: Simplify (- 0) into 0 1545989128.037 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545989128.037 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545989128.038 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1545989128.038 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1545989128.039 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1545989128.040 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1545989128.041 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1545989128.044 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1545989128.045 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1545989128.045 * [misc]backup-simplify: Simplify (- 0) into 0 1545989128.045 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989128.046 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545989128.046 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1545989128.048 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1545989128.048 * [misc]taylor: Taking taylor expansion of 0 in k 1545989128.048 * [misc]backup-simplify: Simplify 0 into 0 1545989128.048 * [misc]backup-simplify: Simplify 0 into 0 1545989128.049 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1545989128.049 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1545989128.052 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1545989128.052 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989128.052 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1545989128.053 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1545989128.053 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1545989128.053 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1545989128.055 * [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))))))) 1545989128.056 * [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))))))) 1545989128.058 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1545989128.059 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1545989128.072 * [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 1545989128.072 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1545989128.072 * [misc]backup-simplify: Simplify (- 0) into 0 1545989128.072 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989128.073 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545989128.073 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1545989128.074 * [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 1545989128.074 * [misc]taylor: Taking taylor expansion of 0 in k 1545989128.074 * [misc]backup-simplify: Simplify 0 into 0 1545989128.074 * [misc]backup-simplify: Simplify 0 into 0 1545989128.075 * [misc]backup-simplify: Simplify 0 into 0 1545989128.075 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1545989128.076 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1545989128.079 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1545989128.079 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989128.079 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1545989128.079 * [misc]backup-simplify: Simplify (- 0) into 0 1545989128.079 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989128.080 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1545989128.081 * [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))))) 1545989128.083 * [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))))) 1545989128.086 * [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))))) 1545989128.086 * [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)))) 1545989128.086 * [misc]approximate: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 1545989128.086 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1545989128.086 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1545989128.086 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1545989128.086 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1545989128.086 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989128.086 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989128.086 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545989128.086 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989128.086 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989128.086 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989128.086 * [misc]taylor: Taking taylor expansion of k in k 1545989128.086 * [misc]backup-simplify: Simplify 0 into 0 1545989128.086 * [misc]backup-simplify: Simplify 1 into 1 1545989128.087 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989128.087 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1545989128.087 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1545989128.087 * [misc]taylor: Taking taylor expansion of 2 in k 1545989128.087 * [misc]backup-simplify: Simplify 2 into 2 1545989128.087 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1545989128.087 * [misc]taylor: Taking taylor expansion of PI in k 1545989128.087 * [misc]backup-simplify: Simplify PI into PI 1545989128.087 * [misc]taylor: Taking taylor expansion of n in k 1545989128.087 * [misc]backup-simplify: Simplify n into n 1545989128.087 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1545989128.087 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1545989128.087 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1545989128.087 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545989128.087 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1545989128.087 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1545989128.087 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1545989128.087 * [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)))) 1545989128.088 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1545989128.088 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1545989128.088 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1545989128.088 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1545989128.088 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989128.088 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989128.088 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989128.088 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989128.088 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989128.088 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989128.088 * [misc]taylor: Taking taylor expansion of k in n 1545989128.088 * [misc]backup-simplify: Simplify k into k 1545989128.088 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989128.088 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1545989128.088 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1545989128.088 * [misc]taylor: Taking taylor expansion of 2 in n 1545989128.088 * [misc]backup-simplify: Simplify 2 into 2 1545989128.088 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545989128.088 * [misc]taylor: Taking taylor expansion of PI in n 1545989128.088 * [misc]backup-simplify: Simplify PI into PI 1545989128.088 * [misc]taylor: Taking taylor expansion of n in n 1545989128.088 * [misc]backup-simplify: Simplify 0 into 0 1545989128.088 * [misc]backup-simplify: Simplify 1 into 1 1545989128.088 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545989128.088 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545989128.089 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545989128.089 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989128.089 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1545989128.089 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1545989128.089 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545989128.090 * [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))) 1545989128.090 * [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)))) 1545989128.090 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1545989128.090 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1545989128.090 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1545989128.090 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1545989128.090 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989128.090 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989128.090 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989128.090 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989128.090 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989128.090 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989128.090 * [misc]taylor: Taking taylor expansion of k in n 1545989128.090 * [misc]backup-simplify: Simplify k into k 1545989128.090 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989128.090 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1545989128.090 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1545989128.090 * [misc]taylor: Taking taylor expansion of 2 in n 1545989128.090 * [misc]backup-simplify: Simplify 2 into 2 1545989128.090 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545989128.090 * [misc]taylor: Taking taylor expansion of PI in n 1545989128.090 * [misc]backup-simplify: Simplify PI into PI 1545989128.090 * [misc]taylor: Taking taylor expansion of n in n 1545989128.090 * [misc]backup-simplify: Simplify 0 into 0 1545989128.090 * [misc]backup-simplify: Simplify 1 into 1 1545989128.090 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545989128.091 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545989128.091 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545989128.091 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989128.091 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1545989128.091 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1545989128.092 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545989128.092 * [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))) 1545989128.092 * [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)))) 1545989128.092 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1545989128.092 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1545989128.092 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1545989128.092 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989128.092 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989128.092 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545989128.093 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989128.093 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989128.093 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989128.093 * [misc]taylor: Taking taylor expansion of k in k 1545989128.093 * [misc]backup-simplify: Simplify 0 into 0 1545989128.093 * [misc]backup-simplify: Simplify 1 into 1 1545989128.093 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989128.093 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1545989128.093 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1545989128.093 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1545989128.093 * [misc]taylor: Taking taylor expansion of 2 in k 1545989128.093 * [misc]backup-simplify: Simplify 2 into 2 1545989128.093 * [misc]taylor: Taking taylor expansion of PI in k 1545989128.093 * [misc]backup-simplify: Simplify PI into PI 1545989128.093 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545989128.093 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545989128.093 * [misc]taylor: Taking taylor expansion of (log n) in k 1545989128.093 * [misc]taylor: Taking taylor expansion of n in k 1545989128.093 * [misc]backup-simplify: Simplify n into n 1545989128.093 * [misc]backup-simplify: Simplify (log n) into (log n) 1545989128.093 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545989128.094 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1545989128.094 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1545989128.094 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1545989128.094 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1545989128.094 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1545989128.095 * [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)))) 1545989128.095 * [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)))) 1545989128.096 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1545989128.096 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1545989128.098 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1545989128.098 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1545989128.098 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1545989128.098 * [misc]backup-simplify: Simplify (- 0) into 0 1545989128.098 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989128.099 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545989128.099 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1545989128.100 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1545989128.100 * [misc]taylor: Taking taylor expansion of 0 in k 1545989128.100 * [misc]backup-simplify: Simplify 0 into 0 1545989128.100 * [misc]backup-simplify: Simplify 0 into 0 1545989128.100 * [misc]backup-simplify: Simplify 0 into 0 1545989128.101 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989128.102 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1545989128.104 * [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 1545989128.105 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545989128.105 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1545989128.105 * [misc]backup-simplify: Simplify (- 0) into 0 1545989128.105 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989128.105 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545989128.106 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1545989128.107 * [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 1545989128.107 * [misc]taylor: Taking taylor expansion of 0 in k 1545989128.107 * [misc]backup-simplify: Simplify 0 into 0 1545989128.107 * [misc]backup-simplify: Simplify 0 into 0 1545989128.107 * [misc]backup-simplify: Simplify 0 into 0 1545989128.107 * [misc]backup-simplify: Simplify 0 into 0 1545989128.108 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989128.109 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1545989128.114 * [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 1545989128.114 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545989128.114 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1545989128.114 * [misc]backup-simplify: Simplify (- 0) into 0 1545989128.115 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989128.115 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545989128.116 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1545989128.118 * [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 1545989128.118 * [misc]taylor: Taking taylor expansion of 0 in k 1545989128.118 * [misc]backup-simplify: Simplify 0 into 0 1545989128.118 * [misc]backup-simplify: Simplify 0 into 0 1545989128.118 * [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))))) 1545989128.118 * [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)) 1545989128.118 * [misc]approximate: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 1545989128.118 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1545989128.118 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1545989128.118 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1545989128.119 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1545989128.119 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545989128.119 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989128.119 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989128.119 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989128.119 * [misc]taylor: Taking taylor expansion of k in k 1545989128.119 * [misc]backup-simplify: Simplify 0 into 0 1545989128.119 * [misc]backup-simplify: Simplify 1 into 1 1545989128.119 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989128.119 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989128.119 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989128.119 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1545989128.119 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1545989128.119 * [misc]taylor: Taking taylor expansion of -2 in k 1545989128.119 * [misc]backup-simplify: Simplify -2 into -2 1545989128.119 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1545989128.119 * [misc]taylor: Taking taylor expansion of PI in k 1545989128.119 * [misc]backup-simplify: Simplify PI into PI 1545989128.119 * [misc]taylor: Taking taylor expansion of n in k 1545989128.119 * [misc]backup-simplify: Simplify n into n 1545989128.119 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1545989128.119 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1545989128.119 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1545989128.119 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545989128.119 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545989128.119 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1545989128.119 * [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))) 1545989128.119 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1545989128.120 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1545989128.120 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1545989128.120 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1545989128.120 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989128.120 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989128.120 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989128.120 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989128.120 * [misc]taylor: Taking taylor expansion of k in n 1545989128.120 * [misc]backup-simplify: Simplify k into k 1545989128.120 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989128.120 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989128.120 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989128.120 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1545989128.120 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1545989128.120 * [misc]taylor: Taking taylor expansion of -2 in n 1545989128.120 * [misc]backup-simplify: Simplify -2 into -2 1545989128.120 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545989128.120 * [misc]taylor: Taking taylor expansion of PI in n 1545989128.120 * [misc]backup-simplify: Simplify PI into PI 1545989128.120 * [misc]taylor: Taking taylor expansion of n in n 1545989128.120 * [misc]backup-simplify: Simplify 0 into 0 1545989128.120 * [misc]backup-simplify: Simplify 1 into 1 1545989128.120 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545989128.120 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1545989128.121 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1545989128.121 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989128.121 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1545989128.121 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545989128.122 * [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))) 1545989128.122 * [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)))) 1545989128.122 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1545989128.122 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1545989128.122 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1545989128.122 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1545989128.122 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989128.122 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989128.122 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989128.122 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989128.122 * [misc]taylor: Taking taylor expansion of k in n 1545989128.122 * [misc]backup-simplify: Simplify k into k 1545989128.122 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989128.122 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989128.122 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989128.122 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1545989128.122 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1545989128.122 * [misc]taylor: Taking taylor expansion of -2 in n 1545989128.122 * [misc]backup-simplify: Simplify -2 into -2 1545989128.122 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545989128.122 * [misc]taylor: Taking taylor expansion of PI in n 1545989128.122 * [misc]backup-simplify: Simplify PI into PI 1545989128.122 * [misc]taylor: Taking taylor expansion of n in n 1545989128.122 * [misc]backup-simplify: Simplify 0 into 0 1545989128.122 * [misc]backup-simplify: Simplify 1 into 1 1545989128.122 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545989128.123 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1545989128.123 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1545989128.123 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989128.123 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1545989128.123 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545989128.124 * [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))) 1545989128.124 * [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)))) 1545989128.124 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1545989128.124 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1545989128.124 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1545989128.124 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545989128.124 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989128.124 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989128.124 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989128.124 * [misc]taylor: Taking taylor expansion of k in k 1545989128.124 * [misc]backup-simplify: Simplify 0 into 0 1545989128.124 * [misc]backup-simplify: Simplify 1 into 1 1545989128.125 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989128.125 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989128.125 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989128.125 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1545989128.125 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1545989128.125 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1545989128.125 * [misc]taylor: Taking taylor expansion of -2 in k 1545989128.125 * [misc]backup-simplify: Simplify -2 into -2 1545989128.125 * [misc]taylor: Taking taylor expansion of PI in k 1545989128.125 * [misc]backup-simplify: Simplify PI into PI 1545989128.125 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1545989128.125 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1545989128.125 * [misc]taylor: Taking taylor expansion of (log n) in k 1545989128.125 * [misc]taylor: Taking taylor expansion of n in k 1545989128.125 * [misc]backup-simplify: Simplify n into n 1545989128.125 * [misc]backup-simplify: Simplify (log n) into (log n) 1545989128.125 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545989128.125 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545989128.126 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1545989128.126 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1545989128.126 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1545989128.127 * [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)))) 1545989128.127 * [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)))) 1545989128.128 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1545989128.129 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1545989128.131 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1545989128.131 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1545989128.132 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1545989128.132 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989128.132 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545989128.133 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1545989128.135 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1545989128.135 * [misc]taylor: Taking taylor expansion of 0 in k 1545989128.135 * [misc]backup-simplify: Simplify 0 into 0 1545989128.135 * [misc]backup-simplify: Simplify 0 into 0 1545989128.135 * [misc]backup-simplify: Simplify 0 into 0 1545989128.136 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989128.138 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1545989128.143 * [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 1545989128.143 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545989128.143 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1545989128.143 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989128.144 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545989128.145 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1545989128.147 * [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 1545989128.147 * [misc]taylor: Taking taylor expansion of 0 in k 1545989128.147 * [misc]backup-simplify: Simplify 0 into 0 1545989128.147 * [misc]backup-simplify: Simplify 0 into 0 1545989128.147 * [misc]backup-simplify: Simplify 0 into 0 1545989128.147 * [misc]backup-simplify: Simplify 0 into 0 1545989128.149 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989128.151 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1545989128.157 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0 1545989128.157 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545989128.158 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1545989128.158 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989128.158 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545989128.159 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 1545989128.161 * [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 1545989128.161 * [misc]taylor: Taking taylor expansion of 0 in k 1545989128.161 * [misc]backup-simplify: Simplify 0 into 0 1545989128.161 * [misc]backup-simplify: Simplify 0 into 0 1545989128.162 * [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))))) 1545989128.162 * * * * [misc]progress: [ 2 / 3 ] generating series at (2 1 1) 1545989128.162 * [misc]backup-simplify: Simplify (* PI (* n 2)) into (* 2 (* n PI)) 1545989128.162 * [misc]approximate: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1545989128.162 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1545989128.162 * [misc]taylor: Taking taylor expansion of 2 in n 1545989128.162 * [misc]backup-simplify: Simplify 2 into 2 1545989128.162 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545989128.162 * [misc]taylor: Taking taylor expansion of n in n 1545989128.162 * [misc]backup-simplify: Simplify 0 into 0 1545989128.162 * [misc]backup-simplify: Simplify 1 into 1 1545989128.162 * [misc]taylor: Taking taylor expansion of PI in n 1545989128.162 * [misc]backup-simplify: Simplify PI into PI 1545989128.162 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1545989128.162 * [misc]taylor: Taking taylor expansion of 2 in n 1545989128.162 * [misc]backup-simplify: Simplify 2 into 2 1545989128.162 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545989128.162 * [misc]taylor: Taking taylor expansion of n in n 1545989128.162 * [misc]backup-simplify: Simplify 0 into 0 1545989128.162 * [misc]backup-simplify: Simplify 1 into 1 1545989128.162 * [misc]taylor: Taking taylor expansion of PI in n 1545989128.162 * [misc]backup-simplify: Simplify PI into PI 1545989128.162 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1545989128.162 * [misc]backup-simplify: Simplify (* 2 0) into 0 1545989128.162 * [misc]backup-simplify: Simplify 0 into 0 1545989128.163 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1545989128.163 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1545989128.163 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545989128.164 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1545989128.165 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1545989128.165 * [misc]backup-simplify: Simplify 0 into 0 1545989128.166 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1545989128.167 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1545989128.167 * [misc]backup-simplify: Simplify 0 into 0 1545989128.168 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1545989128.169 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1545989128.169 * [misc]backup-simplify: Simplify 0 into 0 1545989128.171 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1545989128.172 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1545989128.172 * [misc]backup-simplify: Simplify 0 into 0 1545989128.174 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1545989128.176 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1545989128.176 * [misc]backup-simplify: Simplify 0 into 0 1545989128.180 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1545989128.182 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1545989128.182 * [misc]backup-simplify: Simplify 0 into 0 1545989128.182 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1545989128.182 * [misc]backup-simplify: Simplify (* PI (* (/ 1 n) 2)) into (* 2 (/ PI n)) 1545989128.182 * [misc]approximate: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1545989128.182 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1545989128.182 * [misc]taylor: Taking taylor expansion of 2 in n 1545989128.182 * [misc]backup-simplify: Simplify 2 into 2 1545989128.182 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545989128.182 * [misc]taylor: Taking taylor expansion of PI in n 1545989128.182 * [misc]backup-simplify: Simplify PI into PI 1545989128.182 * [misc]taylor: Taking taylor expansion of n in n 1545989128.182 * [misc]backup-simplify: Simplify 0 into 0 1545989128.182 * [misc]backup-simplify: Simplify 1 into 1 1545989128.183 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545989128.183 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1545989128.183 * [misc]taylor: Taking taylor expansion of 2 in n 1545989128.183 * [misc]backup-simplify: Simplify 2 into 2 1545989128.183 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545989128.183 * [misc]taylor: Taking taylor expansion of PI in n 1545989128.183 * [misc]backup-simplify: Simplify PI into PI 1545989128.183 * [misc]taylor: Taking taylor expansion of n in n 1545989128.183 * [misc]backup-simplify: Simplify 0 into 0 1545989128.183 * [misc]backup-simplify: Simplify 1 into 1 1545989128.183 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545989128.183 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545989128.183 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545989128.184 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1545989128.184 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1545989128.185 * [misc]backup-simplify: Simplify 0 into 0 1545989128.185 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989128.186 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1545989128.186 * [misc]backup-simplify: Simplify 0 into 0 1545989128.187 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989128.189 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1545989128.189 * [misc]backup-simplify: Simplify 0 into 0 1545989128.191 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989128.193 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1545989128.193 * [misc]backup-simplify: Simplify 0 into 0 1545989128.195 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989128.198 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1545989128.198 * [misc]backup-simplify: Simplify 0 into 0 1545989128.200 * [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 1545989128.203 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1545989128.203 * [misc]backup-simplify: Simplify 0 into 0 1545989128.204 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 1545989128.204 * [misc]backup-simplify: Simplify (* PI (* (/ 1 (- n)) 2)) into (* -2 (/ PI n)) 1545989128.204 * [misc]approximate: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1545989128.204 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1545989128.204 * [misc]taylor: Taking taylor expansion of -2 in n 1545989128.204 * [misc]backup-simplify: Simplify -2 into -2 1545989128.204 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545989128.204 * [misc]taylor: Taking taylor expansion of PI in n 1545989128.204 * [misc]backup-simplify: Simplify PI into PI 1545989128.204 * [misc]taylor: Taking taylor expansion of n in n 1545989128.204 * [misc]backup-simplify: Simplify 0 into 0 1545989128.204 * [misc]backup-simplify: Simplify 1 into 1 1545989128.204 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545989128.204 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1545989128.204 * [misc]taylor: Taking taylor expansion of -2 in n 1545989128.204 * [misc]backup-simplify: Simplify -2 into -2 1545989128.204 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545989128.204 * [misc]taylor: Taking taylor expansion of PI in n 1545989128.204 * [misc]backup-simplify: Simplify PI into PI 1545989128.204 * [misc]taylor: Taking taylor expansion of n in n 1545989128.204 * [misc]backup-simplify: Simplify 0 into 0 1545989128.204 * [misc]backup-simplify: Simplify 1 into 1 1545989128.205 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545989128.205 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1545989128.205 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1545989128.206 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1545989128.206 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1545989128.206 * [misc]backup-simplify: Simplify 0 into 0 1545989128.207 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989128.207 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1545989128.207 * [misc]backup-simplify: Simplify 0 into 0 1545989128.208 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989128.209 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1545989128.209 * [misc]backup-simplify: Simplify 0 into 0 1545989128.210 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989128.211 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1545989128.212 * [misc]backup-simplify: Simplify 0 into 0 1545989128.213 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989128.214 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1545989128.214 * [misc]backup-simplify: Simplify 0 into 0 1545989128.216 * [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 1545989128.217 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1545989128.218 * [misc]backup-simplify: Simplify 0 into 0 1545989128.218 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 1545989128.218 * * * * [misc]progress: [ 3 / 3 ] generating series at (2) 1545989128.218 * [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)))) 1545989128.218 * [misc]approximate: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (n k) around 0 1545989128.218 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 1545989128.218 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1545989128.218 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989128.218 * [misc]taylor: Taking taylor expansion of k in k 1545989128.218 * [misc]backup-simplify: Simplify 0 into 0 1545989128.218 * [misc]backup-simplify: Simplify 1 into 1 1545989128.218 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989128.219 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545989128.219 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1545989128.219 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1545989128.219 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1545989128.219 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1545989128.219 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1545989128.219 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989128.219 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989128.219 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1545989128.219 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989128.219 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989128.219 * [misc]taylor: Taking taylor expansion of k in k 1545989128.219 * [misc]backup-simplify: Simplify 0 into 0 1545989128.219 * [misc]backup-simplify: Simplify 1 into 1 1545989128.219 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1545989128.219 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1545989128.219 * [misc]taylor: Taking taylor expansion of 2 in k 1545989128.219 * [misc]backup-simplify: Simplify 2 into 2 1545989128.219 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1545989128.219 * [misc]taylor: Taking taylor expansion of n in k 1545989128.219 * [misc]backup-simplify: Simplify n into n 1545989128.219 * [misc]taylor: Taking taylor expansion of PI in k 1545989128.219 * [misc]backup-simplify: Simplify PI into PI 1545989128.219 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1545989128.220 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1545989128.220 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1545989128.220 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1545989128.220 * [misc]backup-simplify: Simplify (- 0) into 0 1545989128.220 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545989128.220 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1545989128.220 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1545989128.220 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 1545989128.220 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1545989128.220 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989128.220 * [misc]taylor: Taking taylor expansion of k in n 1545989128.220 * [misc]backup-simplify: Simplify k into k 1545989128.220 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989128.220 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1545989128.220 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1545989128.220 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1545989128.220 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1545989128.220 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1545989128.220 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1545989128.220 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1545989128.220 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989128.220 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989128.220 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1545989128.220 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989128.221 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989128.221 * [misc]taylor: Taking taylor expansion of k in n 1545989128.221 * [misc]backup-simplify: Simplify k into k 1545989128.221 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1545989128.221 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1545989128.221 * [misc]taylor: Taking taylor expansion of 2 in n 1545989128.221 * [misc]backup-simplify: Simplify 2 into 2 1545989128.221 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545989128.221 * [misc]taylor: Taking taylor expansion of n in n 1545989128.221 * [misc]backup-simplify: Simplify 0 into 0 1545989128.221 * [misc]backup-simplify: Simplify 1 into 1 1545989128.221 * [misc]taylor: Taking taylor expansion of PI in n 1545989128.221 * [misc]backup-simplify: Simplify PI into PI 1545989128.221 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1545989128.221 * [misc]backup-simplify: Simplify (* 2 0) into 0 1545989128.221 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1545989128.222 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1545989128.222 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545989128.222 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1545989128.222 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1545989128.222 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1545989128.223 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545989128.223 * [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)))) 1545989128.223 * [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))))) 1545989128.223 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 1545989128.224 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1545989128.224 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989128.224 * [misc]taylor: Taking taylor expansion of k in n 1545989128.224 * [misc]backup-simplify: Simplify k into k 1545989128.224 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989128.224 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1545989128.224 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1545989128.224 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1545989128.224 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1545989128.224 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1545989128.224 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1545989128.224 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1545989128.224 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989128.224 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989128.224 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1545989128.224 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989128.224 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989128.224 * [misc]taylor: Taking taylor expansion of k in n 1545989128.224 * [misc]backup-simplify: Simplify k into k 1545989128.224 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1545989128.224 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1545989128.224 * [misc]taylor: Taking taylor expansion of 2 in n 1545989128.224 * [misc]backup-simplify: Simplify 2 into 2 1545989128.224 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545989128.224 * [misc]taylor: Taking taylor expansion of n in n 1545989128.224 * [misc]backup-simplify: Simplify 0 into 0 1545989128.224 * [misc]backup-simplify: Simplify 1 into 1 1545989128.224 * [misc]taylor: Taking taylor expansion of PI in n 1545989128.224 * [misc]backup-simplify: Simplify PI into PI 1545989128.224 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1545989128.224 * [misc]backup-simplify: Simplify (* 2 0) into 0 1545989128.225 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1545989128.225 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1545989128.225 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545989128.225 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1545989128.226 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1545989128.226 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1545989128.226 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545989128.226 * [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)))) 1545989128.227 * [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))))) 1545989128.227 * [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))) 1545989128.227 * [misc]taylor: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k))) in k 1545989128.227 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1545989128.227 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1545989128.228 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1545989128.228 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989128.228 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989128.228 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1545989128.228 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989128.228 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989128.228 * [misc]taylor: Taking taylor expansion of k in k 1545989128.228 * [misc]backup-simplify: Simplify 0 into 0 1545989128.228 * [misc]backup-simplify: Simplify 1 into 1 1545989128.228 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1545989128.228 * [misc]taylor: Taking taylor expansion of (log n) in k 1545989128.228 * [misc]taylor: Taking taylor expansion of n in k 1545989128.228 * [misc]backup-simplify: Simplify n into n 1545989128.228 * [misc]backup-simplify: Simplify (log n) into (log n) 1545989128.228 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1545989128.228 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1545989128.228 * [misc]taylor: Taking taylor expansion of 2 in k 1545989128.228 * [misc]backup-simplify: Simplify 2 into 2 1545989128.228 * [misc]taylor: Taking taylor expansion of PI in k 1545989128.228 * [misc]backup-simplify: Simplify PI into PI 1545989128.228 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545989128.229 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545989128.229 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1545989128.229 * [misc]backup-simplify: Simplify (- 0) into 0 1545989128.229 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545989128.230 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545989128.230 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1545989128.231 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1545989128.231 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1545989128.231 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989128.231 * [misc]taylor: Taking taylor expansion of k in k 1545989128.231 * [misc]backup-simplify: Simplify 0 into 0 1545989128.231 * [misc]backup-simplify: Simplify 1 into 1 1545989128.231 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989128.231 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545989128.232 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1545989128.232 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) into 0 1545989128.232 * [misc]backup-simplify: Simplify 0 into 0 1545989128.233 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1545989128.234 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1545989128.237 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1545989128.237 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1545989128.238 * [misc]backup-simplify: Simplify (- 0) into 0 1545989128.238 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989128.238 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545989128.239 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1545989128.241 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1545989128.241 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 k)) 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))) into 0 1545989128.241 * [misc]taylor: Taking taylor expansion of 0 in k 1545989128.241 * [misc]backup-simplify: Simplify 0 into 0 1545989128.242 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1545989128.243 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1545989128.246 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1545989128.246 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989128.246 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1545989128.247 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1545989128.247 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1545989128.247 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1545989128.249 * [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))))))) 1545989128.251 * [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))))))) 1545989128.252 * [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))))))) 1545989128.254 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1545989128.255 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1545989128.258 * [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 1545989128.258 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1545989128.258 * [misc]backup-simplify: Simplify (- 0) into 0 1545989128.259 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989128.259 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545989128.259 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1545989128.261 * [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 1545989128.261 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545989128.262 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 1545989128.263 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))))) into 0 1545989128.263 * [misc]taylor: Taking taylor expansion of 0 in k 1545989128.263 * [misc]backup-simplify: Simplify 0 into 0 1545989128.263 * [misc]backup-simplify: Simplify 0 into 0 1545989128.263 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1545989128.263 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1545989128.264 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1545989128.265 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1545989128.268 * [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 1545989128.268 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989128.268 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1545989128.268 * [misc]backup-simplify: Simplify (- 0) into 0 1545989128.268 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989128.269 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1545989128.270 * [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))))) 1545989128.273 * [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)))))))) 1545989128.274 * [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)))))))) 1545989128.276 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1545989128.277 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1545989128.281 * [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 1545989128.282 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 1545989128.282 * [misc]backup-simplify: Simplify (- 0) into 0 1545989128.282 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989128.282 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545989128.283 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 1545989128.285 * [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 1545989128.285 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545989128.285 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 1545989128.286 * [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 1545989128.286 * [misc]taylor: Taking taylor expansion of 0 in k 1545989128.286 * [misc]backup-simplify: Simplify 0 into 0 1545989128.286 * [misc]backup-simplify: Simplify 0 into 0 1545989128.286 * [misc]backup-simplify: Simplify 0 into 0 1545989128.286 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989128.287 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1545989128.289 * [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 1545989128.290 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1545989128.299 * [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 1545989128.299 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989128.299 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1545989128.300 * [misc]backup-simplify: Simplify (- 0) into 0 1545989128.300 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989128.301 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 1545989128.304 * [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))))))) 1545989128.313 * [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)))))))))))))) 1545989128.320 * [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)))))))))))))) 1545989128.331 * [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)))))))))))))))))))))) 1545989128.332 * [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))))) 1545989128.332 * [misc]approximate: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0 1545989128.332 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 1545989128.332 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1545989128.332 * [misc]taylor: Taking taylor expansion of k in k 1545989128.332 * [misc]backup-simplify: Simplify 0 into 0 1545989128.332 * [misc]backup-simplify: Simplify 1 into 1 1545989128.332 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545989128.333 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1545989128.333 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1545989128.333 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1545989128.333 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1545989128.333 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1545989128.333 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989128.333 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989128.333 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545989128.333 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989128.333 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989128.333 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989128.333 * [misc]taylor: Taking taylor expansion of k in k 1545989128.333 * [misc]backup-simplify: Simplify 0 into 0 1545989128.333 * [misc]backup-simplify: Simplify 1 into 1 1545989128.333 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989128.334 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1545989128.334 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1545989128.334 * [misc]taylor: Taking taylor expansion of 2 in k 1545989128.334 * [misc]backup-simplify: Simplify 2 into 2 1545989128.334 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1545989128.334 * [misc]taylor: Taking taylor expansion of PI in k 1545989128.334 * [misc]backup-simplify: Simplify PI into PI 1545989128.334 * [misc]taylor: Taking taylor expansion of n in k 1545989128.334 * [misc]backup-simplify: Simplify n into n 1545989128.334 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1545989128.334 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1545989128.334 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1545989128.334 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545989128.334 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1545989128.334 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1545989128.335 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1545989128.335 * [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)))) 1545989128.335 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1545989128.335 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1545989128.335 * [misc]taylor: Taking taylor expansion of k in n 1545989128.335 * [misc]backup-simplify: Simplify k into k 1545989128.335 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1545989128.335 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1545989128.335 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1545989128.335 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1545989128.335 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1545989128.335 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1545989128.335 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989128.335 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989128.335 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989128.335 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989128.335 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989128.335 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989128.335 * [misc]taylor: Taking taylor expansion of k in n 1545989128.335 * [misc]backup-simplify: Simplify k into k 1545989128.335 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989128.336 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1545989128.336 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1545989128.336 * [misc]taylor: Taking taylor expansion of 2 in n 1545989128.336 * [misc]backup-simplify: Simplify 2 into 2 1545989128.336 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545989128.336 * [misc]taylor: Taking taylor expansion of PI in n 1545989128.336 * [misc]backup-simplify: Simplify PI into PI 1545989128.336 * [misc]taylor: Taking taylor expansion of n in n 1545989128.336 * [misc]backup-simplify: Simplify 0 into 0 1545989128.336 * [misc]backup-simplify: Simplify 1 into 1 1545989128.336 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545989128.336 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545989128.337 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545989128.337 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989128.337 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1545989128.337 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1545989128.338 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545989128.338 * [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))) 1545989128.339 * [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)))) 1545989128.339 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1545989128.339 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1545989128.339 * [misc]taylor: Taking taylor expansion of k in n 1545989128.339 * [misc]backup-simplify: Simplify k into k 1545989128.339 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1545989128.339 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1545989128.339 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1545989128.339 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1545989128.339 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1545989128.339 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1545989128.339 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989128.339 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989128.339 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989128.340 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989128.340 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989128.340 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989128.340 * [misc]taylor: Taking taylor expansion of k in n 1545989128.340 * [misc]backup-simplify: Simplify k into k 1545989128.340 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989128.340 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1545989128.340 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1545989128.340 * [misc]taylor: Taking taylor expansion of 2 in n 1545989128.340 * [misc]backup-simplify: Simplify 2 into 2 1545989128.340 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545989128.340 * [misc]taylor: Taking taylor expansion of PI in n 1545989128.340 * [misc]backup-simplify: Simplify PI into PI 1545989128.340 * [misc]taylor: Taking taylor expansion of n in n 1545989128.340 * [misc]backup-simplify: Simplify 0 into 0 1545989128.340 * [misc]backup-simplify: Simplify 1 into 1 1545989128.340 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545989128.340 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545989128.341 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545989128.341 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989128.341 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1545989128.341 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1545989128.342 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545989128.342 * [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))) 1545989128.343 * [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)))) 1545989128.344 * [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)) 1545989128.344 * [misc]taylor: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) in k 1545989128.344 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1545989128.344 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1545989128.344 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1545989128.344 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989128.344 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989128.344 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545989128.344 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989128.344 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989128.344 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989128.344 * [misc]taylor: Taking taylor expansion of k in k 1545989128.344 * [misc]backup-simplify: Simplify 0 into 0 1545989128.344 * [misc]backup-simplify: Simplify 1 into 1 1545989128.344 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989128.344 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1545989128.344 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1545989128.345 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1545989128.345 * [misc]taylor: Taking taylor expansion of 2 in k 1545989128.345 * [misc]backup-simplify: Simplify 2 into 2 1545989128.345 * [misc]taylor: Taking taylor expansion of PI in k 1545989128.345 * [misc]backup-simplify: Simplify PI into PI 1545989128.345 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545989128.345 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545989128.345 * [misc]taylor: Taking taylor expansion of (log n) in k 1545989128.345 * [misc]taylor: Taking taylor expansion of n in k 1545989128.345 * [misc]backup-simplify: Simplify n into n 1545989128.346 * [misc]backup-simplify: Simplify (log n) into (log n) 1545989128.346 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545989128.346 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1545989128.346 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1545989128.346 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1545989128.347 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1545989128.347 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1545989128.348 * [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)))) 1545989128.348 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1545989128.348 * [misc]taylor: Taking taylor expansion of k in k 1545989128.348 * [misc]backup-simplify: Simplify 0 into 0 1545989128.348 * [misc]backup-simplify: Simplify 1 into 1 1545989128.348 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545989128.348 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1545989128.349 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) into 0 1545989128.349 * [misc]backup-simplify: Simplify 0 into 0 1545989128.350 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1545989128.351 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1545989128.354 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1545989128.354 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1545989128.354 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1545989128.354 * [misc]backup-simplify: Simplify (- 0) into 0 1545989128.354 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989128.355 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545989128.356 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1545989128.358 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1545989128.358 * [misc]backup-simplify: Simplify (+ (* (sqrt k) 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0 1545989128.358 * [misc]taylor: Taking taylor expansion of 0 in k 1545989128.358 * [misc]backup-simplify: Simplify 0 into 0 1545989128.359 * [misc]backup-simplify: Simplify 0 into 0 1545989128.359 * [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)))))) 1545989128.360 * [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)))))) 1545989128.362 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989128.363 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1545989128.367 * [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 1545989128.368 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545989128.368 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1545989128.368 * [misc]backup-simplify: Simplify (- 0) into 0 1545989128.368 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989128.369 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545989128.370 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1545989128.372 * [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 1545989128.373 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 1545989128.374 * [misc]backup-simplify: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0 1545989128.374 * [misc]taylor: Taking taylor expansion of 0 in k 1545989128.374 * [misc]backup-simplify: Simplify 0 into 0 1545989128.374 * [misc]backup-simplify: Simplify 0 into 0 1545989128.374 * [misc]backup-simplify: Simplify 0 into 0 1545989128.375 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1545989128.376 * [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)))))) 1545989128.376 * [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)))))) 1545989128.378 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989128.380 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1545989128.387 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 1545989128.388 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545989128.388 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1545989128.388 * [misc]backup-simplify: Simplify (- 0) into 0 1545989128.388 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989128.389 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545989128.390 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1545989128.393 * [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 1545989128.394 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 1545989128.395 * [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 1545989128.395 * [misc]taylor: Taking taylor expansion of 0 in k 1545989128.395 * [misc]backup-simplify: Simplify 0 into 0 1545989128.395 * [misc]backup-simplify: Simplify 0 into 0 1545989128.395 * [misc]backup-simplify: Simplify 0 into 0 1545989128.395 * [misc]backup-simplify: Simplify 0 into 0 1545989128.396 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1545989128.397 * [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)))))) 1545989128.398 * [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)))))) 1545989128.401 * [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)))))))) 1545989128.401 * [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))) 1545989128.401 * [misc]approximate: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (n k) around 0 1545989128.401 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 1545989128.401 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1545989128.401 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1545989128.401 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1545989128.401 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1545989128.401 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545989128.401 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989128.401 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989128.401 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989128.401 * [misc]taylor: Taking taylor expansion of k in k 1545989128.401 * [misc]backup-simplify: Simplify 0 into 0 1545989128.401 * [misc]backup-simplify: Simplify 1 into 1 1545989128.402 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989128.402 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989128.402 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989128.402 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1545989128.402 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1545989128.402 * [misc]taylor: Taking taylor expansion of -2 in k 1545989128.402 * [misc]backup-simplify: Simplify -2 into -2 1545989128.402 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1545989128.402 * [misc]taylor: Taking taylor expansion of PI in k 1545989128.402 * [misc]backup-simplify: Simplify PI into PI 1545989128.402 * [misc]taylor: Taking taylor expansion of n in k 1545989128.402 * [misc]backup-simplify: Simplify n into n 1545989128.402 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1545989128.402 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1545989128.402 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1545989128.402 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545989128.402 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545989128.402 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1545989128.403 * [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))) 1545989128.403 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1545989128.403 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1545989128.403 * [misc]taylor: Taking taylor expansion of -1 in k 1545989128.403 * [misc]backup-simplify: Simplify -1 into -1 1545989128.403 * [misc]taylor: Taking taylor expansion of k in k 1545989128.403 * [misc]backup-simplify: Simplify 0 into 0 1545989128.403 * [misc]backup-simplify: Simplify 1 into 1 1545989128.403 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1545989128.403 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545989128.404 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1545989128.404 * [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)))) 1545989128.404 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 1545989128.404 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1545989128.404 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1545989128.404 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1545989128.404 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1545989128.404 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989128.404 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989128.404 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989128.404 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989128.404 * [misc]taylor: Taking taylor expansion of k in n 1545989128.404 * [misc]backup-simplify: Simplify k into k 1545989128.404 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989128.404 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989128.405 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989128.405 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1545989128.405 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1545989128.405 * [misc]taylor: Taking taylor expansion of -2 in n 1545989128.405 * [misc]backup-simplify: Simplify -2 into -2 1545989128.405 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545989128.405 * [misc]taylor: Taking taylor expansion of PI in n 1545989128.405 * [misc]backup-simplify: Simplify PI into PI 1545989128.405 * [misc]taylor: Taking taylor expansion of n in n 1545989128.405 * [misc]backup-simplify: Simplify 0 into 0 1545989128.405 * [misc]backup-simplify: Simplify 1 into 1 1545989128.405 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545989128.405 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1545989128.406 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1545989128.406 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989128.406 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1545989128.407 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545989128.408 * [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))) 1545989128.408 * [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)))) 1545989128.408 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1545989128.408 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1545989128.408 * [misc]taylor: Taking taylor expansion of -1 in n 1545989128.408 * [misc]backup-simplify: Simplify -1 into -1 1545989128.408 * [misc]taylor: Taking taylor expansion of k in n 1545989128.408 * [misc]backup-simplify: Simplify k into k 1545989128.408 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1545989128.409 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1545989128.409 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1545989128.409 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1545989128.409 * [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))) 1545989128.409 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 1545989128.409 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1545989128.410 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1545989128.410 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1545989128.410 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1545989128.410 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989128.410 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989128.410 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989128.410 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989128.410 * [misc]taylor: Taking taylor expansion of k in n 1545989128.410 * [misc]backup-simplify: Simplify k into k 1545989128.410 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989128.410 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989128.410 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989128.410 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1545989128.410 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1545989128.410 * [misc]taylor: Taking taylor expansion of -2 in n 1545989128.410 * [misc]backup-simplify: Simplify -2 into -2 1545989128.410 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545989128.410 * [misc]taylor: Taking taylor expansion of PI in n 1545989128.410 * [misc]backup-simplify: Simplify PI into PI 1545989128.410 * [misc]taylor: Taking taylor expansion of n in n 1545989128.410 * [misc]backup-simplify: Simplify 0 into 0 1545989128.410 * [misc]backup-simplify: Simplify 1 into 1 1545989128.410 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545989128.411 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1545989128.411 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1545989128.411 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989128.411 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1545989128.412 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545989128.412 * [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))) 1545989128.413 * [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)))) 1545989128.413 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1545989128.413 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1545989128.413 * [misc]taylor: Taking taylor expansion of -1 in n 1545989128.413 * [misc]backup-simplify: Simplify -1 into -1 1545989128.413 * [misc]taylor: Taking taylor expansion of k in n 1545989128.413 * [misc]backup-simplify: Simplify k into k 1545989128.413 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1545989128.413 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1545989128.414 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1545989128.414 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1545989128.414 * [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))) 1545989128.414 * [misc]taylor: Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) in k 1545989128.415 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1545989128.415 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1545989128.415 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1545989128.415 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545989128.415 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989128.415 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989128.415 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989128.415 * [misc]taylor: Taking taylor expansion of k in k 1545989128.415 * [misc]backup-simplify: Simplify 0 into 0 1545989128.415 * [misc]backup-simplify: Simplify 1 into 1 1545989128.415 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989128.415 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989128.415 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989128.415 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1545989128.415 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1545989128.415 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1545989128.415 * [misc]taylor: Taking taylor expansion of -2 in k 1545989128.415 * [misc]backup-simplify: Simplify -2 into -2 1545989128.415 * [misc]taylor: Taking taylor expansion of PI in k 1545989128.415 * [misc]backup-simplify: Simplify PI into PI 1545989128.415 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1545989128.416 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1545989128.416 * [misc]taylor: Taking taylor expansion of (log n) in k 1545989128.416 * [misc]taylor: Taking taylor expansion of n in k 1545989128.416 * [misc]backup-simplify: Simplify n into n 1545989128.416 * [misc]backup-simplify: Simplify (log n) into (log n) 1545989128.416 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545989128.416 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545989128.416 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1545989128.417 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1545989128.417 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1545989128.418 * [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)))) 1545989128.418 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1545989128.418 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1545989128.418 * [misc]taylor: Taking taylor expansion of -1 in k 1545989128.418 * [misc]backup-simplify: Simplify -1 into -1 1545989128.418 * [misc]taylor: Taking taylor expansion of k in k 1545989128.418 * [misc]backup-simplify: Simplify 0 into 0 1545989128.418 * [misc]backup-simplify: Simplify 1 into 1 1545989128.419 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1545989128.419 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545989128.419 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1545989128.420 * [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))))) 1545989128.421 * [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))))) 1545989128.422 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1545989128.422 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1545989128.425 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1545989128.425 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1545989128.425 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1545989128.426 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989128.426 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545989128.427 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1545989128.429 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1545989128.429 * [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 1545989128.429 * [misc]taylor: Taking taylor expansion of 0 in k 1545989128.429 * [misc]backup-simplify: Simplify 0 into 0 1545989128.430 * [misc]backup-simplify: Simplify 0 into 0 1545989128.430 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1545989128.431 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1545989128.432 * [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)))))) 1545989128.433 * [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)))))) 1545989128.434 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989128.435 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1545989128.440 * [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 1545989128.440 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545989128.440 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1545989128.441 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989128.441 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545989128.442 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1545989128.445 * [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 1545989128.445 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545989128.446 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 1545989128.447 * [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 1545989128.447 * [misc]taylor: Taking taylor expansion of 0 in k 1545989128.447 * [misc]backup-simplify: Simplify 0 into 0 1545989128.447 * [misc]backup-simplify: Simplify 0 into 0 1545989128.447 * [misc]backup-simplify: Simplify 0 into 0 1545989128.447 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989128.448 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1545989128.450 * [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)))))) 1545989128.451 * [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)))))) 1545989128.454 * [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))))))))))) 1545989128.455 * * * [misc]progress: simplifying candidates 1545989128.455 * * * * [misc]progress: [ 1 / 77 ] simplifiying candidate # 1545989128.455 * [enter]simplify: Simplifying (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) 1545989128.455 * * [misc]simplify: iters left: 6 (11 enodes) 1545989128.459 * * [misc]simplify: iters left: 5 (21 enodes) 1545989128.466 * * [misc]simplify: iters left: 4 (47 enodes) 1545989128.482 * * [misc]simplify: iters left: 3 (109 enodes) 1545989128.531 * * [misc]simplify: iters left: 2 (300 enodes) 1545989128.758 * [exit]simplify: Simplified to (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) 1545989128.758 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (exp (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI)))) (sqrt k))) 1545989128.758 * * * * [misc]progress: [ 2 / 77 ] simplifiying candidate # 1545989128.758 * * * * [misc]progress: [ 3 / 77 ] simplifiying candidate # 1545989128.758 * [enter]simplify: Simplifying (* PI (* n 2)) 1545989128.758 * * [misc]simplify: iters left: 4 (5 enodes) 1545989128.760 * * [misc]simplify: iters left: 3 (9 enodes) 1545989128.762 * * [misc]simplify: iters left: 2 (15 enodes) 1545989128.766 * * [misc]simplify: iters left: 1 (17 enodes) 1545989128.774 * [exit]simplify: Simplified to (* (* 2 n) PI) 1545989128.774 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* 2 n) PI) (* 1 (- 1/2 (/ k 2)))) (sqrt k))) 1545989128.774 * * * * [misc]progress: [ 4 / 77 ] simplifiying candidate # 1545989128.774 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (/ k 2)) 1545989128.774 * * [misc]simplify: iters left: 5 (8 enodes) 1545989128.777 * * [misc]simplify: iters left: 4 (12 enodes) 1545989128.780 * * [misc]simplify: iters left: 3 (18 enodes) 1545989128.782 * * [misc]simplify: iters left: 2 (20 enodes) 1545989128.784 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ k 2)) 1545989128.784 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (/ (pow (* PI (* n 2)) 1/2) (pow (* (* 2 n) PI) (/ k 2))) (sqrt k))) 1545989128.784 * * * * [misc]progress: [ 5 / 77 ] simplifiying candidate # 1545989128.784 * [enter]simplify: Simplifying (cbrt (- 1/2 (/ k 2))) 1545989128.784 * * [misc]simplify: iters left: 5 (6 enodes) 1545989128.785 * * [misc]simplify: iters left: 4 (8 enodes) 1545989128.786 * * [misc]simplify: iters left: 3 (11 enodes) 1545989128.788 * [exit]simplify: Simplified to (cbrt (- 1/2 (/ k 2))) 1545989128.788 * [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))) 1545989128.788 * * * * [misc]progress: [ 6 / 77 ] simplifiying candidate # 1545989128.788 * [enter]simplify: Simplifying (sqrt (- 1/2 (/ k 2))) 1545989128.788 * * [misc]simplify: iters left: 5 (6 enodes) 1545989128.789 * * [misc]simplify: iters left: 4 (8 enodes) 1545989128.790 * * [misc]simplify: iters left: 3 (11 enodes) 1545989128.791 * [exit]simplify: Simplified to (sqrt (- 1/2 (/ k 2))) 1545989128.791 * [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))) 1545989128.791 * * * * [misc]progress: [ 7 / 77 ] simplifiying candidate # 1545989128.791 * [enter]simplify: Simplifying (- 1/2 (/ k 2)) 1545989128.791 * * [misc]simplify: iters left: 4 (5 enodes) 1545989128.792 * * [misc]simplify: iters left: 3 (7 enodes) 1545989128.793 * * [misc]simplify: iters left: 2 (10 enodes) 1545989128.794 * [exit]simplify: Simplified to (- 1/2 (/ k 2)) 1545989128.794 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (pow (pow (* PI (* n 2)) 1) (- 1/2 (/ k 2))) (sqrt k))) 1545989128.794 * * * * [misc]progress: [ 8 / 77 ] simplifiying candidate # 1545989128.795 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1545989128.795 * * [misc]simplify: iters left: 5 (9 enodes) 1545989128.796 * * [misc]simplify: iters left: 4 (15 enodes) 1545989128.798 * * [misc]simplify: iters left: 3 (21 enodes) 1545989128.801 * * [misc]simplify: iters left: 2 (22 enodes) 1545989128.803 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1545989128.803 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2)))) (sqrt k))) 1545989128.803 * * * * [misc]progress: [ 9 / 77 ] simplifiying candidate # 1545989128.803 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1545989128.803 * * [misc]simplify: iters left: 5 (9 enodes) 1545989128.805 * * [misc]simplify: iters left: 4 (15 enodes) 1545989128.807 * * [misc]simplify: iters left: 3 (21 enodes) 1545989128.809 * * [misc]simplify: iters left: 2 (22 enodes) 1545989128.812 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1545989128.812 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2)))) (sqrt k))) 1545989128.812 * * * * [misc]progress: [ 10 / 77 ] simplifiying candidate # 1545989128.812 * [enter]simplify: Simplifying (pow PI (- 1/2 (/ k 2))) 1545989128.812 * * [misc]simplify: iters left: 5 (7 enodes) 1545989128.813 * * [misc]simplify: iters left: 4 (9 enodes) 1545989128.814 * * [misc]simplify: iters left: 3 (12 enodes) 1545989128.816 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1545989128.816 * [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))) 1545989128.816 * * * * [misc]progress: [ 11 / 77 ] simplifiying candidate # 1545989128.816 * * * * [misc]progress: [ 12 / 77 ] simplifiying candidate # 1545989128.816 * * * * [misc]progress: [ 13 / 77 ] simplifiying candidate # 1545989128.816 * * * * [misc]progress: [ 14 / 77 ] simplifiying candidate # 1545989128.816 * * * * [misc]progress: [ 15 / 77 ] simplifiying candidate # 1545989128.816 * * * * [misc]progress: [ 16 / 77 ] simplifiying candidate # 1545989128.816 * * * * [misc]progress: [ 17 / 77 ] simplifiying candidate # 1545989128.816 * * * * [misc]progress: [ 18 / 77 ] simplifiying candidate # 1545989128.816 * * * * [misc]progress: [ 19 / 77 ] simplifiying candidate # 1545989128.816 * * * * [misc]progress: [ 20 / 77 ] simplifiying candidate # 1545989128.816 * * * * [misc]progress: [ 21 / 77 ] simplifiying candidate # 1545989128.816 * * * * [misc]progress: [ 22 / 77 ] simplifiying candidate # 1545989128.816 * * * * [misc]progress: [ 23 / 77 ] simplifiying candidate # 1545989128.816 * * * * [misc]progress: [ 24 / 77 ] simplifiying candidate # 1545989128.816 * * * * [misc]progress: [ 25 / 77 ] simplifiying candidate # 1545989128.816 * * * * [misc]progress: [ 26 / 77 ] simplifiying candidate # 1545989128.816 * * * * [misc]progress: [ 27 / 77 ] simplifiying candidate # 1545989128.816 * * * * [misc]progress: [ 28 / 77 ] simplifiying candidate # 1545989128.817 * [enter]simplify: Simplifying (- (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) (log (sqrt k))) 1545989128.817 * * [misc]simplify: iters left: 6 (14 enodes) 1545989128.819 * * [misc]simplify: iters left: 5 (26 enodes) 1545989128.823 * * [misc]simplify: iters left: 4 (53 enodes) 1545989128.834 * * [misc]simplify: iters left: 3 (137 enodes) 1545989128.887 * * [misc]simplify: iters left: 2 (487 enodes) 1545989129.494 * [exit]simplify: Simplified to (- (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) (log (sqrt k))) 1545989129.494 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) (log (sqrt k))))) 1545989129.494 * * * * [misc]progress: [ 29 / 77 ] simplifiying candidate # 1545989129.494 * [enter]simplify: Simplifying (- (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) (log (sqrt k))) 1545989129.494 * * [misc]simplify: iters left: 6 (14 enodes) 1545989129.497 * * [misc]simplify: iters left: 5 (26 enodes) 1545989129.501 * * [misc]simplify: iters left: 4 (53 enodes) 1545989129.514 * * [misc]simplify: iters left: 3 (137 enodes) 1545989129.566 * * [misc]simplify: iters left: 2 (487 enodes) 1545989130.014 * [exit]simplify: Simplified to (- (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) (log (sqrt k))) 1545989130.014 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) (log (sqrt k))))) 1545989130.014 * * * * [misc]progress: [ 30 / 77 ] simplifiying candidate # 1545989130.015 * [enter]simplify: Simplifying (- (log (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (log (sqrt k))) 1545989130.015 * * [misc]simplify: iters left: 6 (14 enodes) 1545989130.017 * * [misc]simplify: iters left: 5 (24 enodes) 1545989130.020 * * [misc]simplify: iters left: 4 (42 enodes) 1545989130.029 * * [misc]simplify: iters left: 3 (71 enodes) 1545989130.059 * * [misc]simplify: iters left: 2 (208 enodes) 1545989130.255 * [exit]simplify: Simplified to (- (* (log (* (* 2 n) PI)) (- 1/2 (/ k 2))) (log (sqrt k))) 1545989130.255 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (log (* (* 2 n) PI)) (- 1/2 (/ k 2))) (log (sqrt k))))) 1545989130.255 * * * * [misc]progress: [ 31 / 77 ] simplifiying candidate # 1545989130.255 * * * * [misc]progress: [ 32 / 77 ] simplifiying candidate # 1545989130.255 * * * * [misc]progress: [ 33 / 77 ] simplifiying candidate # 1545989130.256 * [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))) 1545989130.256 * * [misc]simplify: iters left: 6 (16 enodes) 1545989130.258 * * [misc]simplify: iters left: 5 (31 enodes) 1545989130.265 * * [misc]simplify: iters left: 4 (67 enodes) 1545989130.276 * * [misc]simplify: iters left: 3 (124 enodes) 1545989130.320 * * [misc]simplify: iters left: 2 (195 enodes) 1545989130.402 * * [misc]simplify: iters left: 1 (309 enodes) 1545989130.575 * [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)))) 1545989130.575 * [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)))))) 1545989130.575 * * * * [misc]progress: [ 34 / 77 ] simplifiying candidate # 1545989130.575 * * * * [misc]progress: [ 35 / 77 ] simplifiying candidate # 1545989130.575 * * * * [misc]progress: [ 36 / 77 ] simplifiying candidate # 1545989130.575 * * * * [misc]progress: [ 37 / 77 ] simplifiying candidate # 1545989130.575 * * * * [misc]progress: [ 38 / 77 ] simplifiying candidate # 1545989130.576 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1545989130.576 * * [misc]simplify: iters left: 6 (12 enodes) 1545989130.577 * * [misc]simplify: iters left: 5 (19 enodes) 1545989130.581 * * [misc]simplify: iters left: 4 (25 enodes) 1545989130.586 * * [misc]simplify: iters left: 3 (26 enodes) 1545989130.592 * [exit]simplify: Simplified to (/ (sqrt (* (* 2 n) PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1545989130.592 * [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))))) 1545989130.592 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (sqrt k))) 1545989130.593 * * [misc]simplify: iters left: 6 (12 enodes) 1545989130.596 * * [misc]simplify: iters left: 5 (18 enodes) 1545989130.601 * * [misc]simplify: iters left: 4 (24 enodes) 1545989130.607 * * [misc]simplify: iters left: 3 (25 enodes) 1545989130.614 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt k))) 1545989130.614 * [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))))) 1545989130.614 * * * * [misc]progress: [ 39 / 77 ] simplifiying candidate # 1545989130.614 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (sqrt (sqrt k))) 1545989130.614 * * [misc]simplify: iters left: 6 (11 enodes) 1545989130.617 * * [misc]simplify: iters left: 5 (16 enodes) 1545989130.622 * * [misc]simplify: iters left: 4 (22 enodes) 1545989130.627 * * [misc]simplify: iters left: 3 (24 enodes) 1545989130.633 * [exit]simplify: Simplified to (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) 1545989130.633 * [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))))) 1545989130.634 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k))) 1545989130.634 * * [misc]simplify: iters left: 6 (12 enodes) 1545989130.637 * * [misc]simplify: iters left: 5 (18 enodes) 1545989130.642 * * [misc]simplify: iters left: 4 (24 enodes) 1545989130.648 * * [misc]simplify: iters left: 3 (25 enodes) 1545989130.655 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k))) 1545989130.655 * [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))))) 1545989130.655 * * * * [misc]progress: [ 40 / 77 ] simplifiying candidate # 1545989130.655 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) 1) 1545989130.655 * * [misc]simplify: iters left: 6 (9 enodes) 1545989130.658 * * [misc]simplify: iters left: 5 (16 enodes) 1545989130.663 * * [misc]simplify: iters left: 4 (24 enodes) 1545989130.669 * * [misc]simplify: iters left: 3 (26 enodes) 1545989130.674 * [exit]simplify: Simplified to (sqrt (* (* PI 2) n)) 1545989130.674 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) 1545989130.675 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)) 1545989130.675 * * [misc]simplify: iters left: 6 (11 enodes) 1545989130.678 * * [misc]simplify: iters left: 5 (17 enodes) 1545989130.683 * * [misc]simplify: iters left: 4 (23 enodes) 1545989130.689 * * [misc]simplify: iters left: 3 (24 enodes) 1545989130.695 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)) 1545989130.695 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)))) 1545989130.695 * * * * [misc]progress: [ 41 / 77 ] simplifiying candidate # 1545989130.696 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1545989130.696 * * [misc]simplify: iters left: 6 (12 enodes) 1545989130.699 * * [misc]simplify: iters left: 5 (19 enodes) 1545989130.704 * * [misc]simplify: iters left: 4 (25 enodes) 1545989130.707 * * [misc]simplify: iters left: 3 (26 enodes) 1545989130.710 * [exit]simplify: Simplified to (/ (sqrt (* (* 2 n) PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1545989130.710 * [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))))) 1545989130.710 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (sqrt k))) 1545989130.710 * * [misc]simplify: iters left: 6 (12 enodes) 1545989130.712 * * [misc]simplify: iters left: 5 (18 enodes) 1545989130.715 * * [misc]simplify: iters left: 4 (24 enodes) 1545989130.718 * * [misc]simplify: iters left: 3 (25 enodes) 1545989130.722 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt k))) 1545989130.722 * [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))))) 1545989130.722 * * * * [misc]progress: [ 42 / 77 ] simplifiying candidate # 1545989130.722 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (sqrt (sqrt k))) 1545989130.722 * * [misc]simplify: iters left: 6 (11 enodes) 1545989130.724 * * [misc]simplify: iters left: 5 (16 enodes) 1545989130.726 * * [misc]simplify: iters left: 4 (22 enodes) 1545989130.728 * * [misc]simplify: iters left: 3 (24 enodes) 1545989130.731 * [exit]simplify: Simplified to (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) 1545989130.731 * [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))))) 1545989130.731 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k))) 1545989130.731 * * [misc]simplify: iters left: 6 (12 enodes) 1545989130.735 * * [misc]simplify: iters left: 5 (18 enodes) 1545989130.740 * * [misc]simplify: iters left: 4 (24 enodes) 1545989130.746 * * [misc]simplify: iters left: 3 (25 enodes) 1545989130.753 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k))) 1545989130.753 * [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))))) 1545989130.753 * * * * [misc]progress: [ 43 / 77 ] simplifiying candidate # 1545989130.753 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) 1) 1545989130.753 * * [misc]simplify: iters left: 6 (9 enodes) 1545989130.756 * * [misc]simplify: iters left: 5 (16 enodes) 1545989130.761 * * [misc]simplify: iters left: 4 (24 enodes) 1545989130.767 * * [misc]simplify: iters left: 3 (26 enodes) 1545989130.772 * [exit]simplify: Simplified to (sqrt (* (* PI 2) n)) 1545989130.772 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) 1545989130.772 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)) 1545989130.772 * * [misc]simplify: iters left: 6 (11 enodes) 1545989130.774 * * [misc]simplify: iters left: 5 (17 enodes) 1545989130.776 * * [misc]simplify: iters left: 4 (23 enodes) 1545989130.779 * * [misc]simplify: iters left: 3 (24 enodes) 1545989130.782 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)) 1545989130.782 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)))) 1545989130.782 * * * * [misc]progress: [ 44 / 77 ] simplifiying candidate # 1545989130.782 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1545989130.782 * * [misc]simplify: iters left: 6 (11 enodes) 1545989130.784 * * [misc]simplify: iters left: 5 (15 enodes) 1545989130.786 * * [misc]simplify: iters left: 4 (18 enodes) 1545989130.788 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1545989130.788 * [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))))) 1545989130.789 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1545989130.789 * * [misc]simplify: iters left: 6 (11 enodes) 1545989130.790 * * [misc]simplify: iters left: 5 (14 enodes) 1545989130.792 * * [misc]simplify: iters left: 4 (17 enodes) 1545989130.794 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1545989130.794 * [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))))) 1545989130.794 * * * * [misc]progress: [ 45 / 77 ] simplifiying candidate # 1545989130.794 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1545989130.794 * * [misc]simplify: iters left: 6 (10 enodes) 1545989130.796 * * [misc]simplify: iters left: 5 (12 enodes) 1545989130.797 * * [misc]simplify: iters left: 4 (15 enodes) 1545989130.799 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1545989130.799 * [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))))) 1545989130.800 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1545989130.800 * * [misc]simplify: iters left: 6 (11 enodes) 1545989130.803 * * [misc]simplify: iters left: 5 (14 enodes) 1545989130.807 * * [misc]simplify: iters left: 4 (17 enodes) 1545989130.812 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1545989130.812 * [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))))) 1545989130.812 * * * * [misc]progress: [ 46 / 77 ] simplifiying candidate # 1545989130.812 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) 1) 1545989130.812 * * [misc]simplify: iters left: 6 (9 enodes) 1545989130.815 * * [misc]simplify: iters left: 5 (13 enodes) 1545989130.820 * * [misc]simplify: iters left: 4 (18 enodes) 1545989130.824 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1545989130.824 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1545989130.825 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)) 1545989130.825 * * [misc]simplify: iters left: 6 (10 enodes) 1545989130.828 * * [misc]simplify: iters left: 5 (13 enodes) 1545989130.832 * * [misc]simplify: iters left: 4 (16 enodes) 1545989130.836 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)) 1545989130.836 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1545989130.836 * * * * [misc]progress: [ 47 / 77 ] simplifiying candidate # 1545989130.837 * [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)))) 1545989130.837 * * [misc]simplify: iters left: 6 (16 enodes) 1545989130.842 * * [misc]simplify: iters left: 5 (28 enodes) 1545989130.850 * * [misc]simplify: iters left: 4 (46 enodes) 1545989130.863 * * [misc]simplify: iters left: 3 (50 enodes) 1545989130.875 * * [misc]simplify: iters left: 2 (53 enodes) 1545989130.889 * [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)))) 1545989130.889 * [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))))) 1545989130.889 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1545989130.889 * * [misc]simplify: iters left: 6 (14 enodes) 1545989130.893 * * [misc]simplify: iters left: 5 (20 enodes) 1545989130.899 * * [misc]simplify: iters left: 4 (29 enodes) 1545989130.907 * * [misc]simplify: iters left: 3 (30 enodes) 1545989130.913 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1545989130.914 * [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))))) 1545989130.914 * * * * [misc]progress: [ 48 / 77 ] simplifiying candidate # 1545989130.914 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) 1545989130.914 * * [misc]simplify: iters left: 6 (15 enodes) 1545989130.918 * * [misc]simplify: iters left: 5 (23 enodes) 1545989130.925 * * [misc]simplify: iters left: 4 (34 enodes) 1545989130.936 * * [misc]simplify: iters left: 3 (37 enodes) 1545989130.945 * [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)))))) 1545989130.946 * [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))))) 1545989130.946 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1545989130.946 * * [misc]simplify: iters left: 6 (14 enodes) 1545989130.950 * * [misc]simplify: iters left: 5 (20 enodes) 1545989130.956 * * [misc]simplify: iters left: 4 (29 enodes) 1545989130.963 * * [misc]simplify: iters left: 3 (30 enodes) 1545989130.971 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1545989130.971 * [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))))) 1545989130.971 * * * * [misc]progress: [ 49 / 77 ] simplifiying candidate # 1545989130.972 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1) 1545989130.972 * * [misc]simplify: iters left: 6 (14 enodes) 1545989130.976 * * [misc]simplify: iters left: 5 (24 enodes) 1545989130.983 * * [misc]simplify: iters left: 4 (39 enodes) 1545989130.993 * * [misc]simplify: iters left: 3 (54 enodes) 1545989131.003 * * [misc]simplify: iters left: 2 (80 enodes) 1545989131.013 * [exit]simplify: Simplified to (* (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))) 1545989131.013 * [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)))) 1545989131.013 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt k)) 1545989131.013 * * [misc]simplify: iters left: 6 (13 enodes) 1545989131.015 * * [misc]simplify: iters left: 5 (19 enodes) 1545989131.017 * * [misc]simplify: iters left: 4 (28 enodes) 1545989131.021 * * [misc]simplify: iters left: 3 (30 enodes) 1545989131.024 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt k)) 1545989131.024 * [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)))) 1545989131.024 * * * * [misc]progress: [ 50 / 77 ] simplifiying candidate # 1545989131.025 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1545989131.025 * * [misc]simplify: iters left: 6 (15 enodes) 1545989131.027 * * [misc]simplify: iters left: 5 (23 enodes) 1545989131.030 * * [misc]simplify: iters left: 4 (32 enodes) 1545989131.034 * * [misc]simplify: iters left: 3 (34 enodes) 1545989131.038 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1545989131.038 * [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))))) 1545989131.038 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1545989131.038 * * [misc]simplify: iters left: 6 (14 enodes) 1545989131.040 * * [misc]simplify: iters left: 5 (20 enodes) 1545989131.043 * * [misc]simplify: iters left: 4 (29 enodes) 1545989131.046 * * [misc]simplify: iters left: 3 (30 enodes) 1545989131.050 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1545989131.050 * [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))))) 1545989131.050 * * * * [misc]progress: [ 51 / 77 ] simplifiying candidate # 1545989131.050 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1545989131.050 * * [misc]simplify: iters left: 6 (14 enodes) 1545989131.052 * * [misc]simplify: iters left: 5 (20 enodes) 1545989131.055 * * [misc]simplify: iters left: 4 (29 enodes) 1545989131.059 * * [misc]simplify: iters left: 3 (30 enodes) 1545989131.062 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1545989131.062 * [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))))) 1545989131.062 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1545989131.062 * * [misc]simplify: iters left: 6 (14 enodes) 1545989131.064 * * [misc]simplify: iters left: 5 (20 enodes) 1545989131.067 * * [misc]simplify: iters left: 4 (29 enodes) 1545989131.070 * * [misc]simplify: iters left: 3 (30 enodes) 1545989131.074 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1545989131.074 * [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))))) 1545989131.074 * * * * [misc]progress: [ 52 / 77 ] simplifiying candidate # 1545989131.074 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1) 1545989131.074 * * [misc]simplify: iters left: 6 (13 enodes) 1545989131.076 * * [misc]simplify: iters left: 5 (21 enodes) 1545989131.079 * * [misc]simplify: iters left: 4 (32 enodes) 1545989131.086 * * [misc]simplify: iters left: 3 (33 enodes) 1545989131.093 * [exit]simplify: Simplified to (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) 1545989131.093 * [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)))) 1545989131.094 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt k)) 1545989131.094 * * [misc]simplify: iters left: 6 (13 enodes) 1545989131.098 * * [misc]simplify: iters left: 5 (19 enodes) 1545989131.103 * * [misc]simplify: iters left: 4 (28 enodes) 1545989131.111 * * [misc]simplify: iters left: 3 (30 enodes) 1545989131.118 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt k)) 1545989131.118 * [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)))) 1545989131.118 * * * * [misc]progress: [ 53 / 77 ] simplifiying candidate # 1545989131.118 * [enter]simplify: Simplifying (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1545989131.119 * * [misc]simplify: iters left: 6 (6 enodes) 1545989131.120 * * [misc]simplify: iters left: 5 (10 enodes) 1545989131.123 * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) 1545989131.123 * [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))))) 1545989131.123 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1545989131.123 * * [misc]simplify: iters left: 6 (13 enodes) 1545989131.127 * * [misc]simplify: iters left: 5 (19 enodes) 1545989131.132 * * [misc]simplify: iters left: 4 (28 enodes) 1545989131.140 * * [misc]simplify: iters left: 3 (30 enodes) 1545989131.147 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1545989131.147 * [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))))) 1545989131.147 * * * * [misc]progress: [ 54 / 77 ] simplifiying candidate # 1545989131.148 * [enter]simplify: Simplifying (/ 1 (sqrt (sqrt k))) 1545989131.148 * * [misc]simplify: iters left: 4 (5 enodes) 1545989131.149 * * [misc]simplify: iters left: 3 (7 enodes) 1545989131.151 * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt k))) 1545989131.151 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) 1545989131.151 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1545989131.151 * * [misc]simplify: iters left: 6 (13 enodes) 1545989131.155 * * [misc]simplify: iters left: 5 (19 enodes) 1545989131.161 * * [misc]simplify: iters left: 4 (28 enodes) 1545989131.167 * * [misc]simplify: iters left: 3 (30 enodes) 1545989131.176 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1545989131.176 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) 1545989131.176 * * * * [misc]progress: [ 55 / 77 ] simplifiying candidate # 1545989131.177 * [enter]simplify: Simplifying (/ 1 1) 1545989131.177 * * [misc]simplify: iters left: 2 (2 enodes) 1545989131.177 * * [misc]simplify: iters left: 1 (4 enodes) 1545989131.178 * [exit]simplify: Simplified to 1 1545989131.178 * [misc]simplify: Simplified (2 1) to (λ (k n) (* 1 (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))) 1545989131.178 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)) 1545989131.178 * * [misc]simplify: iters left: 6 (12 enodes) 1545989131.182 * * [misc]simplify: iters left: 5 (18 enodes) 1545989131.187 * * [misc]simplify: iters left: 4 (27 enodes) 1545989131.194 * * [misc]simplify: iters left: 3 (29 enodes) 1545989131.201 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k)) 1545989131.202 * [misc]simplify: Simplified (2 2) to (λ (k n) (* 1 (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k)))) 1545989131.202 * * * * [misc]progress: [ 56 / 77 ] simplifiying candidate # 1545989131.202 * * * * [misc]progress: [ 57 / 77 ] simplifiying candidate # 1545989131.202 * * * * [misc]progress: [ 58 / 77 ] simplifiying candidate # 1545989131.202 * * * * [misc]progress: [ 59 / 77 ] simplifiying candidate # 1545989131.202 * [enter]simplify: Simplifying (cbrt (sqrt k)) 1545989131.202 * * [misc]simplify: iters left: 2 (3 enodes) 1545989131.203 * [exit]simplify: Simplified to (cbrt (sqrt k)) 1545989131.203 * [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)))) 1545989131.203 * * * * [misc]progress: [ 60 / 77 ] simplifiying candidate # 1545989131.203 * [enter]simplify: Simplifying (sqrt (sqrt k)) 1545989131.203 * * [misc]simplify: iters left: 2 (3 enodes) 1545989131.204 * [exit]simplify: Simplified to (sqrt (sqrt k)) 1545989131.204 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k)))) 1545989131.204 * * * * [misc]progress: [ 61 / 77 ] simplifiying candidate # 1545989131.204 * [enter]simplify: Simplifying (sqrt k) 1545989131.204 * * [misc]simplify: iters left: 1 (2 enodes) 1545989131.205 * [exit]simplify: Simplified to (sqrt k) 1545989131.205 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) 1) (sqrt k))) 1545989131.205 * * * * [misc]progress: [ 62 / 77 ] simplifiying candidate # 1545989131.205 * [enter]simplify: Simplifying (pow (* PI (* n 2)) 1/2) 1545989131.205 * * [misc]simplify: iters left: 5 (7 enodes) 1545989131.208 * * [misc]simplify: iters left: 4 (12 enodes) 1545989131.211 * * [misc]simplify: iters left: 3 (18 enodes) 1545989131.216 * * [misc]simplify: iters left: 2 (20 enodes) 1545989131.220 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1545989131.220 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2)))))) 1545989131.221 * * * * [misc]progress: [ 63 / 77 ] simplifiying candidate # 1545989131.221 * [enter]simplify: Simplifying (pow (* PI (* n 2)) 1/2) 1545989131.221 * * [misc]simplify: iters left: 5 (7 enodes) 1545989131.223 * * [misc]simplify: iters left: 4 (12 enodes) 1545989131.226 * * [misc]simplify: iters left: 3 (18 enodes) 1545989131.231 * * [misc]simplify: iters left: 2 (20 enodes) 1545989131.235 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1545989131.236 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2)))))) 1545989131.236 * * * * [misc]progress: [ 64 / 77 ] simplifiying candidate # 1545989131.236 * [enter]simplify: Simplifying (pow PI (- 1/2 (/ k 2))) 1545989131.236 * * [misc]simplify: iters left: 5 (7 enodes) 1545989131.238 * * [misc]simplify: iters left: 4 (9 enodes) 1545989131.240 * * [misc]simplify: iters left: 3 (12 enodes) 1545989131.243 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1545989131.243 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (pow PI (- 1/2 (/ k 2))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2)))))) 1545989131.244 * * * * [misc]progress: [ 65 / 77 ] simplifiying candidate # 1545989131.244 * [enter]simplify: Simplifying (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1545989131.244 * * [misc]simplify: iters left: 6 (12 enodes) 1545989131.245 * * [misc]simplify: iters left: 5 (18 enodes) 1545989131.248 * * [misc]simplify: iters left: 4 (27 enodes) 1545989131.251 * * [misc]simplify: iters left: 3 (29 enodes) 1545989131.255 * [exit]simplify: Simplified to (* (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) 1545989131.255 * [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))))))) 1545989131.255 * * * * [misc]progress: [ 66 / 77 ] simplifiying candidate # 1545989131.255 * [enter]simplify: Simplifying (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1545989131.255 * * [misc]simplify: iters left: 6 (11 enodes) 1545989131.256 * * [misc]simplify: iters left: 5 (17 enodes) 1545989131.259 * * [misc]simplify: iters left: 4 (26 enodes) 1545989131.262 * * [misc]simplify: iters left: 3 (27 enodes) 1545989131.265 * [exit]simplify: Simplified to (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) 1545989131.265 * [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))))))) 1545989131.265 * * * * [misc]progress: [ 67 / 77 ] simplifiying candidate # 1545989131.265 * * * * [misc]progress: [ 68 / 77 ] simplifiying candidate # 1545989131.265 * [enter]simplify: Simplifying (pow (* PI (* n 2)) 1/2) 1545989131.265 * * [misc]simplify: iters left: 5 (7 enodes) 1545989131.266 * * [misc]simplify: iters left: 4 (12 enodes) 1545989131.268 * * [misc]simplify: iters left: 3 (18 enodes) 1545989131.270 * * [misc]simplify: iters left: 2 (20 enodes) 1545989131.272 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1545989131.272 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2))))) 1545989131.272 * * * * [misc]progress: [ 69 / 77 ] simplifiying candidate # 1545989131.273 * [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))))) 1545989131.273 * * [misc]simplify: iters left: 6 (37 enodes) 1545989131.285 * * [misc]simplify: iters left: 5 (105 enodes) 1545989131.329 * * [misc]simplify: iters left: 4 (339 enodes) 1545989131.568 * [exit]simplify: Simplified to (+ (+ (* (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) -1/2) (+ (* (* (* k (log n)) (* k (log n))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (pow (* PI 2) 1/2) (pow n 1/2)))) (* (* k k) (+ (* (* (log (* PI 2)) (log (* PI 2))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (* (* (log n) (pow n 1/2)) (pow (* PI 2) 1/2)) (* (log (* PI 2)) 1/4))))) 1545989131.569 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (+ (+ (* (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) -1/2) (+ (* (* (* k (log n)) (* k (log n))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (pow (* PI 2) 1/2) (pow n 1/2)))) (* (* k k) (+ (* (* (log (* PI 2)) (log (* PI 2))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (* (* (log n) (pow n 1/2)) (pow (* PI 2) 1/2)) (* (log (* PI 2)) 1/4))))) (sqrt k))) 1545989131.569 * * * * [misc]progress: [ 70 / 77 ] simplifiying candidate # 1545989131.569 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 1545989131.569 * * [misc]simplify: iters left: 6 (15 enodes) 1545989131.576 * * [misc]simplify: iters left: 5 (33 enodes) 1545989131.586 * * [misc]simplify: iters left: 4 (64 enodes) 1545989131.610 * * [misc]simplify: iters left: 3 (171 enodes) 1545989131.691 * [exit]simplify: Simplified to (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow n (- 1/2 (* 1/2 k)))) 1545989131.691 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow n (- 1/2 (* 1/2 k)))) (sqrt k))) 1545989131.691 * * * * [misc]progress: [ 71 / 77 ] simplifiying candidate # 1545989131.692 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 1545989131.692 * * [misc]simplify: iters left: 6 (15 enodes) 1545989131.698 * * [misc]simplify: iters left: 5 (30 enodes) 1545989131.708 * * [misc]simplify: iters left: 4 (65 enodes) 1545989131.735 * * [misc]simplify: iters left: 3 (200 enodes) 1545989131.861 * [exit]simplify: Simplified to (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))) 1545989131.861 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))) (sqrt k))) 1545989131.861 * * * * [misc]progress: [ 72 / 77 ] simplifiying candidate # 1545989131.865 * [enter]simplify: Simplifying (* 2 (* n PI)) 1545989131.865 * * [misc]simplify: iters left: 4 (5 enodes) 1545989131.867 * * [misc]simplify: iters left: 3 (9 enodes) 1545989131.869 * * [misc]simplify: iters left: 2 (15 enodes) 1545989131.873 * * [misc]simplify: iters left: 1 (17 enodes) 1545989131.877 * [exit]simplify: Simplified to (* (* PI n) 2) 1545989131.877 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt k))) 1545989131.877 * * * * [misc]progress: [ 73 / 77 ] simplifiying candidate # 1545989131.877 * [enter]simplify: Simplifying (* 2 (* n PI)) 1545989131.878 * * [misc]simplify: iters left: 4 (5 enodes) 1545989131.879 * * [misc]simplify: iters left: 3 (9 enodes) 1545989131.882 * * [misc]simplify: iters left: 2 (15 enodes) 1545989131.884 * * [misc]simplify: iters left: 1 (17 enodes) 1545989131.886 * [exit]simplify: Simplified to (* (* PI n) 2) 1545989131.886 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt k))) 1545989131.886 * * * * [misc]progress: [ 74 / 77 ] simplifiying candidate # 1545989131.886 * [enter]simplify: Simplifying (* 2 (* n PI)) 1545989131.887 * * [misc]simplify: iters left: 4 (5 enodes) 1545989131.887 * * [misc]simplify: iters left: 3 (9 enodes) 1545989131.888 * * [misc]simplify: iters left: 2 (15 enodes) 1545989131.891 * * [misc]simplify: iters left: 1 (17 enodes) 1545989131.892 * [exit]simplify: Simplified to (* (* PI n) 2) 1545989131.892 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt k))) 1545989131.893 * * * * [misc]progress: [ 75 / 77 ] simplifiying candidate # 1545989131.893 * [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)))))))))))))))))))))) 1545989131.893 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1545989131.893 * * * * [misc]progress: [ 76 / 77 ] simplifiying candidate # 1545989131.893 * [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)))))))) 1545989131.893 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1545989131.893 * * * * [misc]progress: [ 77 / 77 ] simplifiying candidate # 1545989131.893 * [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))))))))))) 1545989131.893 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1545989131.893 * * * [misc]progress: adding candidates to table 1545989133.026 * * [misc]progress: iteration 2 / 4 1545989133.026 * * * [misc]progress: picking best candidate 1545989133.099 * * * * [misc]pick: Picked # 1545989133.099 * * * [misc]progress: localizing error 1545989133.115 * * * [misc]progress: generating rewritten candidates 1545989133.115 * * * * [misc]progress: [ 1 / 4 ] rewriting at (2 1 1) 1545989133.118 * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 1 1 1) 1545989133.120 * * * * [misc]progress: [ 3 / 4 ] rewriting at (2 1) 1545989133.130 * * * * [misc]progress: [ 4 / 4 ] rewriting at (2 2) 1545989133.133 * * * [misc]progress: generating series expansions 1545989133.133 * * * * [misc]progress: [ 1 / 4 ] generating series at (2 1 1) 1545989133.134 * [misc]backup-simplify: Simplify (pow (* PI (* n 2)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 1545989133.134 * [misc]approximate: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 1545989133.134 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1545989133.134 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1545989133.134 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1545989133.134 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1545989133.134 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989133.134 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989133.134 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1545989133.134 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989133.134 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989133.134 * [misc]taylor: Taking taylor expansion of k in k 1545989133.134 * [misc]backup-simplify: Simplify 0 into 0 1545989133.134 * [misc]backup-simplify: Simplify 1 into 1 1545989133.134 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1545989133.134 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1545989133.134 * [misc]taylor: Taking taylor expansion of 2 in k 1545989133.134 * [misc]backup-simplify: Simplify 2 into 2 1545989133.134 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1545989133.134 * [misc]taylor: Taking taylor expansion of n in k 1545989133.134 * [misc]backup-simplify: Simplify n into n 1545989133.134 * [misc]taylor: Taking taylor expansion of PI in k 1545989133.134 * [misc]backup-simplify: Simplify PI into PI 1545989133.134 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1545989133.134 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1545989133.135 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1545989133.135 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1545989133.135 * [misc]backup-simplify: Simplify (- 0) into 0 1545989133.135 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545989133.135 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1545989133.135 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1545989133.135 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1545989133.136 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1545989133.136 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1545989133.136 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1545989133.136 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989133.136 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989133.136 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1545989133.136 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989133.136 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989133.136 * [misc]taylor: Taking taylor expansion of k in n 1545989133.136 * [misc]backup-simplify: Simplify k into k 1545989133.136 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1545989133.136 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1545989133.136 * [misc]taylor: Taking taylor expansion of 2 in n 1545989133.136 * [misc]backup-simplify: Simplify 2 into 2 1545989133.136 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545989133.136 * [misc]taylor: Taking taylor expansion of n in n 1545989133.136 * [misc]backup-simplify: Simplify 0 into 0 1545989133.136 * [misc]backup-simplify: Simplify 1 into 1 1545989133.136 * [misc]taylor: Taking taylor expansion of PI in n 1545989133.136 * [misc]backup-simplify: Simplify PI into PI 1545989133.137 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1545989133.137 * [misc]backup-simplify: Simplify (* 2 0) into 0 1545989133.137 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1545989133.138 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1545989133.139 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545989133.139 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1545989133.139 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1545989133.139 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1545989133.139 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545989133.140 * [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)))) 1545989133.141 * [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))))) 1545989133.141 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1545989133.141 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1545989133.141 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1545989133.141 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1545989133.141 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989133.141 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989133.141 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1545989133.141 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989133.141 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989133.141 * [misc]taylor: Taking taylor expansion of k in n 1545989133.141 * [misc]backup-simplify: Simplify k into k 1545989133.141 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1545989133.141 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1545989133.141 * [misc]taylor: Taking taylor expansion of 2 in n 1545989133.141 * [misc]backup-simplify: Simplify 2 into 2 1545989133.141 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545989133.141 * [misc]taylor: Taking taylor expansion of n in n 1545989133.141 * [misc]backup-simplify: Simplify 0 into 0 1545989133.141 * [misc]backup-simplify: Simplify 1 into 1 1545989133.141 * [misc]taylor: Taking taylor expansion of PI in n 1545989133.141 * [misc]backup-simplify: Simplify PI into PI 1545989133.142 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1545989133.142 * [misc]backup-simplify: Simplify (* 2 0) into 0 1545989133.142 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1545989133.143 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1545989133.144 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545989133.144 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1545989133.144 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1545989133.144 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1545989133.145 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545989133.145 * [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)))) 1545989133.146 * [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))))) 1545989133.146 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1545989133.146 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1545989133.146 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1545989133.146 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989133.146 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989133.146 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1545989133.146 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989133.146 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989133.146 * [misc]taylor: Taking taylor expansion of k in k 1545989133.146 * [misc]backup-simplify: Simplify 0 into 0 1545989133.146 * [misc]backup-simplify: Simplify 1 into 1 1545989133.146 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1545989133.146 * [misc]taylor: Taking taylor expansion of (log n) in k 1545989133.146 * [misc]taylor: Taking taylor expansion of n in k 1545989133.146 * [misc]backup-simplify: Simplify n into n 1545989133.146 * [misc]backup-simplify: Simplify (log n) into (log n) 1545989133.146 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1545989133.146 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1545989133.146 * [misc]taylor: Taking taylor expansion of 2 in k 1545989133.147 * [misc]backup-simplify: Simplify 2 into 2 1545989133.147 * [misc]taylor: Taking taylor expansion of PI in k 1545989133.147 * [misc]backup-simplify: Simplify PI into PI 1545989133.147 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545989133.147 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545989133.147 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1545989133.148 * [misc]backup-simplify: Simplify (- 0) into 0 1545989133.148 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545989133.148 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545989133.149 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1545989133.149 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1545989133.151 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1545989133.152 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1545989133.153 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1545989133.155 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1545989133.156 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1545989133.156 * [misc]backup-simplify: Simplify (- 0) into 0 1545989133.156 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989133.156 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545989133.157 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1545989133.159 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1545989133.159 * [misc]taylor: Taking taylor expansion of 0 in k 1545989133.159 * [misc]backup-simplify: Simplify 0 into 0 1545989133.159 * [misc]backup-simplify: Simplify 0 into 0 1545989133.160 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1545989133.160 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1545989133.162 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1545989133.163 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989133.163 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1545989133.163 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1545989133.163 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1545989133.164 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1545989133.165 * [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))))))) 1545989133.167 * [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))))))) 1545989133.168 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1545989133.170 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1545989133.175 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1545989133.175 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1545989133.175 * [misc]backup-simplify: Simplify (- 0) into 0 1545989133.175 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989133.176 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545989133.177 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1545989133.179 * [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 1545989133.179 * [misc]taylor: Taking taylor expansion of 0 in k 1545989133.179 * [misc]backup-simplify: Simplify 0 into 0 1545989133.179 * [misc]backup-simplify: Simplify 0 into 0 1545989133.179 * [misc]backup-simplify: Simplify 0 into 0 1545989133.181 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1545989133.182 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1545989133.187 * [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 1545989133.187 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989133.187 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1545989133.188 * [misc]backup-simplify: Simplify (- 0) into 0 1545989133.188 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989133.189 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1545989133.191 * [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))))) 1545989133.193 * [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))))) 1545989133.198 * [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))))) 1545989133.198 * [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)))) 1545989133.198 * [misc]approximate: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 1545989133.198 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1545989133.198 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1545989133.199 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1545989133.199 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1545989133.199 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989133.199 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989133.199 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545989133.199 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989133.199 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989133.199 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989133.199 * [misc]taylor: Taking taylor expansion of k in k 1545989133.199 * [misc]backup-simplify: Simplify 0 into 0 1545989133.199 * [misc]backup-simplify: Simplify 1 into 1 1545989133.199 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989133.199 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1545989133.199 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1545989133.199 * [misc]taylor: Taking taylor expansion of 2 in k 1545989133.199 * [misc]backup-simplify: Simplify 2 into 2 1545989133.199 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1545989133.199 * [misc]taylor: Taking taylor expansion of PI in k 1545989133.199 * [misc]backup-simplify: Simplify PI into PI 1545989133.199 * [misc]taylor: Taking taylor expansion of n in k 1545989133.199 * [misc]backup-simplify: Simplify n into n 1545989133.199 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1545989133.199 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1545989133.199 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1545989133.200 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545989133.200 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1545989133.200 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1545989133.200 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1545989133.201 * [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)))) 1545989133.201 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1545989133.201 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1545989133.201 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1545989133.201 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1545989133.201 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989133.201 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989133.201 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989133.201 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989133.201 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989133.201 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989133.201 * [misc]taylor: Taking taylor expansion of k in n 1545989133.201 * [misc]backup-simplify: Simplify k into k 1545989133.201 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989133.201 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1545989133.201 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1545989133.201 * [misc]taylor: Taking taylor expansion of 2 in n 1545989133.201 * [misc]backup-simplify: Simplify 2 into 2 1545989133.201 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545989133.201 * [misc]taylor: Taking taylor expansion of PI in n 1545989133.201 * [misc]backup-simplify: Simplify PI into PI 1545989133.201 * [misc]taylor: Taking taylor expansion of n in n 1545989133.201 * [misc]backup-simplify: Simplify 0 into 0 1545989133.201 * [misc]backup-simplify: Simplify 1 into 1 1545989133.202 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545989133.202 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545989133.202 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545989133.203 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989133.203 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1545989133.203 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1545989133.203 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545989133.204 * [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))) 1545989133.205 * [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)))) 1545989133.205 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1545989133.205 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1545989133.205 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1545989133.205 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1545989133.205 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989133.205 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989133.205 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989133.205 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989133.205 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989133.205 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989133.205 * [misc]taylor: Taking taylor expansion of k in n 1545989133.205 * [misc]backup-simplify: Simplify k into k 1545989133.205 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989133.205 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1545989133.205 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1545989133.205 * [misc]taylor: Taking taylor expansion of 2 in n 1545989133.205 * [misc]backup-simplify: Simplify 2 into 2 1545989133.205 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545989133.205 * [misc]taylor: Taking taylor expansion of PI in n 1545989133.205 * [misc]backup-simplify: Simplify PI into PI 1545989133.205 * [misc]taylor: Taking taylor expansion of n in n 1545989133.205 * [misc]backup-simplify: Simplify 0 into 0 1545989133.205 * [misc]backup-simplify: Simplify 1 into 1 1545989133.205 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545989133.206 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545989133.206 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545989133.206 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989133.206 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1545989133.207 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1545989133.207 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545989133.208 * [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))) 1545989133.208 * [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)))) 1545989133.208 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1545989133.209 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1545989133.209 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1545989133.209 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989133.209 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989133.209 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545989133.209 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989133.209 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989133.209 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989133.209 * [misc]taylor: Taking taylor expansion of k in k 1545989133.209 * [misc]backup-simplify: Simplify 0 into 0 1545989133.209 * [misc]backup-simplify: Simplify 1 into 1 1545989133.209 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989133.209 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1545989133.209 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1545989133.209 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1545989133.209 * [misc]taylor: Taking taylor expansion of 2 in k 1545989133.209 * [misc]backup-simplify: Simplify 2 into 2 1545989133.209 * [misc]taylor: Taking taylor expansion of PI in k 1545989133.209 * [misc]backup-simplify: Simplify PI into PI 1545989133.209 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545989133.210 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545989133.210 * [misc]taylor: Taking taylor expansion of (log n) in k 1545989133.210 * [misc]taylor: Taking taylor expansion of n in k 1545989133.210 * [misc]backup-simplify: Simplify n into n 1545989133.210 * [misc]backup-simplify: Simplify (log n) into (log n) 1545989133.210 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545989133.210 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1545989133.210 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1545989133.210 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1545989133.211 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1545989133.211 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1545989133.212 * [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)))) 1545989133.213 * [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)))) 1545989133.214 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1545989133.214 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1545989133.216 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1545989133.216 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1545989133.217 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1545989133.217 * [misc]backup-simplify: Simplify (- 0) into 0 1545989133.217 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989133.217 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545989133.218 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1545989133.218 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1545989133.219 * [misc]taylor: Taking taylor expansion of 0 in k 1545989133.219 * [misc]backup-simplify: Simplify 0 into 0 1545989133.219 * [misc]backup-simplify: Simplify 0 into 0 1545989133.219 * [misc]backup-simplify: Simplify 0 into 0 1545989133.219 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989133.220 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1545989133.223 * [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 1545989133.223 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545989133.223 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1545989133.223 * [misc]backup-simplify: Simplify (- 0) into 0 1545989133.223 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989133.224 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545989133.224 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1545989133.226 * [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 1545989133.226 * [misc]taylor: Taking taylor expansion of 0 in k 1545989133.226 * [misc]backup-simplify: Simplify 0 into 0 1545989133.226 * [misc]backup-simplify: Simplify 0 into 0 1545989133.226 * [misc]backup-simplify: Simplify 0 into 0 1545989133.226 * [misc]backup-simplify: Simplify 0 into 0 1545989133.227 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989133.228 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1545989133.235 * [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 1545989133.235 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545989133.235 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1545989133.236 * [misc]backup-simplify: Simplify (- 0) into 0 1545989133.236 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989133.236 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545989133.237 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1545989133.239 * [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 1545989133.239 * [misc]taylor: Taking taylor expansion of 0 in k 1545989133.239 * [misc]backup-simplify: Simplify 0 into 0 1545989133.239 * [misc]backup-simplify: Simplify 0 into 0 1545989133.239 * [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))))) 1545989133.240 * [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)) 1545989133.240 * [misc]approximate: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 1545989133.240 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1545989133.240 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1545989133.240 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1545989133.240 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1545989133.240 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545989133.240 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989133.240 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989133.240 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989133.240 * [misc]taylor: Taking taylor expansion of k in k 1545989133.240 * [misc]backup-simplify: Simplify 0 into 0 1545989133.240 * [misc]backup-simplify: Simplify 1 into 1 1545989133.240 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989133.240 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989133.240 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989133.240 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1545989133.240 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1545989133.240 * [misc]taylor: Taking taylor expansion of -2 in k 1545989133.240 * [misc]backup-simplify: Simplify -2 into -2 1545989133.240 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1545989133.240 * [misc]taylor: Taking taylor expansion of PI in k 1545989133.240 * [misc]backup-simplify: Simplify PI into PI 1545989133.240 * [misc]taylor: Taking taylor expansion of n in k 1545989133.240 * [misc]backup-simplify: Simplify n into n 1545989133.240 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1545989133.240 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1545989133.240 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1545989133.240 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545989133.240 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545989133.241 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1545989133.241 * [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))) 1545989133.241 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1545989133.241 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1545989133.241 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1545989133.241 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1545989133.241 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989133.241 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989133.241 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989133.241 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989133.241 * [misc]taylor: Taking taylor expansion of k in n 1545989133.241 * [misc]backup-simplify: Simplify k into k 1545989133.241 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989133.241 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989133.241 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989133.241 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1545989133.241 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1545989133.241 * [misc]taylor: Taking taylor expansion of -2 in n 1545989133.241 * [misc]backup-simplify: Simplify -2 into -2 1545989133.241 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545989133.241 * [misc]taylor: Taking taylor expansion of PI in n 1545989133.241 * [misc]backup-simplify: Simplify PI into PI 1545989133.241 * [misc]taylor: Taking taylor expansion of n in n 1545989133.241 * [misc]backup-simplify: Simplify 0 into 0 1545989133.241 * [misc]backup-simplify: Simplify 1 into 1 1545989133.241 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545989133.241 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1545989133.242 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1545989133.242 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989133.242 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1545989133.242 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545989133.243 * [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))) 1545989133.243 * [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)))) 1545989133.243 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1545989133.243 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1545989133.243 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1545989133.243 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1545989133.243 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989133.243 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989133.243 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989133.243 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989133.243 * [misc]taylor: Taking taylor expansion of k in n 1545989133.243 * [misc]backup-simplify: Simplify k into k 1545989133.243 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989133.243 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989133.243 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989133.243 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1545989133.243 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1545989133.243 * [misc]taylor: Taking taylor expansion of -2 in n 1545989133.243 * [misc]backup-simplify: Simplify -2 into -2 1545989133.243 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545989133.243 * [misc]taylor: Taking taylor expansion of PI in n 1545989133.243 * [misc]backup-simplify: Simplify PI into PI 1545989133.243 * [misc]taylor: Taking taylor expansion of n in n 1545989133.243 * [misc]backup-simplify: Simplify 0 into 0 1545989133.243 * [misc]backup-simplify: Simplify 1 into 1 1545989133.244 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545989133.244 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1545989133.244 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1545989133.244 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989133.244 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1545989133.245 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545989133.245 * [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))) 1545989133.245 * [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)))) 1545989133.245 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1545989133.245 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1545989133.245 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1545989133.245 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545989133.246 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989133.246 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989133.246 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989133.246 * [misc]taylor: Taking taylor expansion of k in k 1545989133.246 * [misc]backup-simplify: Simplify 0 into 0 1545989133.246 * [misc]backup-simplify: Simplify 1 into 1 1545989133.246 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989133.246 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989133.246 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989133.246 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1545989133.246 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1545989133.246 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1545989133.246 * [misc]taylor: Taking taylor expansion of -2 in k 1545989133.246 * [misc]backup-simplify: Simplify -2 into -2 1545989133.246 * [misc]taylor: Taking taylor expansion of PI in k 1545989133.246 * [misc]backup-simplify: Simplify PI into PI 1545989133.246 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1545989133.246 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1545989133.246 * [misc]taylor: Taking taylor expansion of (log n) in k 1545989133.246 * [misc]taylor: Taking taylor expansion of n in k 1545989133.246 * [misc]backup-simplify: Simplify n into n 1545989133.246 * [misc]backup-simplify: Simplify (log n) into (log n) 1545989133.246 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545989133.247 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545989133.247 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1545989133.247 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1545989133.247 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1545989133.248 * [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)))) 1545989133.249 * [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)))) 1545989133.250 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1545989133.250 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1545989133.253 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1545989133.254 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1545989133.254 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1545989133.254 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989133.255 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545989133.255 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1545989133.257 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1545989133.257 * [misc]taylor: Taking taylor expansion of 0 in k 1545989133.257 * [misc]backup-simplify: Simplify 0 into 0 1545989133.257 * [misc]backup-simplify: Simplify 0 into 0 1545989133.257 * [misc]backup-simplify: Simplify 0 into 0 1545989133.259 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989133.260 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1545989133.265 * [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 1545989133.265 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545989133.265 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1545989133.265 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989133.266 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545989133.267 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1545989133.269 * [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 1545989133.269 * [misc]taylor: Taking taylor expansion of 0 in k 1545989133.269 * [misc]backup-simplify: Simplify 0 into 0 1545989133.269 * [misc]backup-simplify: Simplify 0 into 0 1545989133.269 * [misc]backup-simplify: Simplify 0 into 0 1545989133.269 * [misc]backup-simplify: Simplify 0 into 0 1545989133.271 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989133.273 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1545989133.281 * [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 1545989133.281 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545989133.282 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1545989133.282 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989133.283 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545989133.284 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 1545989133.287 * [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 1545989133.287 * [misc]taylor: Taking taylor expansion of 0 in k 1545989133.287 * [misc]backup-simplify: Simplify 0 into 0 1545989133.287 * [misc]backup-simplify: Simplify 0 into 0 1545989133.288 * [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))))) 1545989133.288 * * * * [misc]progress: [ 2 / 4 ] generating series at (2 1 1 1) 1545989133.288 * [misc]backup-simplify: Simplify (* PI (* n 2)) into (* 2 (* n PI)) 1545989133.288 * [misc]approximate: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1545989133.288 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1545989133.289 * [misc]taylor: Taking taylor expansion of 2 in n 1545989133.289 * [misc]backup-simplify: Simplify 2 into 2 1545989133.289 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545989133.289 * [misc]taylor: Taking taylor expansion of n in n 1545989133.289 * [misc]backup-simplify: Simplify 0 into 0 1545989133.289 * [misc]backup-simplify: Simplify 1 into 1 1545989133.289 * [misc]taylor: Taking taylor expansion of PI in n 1545989133.289 * [misc]backup-simplify: Simplify PI into PI 1545989133.289 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1545989133.289 * [misc]taylor: Taking taylor expansion of 2 in n 1545989133.289 * [misc]backup-simplify: Simplify 2 into 2 1545989133.289 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545989133.289 * [misc]taylor: Taking taylor expansion of n in n 1545989133.289 * [misc]backup-simplify: Simplify 0 into 0 1545989133.289 * [misc]backup-simplify: Simplify 1 into 1 1545989133.289 * [misc]taylor: Taking taylor expansion of PI in n 1545989133.289 * [misc]backup-simplify: Simplify PI into PI 1545989133.289 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1545989133.290 * [misc]backup-simplify: Simplify (* 2 0) into 0 1545989133.290 * [misc]backup-simplify: Simplify 0 into 0 1545989133.290 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1545989133.291 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1545989133.291 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545989133.292 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1545989133.293 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1545989133.293 * [misc]backup-simplify: Simplify 0 into 0 1545989133.295 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1545989133.296 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1545989133.296 * [misc]backup-simplify: Simplify 0 into 0 1545989133.298 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1545989133.300 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1545989133.300 * [misc]backup-simplify: Simplify 0 into 0 1545989133.303 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1545989133.306 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1545989133.306 * [misc]backup-simplify: Simplify 0 into 0 1545989133.310 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1545989133.313 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1545989133.313 * [misc]backup-simplify: Simplify 0 into 0 1545989133.318 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1545989133.322 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1545989133.322 * [misc]backup-simplify: Simplify 0 into 0 1545989133.322 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1545989133.322 * [misc]backup-simplify: Simplify (* PI (* (/ 1 n) 2)) into (* 2 (/ PI n)) 1545989133.322 * [misc]approximate: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1545989133.322 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1545989133.322 * [misc]taylor: Taking taylor expansion of 2 in n 1545989133.323 * [misc]backup-simplify: Simplify 2 into 2 1545989133.323 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545989133.323 * [misc]taylor: Taking taylor expansion of PI in n 1545989133.323 * [misc]backup-simplify: Simplify PI into PI 1545989133.323 * [misc]taylor: Taking taylor expansion of n in n 1545989133.323 * [misc]backup-simplify: Simplify 0 into 0 1545989133.323 * [misc]backup-simplify: Simplify 1 into 1 1545989133.323 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545989133.323 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1545989133.323 * [misc]taylor: Taking taylor expansion of 2 in n 1545989133.323 * [misc]backup-simplify: Simplify 2 into 2 1545989133.323 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545989133.323 * [misc]taylor: Taking taylor expansion of PI in n 1545989133.323 * [misc]backup-simplify: Simplify PI into PI 1545989133.323 * [misc]taylor: Taking taylor expansion of n in n 1545989133.323 * [misc]backup-simplify: Simplify 0 into 0 1545989133.323 * [misc]backup-simplify: Simplify 1 into 1 1545989133.323 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545989133.324 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545989133.324 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545989133.325 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1545989133.326 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1545989133.326 * [misc]backup-simplify: Simplify 0 into 0 1545989133.327 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989133.328 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1545989133.328 * [misc]backup-simplify: Simplify 0 into 0 1545989133.330 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989133.332 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1545989133.332 * [misc]backup-simplify: Simplify 0 into 0 1545989133.334 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989133.336 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1545989133.336 * [misc]backup-simplify: Simplify 0 into 0 1545989133.338 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989133.341 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1545989133.341 * [misc]backup-simplify: Simplify 0 into 0 1545989133.343 * [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 1545989133.347 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1545989133.347 * [misc]backup-simplify: Simplify 0 into 0 1545989133.347 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 1545989133.348 * [misc]backup-simplify: Simplify (* PI (* (/ 1 (- n)) 2)) into (* -2 (/ PI n)) 1545989133.348 * [misc]approximate: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1545989133.348 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1545989133.348 * [misc]taylor: Taking taylor expansion of -2 in n 1545989133.348 * [misc]backup-simplify: Simplify -2 into -2 1545989133.348 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545989133.348 * [misc]taylor: Taking taylor expansion of PI in n 1545989133.348 * [misc]backup-simplify: Simplify PI into PI 1545989133.348 * [misc]taylor: Taking taylor expansion of n in n 1545989133.348 * [misc]backup-simplify: Simplify 0 into 0 1545989133.348 * [misc]backup-simplify: Simplify 1 into 1 1545989133.348 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545989133.348 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1545989133.348 * [misc]taylor: Taking taylor expansion of -2 in n 1545989133.348 * [misc]backup-simplify: Simplify -2 into -2 1545989133.348 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545989133.348 * [misc]taylor: Taking taylor expansion of PI in n 1545989133.348 * [misc]backup-simplify: Simplify PI into PI 1545989133.348 * [misc]taylor: Taking taylor expansion of n in n 1545989133.348 * [misc]backup-simplify: Simplify 0 into 0 1545989133.348 * [misc]backup-simplify: Simplify 1 into 1 1545989133.349 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545989133.349 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1545989133.349 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1545989133.350 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1545989133.351 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1545989133.351 * [misc]backup-simplify: Simplify 0 into 0 1545989133.353 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989133.354 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1545989133.354 * [misc]backup-simplify: Simplify 0 into 0 1545989133.356 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989133.358 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1545989133.358 * [misc]backup-simplify: Simplify 0 into 0 1545989133.360 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989133.362 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1545989133.362 * [misc]backup-simplify: Simplify 0 into 0 1545989133.364 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989133.365 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1545989133.365 * [misc]backup-simplify: Simplify 0 into 0 1545989133.367 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989133.369 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1545989133.369 * [misc]backup-simplify: Simplify 0 into 0 1545989133.369 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 1545989133.369 * * * * [misc]progress: [ 3 / 4 ] generating series at (2 1) 1545989133.369 * [misc]backup-simplify: Simplify (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) into (* (pow (/ 1 k) 1/4) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) 1545989133.369 * [misc]approximate: Taking taylor expansion of (* (pow (/ 1 k) 1/4) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (n k) around 0 1545989133.369 * [misc]taylor: Taking taylor expansion of (* (pow (/ 1 k) 1/4) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 1545989133.369 * [misc]taylor: Taking taylor expansion of (pow (/ 1 k) 1/4) in k 1545989133.369 * [misc]taylor: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k 1545989133.369 * [misc]taylor: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k 1545989133.369 * [misc]taylor: Taking taylor expansion of 1/4 in k 1545989133.369 * [misc]backup-simplify: Simplify 1/4 into 1/4 1545989133.369 * [misc]taylor: Taking taylor expansion of (log (/ 1 k)) in k 1545989133.369 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989133.369 * [misc]taylor: Taking taylor expansion of k in k 1545989133.369 * [misc]backup-simplify: Simplify 0 into 0 1545989133.369 * [misc]backup-simplify: Simplify 1 into 1 1545989133.369 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989133.369 * [misc]backup-simplify: Simplify (log 1) into 0 1545989133.370 * [misc]backup-simplify: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 1545989133.370 * [misc]backup-simplify: Simplify (* 1/4 (- (log k))) into (* -1/4 (log k)) 1545989133.370 * [misc]backup-simplify: Simplify (exp (* -1/4 (log k))) into (pow k -1/4) 1545989133.370 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1545989133.370 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1545989133.370 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1545989133.370 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1545989133.370 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989133.370 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989133.370 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1545989133.370 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989133.370 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989133.370 * [misc]taylor: Taking taylor expansion of k in k 1545989133.370 * [misc]backup-simplify: Simplify 0 into 0 1545989133.370 * [misc]backup-simplify: Simplify 1 into 1 1545989133.370 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1545989133.370 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1545989133.370 * [misc]taylor: Taking taylor expansion of 2 in k 1545989133.370 * [misc]backup-simplify: Simplify 2 into 2 1545989133.370 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1545989133.370 * [misc]taylor: Taking taylor expansion of n in k 1545989133.370 * [misc]backup-simplify: Simplify n into n 1545989133.370 * [misc]taylor: Taking taylor expansion of PI in k 1545989133.370 * [misc]backup-simplify: Simplify PI into PI 1545989133.370 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1545989133.370 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1545989133.370 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1545989133.370 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1545989133.370 * [misc]backup-simplify: Simplify (- 0) into 0 1545989133.370 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545989133.371 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1545989133.371 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1545989133.371 * [misc]taylor: Taking taylor expansion of (* (pow (/ 1 k) 1/4) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 1545989133.371 * [misc]taylor: Taking taylor expansion of (pow (/ 1 k) 1/4) in n 1545989133.371 * [misc]taylor: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in n 1545989133.371 * [misc]taylor: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in n 1545989133.371 * [misc]taylor: Taking taylor expansion of 1/4 in n 1545989133.371 * [misc]backup-simplify: Simplify 1/4 into 1/4 1545989133.371 * [misc]taylor: Taking taylor expansion of (log (/ 1 k)) in n 1545989133.371 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989133.371 * [misc]taylor: Taking taylor expansion of k in n 1545989133.371 * [misc]backup-simplify: Simplify k into k 1545989133.371 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989133.371 * [misc]backup-simplify: Simplify (log (/ 1 k)) into (log (/ 1 k)) 1545989133.371 * [misc]backup-simplify: Simplify (* 1/4 (log (/ 1 k))) into (* 1/4 (log (/ 1 k))) 1545989133.371 * [misc]backup-simplify: Simplify (exp (* 1/4 (log (/ 1 k)))) into (pow (/ 1 k) 1/4) 1545989133.371 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1545989133.371 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1545989133.371 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1545989133.371 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1545989133.371 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989133.371 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989133.371 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1545989133.371 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989133.371 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989133.371 * [misc]taylor: Taking taylor expansion of k in n 1545989133.371 * [misc]backup-simplify: Simplify k into k 1545989133.371 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1545989133.371 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1545989133.371 * [misc]taylor: Taking taylor expansion of 2 in n 1545989133.371 * [misc]backup-simplify: Simplify 2 into 2 1545989133.371 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545989133.371 * [misc]taylor: Taking taylor expansion of n in n 1545989133.371 * [misc]backup-simplify: Simplify 0 into 0 1545989133.371 * [misc]backup-simplify: Simplify 1 into 1 1545989133.371 * [misc]taylor: Taking taylor expansion of PI in n 1545989133.371 * [misc]backup-simplify: Simplify PI into PI 1545989133.372 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1545989133.372 * [misc]backup-simplify: Simplify (* 2 0) into 0 1545989133.372 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1545989133.372 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1545989133.373 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545989133.373 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1545989133.373 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1545989133.373 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1545989133.373 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545989133.374 * [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)))) 1545989133.374 * [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))))) 1545989133.374 * [misc]taylor: Taking taylor expansion of (* (pow (/ 1 k) 1/4) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 1545989133.374 * [misc]taylor: Taking taylor expansion of (pow (/ 1 k) 1/4) in n 1545989133.374 * [misc]taylor: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in n 1545989133.374 * [misc]taylor: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in n 1545989133.374 * [misc]taylor: Taking taylor expansion of 1/4 in n 1545989133.374 * [misc]backup-simplify: Simplify 1/4 into 1/4 1545989133.374 * [misc]taylor: Taking taylor expansion of (log (/ 1 k)) in n 1545989133.374 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989133.374 * [misc]taylor: Taking taylor expansion of k in n 1545989133.374 * [misc]backup-simplify: Simplify k into k 1545989133.374 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989133.374 * [misc]backup-simplify: Simplify (log (/ 1 k)) into (log (/ 1 k)) 1545989133.374 * [misc]backup-simplify: Simplify (* 1/4 (log (/ 1 k))) into (* 1/4 (log (/ 1 k))) 1545989133.374 * [misc]backup-simplify: Simplify (exp (* 1/4 (log (/ 1 k)))) into (pow (/ 1 k) 1/4) 1545989133.374 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1545989133.374 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1545989133.374 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1545989133.374 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1545989133.374 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989133.374 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989133.375 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1545989133.375 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989133.375 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989133.375 * [misc]taylor: Taking taylor expansion of k in n 1545989133.375 * [misc]backup-simplify: Simplify k into k 1545989133.375 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1545989133.375 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1545989133.375 * [misc]taylor: Taking taylor expansion of 2 in n 1545989133.375 * [misc]backup-simplify: Simplify 2 into 2 1545989133.375 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545989133.375 * [misc]taylor: Taking taylor expansion of n in n 1545989133.375 * [misc]backup-simplify: Simplify 0 into 0 1545989133.375 * [misc]backup-simplify: Simplify 1 into 1 1545989133.375 * [misc]taylor: Taking taylor expansion of PI in n 1545989133.375 * [misc]backup-simplify: Simplify PI into PI 1545989133.375 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1545989133.376 * [misc]backup-simplify: Simplify (* 2 0) into 0 1545989133.376 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1545989133.376 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1545989133.377 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545989133.377 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1545989133.377 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1545989133.377 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1545989133.377 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545989133.378 * [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)))) 1545989133.378 * [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))))) 1545989133.379 * [misc]backup-simplify: Simplify (* (pow (/ 1 k) 1/4) (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (pow (/ 1 k) 1/4)) 1545989133.379 * [misc]taylor: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (pow (/ 1 k) 1/4)) in k 1545989133.379 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1545989133.379 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1545989133.379 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1545989133.379 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989133.379 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989133.379 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1545989133.379 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989133.379 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989133.379 * [misc]taylor: Taking taylor expansion of k in k 1545989133.379 * [misc]backup-simplify: Simplify 0 into 0 1545989133.379 * [misc]backup-simplify: Simplify 1 into 1 1545989133.379 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1545989133.379 * [misc]taylor: Taking taylor expansion of (log n) in k 1545989133.379 * [misc]taylor: Taking taylor expansion of n in k 1545989133.379 * [misc]backup-simplify: Simplify n into n 1545989133.379 * [misc]backup-simplify: Simplify (log n) into (log n) 1545989133.379 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1545989133.379 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1545989133.379 * [misc]taylor: Taking taylor expansion of 2 in k 1545989133.379 * [misc]backup-simplify: Simplify 2 into 2 1545989133.379 * [misc]taylor: Taking taylor expansion of PI in k 1545989133.379 * [misc]backup-simplify: Simplify PI into PI 1545989133.379 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545989133.379 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545989133.380 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1545989133.380 * [misc]backup-simplify: Simplify (- 0) into 0 1545989133.380 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545989133.380 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545989133.380 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1545989133.381 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1545989133.381 * [misc]taylor: Taking taylor expansion of (pow (/ 1 k) 1/4) in k 1545989133.381 * [misc]taylor: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k 1545989133.381 * [misc]taylor: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k 1545989133.381 * [misc]taylor: Taking taylor expansion of 1/4 in k 1545989133.381 * [misc]backup-simplify: Simplify 1/4 into 1/4 1545989133.381 * [misc]taylor: Taking taylor expansion of (log (/ 1 k)) in k 1545989133.381 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989133.381 * [misc]taylor: Taking taylor expansion of k in k 1545989133.381 * [misc]backup-simplify: Simplify 0 into 0 1545989133.381 * [misc]backup-simplify: Simplify 1 into 1 1545989133.381 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989133.381 * [misc]backup-simplify: Simplify (log 1) into 0 1545989133.381 * [misc]backup-simplify: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 1545989133.381 * [misc]backup-simplify: Simplify (* 1/4 (- (log k))) into (* -1/4 (log k)) 1545989133.381 * [misc]backup-simplify: Simplify (exp (* -1/4 (log k))) into (pow k -1/4) 1545989133.382 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k -1/4)) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (/ 1 k) 1/4)) 1545989133.382 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (/ 1 k) 1/4)) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (/ 1 k) 1/4)) 1545989133.383 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1545989133.383 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1545989133.385 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1545989133.385 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1545989133.385 * [misc]backup-simplify: Simplify (- 0) into 0 1545989133.385 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989133.386 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545989133.386 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1545989133.387 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1545989133.387 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1545989133.388 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (/ 1 k) 1)))) 1) into 0 1545989133.388 * [misc]backup-simplify: Simplify (+ (* 1/4 0) (* 0 (log (/ 1 k)))) into 0 1545989133.388 * [misc]backup-simplify: Simplify (* (exp (* 1/4 (log (/ 1 k)))) (+ (* (/ (pow 0 1) 1)))) into 0 1545989133.389 * [misc]backup-simplify: Simplify (+ (* (pow (/ 1 k) 1/4) 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))) into 0 1545989133.389 * [misc]taylor: Taking taylor expansion of 0 in k 1545989133.389 * [misc]backup-simplify: Simplify 0 into 0 1545989133.389 * [misc]backup-simplify: Simplify 0 into 0 1545989133.389 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1545989133.390 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 1545989133.391 * [misc]backup-simplify: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 1545989133.391 * [misc]backup-simplify: Simplify (+ (* 1/4 0) (* 0 (- (log k)))) into 0 1545989133.391 * [misc]backup-simplify: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 1545989133.392 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1545989133.393 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1545989133.396 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1545989133.396 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989133.396 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1545989133.396 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1545989133.396 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1545989133.397 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1545989133.399 * [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))))))) 1545989133.401 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (pow k -1/4))) into (- (+ (* 1/2 (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)) (pow (/ 1 k) 1/4))) (* 1/2 (* (* (log (* 2 PI)) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (pow (/ 1 k) 1/4))))) 1545989133.403 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)) (pow (/ 1 k) 1/4))) (* 1/2 (* (* (log (* 2 PI)) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (pow (/ 1 k) 1/4))))) into (- (+ (* 1/2 (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)) (pow (/ 1 k) 1/4))) (* 1/2 (* (* (log (* 2 PI)) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (pow (/ 1 k) 1/4))))) 1545989133.404 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1545989133.406 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1545989133.411 * [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 1545989133.412 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1545989133.412 * [misc]backup-simplify: Simplify (- 0) into 0 1545989133.412 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989133.413 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1545989133.414 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1545989133.416 * [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 1545989133.416 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545989133.418 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (/ 1 k) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (/ 1 k) 1)))) 2) into 0 1545989133.418 * [misc]backup-simplify: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (log (/ 1 k))))) into 0 1545989133.420 * [misc]backup-simplify: Simplify (* (exp (* 1/4 (log (/ 1 k)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1545989133.421 * [misc]backup-simplify: Simplify (+ (* (pow (/ 1 k) 1/4) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))))) into 0 1545989133.421 * [misc]taylor: Taking taylor expansion of 0 in k 1545989133.421 * [misc]backup-simplify: Simplify 0 into 0 1545989133.421 * [misc]backup-simplify: Simplify 0 into 0 1545989133.421 * [misc]backup-simplify: Simplify 0 into 0 1545989133.421 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989133.426 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 1545989133.426 * [misc]backup-simplify: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 1545989133.426 * [misc]backup-simplify: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (- (log k))))) into 0 1545989133.428 * [misc]backup-simplify: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1545989133.429 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1545989133.429 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1545989133.432 * [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 1545989133.432 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989133.432 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1545989133.432 * [misc]backup-simplify: Simplify (- 0) into 0 1545989133.433 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989133.433 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1545989133.434 * [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))))) 1545989133.437 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 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))))) (pow k -1/4)))) into (+ (* 1/8 (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2)) (pow (/ 1 k) 1/4))) (+ (* 1/8 (* (pow (/ 1 k) 1/4) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2)))) (* 1/4 (* (pow (/ 1 k) 1/4) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI)))))))) 1545989133.440 * [misc]backup-simplify: Simplify (+ (* 1/8 (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2)) (pow (/ 1 k) 1/4))) (+ (* 1/8 (* (pow (/ 1 k) 1/4) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2)))) (* 1/4 (* (pow (/ 1 k) 1/4) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI)))))))) into (+ (* 1/8 (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2)) (pow (/ 1 k) 1/4))) (+ (* 1/8 (* (pow (/ 1 k) 1/4) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2)))) (* 1/4 (* (pow (/ 1 k) 1/4) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI)))))))) 1545989133.445 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/8 (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2)) (pow (/ 1 k) 1/4))) (+ (* 1/8 (* (pow (/ 1 k) 1/4) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2)))) (* 1/4 (* (pow (/ 1 k) 1/4) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI)))))))) (pow (* k 1) 2)) (+ (* (- (+ (* 1/2 (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)) (pow (/ 1 k) 1/4))) (* 1/2 (* (* (log (* 2 PI)) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (pow (/ 1 k) 1/4))))) (* k 1)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (/ 1 k) 1/4)))) into (- (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (/ 1 k) 1/4)) (+ (* 1/8 (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2)) (pow (pow k 7) 1/4))) (+ (* 1/4 (* (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))) (pow (pow k 7) 1/4))) (* 1/8 (* (* (pow (log (* 2 PI)) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (pow (pow k 7) 1/4)))))) (+ (* 1/2 (* (* (log (* 2 PI)) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (pow (pow k 3) 1/4))) (* 1/2 (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)) (pow (pow k 3) 1/4))))) 1545989133.445 * [misc]backup-simplify: Simplify (/ (pow (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2))) (sqrt (sqrt (/ 1 k)))) into (* (pow k 1/4) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 1545989133.445 * [misc]approximate: Taking taylor expansion of (* (pow k 1/4) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0 1545989133.445 * [misc]taylor: Taking taylor expansion of (* (pow k 1/4) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 1545989133.445 * [misc]taylor: Taking taylor expansion of (pow k 1/4) in k 1545989133.445 * [misc]taylor: Taking taylor expansion of (exp (* 1/4 (log k))) in k 1545989133.445 * [misc]taylor: Taking taylor expansion of (* 1/4 (log k)) in k 1545989133.445 * [misc]taylor: Taking taylor expansion of 1/4 in k 1545989133.445 * [misc]backup-simplify: Simplify 1/4 into 1/4 1545989133.445 * [misc]taylor: Taking taylor expansion of (log k) in k 1545989133.445 * [misc]taylor: Taking taylor expansion of k in k 1545989133.445 * [misc]backup-simplify: Simplify 0 into 0 1545989133.445 * [misc]backup-simplify: Simplify 1 into 1 1545989133.446 * [misc]backup-simplify: Simplify (log 1) into 0 1545989133.446 * [misc]backup-simplify: Simplify (+ (* (- -1) (log k)) 0) into (log k) 1545989133.446 * [misc]backup-simplify: Simplify (* 1/4 (log k)) into (* 1/4 (log k)) 1545989133.446 * [misc]backup-simplify: Simplify (exp (* 1/4 (log k))) into (pow k 1/4) 1545989133.446 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1545989133.446 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1545989133.446 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1545989133.446 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1545989133.446 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989133.446 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989133.446 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545989133.446 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989133.446 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989133.446 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989133.446 * [misc]taylor: Taking taylor expansion of k in k 1545989133.446 * [misc]backup-simplify: Simplify 0 into 0 1545989133.446 * [misc]backup-simplify: Simplify 1 into 1 1545989133.446 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989133.446 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1545989133.446 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1545989133.446 * [misc]taylor: Taking taylor expansion of 2 in k 1545989133.446 * [misc]backup-simplify: Simplify 2 into 2 1545989133.446 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1545989133.446 * [misc]taylor: Taking taylor expansion of PI in k 1545989133.446 * [misc]backup-simplify: Simplify PI into PI 1545989133.446 * [misc]taylor: Taking taylor expansion of n in k 1545989133.446 * [misc]backup-simplify: Simplify n into n 1545989133.446 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1545989133.446 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1545989133.446 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1545989133.446 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545989133.447 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1545989133.447 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1545989133.447 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1545989133.447 * [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)))) 1545989133.447 * [misc]taylor: Taking taylor expansion of (* (pow k 1/4) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1545989133.447 * [misc]taylor: Taking taylor expansion of (pow k 1/4) in n 1545989133.447 * [misc]taylor: Taking taylor expansion of (exp (* 1/4 (log k))) in n 1545989133.447 * [misc]taylor: Taking taylor expansion of (* 1/4 (log k)) in n 1545989133.447 * [misc]taylor: Taking taylor expansion of 1/4 in n 1545989133.447 * [misc]backup-simplify: Simplify 1/4 into 1/4 1545989133.447 * [misc]taylor: Taking taylor expansion of (log k) in n 1545989133.447 * [misc]taylor: Taking taylor expansion of k in n 1545989133.447 * [misc]backup-simplify: Simplify k into k 1545989133.447 * [misc]backup-simplify: Simplify (log k) into (log k) 1545989133.447 * [misc]backup-simplify: Simplify (* 1/4 (log k)) into (* 1/4 (log k)) 1545989133.447 * [misc]backup-simplify: Simplify (exp (* 1/4 (log k))) into (pow k 1/4) 1545989133.447 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1545989133.447 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1545989133.447 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1545989133.447 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1545989133.447 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989133.447 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989133.447 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989133.447 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989133.447 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989133.447 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989133.447 * [misc]taylor: Taking taylor expansion of k in n 1545989133.447 * [misc]backup-simplify: Simplify k into k 1545989133.447 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989133.447 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1545989133.447 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1545989133.447 * [misc]taylor: Taking taylor expansion of 2 in n 1545989133.447 * [misc]backup-simplify: Simplify 2 into 2 1545989133.447 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545989133.447 * [misc]taylor: Taking taylor expansion of PI in n 1545989133.447 * [misc]backup-simplify: Simplify PI into PI 1545989133.447 * [misc]taylor: Taking taylor expansion of n in n 1545989133.447 * [misc]backup-simplify: Simplify 0 into 0 1545989133.447 * [misc]backup-simplify: Simplify 1 into 1 1545989133.448 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545989133.448 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545989133.448 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545989133.448 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989133.448 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1545989133.448 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1545989133.449 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545989133.449 * [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))) 1545989133.450 * [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)))) 1545989133.450 * [misc]taylor: Taking taylor expansion of (* (pow k 1/4) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1545989133.450 * [misc]taylor: Taking taylor expansion of (pow k 1/4) in n 1545989133.450 * [misc]taylor: Taking taylor expansion of (exp (* 1/4 (log k))) in n 1545989133.450 * [misc]taylor: Taking taylor expansion of (* 1/4 (log k)) in n 1545989133.450 * [misc]taylor: Taking taylor expansion of 1/4 in n 1545989133.450 * [misc]backup-simplify: Simplify 1/4 into 1/4 1545989133.450 * [misc]taylor: Taking taylor expansion of (log k) in n 1545989133.450 * [misc]taylor: Taking taylor expansion of k in n 1545989133.450 * [misc]backup-simplify: Simplify k into k 1545989133.450 * [misc]backup-simplify: Simplify (log k) into (log k) 1545989133.450 * [misc]backup-simplify: Simplify (* 1/4 (log k)) into (* 1/4 (log k)) 1545989133.450 * [misc]backup-simplify: Simplify (exp (* 1/4 (log k))) into (pow k 1/4) 1545989133.450 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1545989133.450 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1545989133.450 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1545989133.450 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1545989133.450 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989133.450 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989133.450 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989133.450 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989133.450 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989133.450 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989133.450 * [misc]taylor: Taking taylor expansion of k in n 1545989133.450 * [misc]backup-simplify: Simplify k into k 1545989133.450 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989133.450 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1545989133.450 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1545989133.450 * [misc]taylor: Taking taylor expansion of 2 in n 1545989133.450 * [misc]backup-simplify: Simplify 2 into 2 1545989133.450 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545989133.450 * [misc]taylor: Taking taylor expansion of PI in n 1545989133.450 * [misc]backup-simplify: Simplify PI into PI 1545989133.450 * [misc]taylor: Taking taylor expansion of n in n 1545989133.450 * [misc]backup-simplify: Simplify 0 into 0 1545989133.450 * [misc]backup-simplify: Simplify 1 into 1 1545989133.450 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545989133.451 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545989133.451 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545989133.451 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989133.451 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1545989133.451 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1545989133.452 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545989133.452 * [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))) 1545989133.452 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 1545989133.453 * [misc]backup-simplify: Simplify (* (pow k 1/4) (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)))) (pow k 1/4)) 1545989133.453 * [misc]taylor: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (pow k 1/4)) in k 1545989133.453 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1545989133.453 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1545989133.453 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1545989133.453 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989133.453 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989133.453 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545989133.453 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989133.453 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989133.453 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989133.453 * [misc]taylor: Taking taylor expansion of k in k 1545989133.453 * [misc]backup-simplify: Simplify 0 into 0 1545989133.453 * [misc]backup-simplify: Simplify 1 into 1 1545989133.453 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989133.453 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1545989133.453 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1545989133.453 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1545989133.453 * [misc]taylor: Taking taylor expansion of 2 in k 1545989133.453 * [misc]backup-simplify: Simplify 2 into 2 1545989133.453 * [misc]taylor: Taking taylor expansion of PI in k 1545989133.453 * [misc]backup-simplify: Simplify PI into PI 1545989133.453 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1545989133.454 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1545989133.454 * [misc]taylor: Taking taylor expansion of (log n) in k 1545989133.454 * [misc]taylor: Taking taylor expansion of n in k 1545989133.454 * [misc]backup-simplify: Simplify n into n 1545989133.454 * [misc]backup-simplify: Simplify (log n) into (log n) 1545989133.454 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545989133.454 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1545989133.454 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1545989133.454 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1545989133.454 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1545989133.455 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1545989133.455 * [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)))) 1545989133.455 * [misc]taylor: Taking taylor expansion of (pow k 1/4) in k 1545989133.455 * [misc]taylor: Taking taylor expansion of (exp (* 1/4 (log k))) in k 1545989133.455 * [misc]taylor: Taking taylor expansion of (* 1/4 (log k)) in k 1545989133.455 * [misc]taylor: Taking taylor expansion of 1/4 in k 1545989133.455 * [misc]backup-simplify: Simplify 1/4 into 1/4 1545989133.455 * [misc]taylor: Taking taylor expansion of (log k) in k 1545989133.455 * [misc]taylor: Taking taylor expansion of k in k 1545989133.455 * [misc]backup-simplify: Simplify 0 into 0 1545989133.455 * [misc]backup-simplify: Simplify 1 into 1 1545989133.455 * [misc]backup-simplify: Simplify (log 1) into 0 1545989133.456 * [misc]backup-simplify: Simplify (+ (* (- -1) (log k)) 0) into (log k) 1545989133.456 * [misc]backup-simplify: Simplify (* 1/4 (log k)) into (* 1/4 (log k)) 1545989133.456 * [misc]backup-simplify: Simplify (exp (* 1/4 (log k))) into (pow k 1/4) 1545989133.456 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (pow k 1/4)) into (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (pow k 1/4)) 1545989133.456 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (pow k 1/4)) into (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (pow k 1/4)) 1545989133.457 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1545989133.458 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1545989133.459 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1545989133.459 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1545989133.460 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1545989133.460 * [misc]backup-simplify: Simplify (- 0) into 0 1545989133.460 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989133.460 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545989133.461 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1545989133.462 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1545989133.462 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow k 1)))) 1) into 0 1545989133.462 * [misc]backup-simplify: Simplify (+ (* 1/4 0) (* 0 (log k))) into 0 1545989133.463 * [misc]backup-simplify: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 1545989133.463 * [misc]backup-simplify: Simplify (+ (* (pow k 1/4) 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0 1545989133.463 * [misc]taylor: Taking taylor expansion of 0 in k 1545989133.463 * [misc]backup-simplify: Simplify 0 into 0 1545989133.463 * [misc]backup-simplify: Simplify 0 into 0 1545989133.465 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 1545989133.465 * [misc]backup-simplify: Simplify (+ (* (- -1) (log k)) 0) into (log k) 1545989133.465 * [misc]backup-simplify: Simplify (+ (* 1/4 0) (* 0 (log k))) into 0 1545989133.466 * [misc]backup-simplify: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 1545989133.466 * [misc]backup-simplify: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) (* 0 (pow k 1/4))) into 0 1545989133.466 * [misc]backup-simplify: Simplify 0 into 0 1545989133.467 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989133.468 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1545989133.471 * [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 1545989133.471 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545989133.471 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1545989133.471 * [misc]backup-simplify: Simplify (- 0) into 0 1545989133.471 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989133.472 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545989133.472 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1545989133.474 * [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 1545989133.475 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow k 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow k 1)))) 2) into 0 1545989133.475 * [misc]backup-simplify: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (log k)))) into 0 1545989133.476 * [misc]backup-simplify: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1545989133.476 * [misc]backup-simplify: Simplify (+ (* (pow k 1/4) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0 1545989133.476 * [misc]taylor: Taking taylor expansion of 0 in k 1545989133.476 * [misc]backup-simplify: Simplify 0 into 0 1545989133.477 * [misc]backup-simplify: Simplify 0 into 0 1545989133.477 * [misc]backup-simplify: Simplify 0 into 0 1545989133.479 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 1545989133.479 * [misc]backup-simplify: Simplify (+ (* (- -1) (log k)) 0) into (log k) 1545989133.480 * [misc]backup-simplify: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (log k)))) into 0 1545989133.481 * [misc]backup-simplify: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1545989133.482 * [misc]backup-simplify: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) (+ (* 0 0) (* 0 (pow k 1/4)))) into 0 1545989133.482 * [misc]backup-simplify: Simplify 0 into 0 1545989133.484 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989133.486 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1545989133.494 * [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 1545989133.494 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545989133.495 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1545989133.495 * [misc]backup-simplify: Simplify (- 0) into 0 1545989133.495 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989133.497 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1545989133.498 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1545989133.502 * [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 1545989133.504 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow k 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow k 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow k 1)))) 6) into 0 1545989133.505 * [misc]backup-simplify: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k))))) into 0 1545989133.508 * [misc]backup-simplify: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1545989133.509 * [misc]backup-simplify: Simplify (+ (* (pow k 1/4) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))) into 0 1545989133.509 * [misc]taylor: Taking taylor expansion of 0 in k 1545989133.509 * [misc]backup-simplify: Simplify 0 into 0 1545989133.509 * [misc]backup-simplify: Simplify 0 into 0 1545989133.510 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))) (pow (/ 1 k) 1/4)) into (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow (/ 1 k) 1/4)) 1545989133.511 * [misc]backup-simplify: Simplify (/ (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (sqrt (/ 1 (- k))))) into (* (sqrt (/ 1 (sqrt (/ -1 k)))) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) 1545989133.511 * [misc]approximate: Taking taylor expansion of (* (sqrt (/ 1 (sqrt (/ -1 k)))) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in (n k) around 0 1545989133.511 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 (sqrt (/ -1 k)))) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in k 1545989133.511 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in k 1545989133.511 * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 1545989133.511 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1545989133.511 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1545989133.511 * [misc]taylor: Taking taylor expansion of -1 in k 1545989133.511 * [misc]backup-simplify: Simplify -1 into -1 1545989133.511 * [misc]taylor: Taking taylor expansion of k in k 1545989133.511 * [misc]backup-simplify: Simplify 0 into 0 1545989133.511 * [misc]backup-simplify: Simplify 1 into 1 1545989133.511 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1545989133.511 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545989133.512 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1545989133.512 * [misc]backup-simplify: Simplify (/ 1 +nan.0) into +nan.0 1545989133.512 * [misc]backup-simplify: Simplify (sqrt +nan.0) into (sqrt +nan.0) 1545989133.513 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1545989133.514 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1545989133.515 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 1545989133.515 * [misc]backup-simplify: Simplify (/ (- +nan.0) (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0)) 1545989133.515 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1545989133.516 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1545989133.516 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1545989133.516 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1545989133.516 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545989133.516 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989133.516 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989133.516 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989133.516 * [misc]taylor: Taking taylor expansion of k in k 1545989133.516 * [misc]backup-simplify: Simplify 0 into 0 1545989133.516 * [misc]backup-simplify: Simplify 1 into 1 1545989133.516 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989133.516 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989133.516 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989133.516 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1545989133.516 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1545989133.516 * [misc]taylor: Taking taylor expansion of -2 in k 1545989133.516 * [misc]backup-simplify: Simplify -2 into -2 1545989133.516 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1545989133.516 * [misc]taylor: Taking taylor expansion of PI in k 1545989133.516 * [misc]backup-simplify: Simplify PI into PI 1545989133.516 * [misc]taylor: Taking taylor expansion of n in k 1545989133.516 * [misc]backup-simplify: Simplify n into n 1545989133.516 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1545989133.516 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1545989133.517 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1545989133.517 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545989133.517 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545989133.517 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1545989133.517 * [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))) 1545989133.517 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 (sqrt (/ -1 k)))) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1545989133.517 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in n 1545989133.517 * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in n 1545989133.518 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1545989133.518 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1545989133.518 * [misc]taylor: Taking taylor expansion of -1 in n 1545989133.518 * [misc]backup-simplify: Simplify -1 into -1 1545989133.518 * [misc]taylor: Taking taylor expansion of k in n 1545989133.518 * [misc]backup-simplify: Simplify k into k 1545989133.518 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1545989133.518 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1545989133.518 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1545989133.518 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1545989133.518 * [misc]backup-simplify: Simplify (/ 1 (sqrt (/ -1 k))) into (/ 1 (sqrt (/ -1 k))) 1545989133.518 * [misc]backup-simplify: Simplify (sqrt (/ 1 (sqrt (/ -1 k)))) into (sqrt (/ 1 (sqrt (/ -1 k)))) 1545989133.518 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0 1545989133.519 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 (sqrt (/ -1 k)))))) into 0 1545989133.519 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1545989133.519 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1545989133.519 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1545989133.519 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1545989133.519 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989133.519 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989133.519 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989133.519 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989133.519 * [misc]taylor: Taking taylor expansion of k in n 1545989133.519 * [misc]backup-simplify: Simplify k into k 1545989133.519 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989133.519 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989133.519 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989133.519 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1545989133.519 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1545989133.519 * [misc]taylor: Taking taylor expansion of -2 in n 1545989133.519 * [misc]backup-simplify: Simplify -2 into -2 1545989133.519 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545989133.519 * [misc]taylor: Taking taylor expansion of PI in n 1545989133.519 * [misc]backup-simplify: Simplify PI into PI 1545989133.519 * [misc]taylor: Taking taylor expansion of n in n 1545989133.519 * [misc]backup-simplify: Simplify 0 into 0 1545989133.519 * [misc]backup-simplify: Simplify 1 into 1 1545989133.520 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545989133.520 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1545989133.520 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1545989133.520 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989133.521 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1545989133.521 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545989133.522 * [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))) 1545989133.522 * [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)))) 1545989133.522 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 (sqrt (/ -1 k)))) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1545989133.523 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in n 1545989133.523 * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in n 1545989133.523 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1545989133.523 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1545989133.523 * [misc]taylor: Taking taylor expansion of -1 in n 1545989133.523 * [misc]backup-simplify: Simplify -1 into -1 1545989133.523 * [misc]taylor: Taking taylor expansion of k in n 1545989133.523 * [misc]backup-simplify: Simplify k into k 1545989133.523 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1545989133.523 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1545989133.523 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1545989133.523 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1545989133.523 * [misc]backup-simplify: Simplify (/ 1 (sqrt (/ -1 k))) into (/ 1 (sqrt (/ -1 k))) 1545989133.523 * [misc]backup-simplify: Simplify (sqrt (/ 1 (sqrt (/ -1 k)))) into (sqrt (/ 1 (sqrt (/ -1 k)))) 1545989133.523 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0 1545989133.524 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 (sqrt (/ -1 k)))))) into 0 1545989133.524 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1545989133.524 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1545989133.524 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1545989133.524 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1545989133.524 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989133.524 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989133.524 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989133.524 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989133.524 * [misc]taylor: Taking taylor expansion of k in n 1545989133.524 * [misc]backup-simplify: Simplify k into k 1545989133.524 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989133.524 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989133.524 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989133.524 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1545989133.524 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1545989133.524 * [misc]taylor: Taking taylor expansion of -2 in n 1545989133.524 * [misc]backup-simplify: Simplify -2 into -2 1545989133.524 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1545989133.524 * [misc]taylor: Taking taylor expansion of PI in n 1545989133.524 * [misc]backup-simplify: Simplify PI into PI 1545989133.524 * [misc]taylor: Taking taylor expansion of n in n 1545989133.524 * [misc]backup-simplify: Simplify 0 into 0 1545989133.524 * [misc]backup-simplify: Simplify 1 into 1 1545989133.525 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1545989133.525 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1545989133.525 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1545989133.525 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989133.525 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1545989133.526 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545989133.527 * [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))) 1545989133.527 * [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)))) 1545989133.528 * [misc]backup-simplify: Simplify (* (sqrt (/ 1 (sqrt (/ -1 k)))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (* (sqrt (/ 1 (sqrt (/ -1 k)))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 1545989133.528 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 (sqrt (/ -1 k)))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) in k 1545989133.528 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in k 1545989133.528 * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 1545989133.528 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1545989133.528 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1545989133.528 * [misc]taylor: Taking taylor expansion of -1 in k 1545989133.528 * [misc]backup-simplify: Simplify -1 into -1 1545989133.528 * [misc]taylor: Taking taylor expansion of k in k 1545989133.529 * [misc]backup-simplify: Simplify 0 into 0 1545989133.529 * [misc]backup-simplify: Simplify 1 into 1 1545989133.529 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1545989133.529 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545989133.529 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1545989133.529 * [misc]backup-simplify: Simplify (/ 1 +nan.0) into +nan.0 1545989133.530 * [misc]backup-simplify: Simplify (sqrt +nan.0) into (sqrt +nan.0) 1545989133.530 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1545989133.531 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1545989133.532 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 1545989133.532 * [misc]backup-simplify: Simplify (/ (- +nan.0) (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0)) 1545989133.532 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1545989133.533 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1545989133.533 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1545989133.533 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545989133.533 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989133.533 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989133.533 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989133.533 * [misc]taylor: Taking taylor expansion of k in k 1545989133.533 * [misc]backup-simplify: Simplify 0 into 0 1545989133.533 * [misc]backup-simplify: Simplify 1 into 1 1545989133.533 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989133.533 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989133.533 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989133.533 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1545989133.533 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1545989133.533 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1545989133.533 * [misc]taylor: Taking taylor expansion of -2 in k 1545989133.533 * [misc]backup-simplify: Simplify -2 into -2 1545989133.533 * [misc]taylor: Taking taylor expansion of PI in k 1545989133.533 * [misc]backup-simplify: Simplify PI into PI 1545989133.533 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1545989133.534 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1545989133.534 * [misc]taylor: Taking taylor expansion of (log n) in k 1545989133.534 * [misc]taylor: Taking taylor expansion of n in k 1545989133.534 * [misc]backup-simplify: Simplify n into n 1545989133.534 * [misc]backup-simplify: Simplify (log n) into (log n) 1545989133.534 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545989133.534 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545989133.535 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1545989133.535 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1545989133.536 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1545989133.536 * [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)))) 1545989133.537 * [misc]backup-simplify: Simplify (* (sqrt +nan.0) (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)))) (sqrt +nan.0)) 1545989133.538 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt +nan.0)) into (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt +nan.0)) 1545989133.539 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1545989133.540 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1545989133.542 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1545989133.543 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1545989133.543 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1545989133.543 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989133.544 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545989133.544 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1545989133.546 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1545989133.547 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 (sqrt (/ -1 k)))) 0) (* 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into 0 1545989133.547 * [misc]taylor: Taking taylor expansion of 0 in k 1545989133.547 * [misc]backup-simplify: Simplify 0 into 0 1545989133.547 * [misc]backup-simplify: Simplify 0 into 0 1545989133.548 * [misc]backup-simplify: Simplify (+ (* (sqrt +nan.0) 0) (* (/ +nan.0 (sqrt +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)))) (sqrt +nan.0)))) 1545989133.549 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt +nan.0)))) into (- (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt +nan.0)))) 1545989133.550 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989133.552 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1545989133.557 * [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 1545989133.557 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545989133.557 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1545989133.557 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989133.558 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1545989133.559 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1545989133.561 * [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 1545989133.561 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545989133.562 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 1545989133.562 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0 1545989133.564 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 (sqrt (/ -1 k)))))) into 0 1545989133.565 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 (sqrt (/ -1 k)))) 0) (+ (* 0 0) (* 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) into 0 1545989133.565 * [misc]taylor: Taking taylor expansion of 0 in k 1545989133.565 * [misc]backup-simplify: Simplify 0 into 0 1545989133.565 * [misc]backup-simplify: Simplify 0 into 0 1545989133.565 * [misc]backup-simplify: Simplify 0 into 0 1545989133.565 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989133.567 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1545989133.568 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 1545989133.570 * [misc]backup-simplify: Simplify (/ (- (- +nan.0) (pow (/ +nan.0 (sqrt +nan.0)) 2) (+)) (* 2 (sqrt +nan.0))) into (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0))) 1545989133.573 * [misc]backup-simplify: Simplify (+ (* (sqrt +nan.0) 0) (+ (* (/ +nan.0 (sqrt +nan.0)) 0) (* (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +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)))) (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt +nan.0)))))) 1545989133.576 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt +nan.0)))))) into (- (+ (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt +nan.0)))))) 1545989133.580 * [misc]backup-simplify: Simplify (+ (* (- (+ (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) (sqrt +nan.0)))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) (sqrt +nan.0)))) (* (/ 1 (- k)) 1)) (* (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) (sqrt +nan.0)))) into (- (* (sqrt +nan.0) (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))) (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (* (sqrt +nan.0) k))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (* (pow (sqrt +nan.0) 3) (pow k 2)))) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (* (sqrt +nan.0) (pow k 2))))))))) 1545989133.580 * * * * [misc]progress: [ 4 / 4 ] generating series at (2 2) 1545989133.581 * [misc]backup-simplify: Simplify (sqrt (sqrt k)) into (pow k 1/4) 1545989133.581 * [misc]approximate: Taking taylor expansion of (pow k 1/4) in (k) around 0 1545989133.581 * [misc]taylor: Taking taylor expansion of (pow k 1/4) in k 1545989133.581 * [misc]taylor: Taking taylor expansion of (exp (* 1/4 (log k))) in k 1545989133.581 * [misc]taylor: Taking taylor expansion of (* 1/4 (log k)) in k 1545989133.581 * [misc]taylor: Taking taylor expansion of 1/4 in k 1545989133.581 * [misc]backup-simplify: Simplify 1/4 into 1/4 1545989133.581 * [misc]taylor: Taking taylor expansion of (log k) in k 1545989133.581 * [misc]taylor: Taking taylor expansion of k in k 1545989133.581 * [misc]backup-simplify: Simplify 0 into 0 1545989133.581 * [misc]backup-simplify: Simplify 1 into 1 1545989133.581 * [misc]backup-simplify: Simplify (log 1) into 0 1545989133.581 * [misc]backup-simplify: Simplify (+ (* (- -1) (log k)) 0) into (log k) 1545989133.581 * [misc]backup-simplify: Simplify (* 1/4 (log k)) into (* 1/4 (log k)) 1545989133.581 * [misc]backup-simplify: Simplify (exp (* 1/4 (log k))) into (pow k 1/4) 1545989133.581 * [misc]taylor: Taking taylor expansion of (pow k 1/4) in k 1545989133.581 * [misc]taylor: Taking taylor expansion of (exp (* 1/4 (log k))) in k 1545989133.581 * [misc]taylor: Taking taylor expansion of (* 1/4 (log k)) in k 1545989133.581 * [misc]taylor: Taking taylor expansion of 1/4 in k 1545989133.582 * [misc]backup-simplify: Simplify 1/4 into 1/4 1545989133.582 * [misc]taylor: Taking taylor expansion of (log k) in k 1545989133.582 * [misc]taylor: Taking taylor expansion of k in k 1545989133.582 * [misc]backup-simplify: Simplify 0 into 0 1545989133.582 * [misc]backup-simplify: Simplify 1 into 1 1545989133.582 * [misc]backup-simplify: Simplify (log 1) into 0 1545989133.582 * [misc]backup-simplify: Simplify (+ (* (- -1) (log k)) 0) into (log k) 1545989133.582 * [misc]backup-simplify: Simplify (* 1/4 (log k)) into (* 1/4 (log k)) 1545989133.582 * [misc]backup-simplify: Simplify (exp (* 1/4 (log k))) into (pow k 1/4) 1545989133.582 * [misc]backup-simplify: Simplify (pow k 1/4) into (pow k 1/4) 1545989133.585 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 1545989133.585 * [misc]backup-simplify: Simplify (+ (* (- -1) (log k)) 0) into (log k) 1545989133.585 * [misc]backup-simplify: Simplify (+ (* 1/4 0) (* 0 (log k))) into 0 1545989133.586 * [misc]backup-simplify: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 1545989133.586 * [misc]backup-simplify: Simplify 0 into 0 1545989133.591 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 1545989133.591 * [misc]backup-simplify: Simplify (+ (* (- -1) (log k)) 0) into (log k) 1545989133.591 * [misc]backup-simplify: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (log k)))) into 0 1545989133.593 * [misc]backup-simplify: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1545989133.593 * [misc]backup-simplify: Simplify 0 into 0 1545989133.600 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 1545989133.601 * [misc]backup-simplify: Simplify (+ (* (- -1) (log k)) 0) into (log k) 1545989133.601 * [misc]backup-simplify: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k))))) into 0 1545989133.604 * [misc]backup-simplify: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1545989133.604 * [misc]backup-simplify: Simplify 0 into 0 1545989133.616 * [misc]backup-simplify: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 1545989133.617 * [misc]backup-simplify: Simplify (+ (* (- -1) (log k)) 0) into (log k) 1545989133.617 * [misc]backup-simplify: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k)))))) into 0 1545989133.622 * [misc]backup-simplify: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1545989133.623 * [misc]backup-simplify: Simplify 0 into 0 1545989133.636 * [misc]backup-simplify: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 1545989133.636 * [misc]backup-simplify: Simplify (+ (* (- -1) (log k)) 0) into (log k) 1545989133.637 * [misc]backup-simplify: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k))))))) into 0 1545989133.642 * [misc]backup-simplify: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1545989133.642 * [misc]backup-simplify: Simplify 0 into 0 1545989133.657 * [misc]backup-simplify: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 1545989133.658 * [misc]backup-simplify: Simplify (+ (* (- -1) (log k)) 0) into (log k) 1545989133.658 * [misc]backup-simplify: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k)))))))) into 0 1545989133.671 * [misc]backup-simplify: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1545989133.671 * [misc]backup-simplify: Simplify 0 into 0 1545989133.671 * [misc]backup-simplify: Simplify (pow k 1/4) into (pow k 1/4) 1545989133.671 * [misc]backup-simplify: Simplify (sqrt (sqrt (/ 1 k))) into (pow (/ 1 k) 1/4) 1545989133.671 * [misc]approximate: Taking taylor expansion of (pow (/ 1 k) 1/4) in (k) around 0 1545989133.671 * [misc]taylor: Taking taylor expansion of (pow (/ 1 k) 1/4) in k 1545989133.671 * [misc]taylor: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k 1545989133.671 * [misc]taylor: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k 1545989133.671 * [misc]taylor: Taking taylor expansion of 1/4 in k 1545989133.671 * [misc]backup-simplify: Simplify 1/4 into 1/4 1545989133.671 * [misc]taylor: Taking taylor expansion of (log (/ 1 k)) in k 1545989133.671 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989133.671 * [misc]taylor: Taking taylor expansion of k in k 1545989133.671 * [misc]backup-simplify: Simplify 0 into 0 1545989133.671 * [misc]backup-simplify: Simplify 1 into 1 1545989133.672 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989133.672 * [misc]backup-simplify: Simplify (log 1) into 0 1545989133.672 * [misc]backup-simplify: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 1545989133.672 * [misc]backup-simplify: Simplify (* 1/4 (- (log k))) into (* -1/4 (log k)) 1545989133.672 * [misc]backup-simplify: Simplify (exp (* -1/4 (log k))) into (pow k -1/4) 1545989133.672 * [misc]taylor: Taking taylor expansion of (pow (/ 1 k) 1/4) in k 1545989133.672 * [misc]taylor: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k 1545989133.672 * [misc]taylor: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k 1545989133.672 * [misc]taylor: Taking taylor expansion of 1/4 in k 1545989133.672 * [misc]backup-simplify: Simplify 1/4 into 1/4 1545989133.672 * [misc]taylor: Taking taylor expansion of (log (/ 1 k)) in k 1545989133.672 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989133.672 * [misc]taylor: Taking taylor expansion of k in k 1545989133.672 * [misc]backup-simplify: Simplify 0 into 0 1545989133.672 * [misc]backup-simplify: Simplify 1 into 1 1545989133.673 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989133.673 * [misc]backup-simplify: Simplify (log 1) into 0 1545989133.673 * [misc]backup-simplify: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 1545989133.673 * [misc]backup-simplify: Simplify (* 1/4 (- (log k))) into (* -1/4 (log k)) 1545989133.673 * [misc]backup-simplify: Simplify (exp (* -1/4 (log k))) into (pow k -1/4) 1545989133.673 * [misc]backup-simplify: Simplify (pow k -1/4) into (pow k -1/4) 1545989133.673 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1545989133.676 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 1545989133.676 * [misc]backup-simplify: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 1545989133.676 * [misc]backup-simplify: Simplify (+ (* 1/4 0) (* 0 (- (log k)))) into 0 1545989133.677 * [misc]backup-simplify: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 1545989133.677 * [misc]backup-simplify: Simplify 0 into 0 1545989133.678 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989133.682 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 1545989133.682 * [misc]backup-simplify: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 1545989133.683 * [misc]backup-simplify: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (- (log k))))) into 0 1545989133.684 * [misc]backup-simplify: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1545989133.684 * [misc]backup-simplify: Simplify 0 into 0 1545989133.684 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989133.688 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 1545989133.688 * [misc]backup-simplify: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 1545989133.689 * [misc]backup-simplify: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k)))))) into 0 1545989133.691 * [misc]backup-simplify: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1545989133.691 * [misc]backup-simplify: Simplify 0 into 0 1545989133.691 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989133.697 * [misc]backup-simplify: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 1545989133.698 * [misc]backup-simplify: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 1545989133.698 * [misc]backup-simplify: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k))))))) into 0 1545989133.701 * [misc]backup-simplify: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1545989133.701 * [misc]backup-simplify: Simplify 0 into 0 1545989133.702 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989133.712 * [misc]backup-simplify: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 1545989133.712 * [misc]backup-simplify: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 1545989133.712 * [misc]backup-simplify: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k)))))))) into 0 1545989133.718 * [misc]backup-simplify: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1545989133.718 * [misc]backup-simplify: Simplify 0 into 0 1545989133.718 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989133.733 * [misc]backup-simplify: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 1545989133.733 * [misc]backup-simplify: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 1545989133.734 * [misc]backup-simplify: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k))))))))) into 0 1545989133.741 * [misc]backup-simplify: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1545989133.742 * [misc]backup-simplify: Simplify 0 into 0 1545989133.743 * [misc]backup-simplify: Simplify (pow (/ 1 k) -1/4) into (pow (/ 1 k) -1/4) 1545989133.743 * [misc]backup-simplify: Simplify (sqrt (sqrt (/ 1 (- k)))) into (sqrt (sqrt (/ -1 k))) 1545989133.743 * [misc]approximate: Taking taylor expansion of (sqrt (sqrt (/ -1 k))) in (k) around 0 1545989133.743 * [misc]taylor: Taking taylor expansion of (sqrt (sqrt (/ -1 k))) in k 1545989133.743 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1545989133.743 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1545989133.743 * [misc]taylor: Taking taylor expansion of -1 in k 1545989133.743 * [misc]backup-simplify: Simplify -1 into -1 1545989133.743 * [misc]taylor: Taking taylor expansion of k in k 1545989133.743 * [misc]backup-simplify: Simplify 0 into 0 1545989133.743 * [misc]backup-simplify: Simplify 1 into 1 1545989133.743 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1545989133.743 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545989133.744 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1545989133.744 * [misc]backup-simplify: Simplify (sqrt +nan.0) into (sqrt +nan.0) 1545989133.744 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1545989133.744 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1545989133.745 * [misc]backup-simplify: Simplify (/ +nan.0 (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0)) 1545989133.745 * [misc]taylor: Taking taylor expansion of (sqrt (sqrt (/ -1 k))) in k 1545989133.745 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1545989133.745 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1545989133.745 * [misc]taylor: Taking taylor expansion of -1 in k 1545989133.745 * [misc]backup-simplify: Simplify -1 into -1 1545989133.745 * [misc]taylor: Taking taylor expansion of k in k 1545989133.745 * [misc]backup-simplify: Simplify 0 into 0 1545989133.745 * [misc]backup-simplify: Simplify 1 into 1 1545989133.745 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1545989133.745 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545989133.745 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1545989133.746 * [misc]backup-simplify: Simplify (sqrt +nan.0) into (sqrt +nan.0) 1545989133.746 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1545989133.747 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1545989133.747 * [misc]backup-simplify: Simplify (/ +nan.0 (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0)) 1545989133.748 * [misc]backup-simplify: Simplify (sqrt +nan.0) into (sqrt +nan.0) 1545989133.748 * [misc]backup-simplify: Simplify (/ +nan.0 (sqrt +nan.0)) into (/ +nan.0 (sqrt +nan.0)) 1545989133.748 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989133.749 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1545989133.750 * [misc]backup-simplify: Simplify (/ (- +nan.0 (pow (/ +nan.0 (sqrt +nan.0)) 2) (+)) (* 2 (sqrt +nan.0))) into (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0))) 1545989133.751 * [misc]backup-simplify: Simplify (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0))) into (* 1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0))) 1545989133.754 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0))) (pow (/ 1 (- k)) 2)) (+ (* (/ +nan.0 (sqrt +nan.0)) (/ 1 (- k))) (sqrt +nan.0))) into (- (sqrt +nan.0) (+ (* +nan.0 (/ 1 (* (sqrt +nan.0) k))) (- (+ (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 3) (pow k 2)))) (- (* +nan.0 (/ 1 (* (sqrt +nan.0) (pow k 2))))))))) 1545989133.754 * * * [misc]progress: simplifying candidates 1545989133.754 * * * * [misc]progress: [ 1 / 113 ] simplifiying candidate # 1545989133.754 * [enter]simplify: Simplifying (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) 1545989133.754 * * [misc]simplify: iters left: 6 (11 enodes) 1545989133.756 * * [misc]simplify: iters left: 5 (21 enodes) 1545989133.759 * * [misc]simplify: iters left: 4 (47 enodes) 1545989133.768 * * [misc]simplify: iters left: 3 (109 enodes) 1545989133.806 * * [misc]simplify: iters left: 2 (300 enodes) 1545989134.088 * [exit]simplify: Simplified to (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) 1545989134.088 * [misc]simplify: Simplified (2 1 1 1) to (λ (k n) (/ (/ (exp (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI)))) (sqrt (sqrt k))) (sqrt (sqrt k)))) 1545989134.088 * * * * [misc]progress: [ 2 / 113 ] simplifiying candidate # 1545989134.088 * * * * [misc]progress: [ 3 / 113 ] simplifiying candidate # 1545989134.089 * [enter]simplify: Simplifying (* PI (* n 2)) 1545989134.089 * * [misc]simplify: iters left: 4 (5 enodes) 1545989134.094 * * [misc]simplify: iters left: 3 (9 enodes) 1545989134.096 * * [misc]simplify: iters left: 2 (15 enodes) 1545989134.100 * * [misc]simplify: iters left: 1 (17 enodes) 1545989134.104 * [exit]simplify: Simplified to (* (* 2 n) PI) 1545989134.105 * [misc]simplify: Simplified (2 1 1 1) to (λ (k n) (/ (/ (pow (* (* 2 n) PI) (* 1 (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (sqrt (sqrt k)))) 1545989134.105 * * * * [misc]progress: [ 4 / 113 ] simplifiying candidate # 1545989134.105 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (/ k 2)) 1545989134.105 * * [misc]simplify: iters left: 5 (8 enodes) 1545989134.108 * * [misc]simplify: iters left: 4 (12 enodes) 1545989134.111 * * [misc]simplify: iters left: 3 (18 enodes) 1545989134.116 * * [misc]simplify: iters left: 2 (20 enodes) 1545989134.121 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ k 2)) 1545989134.121 * [misc]simplify: Simplified (2 1 1 2) to (λ (k n) (/ (/ (/ (pow (* PI (* n 2)) 1/2) (pow (* (* 2 n) PI) (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k)))) 1545989134.121 * * * * [misc]progress: [ 5 / 113 ] simplifiying candidate # 1545989134.121 * [enter]simplify: Simplifying (cbrt (- 1/2 (/ k 2))) 1545989134.121 * * [misc]simplify: iters left: 5 (6 enodes) 1545989134.123 * * [misc]simplify: iters left: 4 (8 enodes) 1545989134.125 * * [misc]simplify: iters left: 3 (11 enodes) 1545989134.128 * [exit]simplify: Simplified to (cbrt (- 1/2 (/ k 2))) 1545989134.128 * [misc]simplify: Simplified (2 1 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 (sqrt k))) (sqrt (sqrt k)))) 1545989134.128 * * * * [misc]progress: [ 6 / 113 ] simplifiying candidate # 1545989134.129 * [enter]simplify: Simplifying (sqrt (- 1/2 (/ k 2))) 1545989134.129 * * [misc]simplify: iters left: 5 (6 enodes) 1545989134.130 * * [misc]simplify: iters left: 4 (8 enodes) 1545989134.133 * * [misc]simplify: iters left: 3 (11 enodes) 1545989134.136 * [exit]simplify: Simplified to (sqrt (- 1/2 (/ k 2))) 1545989134.136 * [misc]simplify: Simplified (2 1 1 2) to (λ (k n) (/ (/ (pow (pow (* PI (* n 2)) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (sqrt (sqrt k)))) 1545989134.136 * * * * [misc]progress: [ 7 / 113 ] simplifiying candidate # 1545989134.136 * [enter]simplify: Simplifying (- 1/2 (/ k 2)) 1545989134.136 * * [misc]simplify: iters left: 4 (5 enodes) 1545989134.137 * * [misc]simplify: iters left: 3 (7 enodes) 1545989134.139 * * [misc]simplify: iters left: 2 (10 enodes) 1545989134.142 * [exit]simplify: Simplified to (- 1/2 (/ k 2)) 1545989134.142 * [misc]simplify: Simplified (2 1 1 2) to (λ (k n) (/ (/ (pow (pow (* PI (* n 2)) 1) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k)))) 1545989134.142 * * * * [misc]progress: [ 8 / 113 ] simplifiying candidate # 1545989134.143 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1545989134.143 * * [misc]simplify: iters left: 5 (9 enodes) 1545989134.145 * * [misc]simplify: iters left: 4 (15 enodes) 1545989134.150 * * [misc]simplify: iters left: 3 (21 enodes) 1545989134.155 * * [misc]simplify: iters left: 2 (22 enodes) 1545989134.160 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1545989134.160 * [misc]simplify: Simplified (2 1 1 2) to (λ (k n) (/ (/ (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2)))) (sqrt (sqrt k))) (sqrt (sqrt k)))) 1545989134.161 * * * * [misc]progress: [ 9 / 113 ] simplifiying candidate # 1545989134.161 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1545989134.161 * * [misc]simplify: iters left: 5 (9 enodes) 1545989134.164 * * [misc]simplify: iters left: 4 (15 enodes) 1545989134.168 * * [misc]simplify: iters left: 3 (21 enodes) 1545989134.173 * * [misc]simplify: iters left: 2 (22 enodes) 1545989134.179 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1545989134.179 * [misc]simplify: Simplified (2 1 1 2) to (λ (k n) (/ (/ (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2)))) (sqrt (sqrt k))) (sqrt (sqrt k)))) 1545989134.179 * * * * [misc]progress: [ 10 / 113 ] simplifiying candidate # 1545989134.179 * [enter]simplify: Simplifying (pow PI (- 1/2 (/ k 2))) 1545989134.179 * * [misc]simplify: iters left: 5 (7 enodes) 1545989134.181 * * [misc]simplify: iters left: 4 (9 enodes) 1545989134.184 * * [misc]simplify: iters left: 3 (12 enodes) 1545989134.187 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1545989134.187 * [misc]simplify: Simplified (2 1 1 1) to (λ (k n) (/ (/ (* (pow PI (- 1/2 (/ k 2))) (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (sqrt (sqrt k)))) 1545989134.187 * * * * [misc]progress: [ 11 / 113 ] simplifiying candidate # 1545989134.187 * * * * [misc]progress: [ 12 / 113 ] simplifiying candidate # 1545989134.187 * * * * [misc]progress: [ 13 / 113 ] simplifiying candidate # 1545989134.187 * * * * [misc]progress: [ 14 / 113 ] simplifiying candidate # 1545989134.187 * * * * [misc]progress: [ 15 / 113 ] simplifiying candidate # 1545989134.188 * * * * [misc]progress: [ 16 / 113 ] simplifiying candidate # 1545989134.188 * * * * [misc]progress: [ 17 / 113 ] simplifiying candidate # 1545989134.188 * * * * [misc]progress: [ 18 / 113 ] simplifiying candidate # 1545989134.188 * * * * [misc]progress: [ 19 / 113 ] simplifiying candidate # 1545989134.188 * * * * [misc]progress: [ 20 / 113 ] simplifiying candidate # 1545989134.188 * * * * [misc]progress: [ 21 / 113 ] simplifiying candidate # 1545989134.188 * * * * [misc]progress: [ 22 / 113 ] simplifiying candidate # 1545989134.188 * * * * [misc]progress: [ 23 / 113 ] simplifiying candidate # 1545989134.188 * * * * [misc]progress: [ 24 / 113 ] simplifiying candidate # 1545989134.188 * * * * [misc]progress: [ 25 / 113 ] simplifiying candidate # 1545989134.188 * * * * [misc]progress: [ 26 / 113 ] simplifiying candidate # 1545989134.188 * * * * [misc]progress: [ 27 / 113 ] simplifiying candidate # 1545989134.188 * * * * [misc]progress: [ 28 / 113 ] simplifiying candidate # 1545989134.189 * [enter]simplify: Simplifying (- (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) (log (sqrt (sqrt k)))) 1545989134.189 * * [misc]simplify: iters left: 6 (15 enodes) 1545989134.193 * * [misc]simplify: iters left: 5 (27 enodes) 1545989134.202 * * [misc]simplify: iters left: 4 (54 enodes) 1545989134.222 * * [misc]simplify: iters left: 3 (138 enodes) 1545989134.280 * * [misc]simplify: iters left: 2 (489 enodes) 1545989134.882 * [exit]simplify: Simplified to (- (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) (log (sqrt (sqrt k)))) 1545989134.883 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (exp (- (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) (log (sqrt (sqrt k))))) (sqrt (sqrt k)))) 1545989134.883 * * * * [misc]progress: [ 29 / 113 ] simplifiying candidate # 1545989134.883 * [enter]simplify: Simplifying (- (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) (log (sqrt (sqrt k)))) 1545989134.883 * * [misc]simplify: iters left: 6 (15 enodes) 1545989134.888 * * [misc]simplify: iters left: 5 (27 enodes) 1545989134.894 * * [misc]simplify: iters left: 4 (54 enodes) 1545989134.904 * * [misc]simplify: iters left: 3 (138 enodes) 1545989134.977 * * [misc]simplify: iters left: 2 (489 enodes) 1545989135.510 * [exit]simplify: Simplified to (- (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) (log (sqrt (sqrt k)))) 1545989135.510 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (exp (- (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) (log (sqrt (sqrt k))))) (sqrt (sqrt k)))) 1545989135.510 * * * * [misc]progress: [ 30 / 113 ] simplifiying candidate # 1545989135.510 * [enter]simplify: Simplifying (- (log (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (log (sqrt (sqrt k)))) 1545989135.510 * * [misc]simplify: iters left: 6 (15 enodes) 1545989135.515 * * [misc]simplify: iters left: 5 (25 enodes) 1545989135.523 * * [misc]simplify: iters left: 4 (43 enodes) 1545989135.535 * * [misc]simplify: iters left: 3 (72 enodes) 1545989135.566 * * [misc]simplify: iters left: 2 (209 enodes) 1545989135.782 * [exit]simplify: Simplified to (- (* (log (* (* PI 2) n)) (- 1/2 (/ k 2))) (log (sqrt (sqrt k)))) 1545989135.782 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (exp (- (* (log (* (* PI 2) n)) (- 1/2 (/ k 2))) (log (sqrt (sqrt k))))) (sqrt (sqrt k)))) 1545989135.783 * * * * [misc]progress: [ 31 / 113 ] simplifiying candidate # 1545989135.783 * * * * [misc]progress: [ 32 / 113 ] simplifiying candidate # 1545989135.783 * * * * [misc]progress: [ 33 / 113 ] simplifiying candidate # 1545989135.783 * [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 (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k)))) 1545989135.783 * * [misc]simplify: iters left: 6 (17 enodes) 1545989135.786 * * [misc]simplify: iters left: 5 (32 enodes) 1545989135.791 * * [misc]simplify: iters left: 4 (70 enodes) 1545989135.807 * * [misc]simplify: iters left: 3 (122 enodes) 1545989135.832 * * [misc]simplify: iters left: 2 (175 enodes) 1545989135.873 * * [misc]simplify: iters left: 1 (192 enodes) 1545989135.918 * [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))) (* (sqrt k) (sqrt (sqrt k))))) 1545989135.918 * [misc]simplify: Simplified (2 1 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))) (* (sqrt k) (sqrt (sqrt k)))))) (sqrt (sqrt k)))) 1545989135.918 * * * * [misc]progress: [ 34 / 113 ] simplifiying candidate # 1545989135.918 * * * * [misc]progress: [ 35 / 113 ] simplifiying candidate # 1545989135.918 * * * * [misc]progress: [ 36 / 113 ] simplifiying candidate # 1545989135.918 * * * * [misc]progress: [ 37 / 113 ] simplifiying candidate # 1545989135.918 * * * * [misc]progress: [ 38 / 113 ] simplifiying candidate # 1545989135.919 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) 1545989135.919 * * [misc]simplify: iters left: 6 (13 enodes) 1545989135.923 * * [misc]simplify: iters left: 5 (20 enodes) 1545989135.929 * * [misc]simplify: iters left: 4 (26 enodes) 1545989135.936 * * [misc]simplify: iters left: 3 (28 enodes) 1545989135.944 * [exit]simplify: Simplified to (/ (/ (sqrt (* (* 2 n) PI)) (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) 1545989135.944 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (* (/ (/ (sqrt (* (* 2 n) PI)) (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt k)))) 1545989135.945 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (sqrt (sqrt k)))) 1545989135.945 * * [misc]simplify: iters left: 6 (13 enodes) 1545989135.949 * * [misc]simplify: iters left: 5 (19 enodes) 1545989135.954 * * [misc]simplify: iters left: 4 (25 enodes) 1545989135.961 * * [misc]simplify: iters left: 3 (26 enodes) 1545989135.968 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt (sqrt k)))) 1545989135.968 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (/ (/ (sqrt (* (* 2 n) PI)) (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt k)))) 1545989135.968 * * * * [misc]progress: [ 39 / 113 ] simplifiying candidate # 1545989135.968 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) 1545989135.969 * * [misc]simplify: iters left: 6 (13 enodes) 1545989135.972 * * [misc]simplify: iters left: 5 (19 enodes) 1545989135.978 * * [misc]simplify: iters left: 4 (25 enodes) 1545989135.984 * * [misc]simplify: iters left: 3 (26 enodes) 1545989135.991 * [exit]simplify: Simplified to (/ (sqrt (* (* 2 n) PI)) (fabs (cbrt (sqrt k)))) 1545989135.991 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (* (/ (sqrt (* (* 2 n) PI)) (fabs (cbrt (sqrt k)))) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (cbrt (sqrt k))))) (sqrt (sqrt k)))) 1545989135.991 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (cbrt (sqrt k)))) 1545989135.991 * * [misc]simplify: iters left: 6 (13 enodes) 1545989135.995 * * [misc]simplify: iters left: 5 (19 enodes) 1545989136.000 * * [misc]simplify: iters left: 4 (25 enodes) 1545989136.007 * * [misc]simplify: iters left: 3 (26 enodes) 1545989136.014 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (cbrt (sqrt k)))) 1545989136.014 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (/ (sqrt (* (* 2 n) PI)) (fabs (cbrt (sqrt k)))) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (cbrt (sqrt k))))) (sqrt (sqrt k)))) 1545989136.014 * * * * [misc]progress: [ 40 / 113 ] simplifiying candidate # 1545989136.014 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (sqrt (sqrt (sqrt k)))) 1545989136.014 * * [misc]simplify: iters left: 6 (12 enodes) 1545989136.018 * * [misc]simplify: iters left: 5 (17 enodes) 1545989136.022 * * [misc]simplify: iters left: 4 (23 enodes) 1545989136.029 * * [misc]simplify: iters left: 3 (24 enodes) 1545989136.034 * [exit]simplify: Simplified to (/ (sqrt (* (* 2 n) PI)) (sqrt (sqrt (sqrt k)))) 1545989136.034 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (* (/ (sqrt (* (* 2 n) PI)) (sqrt (sqrt (sqrt k)))) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt (sqrt k))))) (sqrt (sqrt k)))) 1545989136.035 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt (sqrt k)))) 1545989136.035 * * [misc]simplify: iters left: 6 (13 enodes) 1545989136.039 * * [misc]simplify: iters left: 5 (19 enodes) 1545989136.044 * * [misc]simplify: iters left: 4 (25 enodes) 1545989136.051 * * [misc]simplify: iters left: 3 (26 enodes) 1545989136.057 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt (sqrt k)))) 1545989136.057 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (/ (sqrt (* (* 2 n) PI)) (sqrt (sqrt (sqrt k)))) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt (sqrt k))))) (sqrt (sqrt k)))) 1545989136.057 * * * * [misc]progress: [ 41 / 113 ] simplifiying candidate # 1545989136.057 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (sqrt 1)) 1545989136.058 * * [misc]simplify: iters left: 6 (10 enodes) 1545989136.061 * * [misc]simplify: iters left: 5 (17 enodes) 1545989136.066 * * [misc]simplify: iters left: 4 (23 enodes) 1545989136.071 * * [misc]simplify: iters left: 3 (24 enodes) 1545989136.076 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1545989136.076 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (* (sqrt (* (* 2 n) PI)) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k)))) (sqrt (sqrt k)))) 1545989136.077 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k))) 1545989136.077 * * [misc]simplify: iters left: 6 (12 enodes) 1545989136.080 * * [misc]simplify: iters left: 5 (18 enodes) 1545989136.084 * * [misc]simplify: iters left: 4 (24 enodes) 1545989136.089 * * [misc]simplify: iters left: 3 (25 enodes) 1545989136.096 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k))) 1545989136.096 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (sqrt (* (* 2 n) PI)) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k)))) (sqrt (sqrt k)))) 1545989136.096 * * * * [misc]progress: [ 42 / 113 ] simplifiying candidate # 1545989136.096 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (sqrt (sqrt (sqrt k)))) 1545989136.096 * * [misc]simplify: iters left: 6 (12 enodes) 1545989136.100 * * [misc]simplify: iters left: 5 (17 enodes) 1545989136.104 * * [misc]simplify: iters left: 4 (23 enodes) 1545989136.110 * * [misc]simplify: iters left: 3 (24 enodes) 1545989136.115 * [exit]simplify: Simplified to (/ (sqrt (* (* 2 n) PI)) (sqrt (sqrt (sqrt k)))) 1545989136.115 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (* (/ (sqrt (* (* 2 n) PI)) (sqrt (sqrt (sqrt k)))) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt (sqrt k))))) (sqrt (sqrt k)))) 1545989136.115 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt (sqrt k)))) 1545989136.116 * * [misc]simplify: iters left: 6 (13 enodes) 1545989136.117 * * [misc]simplify: iters left: 5 (19 enodes) 1545989136.120 * * [misc]simplify: iters left: 4 (25 enodes) 1545989136.123 * * [misc]simplify: iters left: 3 (26 enodes) 1545989136.126 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt (sqrt k)))) 1545989136.126 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (/ (sqrt (* (* 2 n) PI)) (sqrt (sqrt (sqrt k)))) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt (sqrt k))))) (sqrt (sqrt k)))) 1545989136.126 * * * * [misc]progress: [ 43 / 113 ] simplifiying candidate # 1545989136.126 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) 1) 1545989136.126 * * [misc]simplify: iters left: 6 (9 enodes) 1545989136.128 * * [misc]simplify: iters left: 5 (16 enodes) 1545989136.130 * * [misc]simplify: iters left: 4 (24 enodes) 1545989136.133 * * [misc]simplify: iters left: 3 (26 enodes) 1545989136.136 * [exit]simplify: Simplified to (sqrt (* (* PI 2) n)) 1545989136.136 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (* (sqrt (* (* PI 2) n)) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k)))) (sqrt (sqrt k)))) 1545989136.136 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k))) 1545989136.136 * * [misc]simplify: iters left: 6 (12 enodes) 1545989136.137 * * [misc]simplify: iters left: 5 (18 enodes) 1545989136.140 * * [misc]simplify: iters left: 4 (24 enodes) 1545989136.143 * * [misc]simplify: iters left: 3 (25 enodes) 1545989136.149 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k))) 1545989136.149 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (sqrt (* (* PI 2) n)) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k)))) (sqrt (sqrt k)))) 1545989136.149 * * * * [misc]progress: [ 44 / 113 ] simplifiying candidate # 1545989136.149 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) 1545989136.149 * * [misc]simplify: iters left: 6 (13 enodes) 1545989136.153 * * [misc]simplify: iters left: 5 (20 enodes) 1545989136.158 * * [misc]simplify: iters left: 4 (26 enodes) 1545989136.165 * * [misc]simplify: iters left: 3 (28 enodes) 1545989136.170 * [exit]simplify: Simplified to (/ (/ (sqrt (* (* 2 n) PI)) (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) 1545989136.170 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (* (/ (/ (sqrt (* (* 2 n) PI)) (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt k)))) 1545989136.170 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (sqrt (sqrt k)))) 1545989136.170 * * [misc]simplify: iters left: 6 (13 enodes) 1545989136.172 * * [misc]simplify: iters left: 5 (19 enodes) 1545989136.174 * * [misc]simplify: iters left: 4 (25 enodes) 1545989136.177 * * [misc]simplify: iters left: 3 (26 enodes) 1545989136.180 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt (sqrt k)))) 1545989136.180 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (/ (/ (sqrt (* (* 2 n) PI)) (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt k)))) 1545989136.180 * * * * [misc]progress: [ 45 / 113 ] simplifiying candidate # 1545989136.181 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) 1545989136.181 * * [misc]simplify: iters left: 6 (13 enodes) 1545989136.182 * * [misc]simplify: iters left: 5 (19 enodes) 1545989136.185 * * [misc]simplify: iters left: 4 (25 enodes) 1545989136.190 * * [misc]simplify: iters left: 3 (26 enodes) 1545989136.196 * [exit]simplify: Simplified to (/ (sqrt (* (* 2 n) PI)) (fabs (cbrt (sqrt k)))) 1545989136.196 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (* (/ (sqrt (* (* 2 n) PI)) (fabs (cbrt (sqrt k)))) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (cbrt (sqrt k))))) (sqrt (sqrt k)))) 1545989136.197 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (cbrt (sqrt k)))) 1545989136.197 * * [misc]simplify: iters left: 6 (13 enodes) 1545989136.200 * * [misc]simplify: iters left: 5 (19 enodes) 1545989136.204 * * [misc]simplify: iters left: 4 (25 enodes) 1545989136.207 * * [misc]simplify: iters left: 3 (26 enodes) 1545989136.210 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (cbrt (sqrt k)))) 1545989136.210 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (/ (sqrt (* (* 2 n) PI)) (fabs (cbrt (sqrt k)))) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (cbrt (sqrt k))))) (sqrt (sqrt k)))) 1545989136.210 * * * * [misc]progress: [ 46 / 113 ] simplifiying candidate # 1545989136.211 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (sqrt (sqrt (sqrt k)))) 1545989136.211 * * [misc]simplify: iters left: 6 (12 enodes) 1545989136.212 * * [misc]simplify: iters left: 5 (17 enodes) 1545989136.215 * * [misc]simplify: iters left: 4 (23 enodes) 1545989136.217 * * [misc]simplify: iters left: 3 (24 enodes) 1545989136.220 * [exit]simplify: Simplified to (/ (sqrt (* (* 2 n) PI)) (sqrt (sqrt (sqrt k)))) 1545989136.220 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (* (/ (sqrt (* (* 2 n) PI)) (sqrt (sqrt (sqrt k)))) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt (sqrt k))))) (sqrt (sqrt k)))) 1545989136.220 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt (sqrt k)))) 1545989136.220 * * [misc]simplify: iters left: 6 (13 enodes) 1545989136.222 * * [misc]simplify: iters left: 5 (19 enodes) 1545989136.225 * * [misc]simplify: iters left: 4 (25 enodes) 1545989136.228 * * [misc]simplify: iters left: 3 (26 enodes) 1545989136.231 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt (sqrt k)))) 1545989136.231 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (/ (sqrt (* (* 2 n) PI)) (sqrt (sqrt (sqrt k)))) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt (sqrt k))))) (sqrt (sqrt k)))) 1545989136.231 * * * * [misc]progress: [ 47 / 113 ] simplifiying candidate # 1545989136.231 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (sqrt 1)) 1545989136.231 * * [misc]simplify: iters left: 6 (10 enodes) 1545989136.233 * * [misc]simplify: iters left: 5 (17 enodes) 1545989136.235 * * [misc]simplify: iters left: 4 (23 enodes) 1545989136.237 * * [misc]simplify: iters left: 3 (24 enodes) 1545989136.240 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1545989136.240 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (* (sqrt (* (* 2 n) PI)) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k)))) (sqrt (sqrt k)))) 1545989136.240 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k))) 1545989136.240 * * [misc]simplify: iters left: 6 (12 enodes) 1545989136.242 * * [misc]simplify: iters left: 5 (18 enodes) 1545989136.244 * * [misc]simplify: iters left: 4 (24 enodes) 1545989136.247 * * [misc]simplify: iters left: 3 (25 enodes) 1545989136.250 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k))) 1545989136.250 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (sqrt (* (* 2 n) PI)) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k)))) (sqrt (sqrt k)))) 1545989136.250 * * * * [misc]progress: [ 48 / 113 ] simplifiying candidate # 1545989136.250 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (sqrt (sqrt (sqrt k)))) 1545989136.250 * * [misc]simplify: iters left: 6 (12 enodes) 1545989136.252 * * [misc]simplify: iters left: 5 (17 enodes) 1545989136.254 * * [misc]simplify: iters left: 4 (23 enodes) 1545989136.258 * * [misc]simplify: iters left: 3 (24 enodes) 1545989136.264 * [exit]simplify: Simplified to (/ (sqrt (* (* 2 n) PI)) (sqrt (sqrt (sqrt k)))) 1545989136.264 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (* (/ (sqrt (* (* 2 n) PI)) (sqrt (sqrt (sqrt k)))) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt (sqrt k))))) (sqrt (sqrt k)))) 1545989136.264 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt (sqrt k)))) 1545989136.265 * * [misc]simplify: iters left: 6 (13 enodes) 1545989136.268 * * [misc]simplify: iters left: 5 (19 enodes) 1545989136.273 * * [misc]simplify: iters left: 4 (25 enodes) 1545989136.282 * * [misc]simplify: iters left: 3 (26 enodes) 1545989136.288 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt (sqrt k)))) 1545989136.288 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (/ (sqrt (* (* 2 n) PI)) (sqrt (sqrt (sqrt k)))) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt (sqrt k))))) (sqrt (sqrt k)))) 1545989136.288 * * * * [misc]progress: [ 49 / 113 ] simplifiying candidate # 1545989136.289 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) 1) 1545989136.289 * * [misc]simplify: iters left: 6 (9 enodes) 1545989136.292 * * [misc]simplify: iters left: 5 (16 enodes) 1545989136.297 * * [misc]simplify: iters left: 4 (24 enodes) 1545989136.302 * * [misc]simplify: iters left: 3 (26 enodes) 1545989136.307 * [exit]simplify: Simplified to (sqrt (* (* PI 2) n)) 1545989136.307 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (* (sqrt (* (* PI 2) n)) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k)))) (sqrt (sqrt k)))) 1545989136.308 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k))) 1545989136.308 * * [misc]simplify: iters left: 6 (12 enodes) 1545989136.312 * * [misc]simplify: iters left: 5 (18 enodes) 1545989136.317 * * [misc]simplify: iters left: 4 (24 enodes) 1545989136.323 * * [misc]simplify: iters left: 3 (25 enodes) 1545989136.330 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k))) 1545989136.330 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (sqrt (* (* PI 2) n)) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k)))) (sqrt (sqrt k)))) 1545989136.330 * * * * [misc]progress: [ 50 / 113 ] simplifiying candidate # 1545989136.331 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) 1545989136.331 * * [misc]simplify: iters left: 6 (12 enodes) 1545989136.335 * * [misc]simplify: iters left: 5 (16 enodes) 1545989136.339 * * [misc]simplify: iters left: 4 (19 enodes) 1545989136.345 * [exit]simplify: Simplified to (/ (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) 1545989136.345 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (* (/ (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt k)))) 1545989136.345 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt (sqrt k)))) 1545989136.345 * * [misc]simplify: iters left: 6 (12 enodes) 1545989136.349 * * [misc]simplify: iters left: 5 (15 enodes) 1545989136.353 * * [misc]simplify: iters left: 4 (18 enodes) 1545989136.358 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt (sqrt k)))) 1545989136.358 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (/ (pow PI (- 1/2 (/ k 2))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt k)))) 1545989136.358 * * * * [misc]progress: [ 51 / 113 ] simplifiying candidate # 1545989136.358 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) 1545989136.358 * * [misc]simplify: iters left: 6 (12 enodes) 1545989136.362 * * [misc]simplify: iters left: 5 (15 enodes) 1545989136.366 * * [misc]simplify: iters left: 4 (18 enodes) 1545989136.371 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (fabs (cbrt (sqrt k)))) 1545989136.371 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (* (/ (pow PI (- 1/2 (/ k 2))) (fabs (cbrt (sqrt k)))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (cbrt (sqrt k))))) (sqrt (sqrt k)))) 1545989136.371 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (cbrt (sqrt k)))) 1545989136.371 * * [misc]simplify: iters left: 6 (12 enodes) 1545989136.375 * * [misc]simplify: iters left: 5 (15 enodes) 1545989136.379 * * [misc]simplify: iters left: 4 (18 enodes) 1545989136.384 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (cbrt (sqrt k)))) 1545989136.384 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (/ (pow PI (- 1/2 (/ k 2))) (fabs (cbrt (sqrt k)))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (cbrt (sqrt k))))) (sqrt (sqrt k)))) 1545989136.384 * * * * [misc]progress: [ 52 / 113 ] simplifiying candidate # 1545989136.384 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt (sqrt k)))) 1545989136.384 * * [misc]simplify: iters left: 6 (11 enodes) 1545989136.387 * * [misc]simplify: iters left: 5 (13 enodes) 1545989136.391 * * [misc]simplify: iters left: 4 (16 enodes) 1545989136.395 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt (sqrt k)))) 1545989136.395 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (* (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt (sqrt k)))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt (sqrt k))))) (sqrt (sqrt k)))) 1545989136.396 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt (sqrt k)))) 1545989136.396 * * [misc]simplify: iters left: 6 (12 enodes) 1545989136.399 * * [misc]simplify: iters left: 5 (15 enodes) 1545989136.403 * * [misc]simplify: iters left: 4 (18 enodes) 1545989136.408 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt (sqrt k)))) 1545989136.408 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt (sqrt k)))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt (sqrt k))))) (sqrt (sqrt k)))) 1545989136.408 * * * * [misc]progress: [ 53 / 113 ] simplifiying candidate # 1545989136.409 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (sqrt 1)) 1545989136.409 * * [misc]simplify: iters left: 6 (10 enodes) 1545989136.412 * * [misc]simplify: iters left: 5 (14 enodes) 1545989136.416 * * [misc]simplify: iters left: 4 (17 enodes) 1545989136.421 * * [misc]simplify: iters left: 3 (19 enodes) 1545989136.424 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1545989136.424 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (* (pow PI (- 1/2 (/ k 2))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (sqrt (sqrt k)))) 1545989136.424 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1545989136.424 * * [misc]simplify: iters left: 6 (11 enodes) 1545989136.426 * * [misc]simplify: iters left: 5 (14 enodes) 1545989136.428 * * [misc]simplify: iters left: 4 (17 enodes) 1545989136.430 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1545989136.431 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (pow PI (- 1/2 (/ k 2))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (sqrt (sqrt k)))) 1545989136.431 * * * * [misc]progress: [ 54 / 113 ] simplifiying candidate # 1545989136.431 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt (sqrt k)))) 1545989136.431 * * [misc]simplify: iters left: 6 (11 enodes) 1545989136.432 * * [misc]simplify: iters left: 5 (13 enodes) 1545989136.434 * * [misc]simplify: iters left: 4 (16 enodes) 1545989136.436 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt (sqrt k)))) 1545989136.436 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (* (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt (sqrt k)))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt (sqrt k))))) (sqrt (sqrt k)))) 1545989136.436 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt (sqrt k)))) 1545989136.436 * * [misc]simplify: iters left: 6 (12 enodes) 1545989136.438 * * [misc]simplify: iters left: 5 (15 enodes) 1545989136.440 * * [misc]simplify: iters left: 4 (18 enodes) 1545989136.442 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt (sqrt k)))) 1545989136.442 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt (sqrt k)))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt (sqrt k))))) (sqrt (sqrt k)))) 1545989136.442 * * * * [misc]progress: [ 55 / 113 ] simplifiying candidate # 1545989136.442 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) 1) 1545989136.442 * * [misc]simplify: iters left: 6 (9 enodes) 1545989136.443 * * [misc]simplify: iters left: 5 (13 enodes) 1545989136.446 * * [misc]simplify: iters left: 4 (18 enodes) 1545989136.447 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1545989136.447 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (* (pow PI (- 1/2 (/ k 2))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (sqrt (sqrt k)))) 1545989136.448 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1545989136.448 * * [misc]simplify: iters left: 6 (11 enodes) 1545989136.449 * * [misc]simplify: iters left: 5 (14 enodes) 1545989136.451 * * [misc]simplify: iters left: 4 (17 enodes) 1545989136.456 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1545989136.456 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (pow PI (- 1/2 (/ k 2))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (sqrt (sqrt k)))) 1545989136.456 * * * * [misc]progress: [ 56 / 113 ] simplifiying candidate # 1545989136.456 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) 1545989136.456 * * [misc]simplify: iters left: 6 (17 enodes) 1545989136.462 * * [misc]simplify: iters left: 5 (29 enodes) 1545989136.470 * * [misc]simplify: iters left: 4 (47 enodes) 1545989136.481 * * [misc]simplify: iters left: 3 (51 enodes) 1545989136.487 * * [misc]simplify: iters left: 2 (54 enodes) 1545989136.494 * [exit]simplify: Simplified to (* (/ (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (sqrt (sqrt k)))) (/ (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (sqrt (sqrt k))))) 1545989136.494 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (* (* (/ (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (sqrt (sqrt k)))) (/ (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (sqrt (sqrt k))))) (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt k)))) 1545989136.494 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (sqrt (sqrt k)))) 1545989136.494 * * [misc]simplify: iters left: 6 (15 enodes) 1545989136.496 * * [misc]simplify: iters left: 5 (21 enodes) 1545989136.499 * * [misc]simplify: iters left: 4 (30 enodes) 1545989136.503 * * [misc]simplify: iters left: 3 (31 enodes) 1545989136.507 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt (sqrt k)))) 1545989136.507 * [misc]simplify: Simplified (2 1 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 (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt k)))) 1545989136.507 * * * * [misc]progress: [ 57 / 113 ] simplifiying candidate # 1545989136.507 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) 1545989136.508 * * [misc]simplify: iters left: 6 (17 enodes) 1545989136.510 * * [misc]simplify: iters left: 5 (26 enodes) 1545989136.513 * * [misc]simplify: iters left: 4 (37 enodes) 1545989136.519 * * [misc]simplify: iters left: 3 (40 enodes) 1545989136.529 * [exit]simplify: Simplified to (* (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (fabs (cbrt (sqrt k)))) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) 1545989136.529 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (* (* (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (fabs (cbrt (sqrt k)))) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (cbrt (sqrt k))))) (sqrt (sqrt k)))) 1545989136.530 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (cbrt (sqrt k)))) 1545989136.530 * * [misc]simplify: iters left: 6 (15 enodes) 1545989136.534 * * [misc]simplify: iters left: 5 (21 enodes) 1545989136.540 * * [misc]simplify: iters left: 4 (30 enodes) 1545989136.548 * * [misc]simplify: iters left: 3 (31 enodes) 1545989136.555 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (cbrt (sqrt k)))) 1545989136.555 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (* (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (fabs (cbrt (sqrt k)))) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (cbrt (sqrt k))))) (sqrt (sqrt k)))) 1545989136.555 * * * * [misc]progress: [ 58 / 113 ] simplifiying candidate # 1545989136.556 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt (sqrt (sqrt k)))) 1545989136.556 * * [misc]simplify: iters left: 6 (16 enodes) 1545989136.560 * * [misc]simplify: iters left: 5 (24 enodes) 1545989136.567 * * [misc]simplify: iters left: 4 (35 enodes) 1545989136.576 * * [misc]simplify: iters left: 3 (37 enodes) 1545989136.586 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (/ (sqrt (sqrt (sqrt k))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))) 1545989136.586 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (* (/ (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (/ (sqrt (sqrt (sqrt k))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))) (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt (sqrt k))))) (sqrt (sqrt k)))) 1545989136.586 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt (sqrt k)))) 1545989136.586 * * [misc]simplify: iters left: 6 (15 enodes) 1545989136.591 * * [misc]simplify: iters left: 5 (21 enodes) 1545989136.596 * * [misc]simplify: iters left: 4 (30 enodes) 1545989136.604 * * [misc]simplify: iters left: 3 (31 enodes) 1545989136.611 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt (sqrt k)))) 1545989136.611 * [misc]simplify: Simplified (2 1 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 (sqrt k)))) (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt (sqrt k))))) (sqrt (sqrt k)))) 1545989136.611 * * * * [misc]progress: [ 59 / 113 ] simplifiying candidate # 1545989136.612 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt 1)) 1545989136.612 * * [misc]simplify: iters left: 6 (15 enodes) 1545989136.617 * * [misc]simplify: iters left: 5 (25 enodes) 1545989136.623 * * [misc]simplify: iters left: 4 (36 enodes) 1545989136.632 * * [misc]simplify: iters left: 3 (41 enodes) 1545989136.637 * * [misc]simplify: iters left: 2 (56 enodes) 1545989136.644 * * [misc]simplify: iters left: 1 (57 enodes) 1545989136.649 * [exit]simplify: Simplified to (* (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) 1545989136.649 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (* (* (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (sqrt k)))) 1545989136.649 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1545989136.649 * * [misc]simplify: iters left: 6 (14 enodes) 1545989136.651 * * [misc]simplify: iters left: 5 (20 enodes) 1545989136.654 * * [misc]simplify: iters left: 4 (29 enodes) 1545989136.657 * * [misc]simplify: iters left: 3 (30 enodes) 1545989136.662 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1545989136.662 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (* (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (sqrt k)))) 1545989136.662 * * * * [misc]progress: [ 60 / 113 ] simplifiying candidate # 1545989136.663 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt (sqrt (sqrt k)))) 1545989136.663 * * [misc]simplify: iters left: 6 (16 enodes) 1545989136.667 * * [misc]simplify: iters left: 5 (24 enodes) 1545989136.673 * * [misc]simplify: iters left: 4 (35 enodes) 1545989136.681 * * [misc]simplify: iters left: 3 (37 enodes) 1545989136.690 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (/ (sqrt (sqrt (sqrt k))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))) 1545989136.690 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (* (/ (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (/ (sqrt (sqrt (sqrt k))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))) (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt (sqrt k))))) (sqrt (sqrt k)))) 1545989136.690 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt (sqrt k)))) 1545989136.690 * * [misc]simplify: iters left: 6 (15 enodes) 1545989136.695 * * [misc]simplify: iters left: 5 (21 enodes) 1545989136.701 * * [misc]simplify: iters left: 4 (30 enodes) 1545989136.709 * * [misc]simplify: iters left: 3 (31 enodes) 1545989136.717 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt (sqrt k)))) 1545989136.717 * [misc]simplify: Simplified (2 1 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 (sqrt k)))) (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt (sqrt k))))) (sqrt (sqrt k)))) 1545989136.717 * * * * [misc]progress: [ 61 / 113 ] simplifiying candidate # 1545989136.717 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1) 1545989136.718 * * [misc]simplify: iters left: 6 (14 enodes) 1545989136.722 * * [misc]simplify: iters left: 5 (24 enodes) 1545989136.730 * * [misc]simplify: iters left: 4 (39 enodes) 1545989136.740 * * [misc]simplify: iters left: 3 (54 enodes) 1545989136.753 * * [misc]simplify: iters left: 2 (80 enodes) 1545989136.774 * [exit]simplify: Simplified to (* (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))) 1545989136.774 * [misc]simplify: Simplified (2 1 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 (sqrt k)))) (sqrt (sqrt k)))) 1545989136.775 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1545989136.775 * * [misc]simplify: iters left: 6 (14 enodes) 1545989136.779 * * [misc]simplify: iters left: 5 (20 enodes) 1545989136.784 * * [misc]simplify: iters left: 4 (29 enodes) 1545989136.792 * * [misc]simplify: iters left: 3 (30 enodes) 1545989136.799 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1545989136.799 * [misc]simplify: Simplified (2 1 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 (sqrt k)))) (sqrt (sqrt k)))) 1545989136.799 * * * * [misc]progress: [ 62 / 113 ] simplifiying candidate # 1545989136.800 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) 1545989136.800 * * [misc]simplify: iters left: 6 (16 enodes) 1545989136.804 * * [misc]simplify: iters left: 5 (24 enodes) 1545989136.811 * * [misc]simplify: iters left: 4 (33 enodes) 1545989136.817 * * [misc]simplify: iters left: 3 (34 enodes) 1545989136.821 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) 1545989136.821 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (* (/ (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt k)))) 1545989136.822 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (sqrt (sqrt k)))) 1545989136.822 * * [misc]simplify: iters left: 6 (15 enodes) 1545989136.824 * * [misc]simplify: iters left: 5 (21 enodes) 1545989136.827 * * [misc]simplify: iters left: 4 (30 enodes) 1545989136.831 * * [misc]simplify: iters left: 3 (31 enodes) 1545989136.834 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt (sqrt k)))) 1545989136.834 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt k)))) 1545989136.835 * * * * [misc]progress: [ 63 / 113 ] simplifiying candidate # 1545989136.835 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) 1545989136.835 * * [misc]simplify: iters left: 6 (16 enodes) 1545989136.837 * * [misc]simplify: iters left: 5 (23 enodes) 1545989136.840 * * [misc]simplify: iters left: 4 (32 enodes) 1545989136.845 * * [misc]simplify: iters left: 3 (34 enodes) 1545989136.850 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (fabs (cbrt (sqrt k)))) 1545989136.850 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (* (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (fabs (cbrt (sqrt k)))) (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (cbrt (sqrt k))))) (sqrt (sqrt k)))) 1545989136.851 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (cbrt (sqrt k)))) 1545989136.851 * * [misc]simplify: iters left: 6 (15 enodes) 1545989136.855 * * [misc]simplify: iters left: 5 (21 enodes) 1545989136.860 * * [misc]simplify: iters left: 4 (30 enodes) 1545989136.864 * * [misc]simplify: iters left: 3 (31 enodes) 1545989136.867 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (cbrt (sqrt k)))) 1545989136.867 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (fabs (cbrt (sqrt k)))) (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (cbrt (sqrt k))))) (sqrt (sqrt k)))) 1545989136.867 * * * * [misc]progress: [ 64 / 113 ] simplifiying candidate # 1545989136.867 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt (sqrt k)))) 1545989136.867 * * [misc]simplify: iters left: 6 (15 enodes) 1545989136.869 * * [misc]simplify: iters left: 5 (21 enodes) 1545989136.873 * * [misc]simplify: iters left: 4 (30 enodes) 1545989136.877 * * [misc]simplify: iters left: 3 (31 enodes) 1545989136.880 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt (sqrt k)))) 1545989136.880 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (* (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt (sqrt k)))) (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt (sqrt k))))) (sqrt (sqrt k)))) 1545989136.880 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt (sqrt k)))) 1545989136.880 * * [misc]simplify: iters left: 6 (15 enodes) 1545989136.882 * * [misc]simplify: iters left: 5 (21 enodes) 1545989136.885 * * [misc]simplify: iters left: 4 (30 enodes) 1545989136.889 * * [misc]simplify: iters left: 3 (31 enodes) 1545989136.892 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt (sqrt k)))) 1545989136.892 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt (sqrt k)))) (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt (sqrt k))))) (sqrt (sqrt k)))) 1545989136.892 * * * * [misc]progress: [ 65 / 113 ] simplifiying candidate # 1545989136.893 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt 1)) 1545989136.893 * * [misc]simplify: iters left: 6 (14 enodes) 1545989136.895 * * [misc]simplify: iters left: 5 (22 enodes) 1545989136.898 * * [misc]simplify: iters left: 4 (31 enodes) 1545989136.902 * * [misc]simplify: iters left: 3 (35 enodes) 1545989136.905 * [exit]simplify: Simplified to (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) 1545989136.906 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (* (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (sqrt k)))) 1545989136.906 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1545989136.906 * * [misc]simplify: iters left: 6 (14 enodes) 1545989136.908 * * [misc]simplify: iters left: 5 (20 enodes) 1545989136.910 * * [misc]simplify: iters left: 4 (29 enodes) 1545989136.916 * * [misc]simplify: iters left: 3 (30 enodes) 1545989136.923 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1545989136.924 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (sqrt k)))) 1545989136.924 * * * * [misc]progress: [ 66 / 113 ] simplifiying candidate # 1545989136.924 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt (sqrt k)))) 1545989136.924 * * [misc]simplify: iters left: 6 (15 enodes) 1545989136.928 * * [misc]simplify: iters left: 5 (21 enodes) 1545989136.934 * * [misc]simplify: iters left: 4 (30 enodes) 1545989136.941 * * [misc]simplify: iters left: 3 (31 enodes) 1545989136.949 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt (sqrt k)))) 1545989136.949 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (* (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt (sqrt k)))) (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt (sqrt k))))) (sqrt (sqrt k)))) 1545989136.949 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt (sqrt k)))) 1545989136.949 * * [misc]simplify: iters left: 6 (15 enodes) 1545989136.953 * * [misc]simplify: iters left: 5 (21 enodes) 1545989136.959 * * [misc]simplify: iters left: 4 (30 enodes) 1545989136.966 * * [misc]simplify: iters left: 3 (31 enodes) 1545989136.973 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt (sqrt k)))) 1545989136.974 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt (sqrt k)))) (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt (sqrt k))))) (sqrt (sqrt k)))) 1545989136.974 * * * * [misc]progress: [ 67 / 113 ] simplifiying candidate # 1545989136.975 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1) 1545989136.975 * * [misc]simplify: iters left: 6 (13 enodes) 1545989136.979 * * [misc]simplify: iters left: 5 (21 enodes) 1545989136.986 * * [misc]simplify: iters left: 4 (32 enodes) 1545989136.992 * * [misc]simplify: iters left: 3 (33 enodes) 1545989136.996 * [exit]simplify: Simplified to (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) 1545989136.996 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (* (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (sqrt k)))) 1545989136.996 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1545989136.996 * * [misc]simplify: iters left: 6 (14 enodes) 1545989136.998 * * [misc]simplify: iters left: 5 (20 enodes) 1545989137.001 * * [misc]simplify: iters left: 4 (29 enodes) 1545989137.004 * * [misc]simplify: iters left: 3 (30 enodes) 1545989137.008 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1545989137.008 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (sqrt k)))) 1545989137.008 * * * * [misc]progress: [ 68 / 113 ] simplifiying candidate # 1545989137.008 * [enter]simplify: Simplifying (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) 1545989137.008 * * [misc]simplify: iters left: 6 (7 enodes) 1545989137.009 * * [misc]simplify: iters left: 5 (11 enodes) 1545989137.011 * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) 1545989137.011 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (* (/ (/ 1 (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt k)))) 1545989137.011 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (cbrt (sqrt (sqrt k)))) 1545989137.011 * * [misc]simplify: iters left: 6 (14 enodes) 1545989137.015 * * [misc]simplify: iters left: 5 (20 enodes) 1545989137.018 * * [misc]simplify: iters left: 4 (29 enodes) 1545989137.021 * * [misc]simplify: iters left: 3 (30 enodes) 1545989137.024 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (cbrt (sqrt (sqrt k)))) 1545989137.025 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt k)))) 1545989137.025 * * * * [misc]progress: [ 69 / 113 ] simplifiying candidate # 1545989137.025 * [enter]simplify: Simplifying (/ 1 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) 1545989137.025 * * [misc]simplify: iters left: 6 (7 enodes) 1545989137.026 * * [misc]simplify: iters left: 5 (10 enodes) 1545989137.027 * [exit]simplify: Simplified to (/ 1 (fabs (cbrt (sqrt k)))) 1545989137.027 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (* (/ 1 (fabs (cbrt (sqrt k)))) (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (cbrt (sqrt k))))) (sqrt (sqrt k)))) 1545989137.027 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (cbrt (sqrt k)))) 1545989137.027 * * [misc]simplify: iters left: 6 (14 enodes) 1545989137.029 * * [misc]simplify: iters left: 5 (20 enodes) 1545989137.032 * * [misc]simplify: iters left: 4 (29 enodes) 1545989137.035 * * [misc]simplify: iters left: 3 (30 enodes) 1545989137.039 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt (cbrt (sqrt k)))) 1545989137.039 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (/ 1 (fabs (cbrt (sqrt k)))) (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt (cbrt (sqrt k))))) (sqrt (sqrt k)))) 1545989137.039 * * * * [misc]progress: [ 70 / 113 ] simplifiying candidate # 1545989137.039 * [enter]simplify: Simplifying (/ 1 (sqrt (sqrt (sqrt k)))) 1545989137.039 * * [misc]simplify: iters left: 5 (6 enodes) 1545989137.040 * * [misc]simplify: iters left: 4 (8 enodes) 1545989137.041 * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt (sqrt k)))) 1545989137.041 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (* (/ 1 (sqrt (sqrt (sqrt k)))) (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt (sqrt k))))) (sqrt (sqrt k)))) 1545989137.041 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt (sqrt k)))) 1545989137.041 * * [misc]simplify: iters left: 6 (14 enodes) 1545989137.043 * * [misc]simplify: iters left: 5 (20 enodes) 1545989137.048 * * [misc]simplify: iters left: 4 (29 enodes) 1545989137.056 * * [misc]simplify: iters left: 3 (30 enodes) 1545989137.063 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt (sqrt (sqrt k)))) 1545989137.063 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (/ 1 (sqrt (sqrt (sqrt k)))) (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt (sqrt (sqrt k))))) (sqrt (sqrt k)))) 1545989137.063 * * * * [misc]progress: [ 71 / 113 ] simplifiying candidate # 1545989137.063 * [enter]simplify: Simplifying (/ 1 (sqrt 1)) 1545989137.063 * * [misc]simplify: iters left: 3 (3 enodes) 1545989137.066 * * [misc]simplify: iters left: 2 (5 enodes) 1545989137.066 * [exit]simplify: Simplified to 1 1545989137.066 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (* 1 (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (sqrt (sqrt k)))) 1545989137.067 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1545989137.067 * * [misc]simplify: iters left: 6 (13 enodes) 1545989137.070 * * [misc]simplify: iters left: 5 (19 enodes) 1545989137.077 * * [misc]simplify: iters left: 4 (28 enodes) 1545989137.089 * * [misc]simplify: iters left: 3 (30 enodes) 1545989137.096 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1545989137.096 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* 1 (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (sqrt (sqrt k)))) 1545989137.096 * * * * [misc]progress: [ 72 / 113 ] simplifiying candidate # 1545989137.096 * [enter]simplify: Simplifying (/ 1 (sqrt (sqrt (sqrt k)))) 1545989137.097 * * [misc]simplify: iters left: 5 (6 enodes) 1545989137.098 * * [misc]simplify: iters left: 4 (8 enodes) 1545989137.100 * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt (sqrt k)))) 1545989137.100 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (* (/ 1 (sqrt (sqrt (sqrt k)))) (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt (sqrt k))))) (sqrt (sqrt k)))) 1545989137.100 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt (sqrt k)))) 1545989137.101 * * [misc]simplify: iters left: 6 (14 enodes) 1545989137.105 * * [misc]simplify: iters left: 5 (20 enodes) 1545989137.111 * * [misc]simplify: iters left: 4 (29 enodes) 1545989137.118 * * [misc]simplify: iters left: 3 (30 enodes) 1545989137.125 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt (sqrt (sqrt k)))) 1545989137.125 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (/ 1 (sqrt (sqrt (sqrt k)))) (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt (sqrt (sqrt k))))) (sqrt (sqrt k)))) 1545989137.125 * * * * [misc]progress: [ 73 / 113 ] simplifiying candidate # 1545989137.126 * [enter]simplify: Simplifying (/ 1 1) 1545989137.126 * * [misc]simplify: iters left: 2 (2 enodes) 1545989137.126 * * [misc]simplify: iters left: 1 (4 enodes) 1545989137.127 * [exit]simplify: Simplified to 1 1545989137.127 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (* 1 (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (sqrt (sqrt k)))) 1545989137.127 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1545989137.127 * * [misc]simplify: iters left: 6 (13 enodes) 1545989137.131 * * [misc]simplify: iters left: 5 (19 enodes) 1545989137.136 * * [misc]simplify: iters left: 4 (28 enodes) 1545989137.144 * * [misc]simplify: iters left: 3 (30 enodes) 1545989137.151 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1545989137.151 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* 1 (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (sqrt (sqrt k)))) 1545989137.151 * * * * [misc]progress: [ 74 / 113 ] simplifiying candidate # 1545989137.151 * * * * [misc]progress: [ 75 / 113 ] simplifiying candidate # 1545989137.151 * * * * [misc]progress: [ 76 / 113 ] simplifiying candidate # 1545989137.151 * * * * [misc]progress: [ 77 / 113 ] simplifiying candidate # 1545989137.151 * [enter]simplify: Simplifying (cbrt (sqrt (sqrt k))) 1545989137.152 * * [misc]simplify: iters left: 3 (4 enodes) 1545989137.153 * [exit]simplify: Simplified to (cbrt (sqrt (sqrt k))) 1545989137.153 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (/ (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt k)))) 1545989137.153 * * * * [misc]progress: [ 78 / 113 ] simplifiying candidate # 1545989137.153 * [enter]simplify: Simplifying (sqrt (cbrt (sqrt k))) 1545989137.153 * * [misc]simplify: iters left: 3 (4 enodes) 1545989137.154 * [exit]simplify: Simplified to (sqrt (cbrt (sqrt k))) 1545989137.154 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (/ (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt k)))) 1545989137.154 * * * * [misc]progress: [ 79 / 113 ] simplifiying candidate # 1545989137.154 * [enter]simplify: Simplifying (sqrt (sqrt (sqrt k))) 1545989137.154 * * [misc]simplify: iters left: 3 (4 enodes) 1545989137.156 * [exit]simplify: Simplified to (sqrt (sqrt (sqrt k))) 1545989137.156 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (/ (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k)))) 1545989137.156 * * * * [misc]progress: [ 80 / 113 ] simplifiying candidate # 1545989137.156 * [enter]simplify: Simplifying (sqrt (sqrt k)) 1545989137.156 * * [misc]simplify: iters left: 2 (3 enodes) 1545989137.157 * [exit]simplify: Simplified to (sqrt (sqrt k)) 1545989137.157 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (/ (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt 1)) (sqrt (sqrt k))) (sqrt (sqrt k)))) 1545989137.157 * * * * [misc]progress: [ 81 / 113 ] simplifiying candidate # 1545989137.157 * [enter]simplify: Simplifying (sqrt (sqrt (sqrt k))) 1545989137.157 * * [misc]simplify: iters left: 3 (4 enodes) 1545989137.158 * [exit]simplify: Simplified to (sqrt (sqrt (sqrt k))) 1545989137.158 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (/ (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k)))) 1545989137.158 * * * * [misc]progress: [ 82 / 113 ] simplifiying candidate # 1545989137.159 * [enter]simplify: Simplifying (sqrt (sqrt k)) 1545989137.159 * * [misc]simplify: iters left: 2 (3 enodes) 1545989137.160 * [exit]simplify: Simplified to (sqrt (sqrt k)) 1545989137.160 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (/ (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) 1) (sqrt (sqrt k))) (sqrt (sqrt k)))) 1545989137.160 * * * * [misc]progress: [ 83 / 113 ] simplifiying candidate # 1545989137.160 * [enter]simplify: Simplifying (pow (* PI (* n 2)) 1/2) 1545989137.160 * * [misc]simplify: iters left: 5 (7 enodes) 1545989137.162 * * [misc]simplify: iters left: 4 (12 enodes) 1545989137.165 * * [misc]simplify: iters left: 3 (18 enodes) 1545989137.170 * * [misc]simplify: iters left: 2 (20 enodes) 1545989137.175 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1545989137.175 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (/ (sqrt (* (* 2 n) PI)) (/ (sqrt (sqrt k)) (pow (* PI (* n 2)) (- (/ k 2))))) (sqrt (sqrt k)))) 1545989137.175 * * * * [misc]progress: [ 84 / 113 ] simplifiying candidate # 1545989137.175 * [enter]simplify: Simplifying (pow (* PI (* n 2)) 1/2) 1545989137.175 * * [misc]simplify: iters left: 5 (7 enodes) 1545989137.177 * * [misc]simplify: iters left: 4 (12 enodes) 1545989137.181 * * [misc]simplify: iters left: 3 (18 enodes) 1545989137.185 * * [misc]simplify: iters left: 2 (20 enodes) 1545989137.190 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1545989137.190 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (/ (sqrt (* (* 2 n) PI)) (/ (sqrt (sqrt k)) (pow (* PI (* n 2)) (- (/ k 2))))) (sqrt (sqrt k)))) 1545989137.190 * * * * [misc]progress: [ 85 / 113 ] simplifiying candidate # 1545989137.190 * [enter]simplify: Simplifying (pow PI (- 1/2 (/ k 2))) 1545989137.190 * * [misc]simplify: iters left: 5 (7 enodes) 1545989137.192 * * [misc]simplify: iters left: 4 (9 enodes) 1545989137.195 * * [misc]simplify: iters left: 3 (12 enodes) 1545989137.198 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1545989137.198 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (/ (pow PI (- 1/2 (/ k 2))) (/ (sqrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2))))) (sqrt (sqrt k)))) 1545989137.198 * * * * [misc]progress: [ 86 / 113 ] simplifiying candidate # 1545989137.198 * [enter]simplify: Simplifying (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1545989137.198 * * [misc]simplify: iters left: 6 (12 enodes) 1545989137.202 * * [misc]simplify: iters left: 5 (18 enodes) 1545989137.207 * * [misc]simplify: iters left: 4 (27 enodes) 1545989137.214 * * [misc]simplify: iters left: 3 (29 enodes) 1545989137.221 * [exit]simplify: Simplified to (* (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) 1545989137.222 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (/ (* (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) (/ (sqrt (sqrt k)) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) (sqrt (sqrt k)))) 1545989137.222 * * * * [misc]progress: [ 87 / 113 ] simplifiying candidate # 1545989137.222 * [enter]simplify: Simplifying (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1545989137.222 * * [misc]simplify: iters left: 6 (11 enodes) 1545989137.226 * * [misc]simplify: iters left: 5 (17 enodes) 1545989137.231 * * [misc]simplify: iters left: 4 (26 enodes) 1545989137.238 * * [misc]simplify: iters left: 3 (27 enodes) 1545989137.244 * [exit]simplify: Simplified to (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) 1545989137.245 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (/ (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) (sqrt (sqrt k)))) 1545989137.245 * * * * [misc]progress: [ 88 / 113 ] simplifiying candidate # 1545989137.245 * * * * [misc]progress: [ 89 / 113 ] simplifiying candidate # 1545989137.245 * [enter]simplify: Simplifying (pow (* PI (* n 2)) 1/2) 1545989137.245 * * [misc]simplify: iters left: 5 (7 enodes) 1545989137.247 * * [misc]simplify: iters left: 4 (12 enodes) 1545989137.251 * * [misc]simplify: iters left: 3 (18 enodes) 1545989137.255 * * [misc]simplify: iters left: 2 (20 enodes) 1545989137.260 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1545989137.260 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (/ (sqrt (* (* 2 n) PI)) (* (sqrt (sqrt k)) (pow (* PI (* n 2)) (/ k 2)))) (sqrt (sqrt k)))) 1545989137.260 * * * * [misc]progress: [ 90 / 113 ] simplifiying candidate # 1545989137.260 * * * * [misc]progress: [ 91 / 113 ] simplifiying candidate # 1545989137.261 * * * * [misc]progress: [ 92 / 113 ] simplifiying candidate # 1545989137.261 * * * * [misc]progress: [ 93 / 113 ] simplifiying candidate # 1545989137.261 * * * * [misc]progress: [ 94 / 113 ] simplifiying candidate # 1545989137.261 * * * * [misc]progress: [ 95 / 113 ] simplifiying candidate # 1545989137.261 * * * * [misc]progress: [ 96 / 113 ] simplifiying candidate # 1545989137.261 * [enter]simplify: Simplifying (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1545989137.261 * * [misc]simplify: iters left: 5 (5 enodes) 1545989137.263 * * [misc]simplify: iters left: 4 (6 enodes) 1545989137.264 * [exit]simplify: Simplified to (fabs (cbrt (sqrt k))) 1545989137.264 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (* (fabs (cbrt (sqrt k))) (sqrt (cbrt (sqrt k)))))) 1545989137.264 * * * * [misc]progress: [ 97 / 113 ] simplifiying candidate # 1545989137.265 * [enter]simplify: Simplifying (sqrt (sqrt (sqrt k))) 1545989137.265 * * [misc]simplify: iters left: 3 (4 enodes) 1545989137.266 * [exit]simplify: Simplified to (sqrt (sqrt (sqrt k))) 1545989137.266 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (* (sqrt (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))))) 1545989137.266 * * * * [misc]progress: [ 98 / 113 ] simplifiying candidate # 1545989137.267 * [enter]simplify: Simplifying (sqrt 1) 1545989137.267 * * [misc]simplify: iters left: 1 (2 enodes) 1545989137.269 * [exit]simplify: Simplified to 1 1545989137.269 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (* 1 (sqrt (sqrt k))))) 1545989137.269 * * * * [misc]progress: [ 99 / 113 ] simplifiying candidate # 1545989137.269 * * * * [misc]progress: [ 100 / 113 ] simplifiying candidate # 1545989137.269 * [enter]simplify: Simplifying (sqrt (sqrt k)) 1545989137.269 * * [misc]simplify: iters left: 2 (3 enodes) 1545989137.270 * [exit]simplify: Simplified to (sqrt (sqrt k)) 1545989137.270 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (fabs (sqrt (sqrt k))))) 1545989137.270 * * * * [misc]progress: [ 101 / 113 ] simplifiying candidate # 1545989137.270 * * * * [misc]progress: [ 102 / 113 ] simplifiying candidate # 1545989137.271 * [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))))) 1545989137.271 * * [misc]simplify: iters left: 6 (37 enodes) 1545989137.286 * * [misc]simplify: iters left: 5 (105 enodes) 1545989137.328 * * [misc]simplify: iters left: 4 (339 enodes) 1545989137.557 * [exit]simplify: Simplified to (+ (+ (* (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) -1/2) (+ (* (* (* k (log n)) (* k (log n))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (pow (* PI 2) 1/2) (pow n 1/2)))) (* (* k k) (+ (* (* (log (* PI 2)) (log (* PI 2))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (* (* (log n) (pow n 1/2)) (pow (* PI 2) 1/2)) (* (log (* PI 2)) 1/4))))) 1545989137.557 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (/ (+ (+ (* (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) -1/2) (+ (* (* (* k (log n)) (* k (log n))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (pow (* PI 2) 1/2) (pow n 1/2)))) (* (* k k) (+ (* (* (log (* PI 2)) (log (* PI 2))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (* (* (log n) (pow n 1/2)) (pow (* PI 2) 1/2)) (* (log (* PI 2)) 1/4))))) (sqrt (sqrt k))) (sqrt (sqrt k)))) 1545989137.557 * * * * [misc]progress: [ 103 / 113 ] simplifiying candidate # 1545989137.558 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 1545989137.558 * * [misc]simplify: iters left: 6 (15 enodes) 1545989137.564 * * [misc]simplify: iters left: 5 (33 enodes) 1545989137.574 * * [misc]simplify: iters left: 4 (64 enodes) 1545989137.598 * * [misc]simplify: iters left: 3 (171 enodes) 1545989137.725 * [exit]simplify: Simplified to (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow n (- 1/2 (* 1/2 k)))) 1545989137.726 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (/ (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow n (- 1/2 (* 1/2 k)))) (sqrt (sqrt k))) (sqrt (sqrt k)))) 1545989137.726 * * * * [misc]progress: [ 104 / 113 ] simplifiying candidate # 1545989137.726 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 1545989137.726 * * [misc]simplify: iters left: 6 (15 enodes) 1545989137.730 * * [misc]simplify: iters left: 5 (30 enodes) 1545989137.738 * * [misc]simplify: iters left: 4 (65 enodes) 1545989137.753 * * [misc]simplify: iters left: 3 (200 enodes) 1545989137.882 * [exit]simplify: Simplified to (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))) 1545989137.882 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (/ (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))) (sqrt (sqrt k))) (sqrt (sqrt k)))) 1545989137.882 * * * * [misc]progress: [ 105 / 113 ] simplifiying candidate # 1545989137.882 * [enter]simplify: Simplifying (* 2 (* n PI)) 1545989137.882 * * [misc]simplify: iters left: 4 (5 enodes) 1545989137.884 * * [misc]simplify: iters left: 3 (9 enodes) 1545989137.887 * * [misc]simplify: iters left: 2 (15 enodes) 1545989137.891 * * [misc]simplify: iters left: 1 (17 enodes) 1545989137.895 * [exit]simplify: Simplified to (* (* PI n) 2) 1545989137.895 * [misc]simplify: Simplified (2 1 1 1) to (λ (k n) (/ (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k)))) 1545989137.895 * * * * [misc]progress: [ 106 / 113 ] simplifiying candidate # 1545989137.895 * [enter]simplify: Simplifying (* 2 (* n PI)) 1545989137.895 * * [misc]simplify: iters left: 4 (5 enodes) 1545989137.897 * * [misc]simplify: iters left: 3 (9 enodes) 1545989137.899 * * [misc]simplify: iters left: 2 (15 enodes) 1545989137.903 * * [misc]simplify: iters left: 1 (17 enodes) 1545989137.907 * [exit]simplify: Simplified to (* (* PI n) 2) 1545989137.907 * [misc]simplify: Simplified (2 1 1 1) to (λ (k n) (/ (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k)))) 1545989137.907 * * * * [misc]progress: [ 107 / 113 ] simplifiying candidate # 1545989137.908 * [enter]simplify: Simplifying (* 2 (* n PI)) 1545989137.908 * * [misc]simplify: iters left: 4 (5 enodes) 1545989137.909 * * [misc]simplify: iters left: 3 (9 enodes) 1545989137.912 * * [misc]simplify: iters left: 2 (15 enodes) 1545989137.916 * * [misc]simplify: iters left: 1 (17 enodes) 1545989137.920 * [exit]simplify: Simplified to (* (* PI n) 2) 1545989137.920 * [misc]simplify: Simplified (2 1 1 1) to (λ (k n) (/ (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k)))) 1545989137.920 * * * * [misc]progress: [ 108 / 113 ] simplifiying candidate # 1545989137.921 * [enter]simplify: Simplifying (- (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (/ 1 k) 1/4)) (+ (* 1/8 (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2)) (pow (pow k 7) 1/4))) (+ (* 1/4 (* (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))) (pow (pow k 7) 1/4))) (* 1/8 (* (* (pow (log (* 2 PI)) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (pow (pow k 7) 1/4)))))) (+ (* 1/2 (* (* (log (* 2 PI)) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (pow (pow k 3) 1/4))) (* 1/2 (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)) (pow (pow k 3) 1/4))))) 1545989137.921 * * [misc]simplify: iters left: 6 (45 enodes) 1545989137.939 * * [misc]simplify: iters left: 5 (119 enodes) 1545989137.987 * * [misc]simplify: iters left: 4 (333 enodes) 1545989138.233 * [exit]simplify: Simplified to (+ (+ (* (- (pow (pow k 3) 1/4)) (* (* (* 1/2 (pow n 1/2)) (pow (* 2 PI) 1/2)) (+ (log n) (log (* 2 PI))))) (+ (* (* (* 1/8 (pow n 1/2)) (pow (* 2 PI) 1/2)) (* (* (log n) (log n)) (pow (pow k 7) 1/4))) (* (pow (/ 1 k) 1/4) (* (pow n 1/2) (pow (* 2 PI) 1/2))))) (* (pow (pow k 7) 1/4) (+ (* (* (log (* 2 PI)) (log (* 2 PI))) (* (* 1/8 (pow n 1/2)) (pow (* 2 PI) 1/2))) (* (* (* (log n) (pow n 1/2)) (pow (* 2 PI) 1/2)) (* 1/4 (log (* 2 PI))))))) 1545989138.234 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (+ (+ (* (- (pow (pow k 3) 1/4)) (* (* (* 1/2 (pow n 1/2)) (pow (* 2 PI) 1/2)) (+ (log n) (log (* 2 PI))))) (+ (* (* (* 1/8 (pow n 1/2)) (pow (* 2 PI) 1/2)) (* (* (log n) (log n)) (pow (pow k 7) 1/4))) (* (pow (/ 1 k) 1/4) (* (pow n 1/2) (pow (* 2 PI) 1/2))))) (* (pow (pow k 7) 1/4) (+ (* (* (log (* 2 PI)) (log (* 2 PI))) (* (* 1/8 (pow n 1/2)) (pow (* 2 PI) 1/2))) (* (* (* (log n) (pow n 1/2)) (pow (* 2 PI) 1/2)) (* 1/4 (log (* 2 PI))))))) (sqrt (sqrt k)))) 1545989138.234 * * * * [misc]progress: [ 109 / 113 ] simplifiying candidate # 1545989138.234 * [enter]simplify: Simplifying (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow (/ 1 k) 1/4)) 1545989138.234 * * [misc]simplify: iters left: 6 (19 enodes) 1545989138.242 * * [misc]simplify: iters left: 5 (38 enodes) 1545989138.254 * * [misc]simplify: iters left: 4 (69 enodes) 1545989138.280 * * [misc]simplify: iters left: 3 (176 enodes) 1545989138.375 * [exit]simplify: Simplified to (* (* (pow (/ 1 k) 1/4) (pow (* 2 PI) (- 1/2 (* 1/2 k)))) (pow n (- 1/2 (* 1/2 k)))) 1545989138.375 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (* (* (pow (/ 1 k) 1/4) (pow (* 2 PI) (- 1/2 (* 1/2 k)))) (pow n (- 1/2 (* 1/2 k)))) (sqrt (sqrt k)))) 1545989138.375 * * * * [misc]progress: [ 110 / 113 ] simplifiying candidate # 1545989138.376 * [enter]simplify: Simplifying (- (* (sqrt +nan.0) (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))) (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (* (sqrt +nan.0) k))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (* (pow (sqrt +nan.0) 3) (pow k 2)))) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (* (sqrt +nan.0) (pow k 2))))))))) 1545989138.376 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ +nan.0 (sqrt (sqrt k)))) 1545989138.376 * * * * [misc]progress: [ 111 / 113 ] simplifiying candidate # 1545989138.376 * [enter]simplify: Simplifying (pow k 1/4) 1545989138.376 * * [misc]simplify: iters left: 1 (3 enodes) 1545989138.377 * [exit]simplify: Simplified to (pow k 1/4) 1545989138.377 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (pow k 1/4))) 1545989138.377 * * * * [misc]progress: [ 112 / 113 ] simplifiying candidate # 1545989138.378 * [enter]simplify: Simplifying (pow (/ 1 k) -1/4) 1545989138.378 * * [misc]simplify: iters left: 3 (5 enodes) 1545989138.379 * * [misc]simplify: iters left: 2 (7 enodes) 1545989138.381 * [exit]simplify: Simplified to (pow (/ 1 k) -1/4) 1545989138.381 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (pow (/ 1 k) -1/4))) 1545989138.381 * * * * [misc]progress: [ 113 / 113 ] simplifiying candidate # 1545989138.381 * [enter]simplify: Simplifying (- (sqrt +nan.0) (+ (* +nan.0 (/ 1 (* (sqrt +nan.0) k))) (- (+ (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 3) (pow k 2)))) (- (* +nan.0 (/ 1 (* (sqrt +nan.0) (pow k 2))))))))) 1545989138.381 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) +nan.0)) 1545989138.381 * * * [misc]progress: adding candidates to table 1545989140.168 * * [misc]progress: iteration 3 / 4 1545989140.168 * * * [misc]progress: picking best candidate 1545989140.221 * * * * [misc]pick: Picked # 1545989140.221 * * * [misc]progress: localizing error 1545989140.251 * * * [misc]progress: generating rewritten candidates 1545989140.251 * * * * [misc]progress: [ 1 / 4 ] rewriting at (2 2 1) 1545989140.254 * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 1) 1545989140.255 * * * * [misc]progress: [ 3 / 4 ] rewriting at (2 2) 1545989140.264 * * * * [misc]progress: [ 4 / 4 ] rewriting at (2) 1545989140.277 * * * [misc]progress: generating series expansions 1545989140.277 * * * * [misc]progress: [ 1 / 4 ] generating series at (2 2 1) 1545989140.278 * [misc]backup-simplify: Simplify (pow (* n 2) (- 1/2 (/ k 2))) into (pow (* 2 n) (- 1/2 (* 1/2 k))) 1545989140.278 * [misc]approximate: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in (n k) around 0 1545989140.278 * [misc]taylor: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in k 1545989140.278 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in k 1545989140.278 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in k 1545989140.278 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1545989140.278 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989140.278 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.278 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1545989140.278 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989140.278 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.278 * [misc]taylor: Taking taylor expansion of k in k 1545989140.278 * [misc]backup-simplify: Simplify 0 into 0 1545989140.278 * [misc]backup-simplify: Simplify 1 into 1 1545989140.278 * [misc]taylor: Taking taylor expansion of (log (* 2 n)) in k 1545989140.278 * [misc]taylor: Taking taylor expansion of (* 2 n) in k 1545989140.278 * [misc]taylor: Taking taylor expansion of 2 in k 1545989140.278 * [misc]backup-simplify: Simplify 2 into 2 1545989140.278 * [misc]taylor: Taking taylor expansion of n in k 1545989140.278 * [misc]backup-simplify: Simplify n into n 1545989140.278 * [misc]backup-simplify: Simplify (* 2 n) into (* 2 n) 1545989140.278 * [misc]backup-simplify: Simplify (log (* 2 n)) into (log (* 2 n)) 1545989140.278 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1545989140.278 * [misc]backup-simplify: Simplify (- 0) into 0 1545989140.278 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545989140.279 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 n))) into (* 1/2 (log (* 2 n))) 1545989140.279 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 n)))) into (pow (* 2 n) 1/2) 1545989140.279 * [misc]taylor: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in n 1545989140.279 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in n 1545989140.279 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in n 1545989140.279 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1545989140.279 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989140.279 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.279 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1545989140.279 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989140.279 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.279 * [misc]taylor: Taking taylor expansion of k in n 1545989140.279 * [misc]backup-simplify: Simplify k into k 1545989140.279 * [misc]taylor: Taking taylor expansion of (log (* 2 n)) in n 1545989140.279 * [misc]taylor: Taking taylor expansion of (* 2 n) in n 1545989140.279 * [misc]taylor: Taking taylor expansion of 2 in n 1545989140.279 * [misc]backup-simplify: Simplify 2 into 2 1545989140.279 * [misc]taylor: Taking taylor expansion of n in n 1545989140.279 * [misc]backup-simplify: Simplify 0 into 0 1545989140.279 * [misc]backup-simplify: Simplify 1 into 1 1545989140.279 * [misc]backup-simplify: Simplify (* 2 0) into 0 1545989140.279 * [misc]backup-simplify: Simplify (+ (* 2 1) (* 0 0)) into 2 1545989140.279 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1545989140.279 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1545989140.279 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1545989140.279 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1545989140.280 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 1545989140.280 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (+ (log 2) (log n))) into (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) 1545989140.280 * [misc]backup-simplify: Simplify (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) into (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) 1545989140.280 * [misc]taylor: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in n 1545989140.280 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in n 1545989140.280 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in n 1545989140.280 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1545989140.280 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989140.280 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.280 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1545989140.280 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989140.280 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.280 * [misc]taylor: Taking taylor expansion of k in n 1545989140.280 * [misc]backup-simplify: Simplify k into k 1545989140.280 * [misc]taylor: Taking taylor expansion of (log (* 2 n)) in n 1545989140.280 * [misc]taylor: Taking taylor expansion of (* 2 n) in n 1545989140.280 * [misc]taylor: Taking taylor expansion of 2 in n 1545989140.280 * [misc]backup-simplify: Simplify 2 into 2 1545989140.280 * [misc]taylor: Taking taylor expansion of n in n 1545989140.280 * [misc]backup-simplify: Simplify 0 into 0 1545989140.280 * [misc]backup-simplify: Simplify 1 into 1 1545989140.280 * [misc]backup-simplify: Simplify (* 2 0) into 0 1545989140.280 * [misc]backup-simplify: Simplify (+ (* 2 1) (* 0 0)) into 2 1545989140.281 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1545989140.281 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1545989140.281 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1545989140.281 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1545989140.281 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 1545989140.281 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (+ (log 2) (log n))) into (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) 1545989140.281 * [misc]backup-simplify: Simplify (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) into (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) 1545989140.281 * [misc]taylor: Taking taylor expansion of (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) in k 1545989140.281 * [misc]taylor: Taking taylor expansion of (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) in k 1545989140.281 * [misc]taylor: Taking taylor expansion of (+ (log 2) (log n)) in k 1545989140.281 * [misc]taylor: Taking taylor expansion of (log 2) in k 1545989140.281 * [misc]taylor: Taking taylor expansion of 2 in k 1545989140.281 * [misc]backup-simplify: Simplify 2 into 2 1545989140.282 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1545989140.282 * [misc]taylor: Taking taylor expansion of (log n) in k 1545989140.282 * [misc]taylor: Taking taylor expansion of n in k 1545989140.282 * [misc]backup-simplify: Simplify n into n 1545989140.282 * [misc]backup-simplify: Simplify (log n) into (log n) 1545989140.282 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1545989140.282 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989140.282 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.282 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1545989140.282 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989140.282 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.282 * [misc]taylor: Taking taylor expansion of k in k 1545989140.282 * [misc]backup-simplify: Simplify 0 into 0 1545989140.282 * [misc]backup-simplify: Simplify 1 into 1 1545989140.282 * [misc]backup-simplify: Simplify (+ (log 2) (log n)) into (+ (log 2) (log n)) 1545989140.282 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1545989140.282 * [misc]backup-simplify: Simplify (- 0) into 0 1545989140.282 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545989140.282 * [misc]backup-simplify: Simplify (* (+ (log 2) (log n)) 1/2) into (* 1/2 (+ (log 2) (log n))) 1545989140.283 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log 2) (log n)))) into (exp (* 1/2 (+ (log 2) (log n)))) 1545989140.283 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log 2) (log n)))) into (exp (* 1/2 (+ (log 2) (log n)))) 1545989140.283 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 1) (* 0 0))) into 0 1545989140.284 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 1545989140.285 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1545989140.285 * [misc]backup-simplify: Simplify (- 0) into 0 1545989140.285 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989140.285 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 1545989140.285 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log 2) (log n)))) into 0 1545989140.286 * [misc]backup-simplify: Simplify (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (+ (* (/ (pow 0 1) 1)))) into 0 1545989140.286 * [misc]taylor: Taking taylor expansion of 0 in k 1545989140.286 * [misc]backup-simplify: Simplify 0 into 0 1545989140.286 * [misc]backup-simplify: Simplify 0 into 0 1545989140.286 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1545989140.286 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1545989140.286 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1545989140.288 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 1545989140.288 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1545989140.289 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989140.289 * [misc]backup-simplify: Simplify (+ (* (+ (log 2) (log n)) -1/2) (* 0 1/2)) into (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 1545989140.289 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) 1545989140.290 * [misc]backup-simplify: Simplify (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) into (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) 1545989140.290 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1545989140.293 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 1545989140.293 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1545989140.293 * [misc]backup-simplify: Simplify (- 0) into 0 1545989140.293 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989140.293 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 1545989140.293 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log 2) (log n))))) into 0 1545989140.295 * [misc]backup-simplify: Simplify (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1545989140.295 * [misc]taylor: Taking taylor expansion of 0 in k 1545989140.295 * [misc]backup-simplify: Simplify 0 into 0 1545989140.295 * [misc]backup-simplify: Simplify 0 into 0 1545989140.295 * [misc]backup-simplify: Simplify 0 into 0 1545989140.295 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1545989140.295 * [misc]backup-simplify: Simplify (- 0) into 0 1545989140.295 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989140.298 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 1545989140.299 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1545989140.299 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989140.299 * [misc]backup-simplify: Simplify (+ (* (+ (log 2) (log n)) 0) (+ (* 0 -1/2) (* 0 1/2))) into 0 1545989140.300 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))) 1545989140.301 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))) into (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))) 1545989140.303 * [misc]backup-simplify: Simplify (+ (* (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) (* k 1)) (exp (* 1/2 (+ (log 2) (log n)))))) into (- (+ (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (* (pow (log 2) 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (pow k 2)))) (+ (* 1/4 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) (pow k 2))))) (* 1/8 (* (exp (* 1/2 (+ (log 2) (log n)))) (* (pow (log n) 2) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) k))) (* 1/2 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) k))))) 1545989140.303 * [misc]backup-simplify: Simplify (pow (* (/ 1 n) 2) (- 1/2 (/ (/ 1 k) 2))) into (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) 1545989140.303 * [misc]approximate: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 1545989140.303 * [misc]taylor: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in k 1545989140.303 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in k 1545989140.303 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in k 1545989140.303 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1545989140.303 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989140.303 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.303 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545989140.303 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989140.303 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.303 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989140.303 * [misc]taylor: Taking taylor expansion of k in k 1545989140.303 * [misc]backup-simplify: Simplify 0 into 0 1545989140.303 * [misc]backup-simplify: Simplify 1 into 1 1545989140.303 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989140.303 * [misc]taylor: Taking taylor expansion of (log (/ 2 n)) in k 1545989140.303 * [misc]taylor: Taking taylor expansion of (/ 2 n) in k 1545989140.303 * [misc]taylor: Taking taylor expansion of 2 in k 1545989140.303 * [misc]backup-simplify: Simplify 2 into 2 1545989140.303 * [misc]taylor: Taking taylor expansion of n in k 1545989140.303 * [misc]backup-simplify: Simplify n into n 1545989140.304 * [misc]backup-simplify: Simplify (/ 2 n) into (/ 2 n) 1545989140.304 * [misc]backup-simplify: Simplify (log (/ 2 n)) into (log (/ 2 n)) 1545989140.304 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545989140.304 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1545989140.304 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1545989140.304 * [misc]backup-simplify: Simplify (* -1/2 (log (/ 2 n))) into (* -1/2 (log (/ 2 n))) 1545989140.304 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) into (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) 1545989140.304 * [misc]taylor: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 1545989140.304 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 1545989140.304 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 1545989140.304 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1545989140.304 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989140.304 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.304 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989140.304 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989140.304 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.304 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989140.304 * [misc]taylor: Taking taylor expansion of k in n 1545989140.304 * [misc]backup-simplify: Simplify k into k 1545989140.304 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989140.304 * [misc]taylor: Taking taylor expansion of (log (/ 2 n)) in n 1545989140.304 * [misc]taylor: Taking taylor expansion of (/ 2 n) in n 1545989140.304 * [misc]taylor: Taking taylor expansion of 2 in n 1545989140.304 * [misc]backup-simplify: Simplify 2 into 2 1545989140.304 * [misc]taylor: Taking taylor expansion of n in n 1545989140.304 * [misc]backup-simplify: Simplify 0 into 0 1545989140.304 * [misc]backup-simplify: Simplify 1 into 1 1545989140.305 * [misc]backup-simplify: Simplify (/ 2 1) into 2 1545989140.305 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1545989140.305 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989140.305 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1545989140.305 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1545989140.305 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 1545989140.305 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 1545989140.305 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 1545989140.305 * [misc]taylor: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 1545989140.305 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 1545989140.306 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 1545989140.306 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1545989140.306 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989140.306 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.306 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989140.306 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989140.306 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.306 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989140.306 * [misc]taylor: Taking taylor expansion of k in n 1545989140.306 * [misc]backup-simplify: Simplify k into k 1545989140.306 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989140.306 * [misc]taylor: Taking taylor expansion of (log (/ 2 n)) in n 1545989140.306 * [misc]taylor: Taking taylor expansion of (/ 2 n) in n 1545989140.306 * [misc]taylor: Taking taylor expansion of 2 in n 1545989140.306 * [misc]backup-simplify: Simplify 2 into 2 1545989140.306 * [misc]taylor: Taking taylor expansion of n in n 1545989140.306 * [misc]backup-simplify: Simplify 0 into 0 1545989140.306 * [misc]backup-simplify: Simplify 1 into 1 1545989140.306 * [misc]backup-simplify: Simplify (/ 2 1) into 2 1545989140.306 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1545989140.306 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989140.306 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1545989140.306 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1545989140.306 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 1545989140.307 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 1545989140.307 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 1545989140.307 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) in k 1545989140.307 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) in k 1545989140.307 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1545989140.307 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989140.307 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.307 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545989140.307 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989140.307 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.307 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989140.307 * [misc]taylor: Taking taylor expansion of k in k 1545989140.307 * [misc]backup-simplify: Simplify 0 into 0 1545989140.307 * [misc]backup-simplify: Simplify 1 into 1 1545989140.307 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989140.307 * [misc]taylor: Taking taylor expansion of (- (log 2) (log n)) in k 1545989140.307 * [misc]taylor: Taking taylor expansion of (log 2) in k 1545989140.307 * [misc]taylor: Taking taylor expansion of 2 in k 1545989140.307 * [misc]backup-simplify: Simplify 2 into 2 1545989140.307 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1545989140.307 * [misc]taylor: Taking taylor expansion of (log n) in k 1545989140.307 * [misc]taylor: Taking taylor expansion of n in k 1545989140.307 * [misc]backup-simplify: Simplify n into n 1545989140.307 * [misc]backup-simplify: Simplify (log n) into (log n) 1545989140.308 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545989140.308 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1545989140.308 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1545989140.308 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1545989140.308 * [misc]backup-simplify: Simplify (+ (log 2) (- (log n))) into (- (log 2) (log n)) 1545989140.308 * [misc]backup-simplify: Simplify (* -1/2 (- (log 2) (log n))) into (* -1/2 (- (log 2) (log n))) 1545989140.308 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 1545989140.308 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 1545989140.309 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)))) into 0 1545989140.310 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 1545989140.310 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1545989140.310 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1545989140.311 * [misc]backup-simplify: Simplify (- 0) into 0 1545989140.311 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989140.311 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 1545989140.311 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log 2) (log n)))) into 0 1545989140.312 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1545989140.312 * [misc]taylor: Taking taylor expansion of 0 in k 1545989140.312 * [misc]backup-simplify: Simplify 0 into 0 1545989140.312 * [misc]backup-simplify: Simplify 0 into 0 1545989140.312 * [misc]backup-simplify: Simplify 0 into 0 1545989140.312 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989140.315 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 1545989140.315 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545989140.315 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1545989140.316 * [misc]backup-simplify: Simplify (- 0) into 0 1545989140.316 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989140.316 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 1545989140.316 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log 2) (log n))))) into 0 1545989140.318 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1545989140.318 * [misc]taylor: Taking taylor expansion of 0 in k 1545989140.318 * [misc]backup-simplify: Simplify 0 into 0 1545989140.318 * [misc]backup-simplify: Simplify 0 into 0 1545989140.318 * [misc]backup-simplify: Simplify 0 into 0 1545989140.318 * [misc]backup-simplify: Simplify 0 into 0 1545989140.318 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989140.322 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 1545989140.322 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545989140.323 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1545989140.323 * [misc]backup-simplify: Simplify (- 0) into 0 1545989140.323 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989140.323 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 1545989140.323 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log 2) (log n)))))) into 0 1545989140.325 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1545989140.325 * [misc]taylor: Taking taylor expansion of 0 in k 1545989140.325 * [misc]backup-simplify: Simplify 0 into 0 1545989140.326 * [misc]backup-simplify: Simplify 0 into 0 1545989140.326 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log 2) (log (/ 1 n))))) into (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) 1545989140.326 * [misc]backup-simplify: Simplify (pow (* (/ 1 (- n)) 2) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) 1545989140.326 * [misc]approximate: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 1545989140.326 * [misc]taylor: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1545989140.326 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in k 1545989140.326 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in k 1545989140.326 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1545989140.326 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545989140.326 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989140.326 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.326 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989140.326 * [misc]taylor: Taking taylor expansion of k in k 1545989140.326 * [misc]backup-simplify: Simplify 0 into 0 1545989140.326 * [misc]backup-simplify: Simplify 1 into 1 1545989140.326 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989140.326 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989140.326 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.326 * [misc]taylor: Taking taylor expansion of (log (/ -2 n)) in k 1545989140.326 * [misc]taylor: Taking taylor expansion of (/ -2 n) in k 1545989140.326 * [misc]taylor: Taking taylor expansion of -2 in k 1545989140.326 * [misc]backup-simplify: Simplify -2 into -2 1545989140.326 * [misc]taylor: Taking taylor expansion of n in k 1545989140.326 * [misc]backup-simplify: Simplify n into n 1545989140.326 * [misc]backup-simplify: Simplify (/ -2 n) into (/ -2 n) 1545989140.326 * [misc]backup-simplify: Simplify (log (/ -2 n)) into (log (/ -2 n)) 1545989140.327 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545989140.327 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545989140.327 * [misc]backup-simplify: Simplify (* 1/2 (log (/ -2 n))) into (* 1/2 (log (/ -2 n))) 1545989140.327 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) into (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) 1545989140.327 * [misc]taylor: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1545989140.327 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 1545989140.327 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 1545989140.327 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1545989140.327 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989140.327 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989140.327 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.327 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989140.327 * [misc]taylor: Taking taylor expansion of k in n 1545989140.327 * [misc]backup-simplify: Simplify k into k 1545989140.327 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989140.327 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989140.327 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.327 * [misc]taylor: Taking taylor expansion of (log (/ -2 n)) in n 1545989140.327 * [misc]taylor: Taking taylor expansion of (/ -2 n) in n 1545989140.327 * [misc]taylor: Taking taylor expansion of -2 in n 1545989140.327 * [misc]backup-simplify: Simplify -2 into -2 1545989140.327 * [misc]taylor: Taking taylor expansion of n in n 1545989140.327 * [misc]backup-simplify: Simplify 0 into 0 1545989140.327 * [misc]backup-simplify: Simplify 1 into 1 1545989140.327 * [misc]backup-simplify: Simplify (/ -2 1) into -2 1545989140.327 * [misc]backup-simplify: Simplify (log -2) into (log -2) 1545989140.328 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989140.328 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1545989140.328 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 1545989140.328 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 1545989140.329 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 1545989140.329 * [misc]taylor: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1545989140.329 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 1545989140.329 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 1545989140.329 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1545989140.329 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989140.329 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989140.329 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.329 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989140.329 * [misc]taylor: Taking taylor expansion of k in n 1545989140.329 * [misc]backup-simplify: Simplify k into k 1545989140.329 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989140.329 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989140.329 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.329 * [misc]taylor: Taking taylor expansion of (log (/ -2 n)) in n 1545989140.329 * [misc]taylor: Taking taylor expansion of (/ -2 n) in n 1545989140.329 * [misc]taylor: Taking taylor expansion of -2 in n 1545989140.329 * [misc]backup-simplify: Simplify -2 into -2 1545989140.329 * [misc]taylor: Taking taylor expansion of n in n 1545989140.329 * [misc]backup-simplify: Simplify 0 into 0 1545989140.329 * [misc]backup-simplify: Simplify 1 into 1 1545989140.330 * [misc]backup-simplify: Simplify (/ -2 1) into -2 1545989140.330 * [misc]backup-simplify: Simplify (log -2) into (log -2) 1545989140.330 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989140.330 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1545989140.330 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 1545989140.331 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 1545989140.331 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 1545989140.331 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) in k 1545989140.331 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) in k 1545989140.331 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1545989140.331 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545989140.331 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989140.331 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.331 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989140.331 * [misc]taylor: Taking taylor expansion of k in k 1545989140.331 * [misc]backup-simplify: Simplify 0 into 0 1545989140.331 * [misc]backup-simplify: Simplify 1 into 1 1545989140.331 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989140.332 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989140.332 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.332 * [misc]taylor: Taking taylor expansion of (- (log -2) (log n)) in k 1545989140.332 * [misc]taylor: Taking taylor expansion of (log -2) in k 1545989140.332 * [misc]taylor: Taking taylor expansion of -2 in k 1545989140.332 * [misc]backup-simplify: Simplify -2 into -2 1545989140.332 * [misc]backup-simplify: Simplify (log -2) into (log -2) 1545989140.332 * [misc]taylor: Taking taylor expansion of (log n) in k 1545989140.332 * [misc]taylor: Taking taylor expansion of n in k 1545989140.332 * [misc]backup-simplify: Simplify n into n 1545989140.332 * [misc]backup-simplify: Simplify (log n) into (log n) 1545989140.332 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545989140.332 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545989140.332 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1545989140.333 * [misc]backup-simplify: Simplify (+ (log -2) (- (log n))) into (- (log -2) (log n)) 1545989140.333 * [misc]backup-simplify: Simplify (* 1/2 (- (log -2) (log n))) into (* 1/2 (- (log -2) (log n))) 1545989140.333 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 1545989140.334 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 1545989140.334 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -2 (/ 0 1)))) into 0 1545989140.336 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -2 1)))) 1) into 0 1545989140.336 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1545989140.337 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1545989140.337 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989140.337 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 1545989140.337 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log -2) (log n)))) into 0 1545989140.339 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1545989140.339 * [misc]taylor: Taking taylor expansion of 0 in k 1545989140.339 * [misc]backup-simplify: Simplify 0 into 0 1545989140.339 * [misc]backup-simplify: Simplify 0 into 0 1545989140.339 * [misc]backup-simplify: Simplify 0 into 0 1545989140.339 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -2 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989140.343 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -2 1)))) 2) into 0 1545989140.343 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545989140.343 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1545989140.344 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989140.344 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 1545989140.344 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log -2) (log n))))) into 0 1545989140.346 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1545989140.346 * [misc]taylor: Taking taylor expansion of 0 in k 1545989140.346 * [misc]backup-simplify: Simplify 0 into 0 1545989140.346 * [misc]backup-simplify: Simplify 0 into 0 1545989140.346 * [misc]backup-simplify: Simplify 0 into 0 1545989140.346 * [misc]backup-simplify: Simplify 0 into 0 1545989140.347 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -2 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989140.353 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow -2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow -2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow -2 1)))) 6) into 0 1545989140.353 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545989140.354 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1545989140.354 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989140.354 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 1545989140.355 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log -2) (log n)))))) into 0 1545989140.358 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1545989140.358 * [misc]taylor: Taking taylor expansion of 0 in k 1545989140.358 * [misc]backup-simplify: Simplify 0 into 0 1545989140.358 * [misc]backup-simplify: Simplify 0 into 0 1545989140.358 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -2) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) 1545989140.358 * * * * [misc]progress: [ 2 / 4 ] generating series at (2 1) 1545989140.358 * [misc]backup-simplify: Simplify (pow PI (- 1/2 (/ k 2))) into (pow PI (- 1/2 (* 1/2 k))) 1545989140.358 * [misc]approximate: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in (k) around 0 1545989140.358 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 1545989140.358 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 1545989140.358 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 1545989140.358 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1545989140.358 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989140.358 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.358 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1545989140.359 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989140.359 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.359 * [misc]taylor: Taking taylor expansion of k in k 1545989140.359 * [misc]backup-simplify: Simplify 0 into 0 1545989140.359 * [misc]backup-simplify: Simplify 1 into 1 1545989140.359 * [misc]taylor: Taking taylor expansion of (log PI) in k 1545989140.359 * [misc]taylor: Taking taylor expansion of PI in k 1545989140.359 * [misc]backup-simplify: Simplify PI into PI 1545989140.359 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1545989140.359 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1545989140.359 * [misc]backup-simplify: Simplify (- 0) into 0 1545989140.360 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545989140.360 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1545989140.361 * [misc]backup-simplify: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 1545989140.361 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 1545989140.361 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 1545989140.361 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 1545989140.361 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1545989140.361 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989140.361 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.361 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1545989140.361 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989140.361 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.361 * [misc]taylor: Taking taylor expansion of k in k 1545989140.361 * [misc]backup-simplify: Simplify 0 into 0 1545989140.361 * [misc]backup-simplify: Simplify 1 into 1 1545989140.361 * [misc]taylor: Taking taylor expansion of (log PI) in k 1545989140.361 * [misc]taylor: Taking taylor expansion of PI in k 1545989140.361 * [misc]backup-simplify: Simplify PI into PI 1545989140.361 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1545989140.361 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1545989140.361 * [misc]backup-simplify: Simplify (- 0) into 0 1545989140.362 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545989140.362 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1545989140.363 * [misc]backup-simplify: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 1545989140.363 * [misc]backup-simplify: Simplify (pow PI 1/2) into (pow PI 1/2) 1545989140.365 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 1545989140.366 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1545989140.366 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1545989140.366 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1545989140.367 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (log PI))) into (- (* 1/2 (log PI))) 1545989140.370 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 1) 1)))) into (* -1/2 (* (log PI) (sqrt PI))) 1545989140.371 * [misc]backup-simplify: Simplify (* -1/2 (* (log PI) (sqrt PI))) into (* -1/2 (* (log PI) (sqrt PI))) 1545989140.375 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 1545989140.376 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1545989140.376 * [misc]backup-simplify: Simplify (- 0) into 0 1545989140.376 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989140.377 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log PI)))) into 0 1545989140.381 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI))) 1545989140.383 * [misc]backup-simplify: Simplify (* 1/8 (* (pow (log PI) 2) (sqrt PI))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI))) 1545989140.386 * [misc]backup-simplify: Simplify (+ (* (* 1/8 (* (pow (log PI) 2) (sqrt PI))) (pow k 2)) (+ (* (* -1/2 (* (log PI) (sqrt PI))) k) (pow PI 1/2))) into (- (+ (pow PI 1/2) (* 1/8 (* (* (pow (log PI) 2) (pow k 2)) (sqrt PI)))) (* 1/2 (* (* (log PI) k) (sqrt PI)))) 1545989140.386 * [misc]backup-simplify: Simplify (pow PI (- 1/2 (/ (/ 1 k) 2))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1545989140.386 * [misc]approximate: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in (k) around 0 1545989140.386 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 1545989140.386 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 1545989140.386 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 1545989140.386 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1545989140.386 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989140.386 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.386 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545989140.386 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989140.386 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.387 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989140.387 * [misc]taylor: Taking taylor expansion of k in k 1545989140.387 * [misc]backup-simplify: Simplify 0 into 0 1545989140.387 * [misc]backup-simplify: Simplify 1 into 1 1545989140.387 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989140.387 * [misc]taylor: Taking taylor expansion of (log PI) in k 1545989140.387 * [misc]taylor: Taking taylor expansion of PI in k 1545989140.387 * [misc]backup-simplify: Simplify PI into PI 1545989140.387 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1545989140.387 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545989140.388 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1545989140.388 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1545989140.388 * [misc]backup-simplify: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 1545989140.389 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1545989140.389 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 1545989140.389 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 1545989140.389 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 1545989140.389 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1545989140.389 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989140.389 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.389 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545989140.389 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989140.389 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.389 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989140.389 * [misc]taylor: Taking taylor expansion of k in k 1545989140.389 * [misc]backup-simplify: Simplify 0 into 0 1545989140.389 * [misc]backup-simplify: Simplify 1 into 1 1545989140.389 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989140.389 * [misc]taylor: Taking taylor expansion of (log PI) in k 1545989140.389 * [misc]taylor: Taking taylor expansion of PI in k 1545989140.389 * [misc]backup-simplify: Simplify PI into PI 1545989140.390 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1545989140.390 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545989140.390 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1545989140.390 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1545989140.390 * [misc]backup-simplify: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 1545989140.391 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1545989140.391 * [misc]backup-simplify: Simplify (pow PI (- 1/2 (* 1/2 (/ 1 k)))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1545989140.393 * [misc]backup-simplify: Simplify 0 into 0 1545989140.393 * [misc]backup-simplify: Simplify 0 into 0 1545989140.393 * [misc]backup-simplify: Simplify 0 into 0 1545989140.393 * [misc]backup-simplify: Simplify 0 into 0 1545989140.393 * [misc]backup-simplify: Simplify 0 into 0 1545989140.393 * [misc]backup-simplify: Simplify 0 into 0 1545989140.393 * [misc]backup-simplify: Simplify (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k))))) into (pow PI (- 1/2 (* 1/2 k))) 1545989140.394 * [misc]backup-simplify: Simplify (pow PI (- 1/2 (/ (/ 1 (- k)) 2))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1545989140.394 * [misc]approximate: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in (k) around 0 1545989140.394 * [misc]taylor: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 1545989140.394 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 1545989140.394 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 1545989140.394 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1545989140.394 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545989140.394 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989140.394 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.394 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989140.394 * [misc]taylor: Taking taylor expansion of k in k 1545989140.394 * [misc]backup-simplify: Simplify 0 into 0 1545989140.394 * [misc]backup-simplify: Simplify 1 into 1 1545989140.394 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989140.394 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989140.394 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.394 * [misc]taylor: Taking taylor expansion of (log PI) in k 1545989140.394 * [misc]taylor: Taking taylor expansion of PI in k 1545989140.395 * [misc]backup-simplify: Simplify PI into PI 1545989140.395 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1545989140.395 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545989140.395 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545989140.396 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1545989140.396 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1545989140.396 * [misc]taylor: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 1545989140.396 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 1545989140.396 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 1545989140.396 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1545989140.396 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545989140.396 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989140.396 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.396 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989140.396 * [misc]taylor: Taking taylor expansion of k in k 1545989140.396 * [misc]backup-simplify: Simplify 0 into 0 1545989140.396 * [misc]backup-simplify: Simplify 1 into 1 1545989140.396 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989140.397 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989140.397 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.397 * [misc]taylor: Taking taylor expansion of (log PI) in k 1545989140.397 * [misc]taylor: Taking taylor expansion of PI in k 1545989140.397 * [misc]backup-simplify: Simplify PI into PI 1545989140.397 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1545989140.397 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545989140.397 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545989140.398 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1545989140.398 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1545989140.398 * [misc]backup-simplify: Simplify (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1545989140.398 * [misc]backup-simplify: Simplify 0 into 0 1545989140.398 * [misc]backup-simplify: Simplify 0 into 0 1545989140.398 * [misc]backup-simplify: Simplify 0 into 0 1545989140.398 * [misc]backup-simplify: Simplify 0 into 0 1545989140.399 * [misc]backup-simplify: Simplify 0 into 0 1545989140.399 * [misc]backup-simplify: Simplify 0 into 0 1545989140.399 * [misc]backup-simplify: Simplify (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)) into (pow PI (- 1/2 (* 1/2 k))) 1545989140.399 * * * * [misc]progress: [ 3 / 4 ] generating series at (2 2) 1545989140.399 * [misc]backup-simplify: Simplify (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)) into (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) 1545989140.399 * [misc]approximate: Taking taylor expansion of (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in (n k) around 0 1545989140.399 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in k 1545989140.399 * [misc]taylor: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in k 1545989140.399 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in k 1545989140.399 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in k 1545989140.399 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1545989140.399 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989140.399 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.399 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1545989140.399 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989140.399 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.399 * [misc]taylor: Taking taylor expansion of k in k 1545989140.399 * [misc]backup-simplify: Simplify 0 into 0 1545989140.400 * [misc]backup-simplify: Simplify 1 into 1 1545989140.400 * [misc]taylor: Taking taylor expansion of (log (* 2 n)) in k 1545989140.400 * [misc]taylor: Taking taylor expansion of (* 2 n) in k 1545989140.400 * [misc]taylor: Taking taylor expansion of 2 in k 1545989140.400 * [misc]backup-simplify: Simplify 2 into 2 1545989140.400 * [misc]taylor: Taking taylor expansion of n in k 1545989140.400 * [misc]backup-simplify: Simplify n into n 1545989140.400 * [misc]backup-simplify: Simplify (* 2 n) into (* 2 n) 1545989140.400 * [misc]backup-simplify: Simplify (log (* 2 n)) into (log (* 2 n)) 1545989140.400 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1545989140.400 * [misc]backup-simplify: Simplify (- 0) into 0 1545989140.400 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545989140.400 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 n))) into (* 1/2 (log (* 2 n))) 1545989140.401 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 n)))) into (pow (* 2 n) 1/2) 1545989140.401 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1545989140.401 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989140.401 * [misc]taylor: Taking taylor expansion of k in k 1545989140.401 * [misc]backup-simplify: Simplify 0 into 0 1545989140.401 * [misc]backup-simplify: Simplify 1 into 1 1545989140.401 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989140.401 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545989140.402 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1545989140.402 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in n 1545989140.402 * [misc]taylor: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in n 1545989140.402 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in n 1545989140.402 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in n 1545989140.402 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1545989140.402 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989140.402 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.402 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1545989140.402 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989140.402 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.402 * [misc]taylor: Taking taylor expansion of k in n 1545989140.402 * [misc]backup-simplify: Simplify k into k 1545989140.402 * [misc]taylor: Taking taylor expansion of (log (* 2 n)) in n 1545989140.402 * [misc]taylor: Taking taylor expansion of (* 2 n) in n 1545989140.402 * [misc]taylor: Taking taylor expansion of 2 in n 1545989140.402 * [misc]backup-simplify: Simplify 2 into 2 1545989140.402 * [misc]taylor: Taking taylor expansion of n in n 1545989140.402 * [misc]backup-simplify: Simplify 0 into 0 1545989140.402 * [misc]backup-simplify: Simplify 1 into 1 1545989140.402 * [misc]backup-simplify: Simplify (* 2 0) into 0 1545989140.403 * [misc]backup-simplify: Simplify (+ (* 2 1) (* 0 0)) into 2 1545989140.403 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1545989140.403 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1545989140.403 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1545989140.403 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1545989140.403 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 1545989140.404 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (+ (log 2) (log n))) into (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) 1545989140.404 * [misc]backup-simplify: Simplify (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) into (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) 1545989140.404 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1545989140.404 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989140.404 * [misc]taylor: Taking taylor expansion of k in n 1545989140.404 * [misc]backup-simplify: Simplify k into k 1545989140.404 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989140.404 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1545989140.404 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1545989140.405 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1545989140.405 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in n 1545989140.405 * [misc]taylor: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in n 1545989140.405 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in n 1545989140.405 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in n 1545989140.405 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1545989140.405 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989140.405 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.405 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1545989140.405 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989140.405 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.405 * [misc]taylor: Taking taylor expansion of k in n 1545989140.405 * [misc]backup-simplify: Simplify k into k 1545989140.405 * [misc]taylor: Taking taylor expansion of (log (* 2 n)) in n 1545989140.405 * [misc]taylor: Taking taylor expansion of (* 2 n) in n 1545989140.405 * [misc]taylor: Taking taylor expansion of 2 in n 1545989140.405 * [misc]backup-simplify: Simplify 2 into 2 1545989140.405 * [misc]taylor: Taking taylor expansion of n in n 1545989140.405 * [misc]backup-simplify: Simplify 0 into 0 1545989140.405 * [misc]backup-simplify: Simplify 1 into 1 1545989140.405 * [misc]backup-simplify: Simplify (* 2 0) into 0 1545989140.406 * [misc]backup-simplify: Simplify (+ (* 2 1) (* 0 0)) into 2 1545989140.406 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1545989140.406 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1545989140.406 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1545989140.406 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1545989140.406 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 1545989140.407 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (+ (log 2) (log n))) into (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) 1545989140.407 * [misc]backup-simplify: Simplify (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) into (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) 1545989140.407 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1545989140.407 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989140.407 * [misc]taylor: Taking taylor expansion of k in n 1545989140.407 * [misc]backup-simplify: Simplify k into k 1545989140.407 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989140.407 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1545989140.407 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1545989140.407 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1545989140.408 * [misc]backup-simplify: Simplify (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) into (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) 1545989140.408 * [misc]taylor: Taking taylor expansion of (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in k 1545989140.408 * [misc]taylor: Taking taylor expansion of (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) in k 1545989140.408 * [misc]taylor: Taking taylor expansion of (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) in k 1545989140.408 * [misc]taylor: Taking taylor expansion of (+ (log 2) (log n)) in k 1545989140.408 * [misc]taylor: Taking taylor expansion of (log 2) in k 1545989140.408 * [misc]taylor: Taking taylor expansion of 2 in k 1545989140.408 * [misc]backup-simplify: Simplify 2 into 2 1545989140.408 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1545989140.408 * [misc]taylor: Taking taylor expansion of (log n) in k 1545989140.408 * [misc]taylor: Taking taylor expansion of n in k 1545989140.408 * [misc]backup-simplify: Simplify n into n 1545989140.409 * [misc]backup-simplify: Simplify (log n) into (log n) 1545989140.409 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1545989140.409 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989140.409 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.409 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1545989140.409 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989140.409 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.409 * [misc]taylor: Taking taylor expansion of k in k 1545989140.409 * [misc]backup-simplify: Simplify 0 into 0 1545989140.409 * [misc]backup-simplify: Simplify 1 into 1 1545989140.409 * [misc]backup-simplify: Simplify (+ (log 2) (log n)) into (+ (log 2) (log n)) 1545989140.409 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1545989140.409 * [misc]backup-simplify: Simplify (- 0) into 0 1545989140.409 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545989140.410 * [misc]backup-simplify: Simplify (* (+ (log 2) (log n)) 1/2) into (* 1/2 (+ (log 2) (log n))) 1545989140.410 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log 2) (log n)))) into (exp (* 1/2 (+ (log 2) (log n)))) 1545989140.410 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1545989140.410 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989140.410 * [misc]taylor: Taking taylor expansion of k in k 1545989140.410 * [misc]backup-simplify: Simplify 0 into 0 1545989140.410 * [misc]backup-simplify: Simplify 1 into 1 1545989140.410 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989140.410 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545989140.411 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1545989140.411 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) 0) into 0 1545989140.411 * [misc]backup-simplify: Simplify 0 into 0 1545989140.412 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 1) (* 0 0))) into 0 1545989140.415 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 1545989140.415 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1545989140.415 * [misc]backup-simplify: Simplify (- 0) into 0 1545989140.415 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989140.416 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 1545989140.416 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log 2) (log n)))) into 0 1545989140.417 * [misc]backup-simplify: Simplify (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (+ (* (/ (pow 0 1) 1)))) into 0 1545989140.418 * [misc]backup-simplify: Simplify (+ (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) 0) (* 0 (sqrt (/ 1 k)))) into 0 1545989140.418 * [misc]taylor: Taking taylor expansion of 0 in k 1545989140.418 * [misc]backup-simplify: Simplify 0 into 0 1545989140.418 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1545989140.418 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1545989140.418 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1545989140.421 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 1545989140.422 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1545989140.422 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989140.422 * [misc]backup-simplify: Simplify (+ (* (+ (log 2) (log n)) -1/2) (* 0 1/2)) into (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 1545989140.423 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) 1545989140.424 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log 2) (log n)))) +nan.0) (* (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) 0)) into (- (* +nan.0 (exp (* 1/2 (+ (log 2) (log n)))))) 1545989140.424 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (+ (log 2) (log n)))))) into (- (* +nan.0 (exp (* 1/2 (+ (log 2) (log n)))))) 1545989140.425 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545989140.425 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 1545989140.426 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1545989140.430 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 1545989140.430 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1545989140.431 * [misc]backup-simplify: Simplify (- 0) into 0 1545989140.431 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989140.431 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 1545989140.432 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log 2) (log n))))) into 0 1545989140.434 * [misc]backup-simplify: Simplify (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1545989140.434 * [misc]backup-simplify: Simplify (+ (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k))))) into 0 1545989140.434 * [misc]taylor: Taking taylor expansion of 0 in k 1545989140.434 * [misc]backup-simplify: Simplify 0 into 0 1545989140.435 * [misc]backup-simplify: Simplify 0 into 0 1545989140.435 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1545989140.436 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1545989140.436 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1545989140.436 * [misc]backup-simplify: Simplify (- 0) into 0 1545989140.437 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989140.441 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 1545989140.442 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1545989140.443 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989140.443 * [misc]backup-simplify: Simplify (+ (* (+ (log 2) (log n)) 0) (+ (* 0 -1/2) (* 0 1/2))) into 0 1545989140.445 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))) 1545989140.447 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log 2) (log n)))) +nan.0) (+ (* (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) +nan.0) (* (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))) 0))) into (- (+ (* +nan.0 (* (log 2) (exp (* 1/2 (+ (log 2) (log n)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (- (* +nan.0 (exp (* 1/2 (+ (log 2) (log n)))))))))) 1545989140.449 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (log 2) (exp (* 1/2 (+ (log 2) (log n)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (- (* +nan.0 (exp (* 1/2 (+ (log 2) (log n)))))))))) into (- (+ (* +nan.0 (* (log 2) (exp (* 1/2 (+ (log 2) (log n)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (- (* +nan.0 (exp (* 1/2 (+ (log 2) (log n)))))))))) 1545989140.449 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545989140.449 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 1545989140.450 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))) into 0 1545989140.457 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 1545989140.457 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 1545989140.458 * [misc]backup-simplify: Simplify (- 0) into 0 1545989140.458 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989140.458 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 1545989140.459 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log 2) (log n)))))) into 0 1545989140.462 * [misc]backup-simplify: Simplify (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1545989140.463 * [misc]backup-simplify: Simplify (+ (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k)))))) into 0 1545989140.463 * [misc]taylor: Taking taylor expansion of 0 in k 1545989140.463 * [misc]backup-simplify: Simplify 0 into 0 1545989140.463 * [misc]backup-simplify: Simplify 0 into 0 1545989140.463 * [misc]backup-simplify: Simplify 0 into 0 1545989140.464 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989140.465 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1545989140.465 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1545989140.465 * [misc]backup-simplify: Simplify (- 0) into 0 1545989140.466 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989140.473 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 1545989140.476 * [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 1545989140.476 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989140.477 * [misc]backup-simplify: Simplify (+ (* (+ (log 2) (log n)) 0) (+ (* 0 0) (+ (* 0 -1/2) (* 0 1/2)))) into 0 1545989140.480 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 3) 6)) (* (/ (pow (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (log 2) (pow (log n) 2))) (+ (* 1/16 (* (pow (log 2) 2) (log n))) (* 1/48 (pow (log 2) 3))))) (exp (* 1/2 (+ (log 2) (log n)))))) 1545989140.485 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log 2) (log n)))) +nan.0) (+ (* (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) +nan.0) (+ (* (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))) +nan.0) (* (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (log 2) (pow (log n) 2))) (+ (* 1/16 (* (pow (log 2) 2) (log n))) (* 1/48 (pow (log 2) 3))))) (exp (* 1/2 (+ (log 2) (log n)))))) 0)))) into (- (+ (* +nan.0 (* (log 2) (exp (* 1/2 (+ (log 2) (log n)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log 2) (log n))))) (- (+ (* +nan.0 (* (pow (log 2) 2) (exp (* 1/2 (+ (log 2) (log n)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2))) (- (* +nan.0 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))))))))))))))) 1545989140.488 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (log 2) (exp (* 1/2 (+ (log 2) (log n)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log 2) (log n))))) (- (+ (* +nan.0 (* (pow (log 2) 2) (exp (* 1/2 (+ (log 2) (log n)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2))) (- (* +nan.0 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))))))))))))))) into (- (+ (* +nan.0 (* (log 2) (exp (* 1/2 (+ (log 2) (log n)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log 2) (log n))))) (- (+ (* +nan.0 (* (pow (log 2) 2) (exp (* 1/2 (+ (log 2) (log n)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2))) (- (* +nan.0 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))))))))))))))) 1545989140.492 * [misc]backup-simplify: Simplify (+ (* (- (+ (* +nan.0 (* (log 2) (exp (* 1/2 (+ (log 2) (log n)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log 2) (log n))))) (- (+ (* +nan.0 (* (pow (log 2) 2) (exp (* 1/2 (+ (log 2) (log n)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2))) (- (* +nan.0 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (log 2) (exp (* 1/2 (+ (log 2) (log n)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (- (* +nan.0 (exp (* 1/2 (+ (log 2) (log n)))))))))) (* k 1)) (- (* +nan.0 (exp (* 1/2 (+ (log 2) (log n)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) k))) (- (+ (* +nan.0 (* (pow (log 2) 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (pow k 2)))) (- (+ (* +nan.0 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) k)) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (pow k 2)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log 2) (log n))))) (- (+ (* +nan.0 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (pow k 2)))))))))))))))))))))) 1545989140.493 * [misc]backup-simplify: Simplify (/ (pow (* (/ 1 n) 2) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) into (* (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) 1545989140.493 * [misc]approximate: Taking taylor expansion of (* (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in (n k) around 0 1545989140.493 * [misc]taylor: Taking taylor expansion of (* (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in k 1545989140.493 * [misc]taylor: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in k 1545989140.493 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in k 1545989140.493 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in k 1545989140.493 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1545989140.493 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989140.493 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.493 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545989140.493 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989140.493 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.493 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989140.493 * [misc]taylor: Taking taylor expansion of k in k 1545989140.493 * [misc]backup-simplify: Simplify 0 into 0 1545989140.493 * [misc]backup-simplify: Simplify 1 into 1 1545989140.493 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989140.493 * [misc]taylor: Taking taylor expansion of (log (/ 2 n)) in k 1545989140.493 * [misc]taylor: Taking taylor expansion of (/ 2 n) in k 1545989140.493 * [misc]taylor: Taking taylor expansion of 2 in k 1545989140.493 * [misc]backup-simplify: Simplify 2 into 2 1545989140.493 * [misc]taylor: Taking taylor expansion of n in k 1545989140.493 * [misc]backup-simplify: Simplify n into n 1545989140.493 * [misc]backup-simplify: Simplify (/ 2 n) into (/ 2 n) 1545989140.493 * [misc]backup-simplify: Simplify (log (/ 2 n)) into (log (/ 2 n)) 1545989140.493 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545989140.493 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1545989140.494 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1545989140.494 * [misc]backup-simplify: Simplify (* -1/2 (log (/ 2 n))) into (* -1/2 (log (/ 2 n))) 1545989140.494 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) into (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) 1545989140.494 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1545989140.494 * [misc]taylor: Taking taylor expansion of k in k 1545989140.494 * [misc]backup-simplify: Simplify 0 into 0 1545989140.494 * [misc]backup-simplify: Simplify 1 into 1 1545989140.494 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545989140.494 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1545989140.494 * [misc]taylor: Taking taylor expansion of (* (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in n 1545989140.494 * [misc]taylor: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 1545989140.494 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 1545989140.494 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 1545989140.495 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1545989140.495 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989140.495 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.495 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989140.495 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989140.495 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.495 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989140.495 * [misc]taylor: Taking taylor expansion of k in n 1545989140.495 * [misc]backup-simplify: Simplify k into k 1545989140.495 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989140.495 * [misc]taylor: Taking taylor expansion of (log (/ 2 n)) in n 1545989140.495 * [misc]taylor: Taking taylor expansion of (/ 2 n) in n 1545989140.495 * [misc]taylor: Taking taylor expansion of 2 in n 1545989140.495 * [misc]backup-simplify: Simplify 2 into 2 1545989140.495 * [misc]taylor: Taking taylor expansion of n in n 1545989140.495 * [misc]backup-simplify: Simplify 0 into 0 1545989140.495 * [misc]backup-simplify: Simplify 1 into 1 1545989140.495 * [misc]backup-simplify: Simplify (/ 2 1) into 2 1545989140.495 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1545989140.495 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989140.495 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1545989140.495 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1545989140.495 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 1545989140.496 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 1545989140.496 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 1545989140.496 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1545989140.496 * [misc]taylor: Taking taylor expansion of k in n 1545989140.496 * [misc]backup-simplify: Simplify k into k 1545989140.496 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1545989140.496 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1545989140.496 * [misc]taylor: Taking taylor expansion of (* (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in n 1545989140.496 * [misc]taylor: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 1545989140.496 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 1545989140.496 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 1545989140.496 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1545989140.496 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989140.496 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.496 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989140.496 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989140.496 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.496 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989140.496 * [misc]taylor: Taking taylor expansion of k in n 1545989140.496 * [misc]backup-simplify: Simplify k into k 1545989140.496 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989140.496 * [misc]taylor: Taking taylor expansion of (log (/ 2 n)) in n 1545989140.496 * [misc]taylor: Taking taylor expansion of (/ 2 n) in n 1545989140.496 * [misc]taylor: Taking taylor expansion of 2 in n 1545989140.496 * [misc]backup-simplify: Simplify 2 into 2 1545989140.496 * [misc]taylor: Taking taylor expansion of n in n 1545989140.496 * [misc]backup-simplify: Simplify 0 into 0 1545989140.496 * [misc]backup-simplify: Simplify 1 into 1 1545989140.496 * [misc]backup-simplify: Simplify (/ 2 1) into 2 1545989140.496 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1545989140.497 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989140.497 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1545989140.497 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1545989140.497 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 1545989140.497 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 1545989140.497 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 1545989140.497 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1545989140.497 * [misc]taylor: Taking taylor expansion of k in n 1545989140.497 * [misc]backup-simplify: Simplify k into k 1545989140.497 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1545989140.497 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1545989140.498 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (sqrt k)) into (* (sqrt k) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) 1545989140.498 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) in k 1545989140.498 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1545989140.498 * [misc]taylor: Taking taylor expansion of k in k 1545989140.498 * [misc]backup-simplify: Simplify 0 into 0 1545989140.498 * [misc]backup-simplify: Simplify 1 into 1 1545989140.498 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545989140.498 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1545989140.498 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) in k 1545989140.498 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) in k 1545989140.498 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1545989140.498 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989140.498 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.498 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545989140.498 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989140.498 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.498 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989140.498 * [misc]taylor: Taking taylor expansion of k in k 1545989140.498 * [misc]backup-simplify: Simplify 0 into 0 1545989140.498 * [misc]backup-simplify: Simplify 1 into 1 1545989140.499 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989140.499 * [misc]taylor: Taking taylor expansion of (- (log 2) (log n)) in k 1545989140.499 * [misc]taylor: Taking taylor expansion of (log 2) in k 1545989140.499 * [misc]taylor: Taking taylor expansion of 2 in k 1545989140.499 * [misc]backup-simplify: Simplify 2 into 2 1545989140.499 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1545989140.499 * [misc]taylor: Taking taylor expansion of (log n) in k 1545989140.499 * [misc]taylor: Taking taylor expansion of n in k 1545989140.499 * [misc]backup-simplify: Simplify n into n 1545989140.499 * [misc]backup-simplify: Simplify (log n) into (log n) 1545989140.499 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545989140.499 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1545989140.499 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1545989140.499 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1545989140.499 * [misc]backup-simplify: Simplify (+ (log 2) (- (log n))) into (- (log 2) (log n)) 1545989140.499 * [misc]backup-simplify: Simplify (* -1/2 (- (log 2) (log n))) into (* -1/2 (- (log 2) (log n))) 1545989140.500 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 1545989140.500 * [misc]backup-simplify: Simplify (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) into 0 1545989140.500 * [misc]backup-simplify: Simplify 0 into 0 1545989140.500 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)))) into 0 1545989140.502 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 1545989140.502 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1545989140.502 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1545989140.502 * [misc]backup-simplify: Simplify (- 0) into 0 1545989140.502 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989140.502 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 1545989140.502 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log 2) (log n)))) into 0 1545989140.503 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1545989140.504 * [misc]backup-simplify: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 0) (* 0 (sqrt k))) into 0 1545989140.504 * [misc]taylor: Taking taylor expansion of 0 in k 1545989140.504 * [misc]backup-simplify: Simplify 0 into 0 1545989140.504 * [misc]backup-simplify: Simplify 0 into 0 1545989140.504 * [misc]backup-simplify: Simplify (+ (* 0 0) (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) 1545989140.504 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) 1545989140.505 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 1545989140.505 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989140.507 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 1545989140.508 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545989140.508 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1545989140.508 * [misc]backup-simplify: Simplify (- 0) into 0 1545989140.508 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989140.508 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 1545989140.509 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log 2) (log n))))) into 0 1545989140.510 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1545989140.510 * [misc]backup-simplify: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 0) (+ (* 0 0) (* 0 (sqrt k)))) into 0 1545989140.510 * [misc]taylor: Taking taylor expansion of 0 in k 1545989140.510 * [misc]backup-simplify: Simplify 0 into 0 1545989140.510 * [misc]backup-simplify: Simplify 0 into 0 1545989140.510 * [misc]backup-simplify: Simplify 0 into 0 1545989140.511 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1545989140.511 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) 1545989140.512 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) 1545989140.512 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 1545989140.513 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989140.519 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 1545989140.519 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545989140.520 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1545989140.520 * [misc]backup-simplify: Simplify (- 0) into 0 1545989140.520 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989140.520 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 1545989140.521 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log 2) (log n)))))) into 0 1545989140.525 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1545989140.525 * [misc]backup-simplify: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt k))))) into 0 1545989140.525 * [misc]taylor: Taking taylor expansion of 0 in k 1545989140.525 * [misc]backup-simplify: Simplify 0 into 0 1545989140.525 * [misc]backup-simplify: Simplify 0 into 0 1545989140.526 * [misc]backup-simplify: Simplify 0 into 0 1545989140.526 * [misc]backup-simplify: Simplify 0 into 0 1545989140.527 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1545989140.528 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* +nan.0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) 1545989140.528 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) 1545989140.530 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log 2) (log (/ 1 n))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log 2) (log (/ 1 n))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log 2) (log (/ 1 n))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) k)) (- (* +nan.0 (/ (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) (pow k 2)))))))) 1545989140.530 * [misc]backup-simplify: Simplify (/ (pow (* (/ 1 (- n)) 2) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) into (/ (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) 1545989140.530 * [misc]approximate: Taking taylor expansion of (/ (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (n k) around 0 1545989140.530 * [misc]taylor: Taking taylor expansion of (/ (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 1545989140.530 * [misc]taylor: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1545989140.530 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in k 1545989140.530 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in k 1545989140.530 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1545989140.531 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545989140.531 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989140.531 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.531 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989140.531 * [misc]taylor: Taking taylor expansion of k in k 1545989140.531 * [misc]backup-simplify: Simplify 0 into 0 1545989140.531 * [misc]backup-simplify: Simplify 1 into 1 1545989140.531 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989140.531 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989140.531 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.531 * [misc]taylor: Taking taylor expansion of (log (/ -2 n)) in k 1545989140.531 * [misc]taylor: Taking taylor expansion of (/ -2 n) in k 1545989140.531 * [misc]taylor: Taking taylor expansion of -2 in k 1545989140.531 * [misc]backup-simplify: Simplify -2 into -2 1545989140.531 * [misc]taylor: Taking taylor expansion of n in k 1545989140.531 * [misc]backup-simplify: Simplify n into n 1545989140.531 * [misc]backup-simplify: Simplify (/ -2 n) into (/ -2 n) 1545989140.531 * [misc]backup-simplify: Simplify (log (/ -2 n)) into (log (/ -2 n)) 1545989140.531 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545989140.532 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545989140.532 * [misc]backup-simplify: Simplify (* 1/2 (log (/ -2 n))) into (* 1/2 (log (/ -2 n))) 1545989140.532 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) into (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) 1545989140.532 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1545989140.532 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1545989140.532 * [misc]taylor: Taking taylor expansion of -1 in k 1545989140.532 * [misc]backup-simplify: Simplify -1 into -1 1545989140.532 * [misc]taylor: Taking taylor expansion of k in k 1545989140.532 * [misc]backup-simplify: Simplify 0 into 0 1545989140.532 * [misc]backup-simplify: Simplify 1 into 1 1545989140.532 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1545989140.532 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545989140.533 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1545989140.533 * [misc]backup-simplify: Simplify (/ (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) +nan.0) into (* +nan.0 (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2))) 1545989140.533 * [misc]taylor: Taking taylor expansion of (/ (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 1545989140.533 * [misc]taylor: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1545989140.533 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 1545989140.533 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 1545989140.533 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1545989140.534 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989140.534 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989140.534 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.534 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989140.534 * [misc]taylor: Taking taylor expansion of k in n 1545989140.534 * [misc]backup-simplify: Simplify k into k 1545989140.534 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989140.534 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989140.534 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.534 * [misc]taylor: Taking taylor expansion of (log (/ -2 n)) in n 1545989140.534 * [misc]taylor: Taking taylor expansion of (/ -2 n) in n 1545989140.534 * [misc]taylor: Taking taylor expansion of -2 in n 1545989140.534 * [misc]backup-simplify: Simplify -2 into -2 1545989140.534 * [misc]taylor: Taking taylor expansion of n in n 1545989140.534 * [misc]backup-simplify: Simplify 0 into 0 1545989140.534 * [misc]backup-simplify: Simplify 1 into 1 1545989140.534 * [misc]backup-simplify: Simplify (/ -2 1) into -2 1545989140.534 * [misc]backup-simplify: Simplify (log -2) into (log -2) 1545989140.534 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989140.535 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1545989140.535 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 1545989140.535 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 1545989140.536 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 1545989140.536 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1545989140.536 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1545989140.536 * [misc]taylor: Taking taylor expansion of -1 in n 1545989140.536 * [misc]backup-simplify: Simplify -1 into -1 1545989140.536 * [misc]taylor: Taking taylor expansion of k in n 1545989140.536 * [misc]backup-simplify: Simplify k into k 1545989140.536 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1545989140.536 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1545989140.536 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1545989140.536 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1545989140.537 * [misc]backup-simplify: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt (/ -1 k))) 1545989140.537 * [misc]taylor: Taking taylor expansion of (/ (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 1545989140.537 * [misc]taylor: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1545989140.537 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 1545989140.537 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 1545989140.537 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1545989140.537 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989140.537 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989140.537 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.537 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989140.537 * [misc]taylor: Taking taylor expansion of k in n 1545989140.537 * [misc]backup-simplify: Simplify k into k 1545989140.537 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989140.537 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989140.537 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.537 * [misc]taylor: Taking taylor expansion of (log (/ -2 n)) in n 1545989140.537 * [misc]taylor: Taking taylor expansion of (/ -2 n) in n 1545989140.537 * [misc]taylor: Taking taylor expansion of -2 in n 1545989140.537 * [misc]backup-simplify: Simplify -2 into -2 1545989140.537 * [misc]taylor: Taking taylor expansion of n in n 1545989140.537 * [misc]backup-simplify: Simplify 0 into 0 1545989140.537 * [misc]backup-simplify: Simplify 1 into 1 1545989140.537 * [misc]backup-simplify: Simplify (/ -2 1) into -2 1545989140.538 * [misc]backup-simplify: Simplify (log -2) into (log -2) 1545989140.538 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989140.538 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1545989140.538 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 1545989140.539 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 1545989140.539 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 1545989140.539 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1545989140.539 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1545989140.539 * [misc]taylor: Taking taylor expansion of -1 in n 1545989140.539 * [misc]backup-simplify: Simplify -1 into -1 1545989140.539 * [misc]taylor: Taking taylor expansion of k in n 1545989140.539 * [misc]backup-simplify: Simplify k into k 1545989140.539 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1545989140.539 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1545989140.539 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1545989140.540 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1545989140.540 * [misc]backup-simplify: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt (/ -1 k))) 1545989140.540 * [misc]taylor: Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt (/ -1 k))) in k 1545989140.540 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) in k 1545989140.540 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) in k 1545989140.540 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1545989140.540 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545989140.541 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989140.541 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.541 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989140.541 * [misc]taylor: Taking taylor expansion of k in k 1545989140.541 * [misc]backup-simplify: Simplify 0 into 0 1545989140.541 * [misc]backup-simplify: Simplify 1 into 1 1545989140.541 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989140.541 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989140.541 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.541 * [misc]taylor: Taking taylor expansion of (- (log -2) (log n)) in k 1545989140.541 * [misc]taylor: Taking taylor expansion of (log -2) in k 1545989140.541 * [misc]taylor: Taking taylor expansion of -2 in k 1545989140.541 * [misc]backup-simplify: Simplify -2 into -2 1545989140.541 * [misc]backup-simplify: Simplify (log -2) into (log -2) 1545989140.541 * [misc]taylor: Taking taylor expansion of (log n) in k 1545989140.541 * [misc]taylor: Taking taylor expansion of n in k 1545989140.541 * [misc]backup-simplify: Simplify n into n 1545989140.541 * [misc]backup-simplify: Simplify (log n) into (log n) 1545989140.541 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545989140.541 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545989140.541 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1545989140.541 * [misc]backup-simplify: Simplify (+ (log -2) (- (log n))) into (- (log -2) (log n)) 1545989140.542 * [misc]backup-simplify: Simplify (* 1/2 (- (log -2) (log n))) into (* 1/2 (- (log -2) (log n))) 1545989140.542 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 1545989140.542 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1545989140.542 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1545989140.542 * [misc]taylor: Taking taylor expansion of -1 in k 1545989140.542 * [misc]backup-simplify: Simplify -1 into -1 1545989140.542 * [misc]taylor: Taking taylor expansion of k in k 1545989140.542 * [misc]backup-simplify: Simplify 0 into 0 1545989140.542 * [misc]backup-simplify: Simplify 1 into 1 1545989140.542 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1545989140.542 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545989140.542 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1545989140.543 * [misc]backup-simplify: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) +nan.0) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))) 1545989140.543 * [misc]backup-simplify: Simplify (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))) 1545989140.543 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -2 (/ 0 1)))) into 0 1545989140.544 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -2 1)))) 1) into 0 1545989140.545 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1545989140.545 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1545989140.545 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989140.545 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 1545989140.545 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log -2) (log n)))) into 0 1545989140.546 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1545989140.546 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0 1545989140.547 * [misc]taylor: Taking taylor expansion of 0 in k 1545989140.547 * [misc]backup-simplify: Simplify 0 into 0 1545989140.547 * [misc]backup-simplify: Simplify 0 into 0 1545989140.547 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1545989140.547 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1545989140.548 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))))) 1545989140.548 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))))) 1545989140.548 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -2 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989140.551 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -2 1)))) 2) into 0 1545989140.551 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545989140.551 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1545989140.551 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989140.552 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 1545989140.552 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log -2) (log n))))) into 0 1545989140.553 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1545989140.553 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545989140.554 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 1545989140.554 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0 1545989140.554 * [misc]taylor: Taking taylor expansion of 0 in k 1545989140.554 * [misc]backup-simplify: Simplify 0 into 0 1545989140.554 * [misc]backup-simplify: Simplify 0 into 0 1545989140.554 * [misc]backup-simplify: Simplify 0 into 0 1545989140.554 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989140.555 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1545989140.556 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))))) 1545989140.556 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))))) 1545989140.557 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -2) (log (/ 1 (- n)))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -2) (log (/ 1 (- n)))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -2) (log (/ 1 (- n))))))))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (pow k 2))) (- (+ (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n)))))) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) k))))))) 1545989140.557 * * * * [misc]progress: [ 4 / 4 ] generating series at (2) 1545989140.557 * [misc]backup-simplify: Simplify (* (pow PI (- 1/2 (/ k 2))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))) into (* (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) 1545989140.557 * [misc]approximate: Taking taylor expansion of (* (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in (k n) around 0 1545989140.557 * [misc]taylor: Taking taylor expansion of (* (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in n 1545989140.557 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) in n 1545989140.558 * [misc]taylor: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in n 1545989140.558 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in n 1545989140.558 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in n 1545989140.558 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1545989140.558 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989140.558 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.558 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1545989140.558 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989140.558 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.558 * [misc]taylor: Taking taylor expansion of k in n 1545989140.558 * [misc]backup-simplify: Simplify k into k 1545989140.558 * [misc]taylor: Taking taylor expansion of (log (* 2 n)) in n 1545989140.558 * [misc]taylor: Taking taylor expansion of (* 2 n) in n 1545989140.558 * [misc]taylor: Taking taylor expansion of 2 in n 1545989140.558 * [misc]backup-simplify: Simplify 2 into 2 1545989140.558 * [misc]taylor: Taking taylor expansion of n in n 1545989140.558 * [misc]backup-simplify: Simplify 0 into 0 1545989140.558 * [misc]backup-simplify: Simplify 1 into 1 1545989140.558 * [misc]backup-simplify: Simplify (* 2 0) into 0 1545989140.558 * [misc]backup-simplify: Simplify (+ (* 2 1) (* 0 0)) into 2 1545989140.558 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1545989140.558 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1545989140.558 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1545989140.558 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1545989140.559 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 1545989140.559 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (+ (log 2) (log n))) into (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) 1545989140.559 * [misc]backup-simplify: Simplify (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) into (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) 1545989140.559 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in n 1545989140.559 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in n 1545989140.559 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in n 1545989140.559 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1545989140.559 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989140.559 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.559 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1545989140.559 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989140.559 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.559 * [misc]taylor: Taking taylor expansion of k in n 1545989140.559 * [misc]backup-simplify: Simplify k into k 1545989140.559 * [misc]taylor: Taking taylor expansion of (log PI) in n 1545989140.559 * [misc]taylor: Taking taylor expansion of PI in n 1545989140.559 * [misc]backup-simplify: Simplify PI into PI 1545989140.559 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1545989140.559 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1545989140.560 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1545989140.560 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1545989140.560 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (log PI)) into (* (- 1/2 (* 1/2 k)) (log PI)) 1545989140.560 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 k)) (log PI))) into (pow PI (- 1/2 (* 1/2 k))) 1545989140.560 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1545989140.560 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989140.560 * [misc]taylor: Taking taylor expansion of k in n 1545989140.560 * [misc]backup-simplify: Simplify k into k 1545989140.560 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989140.560 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1545989140.560 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1545989140.560 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1545989140.560 * [misc]taylor: Taking taylor expansion of (* (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in k 1545989140.560 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) in k 1545989140.560 * [misc]taylor: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in k 1545989140.560 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in k 1545989140.560 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in k 1545989140.560 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1545989140.560 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989140.560 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.560 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1545989140.560 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989140.561 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.561 * [misc]taylor: Taking taylor expansion of k in k 1545989140.561 * [misc]backup-simplify: Simplify 0 into 0 1545989140.561 * [misc]backup-simplify: Simplify 1 into 1 1545989140.561 * [misc]taylor: Taking taylor expansion of (log (* 2 n)) in k 1545989140.561 * [misc]taylor: Taking taylor expansion of (* 2 n) in k 1545989140.561 * [misc]taylor: Taking taylor expansion of 2 in k 1545989140.561 * [misc]backup-simplify: Simplify 2 into 2 1545989140.561 * [misc]taylor: Taking taylor expansion of n in k 1545989140.561 * [misc]backup-simplify: Simplify n into n 1545989140.561 * [misc]backup-simplify: Simplify (* 2 n) into (* 2 n) 1545989140.561 * [misc]backup-simplify: Simplify (log (* 2 n)) into (log (* 2 n)) 1545989140.561 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1545989140.561 * [misc]backup-simplify: Simplify (- 0) into 0 1545989140.561 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545989140.561 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 n))) into (* 1/2 (log (* 2 n))) 1545989140.561 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 n)))) into (pow (* 2 n) 1/2) 1545989140.561 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 1545989140.561 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 1545989140.561 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 1545989140.561 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1545989140.561 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989140.561 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.561 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1545989140.561 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989140.562 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.562 * [misc]taylor: Taking taylor expansion of k in k 1545989140.562 * [misc]backup-simplify: Simplify 0 into 0 1545989140.562 * [misc]backup-simplify: Simplify 1 into 1 1545989140.562 * [misc]taylor: Taking taylor expansion of (log PI) in k 1545989140.562 * [misc]taylor: Taking taylor expansion of PI in k 1545989140.562 * [misc]backup-simplify: Simplify PI into PI 1545989140.562 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1545989140.562 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1545989140.562 * [misc]backup-simplify: Simplify (- 0) into 0 1545989140.562 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545989140.562 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1545989140.563 * [misc]backup-simplify: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 1545989140.563 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1545989140.563 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989140.563 * [misc]taylor: Taking taylor expansion of k in k 1545989140.563 * [misc]backup-simplify: Simplify 0 into 0 1545989140.563 * [misc]backup-simplify: Simplify 1 into 1 1545989140.563 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989140.563 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545989140.564 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1545989140.564 * [misc]taylor: Taking taylor expansion of (* (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in k 1545989140.564 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) in k 1545989140.564 * [misc]taylor: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in k 1545989140.564 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in k 1545989140.564 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in k 1545989140.564 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1545989140.564 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989140.564 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.564 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1545989140.564 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989140.564 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.564 * [misc]taylor: Taking taylor expansion of k in k 1545989140.564 * [misc]backup-simplify: Simplify 0 into 0 1545989140.564 * [misc]backup-simplify: Simplify 1 into 1 1545989140.564 * [misc]taylor: Taking taylor expansion of (log (* 2 n)) in k 1545989140.564 * [misc]taylor: Taking taylor expansion of (* 2 n) in k 1545989140.564 * [misc]taylor: Taking taylor expansion of 2 in k 1545989140.564 * [misc]backup-simplify: Simplify 2 into 2 1545989140.564 * [misc]taylor: Taking taylor expansion of n in k 1545989140.564 * [misc]backup-simplify: Simplify n into n 1545989140.564 * [misc]backup-simplify: Simplify (* 2 n) into (* 2 n) 1545989140.564 * [misc]backup-simplify: Simplify (log (* 2 n)) into (log (* 2 n)) 1545989140.564 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1545989140.564 * [misc]backup-simplify: Simplify (- 0) into 0 1545989140.564 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545989140.564 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 n))) into (* 1/2 (log (* 2 n))) 1545989140.565 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 n)))) into (pow (* 2 n) 1/2) 1545989140.565 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 1545989140.565 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 1545989140.565 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 1545989140.565 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1545989140.565 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989140.565 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.565 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1545989140.565 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989140.565 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.565 * [misc]taylor: Taking taylor expansion of k in k 1545989140.565 * [misc]backup-simplify: Simplify 0 into 0 1545989140.565 * [misc]backup-simplify: Simplify 1 into 1 1545989140.565 * [misc]taylor: Taking taylor expansion of (log PI) in k 1545989140.565 * [misc]taylor: Taking taylor expansion of PI in k 1545989140.565 * [misc]backup-simplify: Simplify PI into PI 1545989140.565 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1545989140.565 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1545989140.565 * [misc]backup-simplify: Simplify (- 0) into 0 1545989140.565 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545989140.566 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1545989140.566 * [misc]backup-simplify: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 1545989140.566 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1545989140.566 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989140.566 * [misc]taylor: Taking taylor expansion of k in k 1545989140.566 * [misc]backup-simplify: Simplify 0 into 0 1545989140.566 * [misc]backup-simplify: Simplify 1 into 1 1545989140.566 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989140.566 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545989140.567 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1545989140.567 * [misc]backup-simplify: Simplify (* (pow (* 2 n) 1/2) (pow PI 1/2)) into (sqrt (* PI (* n 2))) 1545989140.567 * [misc]backup-simplify: Simplify (* (sqrt (* PI (* n 2))) 0) into 0 1545989140.567 * [misc]taylor: Taking taylor expansion of 0 in n 1545989140.567 * [misc]backup-simplify: Simplify 0 into 0 1545989140.567 * [misc]backup-simplify: Simplify 0 into 0 1545989140.568 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 1545989140.569 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1545989140.569 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1545989140.569 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1545989140.569 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (log PI))) into (- (* 1/2 (log PI))) 1545989140.571 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 1) 1)))) into (* -1/2 (* (log PI) (sqrt PI))) 1545989140.571 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 n)) into 0 1545989140.572 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 n) 1)))) 1) into 0 1545989140.572 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1545989140.572 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1545989140.572 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1545989140.572 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 n)))) into (- (* 1/2 (log (* 2 n)))) 1545989140.573 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 n)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 n)))) 1) 1)))) into (* -1/2 (* (sqrt (* n 2)) (log (* 2 n)))) 1545989140.573 * [misc]backup-simplify: Simplify (+ (* (pow (* 2 n) 1/2) (* -1/2 (* (log PI) (sqrt PI)))) (* (* -1/2 (* (sqrt (* n 2)) (log (* 2 n)))) (pow PI 1/2))) into (- (+ (* 1/2 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (* 1/2 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n)))))) 1545989140.574 * [misc]backup-simplify: Simplify (+ (* (sqrt (* PI (* n 2))) +nan.0) (* (- (+ (* 1/2 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (* 1/2 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n)))))) 0)) into (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) 1545989140.574 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 1545989140.575 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 1545989140.575 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1545989140.575 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545989140.575 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1545989140.575 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1545989140.575 * [misc]taylor: Taking taylor expansion of 2 in n 1545989140.575 * [misc]backup-simplify: Simplify 2 into 2 1545989140.575 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1545989140.575 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1545989140.575 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1545989140.575 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545989140.575 * [misc]taylor: Taking taylor expansion of n in n 1545989140.575 * [misc]backup-simplify: Simplify 0 into 0 1545989140.575 * [misc]backup-simplify: Simplify 1 into 1 1545989140.575 * [misc]taylor: Taking taylor expansion of PI in n 1545989140.575 * [misc]backup-simplify: Simplify PI into PI 1545989140.575 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1545989140.576 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1545989140.576 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545989140.576 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1545989140.576 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1545989140.576 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1545989140.576 * [misc]backup-simplify: Simplify (- 0) into 0 1545989140.576 * [misc]backup-simplify: Simplify 0 into 0 1545989140.577 * [misc]backup-simplify: Simplify 0 into 0 1545989140.577 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1545989140.577 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1545989140.580 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 1545989140.580 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1545989140.580 * [misc]backup-simplify: Simplify (- 0) into 0 1545989140.580 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989140.581 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log PI)))) into 0 1545989140.583 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI))) 1545989140.584 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 n))) into 0 1545989140.584 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 n) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 n) 1)))) 2) into 0 1545989140.585 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1545989140.585 * [misc]backup-simplify: Simplify (- 0) into 0 1545989140.585 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989140.585 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 n))))) into 0 1545989140.586 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 n)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* n 2)) (pow (log (* 2 n)) 2))) 1545989140.588 * [misc]backup-simplify: Simplify (+ (* (pow (* 2 n) 1/2) (* 1/8 (* (pow (log PI) 2) (sqrt PI)))) (+ (* (* -1/2 (* (sqrt (* n 2)) (log (* 2 n)))) (* -1/2 (* (log PI) (sqrt PI)))) (* (* 1/8 (* (sqrt (* n 2)) (pow (log (* 2 n)) 2))) (pow PI 1/2)))) into (+ (* 1/8 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (+ (* 1/8 (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (sqrt (* PI n)))) (* 1/4 (* (sqrt (* PI n)) (* (sqrt 2) (* (log (* 2 n)) (log PI))))))) 1545989140.592 * [misc]backup-simplify: Simplify (+ (* (sqrt (* PI (* n 2))) +nan.0) (+ (* (- (+ (* 1/2 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (* 1/2 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n)))))) +nan.0) (* (+ (* 1/8 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (+ (* 1/8 (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (sqrt (* PI n)))) (* 1/4 (* (sqrt (* PI n)) (* (sqrt 2) (* (log (* 2 n)) (log PI))))))) 0))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n))))))))) 1545989140.592 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n))))))))) in n 1545989140.592 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n)))))))) in n 1545989140.593 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) in n 1545989140.593 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1545989140.593 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545989140.593 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (log PI)) (sqrt (* PI n))) in n 1545989140.593 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log PI)) in n 1545989140.593 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1545989140.593 * [misc]taylor: Taking taylor expansion of 2 in n 1545989140.593 * [misc]backup-simplify: Simplify 2 into 2 1545989140.593 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1545989140.593 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1545989140.593 * [misc]taylor: Taking taylor expansion of (log PI) in n 1545989140.593 * [misc]taylor: Taking taylor expansion of PI in n 1545989140.593 * [misc]backup-simplify: Simplify PI into PI 1545989140.593 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1545989140.593 * [misc]taylor: Taking taylor expansion of (sqrt (* PI n)) in n 1545989140.594 * [misc]taylor: Taking taylor expansion of (* PI n) in n 1545989140.594 * [misc]taylor: Taking taylor expansion of PI in n 1545989140.594 * [misc]backup-simplify: Simplify PI into PI 1545989140.594 * [misc]taylor: Taking taylor expansion of n in n 1545989140.594 * [misc]backup-simplify: Simplify 0 into 0 1545989140.594 * [misc]backup-simplify: Simplify 1 into 1 1545989140.594 * [misc]backup-simplify: Simplify (* PI 0) into 0 1545989140.595 * [misc]backup-simplify: Simplify (+ (* PI 1) (* 0 0)) into PI 1545989140.595 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545989140.595 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1545989140.595 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n))))))) in n 1545989140.595 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n)))))) in n 1545989140.595 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 1545989140.595 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1545989140.595 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545989140.595 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1545989140.595 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1545989140.595 * [misc]taylor: Taking taylor expansion of 2 in n 1545989140.595 * [misc]backup-simplify: Simplify 2 into 2 1545989140.596 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1545989140.596 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1545989140.596 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1545989140.596 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545989140.596 * [misc]taylor: Taking taylor expansion of n in n 1545989140.596 * [misc]backup-simplify: Simplify 0 into 0 1545989140.596 * [misc]backup-simplify: Simplify 1 into 1 1545989140.596 * [misc]taylor: Taking taylor expansion of PI in n 1545989140.596 * [misc]backup-simplify: Simplify PI into PI 1545989140.596 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1545989140.597 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1545989140.597 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545989140.598 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1545989140.598 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n))))) in n 1545989140.598 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n)))) in n 1545989140.598 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1545989140.598 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545989140.598 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n))) in n 1545989140.598 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log (* 2 n))) in n 1545989140.598 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1545989140.598 * [misc]taylor: Taking taylor expansion of 2 in n 1545989140.598 * [misc]backup-simplify: Simplify 2 into 2 1545989140.598 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1545989140.598 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1545989140.598 * [misc]taylor: Taking taylor expansion of (log (* 2 n)) in n 1545989140.598 * [misc]taylor: Taking taylor expansion of (* 2 n) in n 1545989140.598 * [misc]taylor: Taking taylor expansion of 2 in n 1545989140.598 * [misc]backup-simplify: Simplify 2 into 2 1545989140.598 * [misc]taylor: Taking taylor expansion of n in n 1545989140.598 * [misc]backup-simplify: Simplify 0 into 0 1545989140.598 * [misc]backup-simplify: Simplify 1 into 1 1545989140.599 * [misc]backup-simplify: Simplify (* 2 0) into 0 1545989140.599 * [misc]backup-simplify: Simplify (+ (* 2 1) (* 0 0)) into 2 1545989140.599 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1545989140.599 * [misc]taylor: Taking taylor expansion of (sqrt (* PI n)) in n 1545989140.599 * [misc]taylor: Taking taylor expansion of (* PI n) in n 1545989140.599 * [misc]taylor: Taking taylor expansion of PI in n 1545989140.599 * [misc]backup-simplify: Simplify PI into PI 1545989140.599 * [misc]taylor: Taking taylor expansion of n in n 1545989140.599 * [misc]backup-simplify: Simplify 0 into 0 1545989140.599 * [misc]backup-simplify: Simplify 1 into 1 1545989140.599 * [misc]backup-simplify: Simplify (* PI 0) into 0 1545989140.600 * [misc]backup-simplify: Simplify (+ (* PI 1) (* 0 0)) into PI 1545989140.600 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545989140.601 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1545989140.601 * [misc]backup-simplify: Simplify (* (sqrt 2) (log PI)) into (* (sqrt 2) (log PI)) 1545989140.602 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (log PI)) 0) into 0 1545989140.602 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1545989140.603 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1545989140.603 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1545989140.603 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 1545989140.603 * [misc]backup-simplify: Simplify (* (sqrt 2) (+ (log 2) (log n))) into (* (+ (log 2) (log n)) (sqrt 2)) 1545989140.604 * [misc]backup-simplify: Simplify (* (* (+ (log 2) (log n)) (sqrt 2)) 0) into 0 1545989140.604 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1545989140.604 * [misc]backup-simplify: Simplify (- 0) into 0 1545989140.604 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989140.604 * [misc]backup-simplify: Simplify (- 0) into 0 1545989140.605 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989140.605 * [misc]backup-simplify: Simplify (- 0) into 0 1545989140.605 * [misc]backup-simplify: Simplify 0 into 0 1545989140.606 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1545989140.608 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1545989140.609 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 1545989140.610 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI))) 1545989140.610 * [misc]backup-simplify: Simplify 0 into 0 1545989140.611 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989140.612 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1545989140.619 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0 1545989140.619 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1545989140.619 * [misc]backup-simplify: Simplify (- 0) into 0 1545989140.619 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989140.621 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log PI))))) into 0 1545989140.628 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 3) 6)) (* (/ (pow (- (* 1/2 (log PI))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (pow (log PI) 3) (sqrt PI))) 1545989140.629 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 n)))) into 0 1545989140.631 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 n) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 n) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 n) 1)))) 6) into 0 1545989140.632 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1545989140.632 * [misc]backup-simplify: Simplify (- 0) into 0 1545989140.632 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989140.633 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log (* 2 n)))))) into 0 1545989140.634 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 n)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 n)))) 3) 6)) (* (/ (pow (- (* 1/2 (log (* 2 n)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (sqrt (* n 2)) (pow (log (* 2 n)) 3))) 1545989140.640 * [misc]backup-simplify: Simplify (+ (* (pow (* 2 n) 1/2) (* -1/48 (* (pow (log PI) 3) (sqrt PI)))) (+ (* (* -1/2 (* (sqrt (* n 2)) (log (* 2 n)))) (* 1/8 (* (pow (log PI) 2) (sqrt PI)))) (+ (* (* 1/8 (* (sqrt (* n 2)) (pow (log (* 2 n)) 2))) (* -1/2 (* (log PI) (sqrt PI)))) (* (* -1/48 (* (sqrt (* n 2)) (pow (log (* 2 n)) 3))) (pow PI 1/2))))) into (- (+ (* 1/48 (* (* (sqrt 2) (pow (log (* 2 n)) 3)) (sqrt (* PI n)))) (+ (* 1/16 (* (sqrt (* PI n)) (* (sqrt 2) (* (log (* 2 n)) (pow (log PI) 2))))) (+ (* 1/48 (* (* (sqrt 2) (pow (log PI) 3)) (sqrt (* PI n)))) (* 1/16 (* (sqrt (* PI n)) (* (sqrt 2) (* (pow (log (* 2 n)) 2) (log PI))))))))) 1545989140.649 * [misc]backup-simplify: Simplify (+ (* (sqrt (* PI (* n 2))) +nan.0) (+ (* (- (+ (* 1/2 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (* 1/2 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n)))))) +nan.0) (+ (* (+ (* 1/8 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (+ (* 1/8 (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (sqrt (* PI n)))) (* 1/4 (* (sqrt (* PI n)) (* (sqrt 2) (* (log (* 2 n)) (log PI))))))) +nan.0) (* (- (+ (* 1/48 (* (* (sqrt 2) (pow (log (* 2 n)) 3)) (sqrt (* PI n)))) (+ (* 1/16 (* (sqrt (* PI n)) (* (sqrt 2) (* (log (* 2 n)) (pow (log PI) 2))))) (+ (* 1/48 (* (* (sqrt 2) (pow (log PI) 3)) (sqrt (* PI n)))) (* 1/16 (* (sqrt (* PI n)) (* (sqrt 2) (* (pow (log (* 2 n)) 2) (log PI))))))))) 0)))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 n)) (log PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n))))))))))))))) 1545989140.650 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 n)) (log PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n))))))))))))))) in n 1545989140.650 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 n)) (log PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n)))))))))))))) in n 1545989140.650 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) in n 1545989140.650 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1545989140.650 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545989140.650 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (log PI)) (sqrt (* PI n))) in n 1545989140.650 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log PI)) in n 1545989140.650 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1545989140.650 * [misc]taylor: Taking taylor expansion of 2 in n 1545989140.650 * [misc]backup-simplify: Simplify 2 into 2 1545989140.650 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1545989140.650 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1545989140.650 * [misc]taylor: Taking taylor expansion of (log PI) in n 1545989140.650 * [misc]taylor: Taking taylor expansion of PI in n 1545989140.651 * [misc]backup-simplify: Simplify PI into PI 1545989140.651 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1545989140.651 * [misc]taylor: Taking taylor expansion of (sqrt (* PI n)) in n 1545989140.651 * [misc]taylor: Taking taylor expansion of (* PI n) in n 1545989140.651 * [misc]taylor: Taking taylor expansion of PI in n 1545989140.651 * [misc]backup-simplify: Simplify PI into PI 1545989140.651 * [misc]taylor: Taking taylor expansion of n in n 1545989140.651 * [misc]backup-simplify: Simplify 0 into 0 1545989140.651 * [misc]backup-simplify: Simplify 1 into 1 1545989140.651 * [misc]backup-simplify: Simplify (* PI 0) into 0 1545989140.652 * [misc]backup-simplify: Simplify (+ (* PI 1) (* 0 0)) into PI 1545989140.652 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545989140.652 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1545989140.652 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 n)) (log PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n))))))))))))) in n 1545989140.653 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 n)) (log PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n)))))))))))) in n 1545989140.653 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) in n 1545989140.653 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1545989140.653 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545989140.653 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n))) in n 1545989140.653 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (log PI) 2)) in n 1545989140.653 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1545989140.653 * [misc]taylor: Taking taylor expansion of 2 in n 1545989140.653 * [misc]backup-simplify: Simplify 2 into 2 1545989140.653 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1545989140.653 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1545989140.653 * [misc]taylor: Taking taylor expansion of (pow (log PI) 2) in n 1545989140.653 * [misc]taylor: Taking taylor expansion of (log PI) in n 1545989140.653 * [misc]taylor: Taking taylor expansion of PI in n 1545989140.653 * [misc]backup-simplify: Simplify PI into PI 1545989140.654 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1545989140.654 * [misc]taylor: Taking taylor expansion of (sqrt (* PI n)) in n 1545989140.654 * [misc]taylor: Taking taylor expansion of (* PI n) in n 1545989140.654 * [misc]taylor: Taking taylor expansion of PI in n 1545989140.654 * [misc]backup-simplify: Simplify PI into PI 1545989140.654 * [misc]taylor: Taking taylor expansion of n in n 1545989140.654 * [misc]backup-simplify: Simplify 0 into 0 1545989140.654 * [misc]backup-simplify: Simplify 1 into 1 1545989140.654 * [misc]backup-simplify: Simplify (* PI 0) into 0 1545989140.655 * [misc]backup-simplify: Simplify (+ (* PI 1) (* 0 0)) into PI 1545989140.655 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545989140.655 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1545989140.655 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 n)) (log PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n))))))))))) in n 1545989140.655 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 n)) (log PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n)))))))))) in n 1545989140.656 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (sqrt (* PI n)))) in n 1545989140.656 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1545989140.656 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545989140.656 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (sqrt (* PI n))) in n 1545989140.656 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (log (* 2 n)) 2)) in n 1545989140.656 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1545989140.656 * [misc]taylor: Taking taylor expansion of 2 in n 1545989140.656 * [misc]backup-simplify: Simplify 2 into 2 1545989140.656 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1545989140.656 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1545989140.656 * [misc]taylor: Taking taylor expansion of (pow (log (* 2 n)) 2) in n 1545989140.656 * [misc]taylor: Taking taylor expansion of (log (* 2 n)) in n 1545989140.656 * [misc]taylor: Taking taylor expansion of (* 2 n) in n 1545989140.656 * [misc]taylor: Taking taylor expansion of 2 in n 1545989140.656 * [misc]backup-simplify: Simplify 2 into 2 1545989140.656 * [misc]taylor: Taking taylor expansion of n in n 1545989140.656 * [misc]backup-simplify: Simplify 0 into 0 1545989140.656 * [misc]backup-simplify: Simplify 1 into 1 1545989140.656 * [misc]backup-simplify: Simplify (* 2 0) into 0 1545989140.657 * [misc]backup-simplify: Simplify (+ (* 2 1) (* 0 0)) into 2 1545989140.657 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1545989140.657 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 1545989140.657 * [misc]taylor: Taking taylor expansion of (sqrt (* PI n)) in n 1545989140.657 * [misc]taylor: Taking taylor expansion of (* PI n) in n 1545989140.657 * [misc]taylor: Taking taylor expansion of PI in n 1545989140.657 * [misc]backup-simplify: Simplify PI into PI 1545989140.657 * [misc]taylor: Taking taylor expansion of n in n 1545989140.657 * [misc]backup-simplify: Simplify 0 into 0 1545989140.657 * [misc]backup-simplify: Simplify 1 into 1 1545989140.658 * [misc]backup-simplify: Simplify (* PI 0) into 0 1545989140.658 * [misc]backup-simplify: Simplify (+ (* PI 1) (* 0 0)) into PI 1545989140.658 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545989140.659 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1545989140.659 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 n)) (log PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n))))))))) in n 1545989140.659 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 n)) (log PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n)))))))) in n 1545989140.659 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (* (log (* 2 n)) (log PI))) (sqrt (* n PI)))) in n 1545989140.659 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1545989140.659 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545989140.659 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (* (log (* 2 n)) (log PI))) (sqrt (* n PI))) in n 1545989140.659 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* (log (* 2 n)) (log PI))) in n 1545989140.659 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1545989140.659 * [misc]taylor: Taking taylor expansion of 2 in n 1545989140.659 * [misc]backup-simplify: Simplify 2 into 2 1545989140.659 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1545989140.660 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1545989140.660 * [misc]taylor: Taking taylor expansion of (* (log (* 2 n)) (log PI)) in n 1545989140.660 * [misc]taylor: Taking taylor expansion of (log (* 2 n)) in n 1545989140.660 * [misc]taylor: Taking taylor expansion of (* 2 n) in n 1545989140.660 * [misc]taylor: Taking taylor expansion of 2 in n 1545989140.660 * [misc]backup-simplify: Simplify 2 into 2 1545989140.660 * [misc]taylor: Taking taylor expansion of n in n 1545989140.660 * [misc]backup-simplify: Simplify 0 into 0 1545989140.660 * [misc]backup-simplify: Simplify 1 into 1 1545989140.660 * [misc]backup-simplify: Simplify (* 2 0) into 0 1545989140.660 * [misc]backup-simplify: Simplify (+ (* 2 1) (* 0 0)) into 2 1545989140.660 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1545989140.660 * [misc]taylor: Taking taylor expansion of (log PI) in n 1545989140.660 * [misc]taylor: Taking taylor expansion of PI in n 1545989140.661 * [misc]backup-simplify: Simplify PI into PI 1545989140.661 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1545989140.661 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1545989140.661 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545989140.661 * [misc]taylor: Taking taylor expansion of n in n 1545989140.661 * [misc]backup-simplify: Simplify 0 into 0 1545989140.661 * [misc]backup-simplify: Simplify 1 into 1 1545989140.661 * [misc]taylor: Taking taylor expansion of PI in n 1545989140.661 * [misc]backup-simplify: Simplify PI into PI 1545989140.661 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1545989140.662 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1545989140.662 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545989140.663 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1545989140.663 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n))))))) in n 1545989140.663 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n)))))) in n 1545989140.663 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 1545989140.663 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1545989140.663 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545989140.663 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1545989140.663 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1545989140.663 * [misc]taylor: Taking taylor expansion of 2 in n 1545989140.663 * [misc]backup-simplify: Simplify 2 into 2 1545989140.663 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1545989140.663 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1545989140.663 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1545989140.663 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545989140.663 * [misc]taylor: Taking taylor expansion of n in n 1545989140.663 * [misc]backup-simplify: Simplify 0 into 0 1545989140.663 * [misc]backup-simplify: Simplify 1 into 1 1545989140.663 * [misc]taylor: Taking taylor expansion of PI in n 1545989140.663 * [misc]backup-simplify: Simplify PI into PI 1545989140.664 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1545989140.664 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1545989140.665 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545989140.665 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1545989140.665 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n))))) in n 1545989140.665 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n)))) in n 1545989140.665 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1545989140.665 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545989140.665 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n))) in n 1545989140.665 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log (* 2 n))) in n 1545989140.665 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1545989140.665 * [misc]taylor: Taking taylor expansion of 2 in n 1545989140.665 * [misc]backup-simplify: Simplify 2 into 2 1545989140.665 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1545989140.666 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1545989140.666 * [misc]taylor: Taking taylor expansion of (log (* 2 n)) in n 1545989140.666 * [misc]taylor: Taking taylor expansion of (* 2 n) in n 1545989140.666 * [misc]taylor: Taking taylor expansion of 2 in n 1545989140.666 * [misc]backup-simplify: Simplify 2 into 2 1545989140.666 * [misc]taylor: Taking taylor expansion of n in n 1545989140.666 * [misc]backup-simplify: Simplify 0 into 0 1545989140.666 * [misc]backup-simplify: Simplify 1 into 1 1545989140.666 * [misc]backup-simplify: Simplify (* 2 0) into 0 1545989140.666 * [misc]backup-simplify: Simplify (+ (* 2 1) (* 0 0)) into 2 1545989140.666 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1545989140.666 * [misc]taylor: Taking taylor expansion of (sqrt (* PI n)) in n 1545989140.667 * [misc]taylor: Taking taylor expansion of (* PI n) in n 1545989140.667 * [misc]taylor: Taking taylor expansion of PI in n 1545989140.667 * [misc]backup-simplify: Simplify PI into PI 1545989140.667 * [misc]taylor: Taking taylor expansion of n in n 1545989140.667 * [misc]backup-simplify: Simplify 0 into 0 1545989140.667 * [misc]backup-simplify: Simplify 1 into 1 1545989140.667 * [misc]backup-simplify: Simplify (* PI 0) into 0 1545989140.668 * [misc]backup-simplify: Simplify (+ (* PI 1) (* 0 0)) into PI 1545989140.668 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545989140.668 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1545989140.669 * [misc]backup-simplify: Simplify (* (sqrt 2) (log PI)) into (* (sqrt 2) (log PI)) 1545989140.670 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (log PI)) 0) into 0 1545989140.670 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1545989140.671 * [misc]backup-simplify: Simplify (* (log PI) (log PI)) into (pow (log PI) 2) 1545989140.674 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow (log PI) 2)) into (* (sqrt 2) (pow (log PI) 2)) 1545989140.676 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (pow (log PI) 2)) 0) into 0 1545989140.676 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1545989140.676 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 1545989140.677 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 1545989140.677 * [misc]backup-simplify: Simplify (* (+ (log 2) (log n)) (+ (log 2) (log n))) into (pow (+ (log 2) (log n)) 2) 1545989140.677 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow (+ (log 2) (log n)) 2)) into (* (pow (+ (log 2) (log n)) 2) (sqrt 2)) 1545989140.678 * [misc]backup-simplify: Simplify (* (* (pow (+ (log 2) (log n)) 2) (sqrt 2)) 0) into 0 1545989140.678 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1545989140.678 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 1545989140.679 * [misc]backup-simplify: Simplify (* (+ (log 2) (log n)) (log PI)) into (* (+ (log 2) (log n)) (log PI)) 1545989140.679 * [misc]backup-simplify: Simplify (* (sqrt 2) (* (+ (log 2) (log n)) (log PI))) into (* (+ (log 2) (log n)) (* (sqrt 2) (log PI))) 1545989140.680 * [misc]backup-simplify: Simplify (* (* (+ (log 2) (log n)) (* (sqrt 2) (log PI))) 0) into 0 1545989140.680 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1545989140.681 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1545989140.681 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1545989140.681 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 1545989140.682 * [misc]backup-simplify: Simplify (* (sqrt 2) (+ (log 2) (log n))) into (* (+ (log 2) (log n)) (sqrt 2)) 1545989140.682 * [misc]backup-simplify: Simplify (* (* (+ (log 2) (log n)) (sqrt 2)) 0) into 0 1545989140.682 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1545989140.683 * [misc]backup-simplify: Simplify (- 0) into 0 1545989140.683 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989140.683 * [misc]backup-simplify: Simplify (- 0) into 0 1545989140.683 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989140.683 * [misc]backup-simplify: Simplify (- 0) into 0 1545989140.683 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989140.684 * [misc]backup-simplify: Simplify (- 0) into 0 1545989140.684 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989140.684 * [misc]backup-simplify: Simplify (- 0) into 0 1545989140.684 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989140.684 * [misc]backup-simplify: Simplify (- 0) into 0 1545989140.684 * [misc]backup-simplify: Simplify 0 into 0 1545989140.687 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 1545989140.688 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (log PI))) into 0 1545989140.690 * [misc]backup-simplify: Simplify (+ (* (* (sqrt 2) (log PI)) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) (* (log PI) PI)))) 1545989140.692 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) (* (log PI) PI))))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) (* (log PI) PI)))) 1545989140.694 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1545989140.695 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1545989140.696 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 1) (* 0 0))) into 0 1545989140.698 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 1545989140.698 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 1545989140.699 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log 2) (log n)))) into 0 1545989140.700 * [misc]backup-simplify: Simplify (+ (* (* (+ (log 2) (log n)) (sqrt 2)) (* +nan.0 PI)) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (log 2) (* (sqrt 2) PI)))))) 1545989140.702 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (log 2) (* (sqrt 2) PI))))))) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (log 2) (* (sqrt 2) PI)))))) 1545989140.704 * [misc]backup-simplify: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (log 2) (* (sqrt 2) PI))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (log 2) (* (sqrt 2) PI)))))) 1545989140.707 * [misc]backup-simplify: Simplify (+ (- (* +nan.0 (* (sqrt 2) PI))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (log 2) (* (sqrt 2) PI))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))) 1545989140.711 * [misc]backup-simplify: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI)))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))) 1545989140.716 * [misc]backup-simplify: Simplify (+ (- (* +nan.0 (* (sqrt 2) (* (log PI) PI)))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI)))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))))) 1545989140.723 * [misc]backup-simplify: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI)))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))))) 1545989140.730 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))))) 1545989140.731 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1545989140.733 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 1545989140.733 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1545989140.735 * [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)))) 1545989140.737 * [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)))) 1545989140.738 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 1545989140.739 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 1545989140.745 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) (pow (* n 1) 2)) (+ (* (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))))) (* n k)) (* (- (* +nan.0 (* (sqrt 2) PI))) (* n 1)))) into (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log PI) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))))))))) 1545989140.745 * [misc]backup-simplify: Simplify (* (pow PI (- 1/2 (/ (/ 1 k) 2))) (/ (pow (* (/ 1 n) 2) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k)))) into (* (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) 1545989140.745 * [misc]approximate: Taking taylor expansion of (* (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in (k n) around 0 1545989140.745 * [misc]taylor: Taking taylor expansion of (* (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in n 1545989140.745 * [misc]taylor: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) in n 1545989140.745 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in n 1545989140.745 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in n 1545989140.745 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in n 1545989140.745 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1545989140.745 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989140.745 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.745 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989140.745 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989140.745 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.745 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989140.745 * [misc]taylor: Taking taylor expansion of k in n 1545989140.745 * [misc]backup-simplify: Simplify k into k 1545989140.745 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989140.745 * [misc]taylor: Taking taylor expansion of (log PI) in n 1545989140.745 * [misc]taylor: Taking taylor expansion of PI in n 1545989140.745 * [misc]backup-simplify: Simplify PI into PI 1545989140.745 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1545989140.746 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989140.746 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1545989140.746 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1545989140.746 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) into (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) 1545989140.746 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1545989140.746 * [misc]taylor: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 1545989140.746 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 1545989140.746 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 1545989140.746 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1545989140.746 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989140.746 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.746 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989140.746 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989140.746 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.746 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989140.746 * [misc]taylor: Taking taylor expansion of k in n 1545989140.746 * [misc]backup-simplify: Simplify k into k 1545989140.746 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989140.746 * [misc]taylor: Taking taylor expansion of (log (/ 2 n)) in n 1545989140.746 * [misc]taylor: Taking taylor expansion of (/ 2 n) in n 1545989140.746 * [misc]taylor: Taking taylor expansion of 2 in n 1545989140.746 * [misc]backup-simplify: Simplify 2 into 2 1545989140.746 * [misc]taylor: Taking taylor expansion of n in n 1545989140.746 * [misc]backup-simplify: Simplify 0 into 0 1545989140.746 * [misc]backup-simplify: Simplify 1 into 1 1545989140.747 * [misc]backup-simplify: Simplify (/ 2 1) into 2 1545989140.747 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1545989140.747 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989140.747 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1545989140.747 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1545989140.747 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 1545989140.747 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 1545989140.747 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 1545989140.747 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1545989140.747 * [misc]taylor: Taking taylor expansion of k in n 1545989140.748 * [misc]backup-simplify: Simplify k into k 1545989140.748 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1545989140.748 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1545989140.748 * [misc]taylor: Taking taylor expansion of (* (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in k 1545989140.748 * [misc]taylor: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) in k 1545989140.748 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 1545989140.748 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 1545989140.748 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 1545989140.748 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1545989140.748 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989140.748 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.748 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545989140.748 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989140.748 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.748 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989140.748 * [misc]taylor: Taking taylor expansion of k in k 1545989140.748 * [misc]backup-simplify: Simplify 0 into 0 1545989140.748 * [misc]backup-simplify: Simplify 1 into 1 1545989140.748 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989140.748 * [misc]taylor: Taking taylor expansion of (log PI) in k 1545989140.748 * [misc]taylor: Taking taylor expansion of PI in k 1545989140.748 * [misc]backup-simplify: Simplify PI into PI 1545989140.748 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1545989140.748 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545989140.748 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1545989140.748 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1545989140.749 * [misc]backup-simplify: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 1545989140.749 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1545989140.749 * [misc]taylor: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in k 1545989140.749 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in k 1545989140.749 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in k 1545989140.749 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1545989140.749 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989140.749 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.749 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545989140.749 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989140.749 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.749 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989140.749 * [misc]taylor: Taking taylor expansion of k in k 1545989140.749 * [misc]backup-simplify: Simplify 0 into 0 1545989140.749 * [misc]backup-simplify: Simplify 1 into 1 1545989140.749 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989140.749 * [misc]taylor: Taking taylor expansion of (log (/ 2 n)) in k 1545989140.749 * [misc]taylor: Taking taylor expansion of (/ 2 n) in k 1545989140.749 * [misc]taylor: Taking taylor expansion of 2 in k 1545989140.749 * [misc]backup-simplify: Simplify 2 into 2 1545989140.749 * [misc]taylor: Taking taylor expansion of n in k 1545989140.749 * [misc]backup-simplify: Simplify n into n 1545989140.749 * [misc]backup-simplify: Simplify (/ 2 n) into (/ 2 n) 1545989140.749 * [misc]backup-simplify: Simplify (log (/ 2 n)) into (log (/ 2 n)) 1545989140.750 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545989140.750 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1545989140.750 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1545989140.750 * [misc]backup-simplify: Simplify (* -1/2 (log (/ 2 n))) into (* -1/2 (log (/ 2 n))) 1545989140.750 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) into (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) 1545989140.750 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1545989140.750 * [misc]taylor: Taking taylor expansion of k in k 1545989140.750 * [misc]backup-simplify: Simplify 0 into 0 1545989140.750 * [misc]backup-simplify: Simplify 1 into 1 1545989140.750 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545989140.750 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1545989140.750 * [misc]taylor: Taking taylor expansion of (* (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in k 1545989140.750 * [misc]taylor: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) in k 1545989140.750 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 1545989140.750 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 1545989140.750 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 1545989140.750 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1545989140.750 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989140.751 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.751 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545989140.751 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989140.751 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.751 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989140.751 * [misc]taylor: Taking taylor expansion of k in k 1545989140.751 * [misc]backup-simplify: Simplify 0 into 0 1545989140.751 * [misc]backup-simplify: Simplify 1 into 1 1545989140.751 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989140.751 * [misc]taylor: Taking taylor expansion of (log PI) in k 1545989140.751 * [misc]taylor: Taking taylor expansion of PI in k 1545989140.751 * [misc]backup-simplify: Simplify PI into PI 1545989140.751 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1545989140.751 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545989140.751 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1545989140.751 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1545989140.752 * [misc]backup-simplify: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 1545989140.752 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1545989140.752 * [misc]taylor: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in k 1545989140.752 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in k 1545989140.752 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in k 1545989140.752 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1545989140.752 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989140.752 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.752 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545989140.752 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989140.752 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.752 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989140.752 * [misc]taylor: Taking taylor expansion of k in k 1545989140.752 * [misc]backup-simplify: Simplify 0 into 0 1545989140.752 * [misc]backup-simplify: Simplify 1 into 1 1545989140.752 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989140.752 * [misc]taylor: Taking taylor expansion of (log (/ 2 n)) in k 1545989140.752 * [misc]taylor: Taking taylor expansion of (/ 2 n) in k 1545989140.752 * [misc]taylor: Taking taylor expansion of 2 in k 1545989140.752 * [misc]backup-simplify: Simplify 2 into 2 1545989140.752 * [misc]taylor: Taking taylor expansion of n in k 1545989140.752 * [misc]backup-simplify: Simplify n into n 1545989140.752 * [misc]backup-simplify: Simplify (/ 2 n) into (/ 2 n) 1545989140.752 * [misc]backup-simplify: Simplify (log (/ 2 n)) into (log (/ 2 n)) 1545989140.752 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545989140.752 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1545989140.753 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1545989140.753 * [misc]backup-simplify: Simplify (* -1/2 (log (/ 2 n))) into (* -1/2 (log (/ 2 n))) 1545989140.753 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) into (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) 1545989140.753 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1545989140.753 * [misc]taylor: Taking taylor expansion of k in k 1545989140.753 * [misc]backup-simplify: Simplify 0 into 0 1545989140.753 * [misc]backup-simplify: Simplify 1 into 1 1545989140.753 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545989140.753 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1545989140.753 * [misc]backup-simplify: Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) into (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) 1545989140.753 * [misc]backup-simplify: Simplify (* (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) 0) into 0 1545989140.754 * [misc]taylor: Taking taylor expansion of 0 in n 1545989140.754 * [misc]backup-simplify: Simplify 0 into 0 1545989140.754 * [misc]backup-simplify: Simplify 0 into 0 1545989140.754 * [misc]backup-simplify: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (* 0 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))) into 0 1545989140.754 * [misc]backup-simplify: Simplify (+ (* (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (* 0 0)) into (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))))) 1545989140.754 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))))) in n 1545989140.754 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))) in n 1545989140.754 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1545989140.754 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545989140.754 * [misc]taylor: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) in n 1545989140.754 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in n 1545989140.754 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in n 1545989140.754 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in n 1545989140.754 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1545989140.754 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989140.754 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.754 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989140.754 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989140.754 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.754 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989140.754 * [misc]taylor: Taking taylor expansion of k in n 1545989140.754 * [misc]backup-simplify: Simplify k into k 1545989140.754 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989140.754 * [misc]taylor: Taking taylor expansion of (log PI) in n 1545989140.754 * [misc]taylor: Taking taylor expansion of PI in n 1545989140.754 * [misc]backup-simplify: Simplify PI into PI 1545989140.755 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1545989140.755 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989140.755 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1545989140.755 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1545989140.755 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) into (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) 1545989140.755 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1545989140.755 * [misc]taylor: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 1545989140.755 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 1545989140.755 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 1545989140.755 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1545989140.755 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989140.755 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.755 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989140.755 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989140.755 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.755 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989140.755 * [misc]taylor: Taking taylor expansion of k in n 1545989140.755 * [misc]backup-simplify: Simplify k into k 1545989140.755 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989140.755 * [misc]taylor: Taking taylor expansion of (log (/ 2 n)) in n 1545989140.755 * [misc]taylor: Taking taylor expansion of (/ 2 n) in n 1545989140.755 * [misc]taylor: Taking taylor expansion of 2 in n 1545989140.755 * [misc]backup-simplify: Simplify 2 into 2 1545989140.755 * [misc]taylor: Taking taylor expansion of n in n 1545989140.755 * [misc]backup-simplify: Simplify 0 into 0 1545989140.755 * [misc]backup-simplify: Simplify 1 into 1 1545989140.756 * [misc]backup-simplify: Simplify (/ 2 1) into 2 1545989140.756 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1545989140.756 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989140.756 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1545989140.756 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1545989140.756 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 1545989140.756 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 1545989140.756 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 1545989140.757 * [misc]backup-simplify: Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) into (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) 1545989140.757 * [misc]backup-simplify: Simplify (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) into (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) 1545989140.757 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) into (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) 1545989140.758 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) into (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) 1545989140.758 * [misc]backup-simplify: Simplify 0 into 0 1545989140.758 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1545989140.759 * [misc]backup-simplify: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (* 0 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))))) into 0 1545989140.759 * [misc]backup-simplify: Simplify (+ (* (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))))) 1545989140.759 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))))) in n 1545989140.759 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))) in n 1545989140.759 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1545989140.759 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545989140.759 * [misc]taylor: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) in n 1545989140.759 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in n 1545989140.759 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in n 1545989140.759 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in n 1545989140.759 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1545989140.759 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989140.759 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.759 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989140.759 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989140.759 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.759 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989140.759 * [misc]taylor: Taking taylor expansion of k in n 1545989140.759 * [misc]backup-simplify: Simplify k into k 1545989140.759 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989140.759 * [misc]taylor: Taking taylor expansion of (log PI) in n 1545989140.759 * [misc]taylor: Taking taylor expansion of PI in n 1545989140.759 * [misc]backup-simplify: Simplify PI into PI 1545989140.760 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1545989140.760 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989140.760 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1545989140.760 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1545989140.760 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) into (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) 1545989140.761 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1545989140.761 * [misc]taylor: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 1545989140.761 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 1545989140.761 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 1545989140.761 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1545989140.761 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989140.761 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.761 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989140.761 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989140.761 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.761 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989140.761 * [misc]taylor: Taking taylor expansion of k in n 1545989140.761 * [misc]backup-simplify: Simplify k into k 1545989140.761 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989140.761 * [misc]taylor: Taking taylor expansion of (log (/ 2 n)) in n 1545989140.761 * [misc]taylor: Taking taylor expansion of (/ 2 n) in n 1545989140.761 * [misc]taylor: Taking taylor expansion of 2 in n 1545989140.761 * [misc]backup-simplify: Simplify 2 into 2 1545989140.761 * [misc]taylor: Taking taylor expansion of n in n 1545989140.761 * [misc]backup-simplify: Simplify 0 into 0 1545989140.761 * [misc]backup-simplify: Simplify 1 into 1 1545989140.762 * [misc]backup-simplify: Simplify (/ 2 1) into 2 1545989140.762 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1545989140.762 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989140.762 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1545989140.762 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1545989140.762 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 1545989140.763 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 1545989140.763 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 1545989140.763 * [misc]backup-simplify: Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) into (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) 1545989140.764 * [misc]backup-simplify: Simplify (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) into (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) 1545989140.764 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) into (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) 1545989140.765 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) into (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) 1545989140.765 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)))) into 0 1545989140.768 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 1545989140.768 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1545989140.768 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1545989140.768 * [misc]backup-simplify: Simplify (- 0) into 0 1545989140.769 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989140.769 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 1545989140.769 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log 2) (log n)))) into 0 1545989140.771 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1545989140.773 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 1545989140.773 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1545989140.773 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1545989140.774 * [misc]backup-simplify: Simplify (- 0) into 0 1545989140.774 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989140.774 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (log PI))) into 0 1545989140.776 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 1545989140.776 * [misc]backup-simplify: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) into 0 1545989140.777 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) into 0 1545989140.777 * [misc]backup-simplify: Simplify (- 0) into 0 1545989140.777 * [misc]backup-simplify: Simplify 0 into 0 1545989140.777 * [misc]backup-simplify: Simplify 0 into 0 1545989140.778 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1545989140.779 * [misc]backup-simplify: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 1545989140.780 * [misc]backup-simplify: Simplify (+ (* (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))))) 1545989140.780 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))))) in n 1545989140.780 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))) in n 1545989140.780 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1545989140.780 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545989140.780 * [misc]taylor: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) in n 1545989140.780 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in n 1545989140.780 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in n 1545989140.780 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in n 1545989140.780 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1545989140.780 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989140.780 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.780 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989140.780 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989140.780 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.780 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989140.780 * [misc]taylor: Taking taylor expansion of k in n 1545989140.780 * [misc]backup-simplify: Simplify k into k 1545989140.781 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989140.781 * [misc]taylor: Taking taylor expansion of (log PI) in n 1545989140.781 * [misc]taylor: Taking taylor expansion of PI in n 1545989140.781 * [misc]backup-simplify: Simplify PI into PI 1545989140.781 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1545989140.781 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989140.781 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1545989140.781 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1545989140.782 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) into (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) 1545989140.782 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1545989140.782 * [misc]taylor: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 1545989140.782 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 1545989140.782 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 1545989140.782 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1545989140.782 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989140.782 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.782 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989140.782 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989140.782 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.782 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989140.782 * [misc]taylor: Taking taylor expansion of k in n 1545989140.782 * [misc]backup-simplify: Simplify k into k 1545989140.782 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989140.783 * [misc]taylor: Taking taylor expansion of (log (/ 2 n)) in n 1545989140.783 * [misc]taylor: Taking taylor expansion of (/ 2 n) in n 1545989140.783 * [misc]taylor: Taking taylor expansion of 2 in n 1545989140.783 * [misc]backup-simplify: Simplify 2 into 2 1545989140.783 * [misc]taylor: Taking taylor expansion of n in n 1545989140.783 * [misc]backup-simplify: Simplify 0 into 0 1545989140.783 * [misc]backup-simplify: Simplify 1 into 1 1545989140.783 * [misc]backup-simplify: Simplify (/ 2 1) into 2 1545989140.783 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1545989140.783 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989140.783 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1545989140.783 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1545989140.784 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 1545989140.784 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 1545989140.784 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 1545989140.785 * [misc]backup-simplify: Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) into (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) 1545989140.785 * [misc]backup-simplify: Simplify (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) into (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) 1545989140.786 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) into (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) 1545989140.786 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) into (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) 1545989140.789 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k))))) (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log 2) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k))))) (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log 2) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k))))) (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log 2) (log (/ 1 n)))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (* (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))) (pow k 2))) (- (+ (* +nan.0 (/ (* (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))) k)) (- (* +nan.0 (/ (* (pow PI (- 1/2 (* 1/2 k))) (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k))))) (pow k 3)))))))) 1545989140.789 * [misc]backup-simplify: Simplify (* (pow PI (- 1/2 (/ (/ 1 (- k)) 2))) (/ (pow (* (/ 1 (- n)) 2) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k))))) into (/ (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) 1545989140.789 * [misc]approximate: Taking taylor expansion of (/ (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) in (k n) around 0 1545989140.790 * [misc]taylor: Taking taylor expansion of (/ (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) in n 1545989140.790 * [misc]taylor: Taking taylor expansion of (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in n 1545989140.790 * [misc]taylor: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1545989140.790 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 1545989140.790 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 1545989140.790 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1545989140.790 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989140.790 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989140.790 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.790 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989140.790 * [misc]taylor: Taking taylor expansion of k in n 1545989140.790 * [misc]backup-simplify: Simplify k into k 1545989140.790 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989140.790 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989140.790 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.790 * [misc]taylor: Taking taylor expansion of (log (/ -2 n)) in n 1545989140.790 * [misc]taylor: Taking taylor expansion of (/ -2 n) in n 1545989140.790 * [misc]taylor: Taking taylor expansion of -2 in n 1545989140.790 * [misc]backup-simplify: Simplify -2 into -2 1545989140.790 * [misc]taylor: Taking taylor expansion of n in n 1545989140.790 * [misc]backup-simplify: Simplify 0 into 0 1545989140.790 * [misc]backup-simplify: Simplify 1 into 1 1545989140.790 * [misc]backup-simplify: Simplify (/ -2 1) into -2 1545989140.791 * [misc]backup-simplify: Simplify (log -2) into (log -2) 1545989140.791 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989140.791 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1545989140.791 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 1545989140.791 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 1545989140.792 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 1545989140.792 * [misc]taylor: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in n 1545989140.792 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in n 1545989140.792 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in n 1545989140.792 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1545989140.792 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989140.792 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989140.792 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.792 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989140.792 * [misc]taylor: Taking taylor expansion of k in n 1545989140.792 * [misc]backup-simplify: Simplify k into k 1545989140.792 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989140.792 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989140.792 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.792 * [misc]taylor: Taking taylor expansion of (log PI) in n 1545989140.792 * [misc]taylor: Taking taylor expansion of PI in n 1545989140.792 * [misc]backup-simplify: Simplify PI into PI 1545989140.793 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1545989140.793 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989140.793 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1545989140.793 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) 1545989140.794 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1545989140.794 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1545989140.794 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1545989140.794 * [misc]taylor: Taking taylor expansion of -1 in n 1545989140.794 * [misc]backup-simplify: Simplify -1 into -1 1545989140.794 * [misc]taylor: Taking taylor expansion of k in n 1545989140.794 * [misc]backup-simplify: Simplify k into k 1545989140.794 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1545989140.794 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1545989140.794 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1545989140.794 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1545989140.795 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 1545989140.795 * [misc]backup-simplify: Simplify (/ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) into (/ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) 1545989140.795 * [misc]taylor: Taking taylor expansion of (/ (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) in k 1545989140.795 * [misc]taylor: Taking taylor expansion of (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in k 1545989140.795 * [misc]taylor: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1545989140.796 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in k 1545989140.796 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in k 1545989140.796 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1545989140.796 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545989140.796 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989140.796 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.796 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989140.796 * [misc]taylor: Taking taylor expansion of k in k 1545989140.796 * [misc]backup-simplify: Simplify 0 into 0 1545989140.796 * [misc]backup-simplify: Simplify 1 into 1 1545989140.796 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989140.796 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989140.796 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.796 * [misc]taylor: Taking taylor expansion of (log (/ -2 n)) in k 1545989140.796 * [misc]taylor: Taking taylor expansion of (/ -2 n) in k 1545989140.796 * [misc]taylor: Taking taylor expansion of -2 in k 1545989140.796 * [misc]backup-simplify: Simplify -2 into -2 1545989140.796 * [misc]taylor: Taking taylor expansion of n in k 1545989140.796 * [misc]backup-simplify: Simplify n into n 1545989140.796 * [misc]backup-simplify: Simplify (/ -2 n) into (/ -2 n) 1545989140.796 * [misc]backup-simplify: Simplify (log (/ -2 n)) into (log (/ -2 n)) 1545989140.797 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545989140.797 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545989140.797 * [misc]backup-simplify: Simplify (* 1/2 (log (/ -2 n))) into (* 1/2 (log (/ -2 n))) 1545989140.797 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) into (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) 1545989140.797 * [misc]taylor: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 1545989140.797 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 1545989140.797 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 1545989140.797 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1545989140.797 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545989140.797 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989140.797 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.797 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989140.797 * [misc]taylor: Taking taylor expansion of k in k 1545989140.797 * [misc]backup-simplify: Simplify 0 into 0 1545989140.797 * [misc]backup-simplify: Simplify 1 into 1 1545989140.798 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989140.798 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989140.798 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.798 * [misc]taylor: Taking taylor expansion of (log PI) in k 1545989140.798 * [misc]taylor: Taking taylor expansion of PI in k 1545989140.798 * [misc]backup-simplify: Simplify PI into PI 1545989140.798 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1545989140.798 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545989140.798 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545989140.799 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1545989140.799 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1545989140.799 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1545989140.799 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1545989140.799 * [misc]taylor: Taking taylor expansion of -1 in k 1545989140.799 * [misc]backup-simplify: Simplify -1 into -1 1545989140.799 * [misc]taylor: Taking taylor expansion of k in k 1545989140.799 * [misc]backup-simplify: Simplify 0 into 0 1545989140.799 * [misc]backup-simplify: Simplify 1 into 1 1545989140.800 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1545989140.800 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545989140.800 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1545989140.800 * [misc]backup-simplify: Simplify (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 1545989140.801 * [misc]backup-simplify: Simplify (/ (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) +nan.0) into (* +nan.0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 1545989140.801 * [misc]taylor: Taking taylor expansion of (/ (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) in k 1545989140.801 * [misc]taylor: Taking taylor expansion of (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in k 1545989140.801 * [misc]taylor: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1545989140.801 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in k 1545989140.801 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in k 1545989140.801 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1545989140.801 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545989140.801 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989140.801 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.801 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989140.801 * [misc]taylor: Taking taylor expansion of k in k 1545989140.801 * [misc]backup-simplify: Simplify 0 into 0 1545989140.801 * [misc]backup-simplify: Simplify 1 into 1 1545989140.801 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989140.801 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989140.801 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.801 * [misc]taylor: Taking taylor expansion of (log (/ -2 n)) in k 1545989140.801 * [misc]taylor: Taking taylor expansion of (/ -2 n) in k 1545989140.802 * [misc]taylor: Taking taylor expansion of -2 in k 1545989140.802 * [misc]backup-simplify: Simplify -2 into -2 1545989140.802 * [misc]taylor: Taking taylor expansion of n in k 1545989140.802 * [misc]backup-simplify: Simplify n into n 1545989140.802 * [misc]backup-simplify: Simplify (/ -2 n) into (/ -2 n) 1545989140.802 * [misc]backup-simplify: Simplify (log (/ -2 n)) into (log (/ -2 n)) 1545989140.802 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545989140.802 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545989140.802 * [misc]backup-simplify: Simplify (* 1/2 (log (/ -2 n))) into (* 1/2 (log (/ -2 n))) 1545989140.802 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) into (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) 1545989140.802 * [misc]taylor: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 1545989140.802 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 1545989140.802 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 1545989140.803 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1545989140.803 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545989140.803 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989140.803 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.803 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989140.803 * [misc]taylor: Taking taylor expansion of k in k 1545989140.803 * [misc]backup-simplify: Simplify 0 into 0 1545989140.803 * [misc]backup-simplify: Simplify 1 into 1 1545989140.803 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989140.803 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989140.803 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.803 * [misc]taylor: Taking taylor expansion of (log PI) in k 1545989140.803 * [misc]taylor: Taking taylor expansion of PI in k 1545989140.803 * [misc]backup-simplify: Simplify PI into PI 1545989140.803 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1545989140.803 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545989140.804 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545989140.804 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1545989140.804 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1545989140.805 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1545989140.805 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1545989140.805 * [misc]taylor: Taking taylor expansion of -1 in k 1545989140.805 * [misc]backup-simplify: Simplify -1 into -1 1545989140.805 * [misc]taylor: Taking taylor expansion of k in k 1545989140.805 * [misc]backup-simplify: Simplify 0 into 0 1545989140.805 * [misc]backup-simplify: Simplify 1 into 1 1545989140.805 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1545989140.805 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545989140.806 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1545989140.806 * [misc]backup-simplify: Simplify (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 1545989140.806 * [misc]backup-simplify: Simplify (/ (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) +nan.0) into (* +nan.0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 1545989140.806 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1545989140.806 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1545989140.806 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545989140.806 * [misc]taylor: Taking taylor expansion of (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in n 1545989140.806 * [misc]taylor: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1545989140.806 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 1545989140.806 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 1545989140.807 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1545989140.807 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989140.807 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989140.807 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.807 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989140.807 * [misc]taylor: Taking taylor expansion of k in n 1545989140.807 * [misc]backup-simplify: Simplify k into k 1545989140.807 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989140.807 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989140.807 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.807 * [misc]taylor: Taking taylor expansion of (log (/ -2 n)) in n 1545989140.807 * [misc]taylor: Taking taylor expansion of (/ -2 n) in n 1545989140.807 * [misc]taylor: Taking taylor expansion of -2 in n 1545989140.807 * [misc]backup-simplify: Simplify -2 into -2 1545989140.807 * [misc]taylor: Taking taylor expansion of n in n 1545989140.807 * [misc]backup-simplify: Simplify 0 into 0 1545989140.807 * [misc]backup-simplify: Simplify 1 into 1 1545989140.807 * [misc]backup-simplify: Simplify (/ -2 1) into -2 1545989140.807 * [misc]backup-simplify: Simplify (log -2) into (log -2) 1545989140.808 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989140.808 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1545989140.808 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 1545989140.808 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 1545989140.809 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 1545989140.809 * [misc]taylor: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in n 1545989140.809 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in n 1545989140.809 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in n 1545989140.809 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1545989140.809 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989140.809 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989140.809 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.809 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989140.809 * [misc]taylor: Taking taylor expansion of k in n 1545989140.809 * [misc]backup-simplify: Simplify k into k 1545989140.809 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989140.809 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989140.809 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.809 * [misc]taylor: Taking taylor expansion of (log PI) in n 1545989140.809 * [misc]taylor: Taking taylor expansion of PI in n 1545989140.809 * [misc]backup-simplify: Simplify PI into PI 1545989140.810 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1545989140.810 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989140.810 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1545989140.810 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) 1545989140.810 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1545989140.811 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 1545989140.811 * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 1545989140.812 * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 1545989140.812 * [misc]backup-simplify: Simplify (+ (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) 0) (* 0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into 0 1545989140.813 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1545989140.814 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1545989140.814 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 1545989140.814 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) in n 1545989140.815 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1545989140.815 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1545989140.815 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545989140.815 * [misc]taylor: Taking taylor expansion of (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in n 1545989140.815 * [misc]taylor: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1545989140.815 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 1545989140.815 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 1545989140.815 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1545989140.815 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989140.815 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989140.815 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.815 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989140.815 * [misc]taylor: Taking taylor expansion of k in n 1545989140.815 * [misc]backup-simplify: Simplify k into k 1545989140.815 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989140.815 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989140.815 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.815 * [misc]taylor: Taking taylor expansion of (log (/ -2 n)) in n 1545989140.815 * [misc]taylor: Taking taylor expansion of (/ -2 n) in n 1545989140.815 * [misc]taylor: Taking taylor expansion of -2 in n 1545989140.815 * [misc]backup-simplify: Simplify -2 into -2 1545989140.815 * [misc]taylor: Taking taylor expansion of n in n 1545989140.815 * [misc]backup-simplify: Simplify 0 into 0 1545989140.815 * [misc]backup-simplify: Simplify 1 into 1 1545989140.815 * [misc]backup-simplify: Simplify (/ -2 1) into -2 1545989140.816 * [misc]backup-simplify: Simplify (log -2) into (log -2) 1545989140.816 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989140.816 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1545989140.816 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 1545989140.817 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 1545989140.817 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 1545989140.817 * [misc]taylor: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in n 1545989140.817 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in n 1545989140.817 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in n 1545989140.817 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1545989140.817 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989140.817 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989140.817 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.817 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989140.817 * [misc]taylor: Taking taylor expansion of k in n 1545989140.817 * [misc]backup-simplify: Simplify k into k 1545989140.817 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989140.817 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989140.817 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.817 * [misc]taylor: Taking taylor expansion of (log PI) in n 1545989140.817 * [misc]taylor: Taking taylor expansion of PI in n 1545989140.817 * [misc]backup-simplify: Simplify PI into PI 1545989140.818 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1545989140.818 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989140.818 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1545989140.818 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) 1545989140.819 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1545989140.820 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 1545989140.820 * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 1545989140.821 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 1545989140.821 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 1545989140.822 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 1545989140.822 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1545989140.823 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1545989140.823 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989140.823 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (log PI))) into 0 1545989140.824 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 1545989140.824 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -2 (/ 0 1)))) into 0 1545989140.825 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -2 1)))) 1) into 0 1545989140.826 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1545989140.826 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1545989140.826 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989140.826 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 1545989140.826 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log -2) (log n)))) into 0 1545989140.827 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1545989140.827 * [misc]backup-simplify: Simplify (+ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 0) (* 0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into 0 1545989140.828 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into 0 1545989140.828 * [misc]backup-simplify: Simplify 0 into 0 1545989140.828 * [misc]backup-simplify: Simplify (+ (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (* 0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into 0 1545989140.828 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989140.829 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1545989140.829 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 1545989140.830 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) in n 1545989140.830 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1545989140.830 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1545989140.830 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545989140.830 * [misc]taylor: Taking taylor expansion of (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in n 1545989140.830 * [misc]taylor: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1545989140.830 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 1545989140.830 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 1545989140.830 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1545989140.830 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989140.830 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989140.830 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.830 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989140.830 * [misc]taylor: Taking taylor expansion of k in n 1545989140.830 * [misc]backup-simplify: Simplify k into k 1545989140.830 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989140.830 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989140.830 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.830 * [misc]taylor: Taking taylor expansion of (log (/ -2 n)) in n 1545989140.830 * [misc]taylor: Taking taylor expansion of (/ -2 n) in n 1545989140.830 * [misc]taylor: Taking taylor expansion of -2 in n 1545989140.830 * [misc]backup-simplify: Simplify -2 into -2 1545989140.830 * [misc]taylor: Taking taylor expansion of n in n 1545989140.830 * [misc]backup-simplify: Simplify 0 into 0 1545989140.830 * [misc]backup-simplify: Simplify 1 into 1 1545989140.830 * [misc]backup-simplify: Simplify (/ -2 1) into -2 1545989140.830 * [misc]backup-simplify: Simplify (log -2) into (log -2) 1545989140.830 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989140.830 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1545989140.830 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 1545989140.831 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 1545989140.831 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 1545989140.831 * [misc]taylor: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in n 1545989140.831 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in n 1545989140.831 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in n 1545989140.831 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1545989140.831 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989140.831 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989140.831 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.831 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989140.831 * [misc]taylor: Taking taylor expansion of k in n 1545989140.831 * [misc]backup-simplify: Simplify k into k 1545989140.831 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989140.831 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989140.831 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989140.831 * [misc]taylor: Taking taylor expansion of (log PI) in n 1545989140.831 * [misc]taylor: Taking taylor expansion of PI in n 1545989140.831 * [misc]backup-simplify: Simplify PI into PI 1545989140.831 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1545989140.831 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989140.831 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1545989140.832 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) 1545989140.832 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1545989140.832 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 1545989140.832 * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 1545989140.833 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 1545989140.833 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 1545989140.834 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -2) (log (/ 1 (- n)))))) (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -2) (log (/ 1 (- n)))))) (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))))) (* 1 (/ 1 (- k)))) (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -2) (log (/ 1 (- n)))))) (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)))))) into (- (+ (* +nan.0 (* (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (pow PI (- 1/2 (* 1/2 k))))) (- (+ (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (pow PI (- 1/2 (* 1/2 k)))) k)) (- (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (pow PI (- 1/2 (* 1/2 k)))) (pow k 2)))))))) 1545989140.834 * * * [misc]progress: simplifying candidates 1545989140.834 * * * * [misc]progress: [ 1 / 133 ] simplifiying candidate # 1545989140.835 * [enter]simplify: Simplifying (* (log (* n 2)) (- 1/2 (/ k 2))) 1545989140.835 * * [misc]simplify: iters left: 6 (9 enodes) 1545989140.837 * * [misc]simplify: iters left: 5 (16 enodes) 1545989140.839 * * [misc]simplify: iters left: 4 (32 enodes) 1545989140.845 * * [misc]simplify: iters left: 3 (68 enodes) 1545989140.861 * * [misc]simplify: iters left: 2 (171 enodes) 1545989140.898 * * [misc]simplify: iters left: 1 (342 enodes) 1545989141.028 * [exit]simplify: Simplified to (* (log (* n 2)) (- 1/2 (/ k 2))) 1545989141.028 * [misc]simplify: Simplified (2 2 1 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (exp (* (log (* n 2)) (- 1/2 (/ k 2)))) (sqrt k)))) 1545989141.028 * * * * [misc]progress: [ 2 / 133 ] simplifiying candidate # 1545989141.028 * * * * [misc]progress: [ 3 / 133 ] simplifiying candidate # 1545989141.028 * [enter]simplify: Simplifying (* n 2) 1545989141.028 * * [misc]simplify: iters left: 2 (3 enodes) 1545989141.028 * * [misc]simplify: iters left: 1 (4 enodes) 1545989141.029 * [exit]simplify: Simplified to (* n 2) 1545989141.029 * [misc]simplify: Simplified (2 2 1 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (pow (* n 2) (* 1 (- 1/2 (/ k 2)))) (sqrt k)))) 1545989141.029 * * * * [misc]progress: [ 4 / 133 ] simplifiying candidate # 1545989141.029 * [enter]simplify: Simplifying (pow (* n 2) (/ k 2)) 1545989141.029 * * [misc]simplify: iters left: 3 (6 enodes) 1545989141.030 * * [misc]simplify: iters left: 2 (7 enodes) 1545989141.031 * [exit]simplify: Simplified to (pow (* n 2) (/ k 2)) 1545989141.031 * [misc]simplify: Simplified (2 2 1 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (/ (pow (* n 2) 1/2) (pow (* n 2) (/ k 2))) (sqrt k)))) 1545989141.031 * * * * [misc]progress: [ 5 / 133 ] simplifiying candidate # 1545989141.031 * [enter]simplify: Simplifying (cbrt (- 1/2 (/ k 2))) 1545989141.031 * * [misc]simplify: iters left: 5 (6 enodes) 1545989141.033 * * [misc]simplify: iters left: 4 (8 enodes) 1545989141.035 * * [misc]simplify: iters left: 3 (11 enodes) 1545989141.038 * [exit]simplify: Simplified to (cbrt (- 1/2 (/ k 2))) 1545989141.038 * [misc]simplify: Simplified (2 2 1 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (pow (pow (* n 2) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))) (sqrt k)))) 1545989141.038 * * * * [misc]progress: [ 6 / 133 ] simplifiying candidate # 1545989141.039 * [enter]simplify: Simplifying (sqrt (- 1/2 (/ k 2))) 1545989141.039 * * [misc]simplify: iters left: 5 (6 enodes) 1545989141.041 * * [misc]simplify: iters left: 4 (8 enodes) 1545989141.043 * * [misc]simplify: iters left: 3 (11 enodes) 1545989141.046 * [exit]simplify: Simplified to (sqrt (- 1/2 (/ k 2))) 1545989141.046 * [misc]simplify: Simplified (2 2 1 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (pow (pow (* n 2) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))) (sqrt k)))) 1545989141.046 * * * * [misc]progress: [ 7 / 133 ] simplifiying candidate # 1545989141.046 * [enter]simplify: Simplifying (- 1/2 (/ k 2)) 1545989141.046 * * [misc]simplify: iters left: 4 (5 enodes) 1545989141.048 * * [misc]simplify: iters left: 3 (7 enodes) 1545989141.050 * * [misc]simplify: iters left: 2 (10 enodes) 1545989141.052 * [exit]simplify: Simplified to (- 1/2 (/ k 2)) 1545989141.053 * [misc]simplify: Simplified (2 2 1 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (pow (pow (* n 2) 1) (- 1/2 (/ k 2))) (sqrt k)))) 1545989141.053 * * * * [misc]progress: [ 8 / 133 ] simplifiying candidate # 1545989141.053 * [enter]simplify: Simplifying (pow (* n 2) (- (/ k 2))) 1545989141.053 * * [misc]simplify: iters left: 5 (7 enodes) 1545989141.055 * * [misc]simplify: iters left: 4 (10 enodes) 1545989141.058 * [exit]simplify: Simplified to (pow (* n 2) (- (/ k 2))) 1545989141.058 * [misc]simplify: Simplified (2 2 1 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (* (pow (* n 2) 1/2) (pow (* n 2) (- (/ k 2)))) (sqrt k)))) 1545989141.058 * * * * [misc]progress: [ 9 / 133 ] simplifiying candidate # 1545989141.058 * [enter]simplify: Simplifying (pow (* n 2) (- (/ k 2))) 1545989141.058 * * [misc]simplify: iters left: 5 (7 enodes) 1545989141.060 * * [misc]simplify: iters left: 4 (10 enodes) 1545989141.063 * [exit]simplify: Simplified to (pow (* n 2) (- (/ k 2))) 1545989141.063 * [misc]simplify: Simplified (2 2 1 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (* (pow (* n 2) 1/2) (pow (* n 2) (- (/ k 2)))) (sqrt k)))) 1545989141.063 * * * * [misc]progress: [ 10 / 133 ] simplifiying candidate # 1545989141.064 * [enter]simplify: Simplifying (pow n (- 1/2 (/ k 2))) 1545989141.064 * * [misc]simplify: iters left: 5 (7 enodes) 1545989141.066 * * [misc]simplify: iters left: 4 (9 enodes) 1545989141.068 * * [misc]simplify: iters left: 3 (12 enodes) 1545989141.071 * [exit]simplify: Simplified to (pow n (- 1/2 (/ k 2))) 1545989141.071 * [misc]simplify: Simplified (2 2 1 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (* (pow n (- 1/2 (/ k 2))) (pow 2 (- 1/2 (/ k 2)))) (sqrt k)))) 1545989141.071 * * * * [misc]progress: [ 11 / 133 ] simplifiying candidate # 1545989141.071 * * * * [misc]progress: [ 12 / 133 ] simplifiying candidate # 1545989141.071 * * * * [misc]progress: [ 13 / 133 ] simplifiying candidate # 1545989141.071 * * * * [misc]progress: [ 14 / 133 ] simplifiying candidate # 1545989141.071 * * * * [misc]progress: [ 15 / 133 ] simplifiying candidate # 1545989141.072 * * * * [misc]progress: [ 16 / 133 ] simplifiying candidate # 1545989141.072 * * * * [misc]progress: [ 17 / 133 ] simplifiying candidate # 1545989141.072 * * * * [misc]progress: [ 18 / 133 ] simplifiying candidate # 1545989141.072 * * * * [misc]progress: [ 19 / 133 ] simplifiying candidate # 1545989141.072 * [enter]simplify: Simplifying (pow PI (/ k 2)) 1545989141.072 * * [misc]simplify: iters left: 3 (5 enodes) 1545989141.073 * [exit]simplify: Simplified to (pow PI (/ k 2)) 1545989141.074 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (/ (pow PI 1/2) (pow PI (/ k 2))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1545989141.074 * * * * [misc]progress: [ 20 / 133 ] simplifiying candidate # 1545989141.074 * [enter]simplify: Simplifying (cbrt (- 1/2 (/ k 2))) 1545989141.074 * * [misc]simplify: iters left: 5 (6 enodes) 1545989141.076 * * [misc]simplify: iters left: 4 (8 enodes) 1545989141.078 * * [misc]simplify: iters left: 3 (11 enodes) 1545989141.081 * [exit]simplify: Simplified to (cbrt (- 1/2 (/ k 2))) 1545989141.081 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (pow (pow PI (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1545989141.081 * * * * [misc]progress: [ 21 / 133 ] simplifiying candidate # 1545989141.081 * [enter]simplify: Simplifying (sqrt (- 1/2 (/ k 2))) 1545989141.081 * * [misc]simplify: iters left: 5 (6 enodes) 1545989141.083 * * [misc]simplify: iters left: 4 (8 enodes) 1545989141.085 * * [misc]simplify: iters left: 3 (11 enodes) 1545989141.088 * [exit]simplify: Simplified to (sqrt (- 1/2 (/ k 2))) 1545989141.088 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (pow (pow PI (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1545989141.088 * * * * [misc]progress: [ 22 / 133 ] simplifiying candidate # 1545989141.088 * [enter]simplify: Simplifying (- 1/2 (/ k 2)) 1545989141.088 * * [misc]simplify: iters left: 4 (5 enodes) 1545989141.089 * * [misc]simplify: iters left: 3 (7 enodes) 1545989141.090 * * [misc]simplify: iters left: 2 (10 enodes) 1545989141.093 * [exit]simplify: Simplified to (- 1/2 (/ k 2)) 1545989141.093 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (pow (pow PI 1) (- 1/2 (/ k 2))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1545989141.093 * * * * [misc]progress: [ 23 / 133 ] simplifiying candidate # 1545989141.093 * [enter]simplify: Simplifying (pow PI (- (/ k 2))) 1545989141.093 * * [misc]simplify: iters left: 5 (6 enodes) 1545989141.094 * * [misc]simplify: iters left: 4 (8 enodes) 1545989141.095 * [exit]simplify: Simplified to (pow PI (/ (- k) 2)) 1545989141.095 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (* (pow PI 1/2) (pow PI (/ (- k) 2))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1545989141.095 * * * * [misc]progress: [ 24 / 133 ] simplifiying candidate # 1545989141.095 * [enter]simplify: Simplifying (pow PI (- (/ k 2))) 1545989141.095 * * [misc]simplify: iters left: 5 (6 enodes) 1545989141.096 * * [misc]simplify: iters left: 4 (8 enodes) 1545989141.097 * [exit]simplify: Simplified to (pow PI (/ (- k) 2)) 1545989141.097 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (* (pow PI 1/2) (pow PI (/ (- k) 2))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1545989141.097 * * * * [misc]progress: [ 25 / 133 ] simplifiying candidate # 1545989141.097 * * * * [misc]progress: [ 26 / 133 ] simplifiying candidate # 1545989141.097 * * * * [misc]progress: [ 27 / 133 ] simplifiying candidate # 1545989141.097 * * * * [misc]progress: [ 28 / 133 ] simplifiying candidate # 1545989141.097 * * * * [misc]progress: [ 29 / 133 ] simplifiying candidate # 1545989141.097 * * * * [misc]progress: [ 30 / 133 ] simplifiying candidate # 1545989141.097 * * * * [misc]progress: [ 31 / 133 ] simplifiying candidate # 1545989141.097 * * * * [misc]progress: [ 32 / 133 ] simplifiying candidate # 1545989141.097 * * * * [misc]progress: [ 33 / 133 ] simplifiying candidate # 1545989141.098 * [enter]simplify: Simplifying (- (* (log (* n 2)) (- 1/2 (/ k 2))) (log (sqrt k))) 1545989141.098 * * [misc]simplify: iters left: 6 (12 enodes) 1545989141.100 * * [misc]simplify: iters left: 5 (21 enodes) 1545989141.104 * * [misc]simplify: iters left: 4 (38 enodes) 1545989141.112 * * [misc]simplify: iters left: 3 (98 enodes) 1545989141.150 * * [misc]simplify: iters left: 2 (325 enodes) 1545989141.313 * [exit]simplify: Simplified to (- (* (log (* n 2)) (- 1/2 (/ k 2))) (log (sqrt k))) 1545989141.313 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (exp (- (* (log (* n 2)) (- 1/2 (/ k 2))) (log (sqrt k)))))) 1545989141.313 * * * * [misc]progress: [ 34 / 133 ] simplifiying candidate # 1545989141.313 * [enter]simplify: Simplifying (- (* (log (* n 2)) (- 1/2 (/ k 2))) (log (sqrt k))) 1545989141.314 * * [misc]simplify: iters left: 6 (12 enodes) 1545989141.317 * * [misc]simplify: iters left: 5 (21 enodes) 1545989141.320 * * [misc]simplify: iters left: 4 (38 enodes) 1545989141.328 * * [misc]simplify: iters left: 3 (98 enodes) 1545989141.360 * * [misc]simplify: iters left: 2 (325 enodes) 1545989141.526 * [exit]simplify: Simplified to (- (* (log (* n 2)) (- 1/2 (/ k 2))) (log (sqrt k))) 1545989141.526 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (exp (- (* (log (* n 2)) (- 1/2 (/ k 2))) (log (sqrt k)))))) 1545989141.526 * * * * [misc]progress: [ 35 / 133 ] simplifiying candidate # 1545989141.527 * [enter]simplify: Simplifying (- (log (pow (* n 2) (- 1/2 (/ k 2)))) (log (sqrt k))) 1545989141.527 * * [misc]simplify: iters left: 6 (12 enodes) 1545989141.530 * * [misc]simplify: iters left: 5 (19 enodes) 1545989141.535 * * [misc]simplify: iters left: 4 (28 enodes) 1545989141.543 * * [misc]simplify: iters left: 3 (44 enodes) 1545989141.559 * * [misc]simplify: iters left: 2 (124 enodes) 1545989141.612 * * [misc]simplify: iters left: 1 (453 enodes) 1545989141.926 * [exit]simplify: Simplified to (- (* (log (* n 2)) (- 1/2 (/ k 2))) (log (sqrt k))) 1545989141.926 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (exp (- (* (log (* n 2)) (- 1/2 (/ k 2))) (log (sqrt k)))))) 1545989141.926 * * * * [misc]progress: [ 36 / 133 ] simplifiying candidate # 1545989141.926 * * * * [misc]progress: [ 37 / 133 ] simplifiying candidate # 1545989141.926 * * * * [misc]progress: [ 38 / 133 ] simplifiying candidate # 1545989141.927 * [enter]simplify: Simplifying (/ (* (* (pow (* n 2) (- 1/2 (/ k 2))) (pow (* n 2) (- 1/2 (/ k 2)))) (pow (* n 2) (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k))) 1545989141.927 * * [misc]simplify: iters left: 6 (14 enodes) 1545989141.929 * * [misc]simplify: iters left: 5 (26 enodes) 1545989141.935 * * [misc]simplify: iters left: 4 (57 enodes) 1545989141.954 * * [misc]simplify: iters left: 3 (112 enodes) 1545989141.978 * * [misc]simplify: iters left: 2 (189 enodes) 1545989142.045 * * [misc]simplify: iters left: 1 (316 enodes) 1545989142.190 * [exit]simplify: Simplified to (* (/ (pow (* n 2) (- 1/2 (/ k 2))) (* k (sqrt k))) (* (pow (* n 2) (- 1/2 (/ k 2))) (pow (* n 2) (- 1/2 (/ k 2))))) 1545989142.190 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (cbrt (* (/ (pow (* n 2) (- 1/2 (/ k 2))) (* k (sqrt k))) (* (pow (* n 2) (- 1/2 (/ k 2))) (pow (* n 2) (- 1/2 (/ k 2)))))))) 1545989142.190 * * * * [misc]progress: [ 39 / 133 ] simplifiying candidate # 1545989142.190 * * * * [misc]progress: [ 40 / 133 ] simplifiying candidate # 1545989142.190 * * * * [misc]progress: [ 41 / 133 ] simplifiying candidate # 1545989142.190 * * * * [misc]progress: [ 42 / 133 ] simplifiying candidate # 1545989142.191 * * * * [misc]progress: [ 43 / 133 ] simplifiying candidate # 1545989142.191 * [enter]simplify: Simplifying (/ (pow (* n 2) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1545989142.191 * * [misc]simplify: iters left: 6 (10 enodes) 1545989142.192 * * [misc]simplify: iters left: 5 (14 enodes) 1545989142.194 * [exit]simplify: Simplified to (/ (sqrt (* n 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1545989142.194 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (/ (sqrt (* n 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n 2) (- (/ k 2))) (cbrt (sqrt k)))))) 1545989142.194 * [enter]simplify: Simplifying (/ (pow (* n 2) (- (/ k 2))) (cbrt (sqrt k))) 1545989142.194 * * [misc]simplify: iters left: 6 (10 enodes) 1545989142.196 * * [misc]simplify: iters left: 5 (13 enodes) 1545989142.197 * [exit]simplify: Simplified to (/ (pow (* n 2) (/ (- k) 2)) (cbrt (sqrt k))) 1545989142.197 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (/ (sqrt (* n 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n 2) (/ (- k) 2)) (cbrt (sqrt k)))))) 1545989142.197 * * * * [misc]progress: [ 44 / 133 ] simplifiying candidate # 1545989142.198 * [enter]simplify: Simplifying (/ (pow (* n 2) 1/2) (sqrt (sqrt k))) 1545989142.198 * * [misc]simplify: iters left: 5 (9 enodes) 1545989142.199 * * [misc]simplify: iters left: 4 (11 enodes) 1545989142.201 * [exit]simplify: Simplified to (/ (sqrt (* n 2)) (sqrt (sqrt k))) 1545989142.201 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (/ (sqrt (* n 2)) (sqrt (sqrt k))) (/ (pow (* n 2) (- (/ k 2))) (sqrt (sqrt k)))))) 1545989142.201 * [enter]simplify: Simplifying (/ (pow (* n 2) (- (/ k 2))) (sqrt (sqrt k))) 1545989142.201 * * [misc]simplify: iters left: 6 (10 enodes) 1545989142.202 * * [misc]simplify: iters left: 5 (13 enodes) 1545989142.204 * [exit]simplify: Simplified to (/ (pow (* n 2) (/ (- k) 2)) (sqrt (sqrt k))) 1545989142.204 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (/ (sqrt (* n 2)) (sqrt (sqrt k))) (/ (pow (* n 2) (/ (- k) 2)) (sqrt (sqrt k)))))) 1545989142.204 * * * * [misc]progress: [ 45 / 133 ] simplifiying candidate # 1545989142.204 * [enter]simplify: Simplifying (/ (pow (* n 2) 1/2) 1) 1545989142.204 * * [misc]simplify: iters left: 5 (7 enodes) 1545989142.205 * * [misc]simplify: iters left: 4 (11 enodes) 1545989142.207 * * [misc]simplify: iters left: 3 (13 enodes) 1545989142.208 * [exit]simplify: Simplified to (sqrt (* n 2)) 1545989142.209 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (sqrt (* n 2)) (/ (pow (* n 2) (- (/ k 2))) (sqrt k))))) 1545989142.209 * [enter]simplify: Simplifying (/ (pow (* n 2) (- (/ k 2))) (sqrt k)) 1545989142.209 * * [misc]simplify: iters left: 6 (9 enodes) 1545989142.210 * * [misc]simplify: iters left: 5 (12 enodes) 1545989142.211 * [exit]simplify: Simplified to (/ (pow (* n 2) (- (/ k 2))) (sqrt k)) 1545989142.211 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (sqrt (* n 2)) (/ (pow (* n 2) (- (/ k 2))) (sqrt k))))) 1545989142.212 * * * * [misc]progress: [ 46 / 133 ] simplifiying candidate # 1545989142.212 * [enter]simplify: Simplifying (/ (pow (* n 2) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1545989142.212 * * [misc]simplify: iters left: 6 (10 enodes) 1545989142.213 * * [misc]simplify: iters left: 5 (14 enodes) 1545989142.215 * [exit]simplify: Simplified to (/ (sqrt (* n 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1545989142.215 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (/ (sqrt (* n 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n 2) (- (/ k 2))) (cbrt (sqrt k)))))) 1545989142.215 * [enter]simplify: Simplifying (/ (pow (* n 2) (- (/ k 2))) (cbrt (sqrt k))) 1545989142.215 * * [misc]simplify: iters left: 6 (10 enodes) 1545989142.218 * * [misc]simplify: iters left: 5 (13 enodes) 1545989142.220 * [exit]simplify: Simplified to (/ (pow (* n 2) (/ (- k) 2)) (cbrt (sqrt k))) 1545989142.220 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (/ (sqrt (* n 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n 2) (/ (- k) 2)) (cbrt (sqrt k)))))) 1545989142.220 * * * * [misc]progress: [ 47 / 133 ] simplifiying candidate # 1545989142.220 * [enter]simplify: Simplifying (/ (pow (* n 2) 1/2) (sqrt (sqrt k))) 1545989142.220 * * [misc]simplify: iters left: 5 (9 enodes) 1545989142.221 * * [misc]simplify: iters left: 4 (11 enodes) 1545989142.222 * [exit]simplify: Simplified to (/ (sqrt (* n 2)) (sqrt (sqrt k))) 1545989142.222 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (/ (sqrt (* n 2)) (sqrt (sqrt k))) (/ (pow (* n 2) (- (/ k 2))) (sqrt (sqrt k)))))) 1545989142.223 * [enter]simplify: Simplifying (/ (pow (* n 2) (- (/ k 2))) (sqrt (sqrt k))) 1545989142.223 * * [misc]simplify: iters left: 6 (10 enodes) 1545989142.224 * * [misc]simplify: iters left: 5 (13 enodes) 1545989142.226 * [exit]simplify: Simplified to (/ (pow (* n 2) (/ (- k) 2)) (sqrt (sqrt k))) 1545989142.226 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (/ (sqrt (* n 2)) (sqrt (sqrt k))) (/ (pow (* n 2) (/ (- k) 2)) (sqrt (sqrt k)))))) 1545989142.226 * * * * [misc]progress: [ 48 / 133 ] simplifiying candidate # 1545989142.226 * [enter]simplify: Simplifying (/ (pow (* n 2) 1/2) 1) 1545989142.226 * * [misc]simplify: iters left: 5 (7 enodes) 1545989142.227 * * [misc]simplify: iters left: 4 (11 enodes) 1545989142.229 * * [misc]simplify: iters left: 3 (13 enodes) 1545989142.230 * [exit]simplify: Simplified to (sqrt (* n 2)) 1545989142.230 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (sqrt (* n 2)) (/ (pow (* n 2) (- (/ k 2))) (sqrt k))))) 1545989142.230 * [enter]simplify: Simplifying (/ (pow (* n 2) (- (/ k 2))) (sqrt k)) 1545989142.230 * * [misc]simplify: iters left: 6 (9 enodes) 1545989142.232 * * [misc]simplify: iters left: 5 (12 enodes) 1545989142.233 * [exit]simplify: Simplified to (/ (pow (* n 2) (- (/ k 2))) (sqrt k)) 1545989142.233 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (sqrt (* n 2)) (/ (pow (* n 2) (- (/ k 2))) (sqrt k))))) 1545989142.233 * * * * [misc]progress: [ 49 / 133 ] simplifiying candidate # 1545989142.233 * [enter]simplify: Simplifying (/ (pow n (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1545989142.234 * * [misc]simplify: iters left: 6 (11 enodes) 1545989142.235 * * [misc]simplify: iters left: 5 (15 enodes) 1545989142.237 * * [misc]simplify: iters left: 4 (18 enodes) 1545989142.240 * [exit]simplify: Simplified to (/ (pow n (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1545989142.240 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (/ (pow n (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow 2 (- 1/2 (/ k 2))) (cbrt (sqrt k)))))) 1545989142.240 * [enter]simplify: Simplifying (/ (pow 2 (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1545989142.240 * * [misc]simplify: iters left: 6 (9 enodes) 1545989142.241 * * [misc]simplify: iters left: 5 (11 enodes) 1545989142.243 * * [misc]simplify: iters left: 4 (14 enodes) 1545989142.244 * [exit]simplify: Simplified to (/ (pow 2 (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1545989142.245 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (/ (pow n (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow 2 (- 1/2 (/ k 2))) (cbrt (sqrt k)))))) 1545989142.245 * * * * [misc]progress: [ 50 / 133 ] simplifiying candidate # 1545989142.245 * [enter]simplify: Simplifying (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1545989142.245 * * [misc]simplify: iters left: 6 (10 enodes) 1545989142.246 * * [misc]simplify: iters left: 5 (12 enodes) 1545989142.248 * * [misc]simplify: iters left: 4 (15 enodes) 1545989142.250 * [exit]simplify: Simplified to (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1545989142.250 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow 2 (- 1/2 (/ k 2))) (sqrt (sqrt k)))))) 1545989142.250 * [enter]simplify: Simplifying (/ (pow 2 (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1545989142.250 * * [misc]simplify: iters left: 6 (9 enodes) 1545989142.251 * * [misc]simplify: iters left: 5 (11 enodes) 1545989142.252 * * [misc]simplify: iters left: 4 (14 enodes) 1545989142.254 * [exit]simplify: Simplified to (/ (pow 2 (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1545989142.254 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow 2 (- 1/2 (/ k 2))) (sqrt (sqrt k)))))) 1545989142.254 * * * * [misc]progress: [ 51 / 133 ] simplifiying candidate # 1545989142.254 * [enter]simplify: Simplifying (/ (pow n (- 1/2 (/ k 2))) 1) 1545989142.254 * * [misc]simplify: iters left: 6 (9 enodes) 1545989142.256 * * [misc]simplify: iters left: 5 (13 enodes) 1545989142.258 * * [misc]simplify: iters left: 4 (18 enodes) 1545989142.260 * [exit]simplify: Simplified to (pow n (- 1/2 (/ k 2))) 1545989142.260 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow 2 (- 1/2 (/ k 2))) (sqrt k))))) 1545989142.261 * [enter]simplify: Simplifying (/ (pow 2 (- 1/2 (/ k 2))) (sqrt k)) 1545989142.261 * * [misc]simplify: iters left: 6 (8 enodes) 1545989142.264 * * [misc]simplify: iters left: 5 (10 enodes) 1545989142.267 * * [misc]simplify: iters left: 4 (13 enodes) 1545989142.270 * [exit]simplify: Simplified to (/ (pow 2 (- 1/2 (/ k 2))) (sqrt k)) 1545989142.270 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow 2 (- 1/2 (/ k 2))) (sqrt k))))) 1545989142.270 * * * * [misc]progress: [ 52 / 133 ] simplifiying candidate # 1545989142.271 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (pow (* n 2) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1545989142.271 * * [misc]simplify: iters left: 6 (14 enodes) 1545989142.275 * * [misc]simplify: iters left: 5 (23 enodes) 1545989142.282 * * [misc]simplify: iters left: 4 (35 enodes) 1545989142.291 * * [misc]simplify: iters left: 3 (38 enodes) 1545989142.298 * * [misc]simplify: iters left: 2 (41 enodes) 1545989142.303 * [exit]simplify: Simplified to (* (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))) 1545989142.303 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (* (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))) (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))) 1545989142.304 * [enter]simplify: Simplifying (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1545989142.304 * * [misc]simplify: iters left: 6 (12 enodes) 1545989142.305 * * [misc]simplify: iters left: 5 (15 enodes) 1545989142.307 * * [misc]simplify: iters left: 4 (18 enodes) 1545989142.311 * [exit]simplify: Simplified to (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1545989142.311 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (/ (* (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (pow (* n 2) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))) 1545989142.311 * * * * [misc]progress: [ 53 / 133 ] simplifiying candidate # 1545989142.311 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (pow (* n 2) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) 1545989142.311 * * [misc]simplify: iters left: 6 (13 enodes) 1545989142.313 * * [misc]simplify: iters left: 5 (18 enodes) 1545989142.315 * * [misc]simplify: iters left: 4 (23 enodes) 1545989142.318 * * [misc]simplify: iters left: 3 (24 enodes) 1545989142.321 * [exit]simplify: Simplified to (* (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (cbrt (pow (* n 2) (- 1/2 (/ k 2))))) 1545989142.321 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (* (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (cbrt (pow (* n 2) (- 1/2 (/ k 2))))) (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))) 1545989142.322 * [enter]simplify: Simplifying (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1545989142.322 * * [misc]simplify: iters left: 6 (12 enodes) 1545989142.323 * * [misc]simplify: iters left: 5 (15 enodes) 1545989142.327 * * [misc]simplify: iters left: 4 (18 enodes) 1545989142.332 * [exit]simplify: Simplified to (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1545989142.332 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (/ (* (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (pow (* n 2) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))) 1545989142.332 * * * * [misc]progress: [ 54 / 133 ] simplifiying candidate # 1545989142.333 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (pow (* n 2) (- 1/2 (/ k 2))))) 1) 1545989142.333 * * [misc]simplify: iters left: 6 (12 enodes) 1545989142.337 * * [misc]simplify: iters left: 5 (19 enodes) 1545989142.342 * * [misc]simplify: iters left: 4 (28 enodes) 1545989142.350 * * [misc]simplify: iters left: 3 (42 enodes) 1545989142.356 * * [misc]simplify: iters left: 2 (68 enodes) 1545989142.364 * [exit]simplify: Simplified to (* (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (pow (* n 2) (- 1/2 (/ k 2))))) 1545989142.364 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (* (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (pow (* n 2) (- 1/2 (/ k 2))))) (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt k))))) 1545989142.364 * [enter]simplify: Simplifying (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt k)) 1545989142.364 * * [misc]simplify: iters left: 6 (11 enodes) 1545989142.366 * * [misc]simplify: iters left: 5 (14 enodes) 1545989142.367 * * [misc]simplify: iters left: 4 (17 enodes) 1545989142.370 * [exit]simplify: Simplified to (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt k)) 1545989142.370 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (* (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (pow (* n 2) (- 1/2 (/ k 2))))) (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt k))))) 1545989142.370 * * * * [misc]progress: [ 55 / 133 ] simplifiying candidate # 1545989142.370 * [enter]simplify: Simplifying (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1545989142.370 * * [misc]simplify: iters left: 6 (13 enodes) 1545989142.372 * * [misc]simplify: iters left: 5 (18 enodes) 1545989142.374 * * [misc]simplify: iters left: 4 (21 enodes) 1545989142.377 * [exit]simplify: Simplified to (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1545989142.377 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))) 1545989142.377 * [enter]simplify: Simplifying (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1545989142.377 * * [misc]simplify: iters left: 6 (12 enodes) 1545989142.379 * * [misc]simplify: iters left: 5 (15 enodes) 1545989142.381 * * [misc]simplify: iters left: 4 (18 enodes) 1545989142.383 * [exit]simplify: Simplified to (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1545989142.383 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))) 1545989142.383 * * * * [misc]progress: [ 56 / 133 ] simplifiying candidate # 1545989142.383 * [enter]simplify: Simplifying (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1545989142.383 * * [misc]simplify: iters left: 6 (12 enodes) 1545989142.385 * * [misc]simplify: iters left: 5 (15 enodes) 1545989142.387 * * [misc]simplify: iters left: 4 (18 enodes) 1545989142.389 * [exit]simplify: Simplified to (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1545989142.389 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))) 1545989142.389 * [enter]simplify: Simplifying (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1545989142.390 * * [misc]simplify: iters left: 6 (12 enodes) 1545989142.391 * * [misc]simplify: iters left: 5 (15 enodes) 1545989142.393 * * [misc]simplify: iters left: 4 (18 enodes) 1545989142.396 * [exit]simplify: Simplified to (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1545989142.397 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))) 1545989142.397 * * * * [misc]progress: [ 57 / 133 ] simplifiying candidate # 1545989142.397 * [enter]simplify: Simplifying (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) 1) 1545989142.397 * * [misc]simplify: iters left: 6 (11 enodes) 1545989142.398 * * [misc]simplify: iters left: 5 (16 enodes) 1545989142.402 * * [misc]simplify: iters left: 4 (21 enodes) 1545989142.404 * [exit]simplify: Simplified to (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) 1545989142.404 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt k))))) 1545989142.404 * [enter]simplify: Simplifying (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt k)) 1545989142.404 * * [misc]simplify: iters left: 6 (11 enodes) 1545989142.406 * * [misc]simplify: iters left: 5 (14 enodes) 1545989142.408 * * [misc]simplify: iters left: 4 (17 enodes) 1545989142.410 * [exit]simplify: Simplified to (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt k)) 1545989142.410 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt k))))) 1545989142.410 * * * * [misc]progress: [ 58 / 133 ] simplifiying candidate # 1545989142.410 * [enter]simplify: Simplifying (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1545989142.411 * * [misc]simplify: iters left: 6 (6 enodes) 1545989142.411 * * [misc]simplify: iters left: 5 (10 enodes) 1545989142.413 * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) 1545989142.413 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k)))))) 1545989142.413 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1545989142.413 * * [misc]simplify: iters left: 6 (11 enodes) 1545989142.414 * * [misc]simplify: iters left: 5 (14 enodes) 1545989142.416 * * [misc]simplify: iters left: 4 (17 enodes) 1545989142.418 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1545989142.418 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k)))))) 1545989142.418 * * * * [misc]progress: [ 59 / 133 ] simplifiying candidate # 1545989142.419 * [enter]simplify: Simplifying (/ 1 (sqrt (sqrt k))) 1545989142.419 * * [misc]simplify: iters left: 4 (5 enodes) 1545989142.419 * * [misc]simplify: iters left: 3 (7 enodes) 1545989142.420 * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt k))) 1545989142.420 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))) 1545989142.420 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1545989142.420 * * [misc]simplify: iters left: 6 (11 enodes) 1545989142.422 * * [misc]simplify: iters left: 5 (14 enodes) 1545989142.424 * * [misc]simplify: iters left: 4 (17 enodes) 1545989142.426 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1545989142.426 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))) 1545989142.426 * * * * [misc]progress: [ 60 / 133 ] simplifiying candidate # 1545989142.426 * [enter]simplify: Simplifying (/ 1 1) 1545989142.426 * * [misc]simplify: iters left: 2 (2 enodes) 1545989142.426 * * [misc]simplify: iters left: 1 (4 enodes) 1545989142.427 * [exit]simplify: Simplified to 1 1545989142.427 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* 1 (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))))) 1545989142.427 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)) 1545989142.427 * * [misc]simplify: iters left: 6 (10 enodes) 1545989142.428 * * [misc]simplify: iters left: 5 (13 enodes) 1545989142.430 * * [misc]simplify: iters left: 4 (16 enodes) 1545989142.432 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)) 1545989142.432 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (* 1 (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))))) 1545989142.432 * * * * [misc]progress: [ 61 / 133 ] simplifiying candidate # 1545989142.433 * * * * [misc]progress: [ 62 / 133 ] simplifiying candidate # 1545989142.433 * * * * [misc]progress: [ 63 / 133 ] simplifiying candidate # 1545989142.433 * * * * [misc]progress: [ 64 / 133 ] simplifiying candidate # 1545989142.433 * [enter]simplify: Simplifying (cbrt (sqrt k)) 1545989142.433 * * [misc]simplify: iters left: 2 (3 enodes) 1545989142.433 * [exit]simplify: Simplified to (cbrt (sqrt k)) 1545989142.433 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (/ (pow (* n 2) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k))))) 1545989142.433 * * * * [misc]progress: [ 65 / 133 ] simplifiying candidate # 1545989142.433 * [enter]simplify: Simplifying (sqrt (sqrt k)) 1545989142.434 * * [misc]simplify: iters left: 2 (3 enodes) 1545989142.434 * [exit]simplify: Simplified to (sqrt (sqrt k)) 1545989142.434 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k))))) 1545989142.434 * * * * [misc]progress: [ 66 / 133 ] simplifiying candidate # 1545989142.434 * [enter]simplify: Simplifying (sqrt k) 1545989142.434 * * [misc]simplify: iters left: 1 (2 enodes) 1545989142.434 * [exit]simplify: Simplified to (sqrt k) 1545989142.434 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (/ (pow (* n 2) (- 1/2 (/ k 2))) 1) (sqrt k)))) 1545989142.435 * * * * [misc]progress: [ 67 / 133 ] simplifiying candidate # 1545989142.435 * [enter]simplify: Simplifying (pow (* n 2) 1/2) 1545989142.435 * * [misc]simplify: iters left: 3 (5 enodes) 1545989142.435 * * [misc]simplify: iters left: 2 (7 enodes) 1545989142.436 * [exit]simplify: Simplified to (sqrt (* n 2)) 1545989142.436 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (sqrt (* n 2)) (/ (sqrt k) (pow (* n 2) (- (/ k 2))))))) 1545989142.436 * * * * [misc]progress: [ 68 / 133 ] simplifiying candidate # 1545989142.436 * [enter]simplify: Simplifying (pow (* n 2) 1/2) 1545989142.437 * * [misc]simplify: iters left: 3 (5 enodes) 1545989142.437 * * [misc]simplify: iters left: 2 (7 enodes) 1545989142.438 * [exit]simplify: Simplified to (sqrt (* n 2)) 1545989142.438 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (sqrt (* n 2)) (/ (sqrt k) (pow (* n 2) (- (/ k 2))))))) 1545989142.438 * * * * [misc]progress: [ 69 / 133 ] simplifiying candidate # 1545989142.438 * [enter]simplify: Simplifying (pow n (- 1/2 (/ k 2))) 1545989142.438 * * [misc]simplify: iters left: 5 (7 enodes) 1545989142.439 * * [misc]simplify: iters left: 4 (9 enodes) 1545989142.440 * * [misc]simplify: iters left: 3 (12 enodes) 1545989142.442 * [exit]simplify: Simplified to (pow n (- 1/2 (/ k 2))) 1545989142.442 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (pow n (- 1/2 (/ k 2))) (/ (sqrt k) (pow 2 (- 1/2 (/ k 2))))))) 1545989142.442 * * * * [misc]progress: [ 70 / 133 ] simplifiying candidate # 1545989142.442 * [enter]simplify: Simplifying (* (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (pow (* n 2) (- 1/2 (/ k 2))))) 1545989142.442 * * [misc]simplify: iters left: 6 (10 enodes) 1545989142.444 * * [misc]simplify: iters left: 5 (13 enodes) 1545989142.445 * * [misc]simplify: iters left: 4 (16 enodes) 1545989142.448 * [exit]simplify: Simplified to (* (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (pow (* n 2) (- 1/2 (/ k 2))))) 1545989142.448 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (* (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (pow (* n 2) (- 1/2 (/ k 2))))) (/ (sqrt k) (cbrt (pow (* n 2) (- 1/2 (/ k 2)))))))) 1545989142.448 * * * * [misc]progress: [ 71 / 133 ] simplifiying candidate # 1545989142.448 * [enter]simplify: Simplifying (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) 1545989142.448 * * [misc]simplify: iters left: 6 (9 enodes) 1545989142.451 * * [misc]simplify: iters left: 5 (12 enodes) 1545989142.454 * * [misc]simplify: iters left: 4 (15 enodes) 1545989142.458 * [exit]simplify: Simplified to (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) 1545989142.459 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* n 2) (- 1/2 (/ k 2)))))))) 1545989142.459 * * * * [misc]progress: [ 72 / 133 ] simplifiying candidate # 1545989142.459 * * * * [misc]progress: [ 73 / 133 ] simplifiying candidate # 1545989142.459 * [enter]simplify: Simplifying (pow (* n 2) 1/2) 1545989142.459 * * [misc]simplify: iters left: 3 (5 enodes) 1545989142.461 * * [misc]simplify: iters left: 2 (7 enodes) 1545989142.462 * [exit]simplify: Simplified to (sqrt (* n 2)) 1545989142.463 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (sqrt (* n 2)) (* (sqrt k) (pow (* n 2) (/ k 2)))))) 1545989142.463 * * * * [misc]progress: [ 74 / 133 ] simplifiying candidate # 1545989142.463 * * * * [misc]progress: [ 75 / 133 ] simplifiying candidate # 1545989142.463 * [enter]simplify: Simplifying (+ (* (log PI) (- 1/2 (/ k 2))) (- (* (log (* n 2)) (- 1/2 (/ k 2))) (log (sqrt k)))) 1545989142.463 * * [misc]simplify: iters left: 6 (16 enodes) 1545989142.469 * * [misc]simplify: iters left: 5 (29 enodes) 1545989142.477 * * [misc]simplify: iters left: 4 (60 enodes) 1545989142.493 * * [misc]simplify: iters left: 3 (191 enodes) 1545989142.618 * [exit]simplify: Simplified to (- (* (+ (log PI) (log (* 2 n))) (- 1/2 (/ k 2))) (log (sqrt k))) 1545989142.618 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (+ (log PI) (log (* 2 n))) (- 1/2 (/ k 2))) (log (sqrt k))))) 1545989142.618 * * * * [misc]progress: [ 76 / 133 ] simplifiying candidate # 1545989142.619 * [enter]simplify: Simplifying (+ (* (log PI) (- 1/2 (/ k 2))) (- (* (log (* n 2)) (- 1/2 (/ k 2))) (log (sqrt k)))) 1545989142.619 * * [misc]simplify: iters left: 6 (16 enodes) 1545989142.624 * * [misc]simplify: iters left: 5 (29 enodes) 1545989142.633 * * [misc]simplify: iters left: 4 (60 enodes) 1545989142.662 * * [misc]simplify: iters left: 3 (191 enodes) 1545989142.807 * [exit]simplify: Simplified to (- (* (+ (log PI) (log (* 2 n))) (- 1/2 (/ k 2))) (log (sqrt k))) 1545989142.807 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (+ (log PI) (log (* 2 n))) (- 1/2 (/ k 2))) (log (sqrt k))))) 1545989142.807 * * * * [misc]progress: [ 77 / 133 ] simplifiying candidate # 1545989142.807 * [enter]simplify: Simplifying (+ (* (log PI) (- 1/2 (/ k 2))) (- (log (pow (* n 2) (- 1/2 (/ k 2)))) (log (sqrt k)))) 1545989142.807 * * [misc]simplify: iters left: 6 (16 enodes) 1545989142.812 * * [misc]simplify: iters left: 5 (27 enodes) 1545989142.821 * * [misc]simplify: iters left: 4 (50 enodes) 1545989142.840 * * [misc]simplify: iters left: 3 (114 enodes) 1545989142.915 * * [misc]simplify: iters left: 2 (426 enodes) 1545989143.432 * [exit]simplify: Simplified to (- (* (+ (log PI) (log (* 2 n))) (- 1/2 (/ k 2))) (log (sqrt k))) 1545989143.432 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (+ (log PI) (log (* 2 n))) (- 1/2 (/ k 2))) (log (sqrt k))))) 1545989143.432 * * * * [misc]progress: [ 78 / 133 ] simplifiying candidate # 1545989143.432 * [enter]simplify: Simplifying (+ (* (log PI) (- 1/2 (/ k 2))) (log (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1545989143.432 * * [misc]simplify: iters left: 6 (15 enodes) 1545989143.437 * * [misc]simplify: iters left: 5 (23 enodes) 1545989143.443 * * [misc]simplify: iters left: 4 (40 enodes) 1545989143.458 * * [misc]simplify: iters left: 3 (82 enodes) 1545989143.475 * * [misc]simplify: iters left: 2 (187 enodes) 1545989143.629 * [exit]simplify: Simplified to (- (* (+ (log PI) (log (* 2 n))) (- 1/2 (/ k 2))) (log (sqrt k))) 1545989143.629 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (+ (log PI) (log (* 2 n))) (- 1/2 (/ k 2))) (log (sqrt k))))) 1545989143.629 * * * * [misc]progress: [ 79 / 133 ] simplifiying candidate # 1545989143.629 * [enter]simplify: Simplifying (+ (log (pow PI (- 1/2 (/ k 2)))) (- (* (log (* n 2)) (- 1/2 (/ k 2))) (log (sqrt k)))) 1545989143.629 * * [misc]simplify: iters left: 6 (16 enodes) 1545989143.635 * * [misc]simplify: iters left: 5 (30 enodes) 1545989143.644 * * [misc]simplify: iters left: 4 (56 enodes) 1545989143.672 * * [misc]simplify: iters left: 3 (161 enodes) 1545989143.793 * [exit]simplify: Simplified to (- (* (+ (log PI) (log (* n 2))) (- 1/2 (/ k 2))) (log (sqrt k))) 1545989143.793 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (+ (log PI) (log (* n 2))) (- 1/2 (/ k 2))) (log (sqrt k))))) 1545989143.793 * * * * [misc]progress: [ 80 / 133 ] simplifiying candidate # 1545989143.793 * [enter]simplify: Simplifying (+ (log (pow PI (- 1/2 (/ k 2)))) (- (* (log (* n 2)) (- 1/2 (/ k 2))) (log (sqrt k)))) 1545989143.794 * * [misc]simplify: iters left: 6 (16 enodes) 1545989143.799 * * [misc]simplify: iters left: 5 (30 enodes) 1545989143.809 * * [misc]simplify: iters left: 4 (56 enodes) 1545989143.831 * * [misc]simplify: iters left: 3 (161 enodes) 1545989143.920 * [exit]simplify: Simplified to (- (* (+ (log PI) (log (* n 2))) (- 1/2 (/ k 2))) (log (sqrt k))) 1545989143.920 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (+ (log PI) (log (* n 2))) (- 1/2 (/ k 2))) (log (sqrt k))))) 1545989143.920 * * * * [misc]progress: [ 81 / 133 ] simplifiying candidate # 1545989143.920 * [enter]simplify: Simplifying (+ (log (pow PI (- 1/2 (/ k 2)))) (- (log (pow (* n 2) (- 1/2 (/ k 2)))) (log (sqrt k)))) 1545989143.920 * * [misc]simplify: iters left: 6 (16 enodes) 1545989143.923 * * [misc]simplify: iters left: 5 (28 enodes) 1545989143.927 * * [misc]simplify: iters left: 4 (46 enodes) 1545989143.934 * * [misc]simplify: iters left: 3 (83 enodes) 1545989143.975 * * [misc]simplify: iters left: 2 (323 enodes) 1545989144.292 * [exit]simplify: Simplified to (- (* (+ (log (* n 2)) (log PI)) (- 1/2 (/ k 2))) (log (sqrt k))) 1545989144.292 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (+ (log (* n 2)) (log PI)) (- 1/2 (/ k 2))) (log (sqrt k))))) 1545989144.292 * * * * [misc]progress: [ 82 / 133 ] simplifiying candidate # 1545989144.292 * [enter]simplify: Simplifying (+ (log (pow PI (- 1/2 (/ k 2)))) (log (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1545989144.292 * * [misc]simplify: iters left: 6 (15 enodes) 1545989144.294 * * [misc]simplify: iters left: 5 (24 enodes) 1545989144.298 * * [misc]simplify: iters left: 4 (36 enodes) 1545989144.303 * * [misc]simplify: iters left: 3 (60 enodes) 1545989144.316 * * [misc]simplify: iters left: 2 (163 enodes) 1545989144.388 * [exit]simplify: Simplified to (- (* (+ (log PI) (log (* n 2))) (- 1/2 (/ k 2))) (log (sqrt k))) 1545989144.388 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (+ (log PI) (log (* n 2))) (- 1/2 (/ k 2))) (log (sqrt k))))) 1545989144.388 * * * * [misc]progress: [ 83 / 133 ] simplifiying candidate # 1545989144.388 * * * * [misc]progress: [ 84 / 133 ] simplifiying candidate # 1545989144.388 * * * * [misc]progress: [ 85 / 133 ] simplifiying candidate # 1545989144.389 * [enter]simplify: Simplifying (* (* (* (pow PI (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))) (pow PI (- 1/2 (/ k 2)))) (/ (* (* (pow (* n 2) (- 1/2 (/ k 2))) (pow (* n 2) (- 1/2 (/ k 2)))) (pow (* n 2) (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))) 1545989144.389 * * [misc]simplify: iters left: 6 (19 enodes) 1545989144.396 * * [misc]simplify: iters left: 5 (37 enodes) 1545989144.410 * * [misc]simplify: iters left: 4 (114 enodes) 1545989144.453 * * [misc]simplify: iters left: 3 (443 enodes) 1545989144.962 * [exit]simplify: Simplified to (* (* (/ (pow (* 2 n) (- 1/2 (/ k 2))) (sqrt k)) (* (pow (* 2 n) (- 1/2 (/ k 2))) (pow (* 2 n) (- 1/2 (/ k 2))))) (* (/ (pow PI (- 1/2 (/ k 2))) k) (* (pow PI (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))))) 1545989144.962 * [misc]simplify: Simplified (2 1) to (λ (k n) (cbrt (* (* (/ (pow (* 2 n) (- 1/2 (/ k 2))) (sqrt k)) (* (pow (* 2 n) (- 1/2 (/ k 2))) (pow (* 2 n) (- 1/2 (/ k 2))))) (* (/ (pow PI (- 1/2 (/ k 2))) k) (* (pow PI (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))))))) 1545989144.962 * * * * [misc]progress: [ 86 / 133 ] simplifiying candidate # 1545989144.962 * [enter]simplify: Simplifying (* (* (* (pow PI (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))) (pow PI (- 1/2 (/ k 2)))) (* (* (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1545989144.963 * * [misc]simplify: iters left: 6 (17 enodes) 1545989144.966 * * [misc]simplify: iters left: 5 (33 enodes) 1545989144.972 * * [misc]simplify: iters left: 4 (87 enodes) 1545989144.994 * * [misc]simplify: iters left: 3 (222 enodes) 1545989145.090 * [exit]simplify: Simplified to (* (* (* (pow PI (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))) (/ (pow (* 2 n) (- 1/2 (/ k 2))) (sqrt k))) (* (/ (pow (* 2 n) (- 1/2 (/ k 2))) k) (* (pow (* 2 n) (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))))) 1545989145.090 * [misc]simplify: Simplified (2 1) to (λ (k n) (cbrt (* (* (* (pow PI (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))) (/ (pow (* 2 n) (- 1/2 (/ k 2))) (sqrt k))) (* (/ (pow (* 2 n) (- 1/2 (/ k 2))) k) (* (pow (* 2 n) (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))))))) 1545989145.090 * * * * [misc]progress: [ 87 / 133 ] simplifiying candidate # 1545989145.090 * * * * [misc]progress: [ 88 / 133 ] simplifiying candidate # 1545989145.090 * * * * [misc]progress: [ 89 / 133 ] simplifiying candidate # 1545989145.090 * * * * [misc]progress: [ 90 / 133 ] simplifiying candidate # 1545989145.090 * [enter]simplify: Simplifying (* (pow PI 1/2) (pow (* n 2) (- 1/2 (/ k 2)))) 1545989145.090 * * [misc]simplify: iters left: 6 (11 enodes) 1545989145.092 * * [misc]simplify: iters left: 5 (16 enodes) 1545989145.094 * * [misc]simplify: iters left: 4 (19 enodes) 1545989145.096 * [exit]simplify: Simplified to (* (sqrt PI) (pow (* n 2) (- 1/2 (/ k 2)))) 1545989145.097 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (* (sqrt PI) (pow (* n 2) (- 1/2 (/ k 2)))) (* (pow PI (/ k 2)) (sqrt k)))) 1545989145.097 * [enter]simplify: Simplifying (* (pow PI (/ k 2)) (sqrt k)) 1545989145.097 * * [misc]simplify: iters left: 5 (7 enodes) 1545989145.098 * * [misc]simplify: iters left: 4 (8 enodes) 1545989145.099 * [exit]simplify: Simplified to (* (pow PI (/ k 2)) (sqrt k)) 1545989145.099 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (* (sqrt PI) (pow (* n 2) (- 1/2 (/ k 2)))) (* (pow PI (/ k 2)) (sqrt k)))) 1545989145.099 * * * * [misc]progress: [ 91 / 133 ] simplifiying candidate # 1545989145.099 * * * * [misc]progress: [ 92 / 133 ] simplifiying candidate # 1545989145.099 * [enter]simplify: Simplifying (cbrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))) 1545989145.099 * * [misc]simplify: iters left: 6 (11 enodes) 1545989145.101 * * [misc]simplify: iters left: 5 (14 enodes) 1545989145.102 * * [misc]simplify: iters left: 4 (17 enodes) 1545989145.105 * [exit]simplify: Simplified to (cbrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))) 1545989145.105 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow PI (- 1/2 (/ k 2))) (* (cbrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))))) (cbrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))))) 1545989145.105 * * * * [misc]progress: [ 93 / 133 ] simplifiying candidate # 1545989145.105 * [enter]simplify: Simplifying (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))) 1545989145.105 * * [misc]simplify: iters left: 6 (11 enodes) 1545989145.107 * * [misc]simplify: iters left: 5 (14 enodes) 1545989145.108 * * [misc]simplify: iters left: 4 (17 enodes) 1545989145.111 * [exit]simplify: Simplified to (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))) 1545989145.111 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow PI (- 1/2 (/ k 2))) (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))))) 1545989145.111 * * * * [misc]progress: [ 94 / 133 ] simplifiying candidate # 1545989145.111 * [enter]simplify: Simplifying (/ (pow (* n 2) (- (/ k 2))) (cbrt (sqrt k))) 1545989145.111 * * [misc]simplify: iters left: 6 (10 enodes) 1545989145.112 * * [misc]simplify: iters left: 5 (13 enodes) 1545989145.114 * [exit]simplify: Simplified to (/ (pow (* n 2) (/ (- k) 2)) (cbrt (sqrt k))) 1545989145.114 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow PI (- 1/2 (/ k 2))) (/ (pow (* n 2) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow (* n 2) (/ (- k) 2)) (cbrt (sqrt k))))) 1545989145.114 * * * * [misc]progress: [ 95 / 133 ] simplifiying candidate # 1545989145.114 * [enter]simplify: Simplifying (/ (pow (* n 2) (- (/ k 2))) (sqrt (sqrt k))) 1545989145.114 * * [misc]simplify: iters left: 6 (10 enodes) 1545989145.116 * * [misc]simplify: iters left: 5 (13 enodes) 1545989145.117 * [exit]simplify: Simplified to (/ (pow (* n 2) (/ (- k) 2)) (sqrt (sqrt k))) 1545989145.118 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow PI (- 1/2 (/ k 2))) (/ (pow (* n 2) 1/2) (sqrt (sqrt k)))) (/ (pow (* n 2) (/ (- k) 2)) (sqrt (sqrt k))))) 1545989145.118 * * * * [misc]progress: [ 96 / 133 ] simplifiying candidate # 1545989145.118 * [enter]simplify: Simplifying (/ (pow (* n 2) (- (/ k 2))) (sqrt k)) 1545989145.118 * * [misc]simplify: iters left: 6 (9 enodes) 1545989145.119 * * [misc]simplify: iters left: 5 (12 enodes) 1545989145.121 * [exit]simplify: Simplified to (/ (pow (* n 2) (- (/ k 2))) (sqrt k)) 1545989145.121 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow PI (- 1/2 (/ k 2))) (/ (pow (* n 2) 1/2) 1)) (/ (pow (* n 2) (- (/ k 2))) (sqrt k)))) 1545989145.121 * * * * [misc]progress: [ 97 / 133 ] simplifiying candidate # 1545989145.121 * [enter]simplify: Simplifying (/ (pow (* n 2) (- (/ k 2))) (cbrt (sqrt k))) 1545989145.121 * * [misc]simplify: iters left: 6 (10 enodes) 1545989145.123 * * [misc]simplify: iters left: 5 (13 enodes) 1545989145.126 * [exit]simplify: Simplified to (/ (pow (* n 2) (/ (- k) 2)) (cbrt (sqrt k))) 1545989145.126 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow PI (- 1/2 (/ k 2))) (/ (pow (* n 2) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow (* n 2) (/ (- k) 2)) (cbrt (sqrt k))))) 1545989145.126 * * * * [misc]progress: [ 98 / 133 ] simplifiying candidate # 1545989145.126 * [enter]simplify: Simplifying (/ (pow (* n 2) (- (/ k 2))) (sqrt (sqrt k))) 1545989145.127 * * [misc]simplify: iters left: 6 (10 enodes) 1545989145.128 * * [misc]simplify: iters left: 5 (13 enodes) 1545989145.130 * [exit]simplify: Simplified to (/ (pow (* n 2) (/ (- k) 2)) (sqrt (sqrt k))) 1545989145.130 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow PI (- 1/2 (/ k 2))) (/ (pow (* n 2) 1/2) (sqrt (sqrt k)))) (/ (pow (* n 2) (/ (- k) 2)) (sqrt (sqrt k))))) 1545989145.130 * * * * [misc]progress: [ 99 / 133 ] simplifiying candidate # 1545989145.130 * [enter]simplify: Simplifying (/ (pow (* n 2) (- (/ k 2))) (sqrt k)) 1545989145.130 * * [misc]simplify: iters left: 6 (9 enodes) 1545989145.131 * * [misc]simplify: iters left: 5 (12 enodes) 1545989145.134 * [exit]simplify: Simplified to (/ (pow (* n 2) (- (/ k 2))) (sqrt k)) 1545989145.134 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow PI (- 1/2 (/ k 2))) (/ (pow (* n 2) 1/2) 1)) (/ (pow (* n 2) (- (/ k 2))) (sqrt k)))) 1545989145.134 * * * * [misc]progress: [ 100 / 133 ] simplifiying candidate # 1545989145.135 * [enter]simplify: Simplifying (/ (pow 2 (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1545989145.135 * * [misc]simplify: iters left: 6 (9 enodes) 1545989145.137 * * [misc]simplify: iters left: 5 (11 enodes) 1545989145.141 * * [misc]simplify: iters left: 4 (14 enodes) 1545989145.145 * [exit]simplify: Simplified to (/ (pow 2 (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1545989145.145 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow PI (- 1/2 (/ k 2))) (/ (pow n (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow 2 (- 1/2 (/ k 2))) (cbrt (sqrt k))))) 1545989145.145 * * * * [misc]progress: [ 101 / 133 ] simplifiying candidate # 1545989145.145 * [enter]simplify: Simplifying (/ (pow 2 (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1545989145.145 * * [misc]simplify: iters left: 6 (9 enodes) 1545989145.148 * * [misc]simplify: iters left: 5 (11 enodes) 1545989145.151 * * [misc]simplify: iters left: 4 (14 enodes) 1545989145.155 * [exit]simplify: Simplified to (/ (pow 2 (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1545989145.155 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow PI (- 1/2 (/ k 2))) (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (/ (pow 2 (- 1/2 (/ k 2))) (sqrt (sqrt k))))) 1545989145.155 * * * * [misc]progress: [ 102 / 133 ] simplifiying candidate # 1545989145.155 * [enter]simplify: Simplifying (/ (pow 2 (- 1/2 (/ k 2))) (sqrt k)) 1545989145.155 * * [misc]simplify: iters left: 6 (8 enodes) 1545989145.158 * * [misc]simplify: iters left: 5 (10 enodes) 1545989145.161 * * [misc]simplify: iters left: 4 (13 enodes) 1545989145.164 * [exit]simplify: Simplified to (/ (pow 2 (- 1/2 (/ k 2))) (sqrt k)) 1545989145.164 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow PI (- 1/2 (/ k 2))) (/ (pow n (- 1/2 (/ k 2))) 1)) (/ (pow 2 (- 1/2 (/ k 2))) (sqrt k)))) 1545989145.164 * * * * [misc]progress: [ 103 / 133 ] simplifiying candidate # 1545989145.165 * [enter]simplify: Simplifying (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1545989145.165 * * [misc]simplify: iters left: 6 (12 enodes) 1545989145.168 * * [misc]simplify: iters left: 5 (15 enodes) 1545989145.172 * * [misc]simplify: iters left: 4 (18 enodes) 1545989145.177 * [exit]simplify: Simplified to (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1545989145.177 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow PI (- 1/2 (/ k 2))) (/ (* (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (pow (* n 2) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))) 1545989145.177 * * * * [misc]progress: [ 104 / 133 ] simplifiying candidate # 1545989145.178 * [enter]simplify: Simplifying (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1545989145.178 * * [misc]simplify: iters left: 6 (12 enodes) 1545989145.181 * * [misc]simplify: iters left: 5 (15 enodes) 1545989145.185 * * [misc]simplify: iters left: 4 (18 enodes) 1545989145.190 * [exit]simplify: Simplified to (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1545989145.190 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow PI (- 1/2 (/ k 2))) (/ (* (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (pow (* n 2) (- 1/2 (/ k 2))))) (sqrt (sqrt k)))) (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) 1545989145.190 * * * * [misc]progress: [ 105 / 133 ] simplifiying candidate # 1545989145.191 * [enter]simplify: Simplifying (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt k)) 1545989145.191 * * [misc]simplify: iters left: 6 (11 enodes) 1545989145.194 * * [misc]simplify: iters left: 5 (14 enodes) 1545989145.198 * * [misc]simplify: iters left: 4 (17 enodes) 1545989145.202 * [exit]simplify: Simplified to (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt k)) 1545989145.203 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow PI (- 1/2 (/ k 2))) (/ (* (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (pow (* n 2) (- 1/2 (/ k 2))))) 1)) (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt k)))) 1545989145.203 * * * * [misc]progress: [ 106 / 133 ] simplifiying candidate # 1545989145.203 * [enter]simplify: Simplifying (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1545989145.203 * * [misc]simplify: iters left: 6 (12 enodes) 1545989145.206 * * [misc]simplify: iters left: 5 (15 enodes) 1545989145.210 * * [misc]simplify: iters left: 4 (18 enodes) 1545989145.215 * [exit]simplify: Simplified to (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1545989145.215 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow PI (- 1/2 (/ k 2))) (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))) 1545989145.215 * * * * [misc]progress: [ 107 / 133 ] simplifiying candidate # 1545989145.215 * [enter]simplify: Simplifying (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1545989145.215 * * [misc]simplify: iters left: 6 (12 enodes) 1545989145.218 * * [misc]simplify: iters left: 5 (15 enodes) 1545989145.222 * * [misc]simplify: iters left: 4 (18 enodes) 1545989145.227 * [exit]simplify: Simplified to (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1545989145.227 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow PI (- 1/2 (/ k 2))) (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) 1545989145.227 * * * * [misc]progress: [ 108 / 133 ] simplifiying candidate # 1545989145.228 * [enter]simplify: Simplifying (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt k)) 1545989145.228 * * [misc]simplify: iters left: 6 (11 enodes) 1545989145.231 * * [misc]simplify: iters left: 5 (14 enodes) 1545989145.235 * * [misc]simplify: iters left: 4 (17 enodes) 1545989145.240 * [exit]simplify: Simplified to (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt k)) 1545989145.240 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow PI (- 1/2 (/ k 2))) (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) 1)) (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt k)))) 1545989145.240 * * * * [misc]progress: [ 109 / 133 ] simplifiying candidate # 1545989145.240 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1545989145.240 * * [misc]simplify: iters left: 6 (11 enodes) 1545989145.243 * * [misc]simplify: iters left: 5 (14 enodes) 1545989145.247 * * [misc]simplify: iters left: 4 (17 enodes) 1545989145.252 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1545989145.252 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow PI (- 1/2 (/ k 2))) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))))) 1545989145.252 * * * * [misc]progress: [ 110 / 133 ] simplifiying candidate # 1545989145.252 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1545989145.253 * * [misc]simplify: iters left: 6 (11 enodes) 1545989145.256 * * [misc]simplify: iters left: 5 (14 enodes) 1545989145.260 * * [misc]simplify: iters left: 4 (17 enodes) 1545989145.265 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1545989145.265 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow PI (- 1/2 (/ k 2))) (/ 1 (sqrt (sqrt k)))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) 1545989145.265 * * * * [misc]progress: [ 111 / 133 ] simplifiying candidate # 1545989145.266 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)) 1545989145.266 * * [misc]simplify: iters left: 6 (10 enodes) 1545989145.269 * * [misc]simplify: iters left: 5 (13 enodes) 1545989145.273 * * [misc]simplify: iters left: 4 (16 enodes) 1545989145.278 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)) 1545989145.278 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow PI (- 1/2 (/ k 2))) (/ 1 1)) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1545989145.278 * * * * [misc]progress: [ 112 / 133 ] simplifiying candidate # 1545989145.278 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)) 1545989145.278 * * [misc]simplify: iters left: 6 (10 enodes) 1545989145.281 * * [misc]simplify: iters left: 5 (13 enodes) 1545989145.285 * * [misc]simplify: iters left: 4 (16 enodes) 1545989145.289 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)) 1545989145.289 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow PI (- 1/2 (/ k 2))) 1) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1545989145.289 * * * * [misc]progress: [ 113 / 133 ] simplifiying candidate # 1545989145.289 * [enter]simplify: Simplifying (/ 1 (sqrt k)) 1545989145.289 * * [misc]simplify: iters left: 3 (4 enodes) 1545989145.291 * * [misc]simplify: iters left: 2 (6 enodes) 1545989145.292 * [exit]simplify: Simplified to (/ 1 (sqrt k)) 1545989145.292 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow PI (- 1/2 (/ k 2))) (pow (* n 2) (- 1/2 (/ k 2)))) (/ 1 (sqrt k)))) 1545989145.292 * * * * [misc]progress: [ 114 / 133 ] simplifiying candidate # 1545989145.293 * [enter]simplify: Simplifying (pow PI 1/2) 1545989145.293 * * [misc]simplify: iters left: 1 (3 enodes) 1545989145.294 * [exit]simplify: Simplified to (sqrt PI) 1545989145.294 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt PI) (* (pow PI (- (/ k 2))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))))) 1545989145.294 * * * * [misc]progress: [ 115 / 133 ] simplifiying candidate # 1545989145.294 * [enter]simplify: Simplifying (pow PI 1/2) 1545989145.294 * * [misc]simplify: iters left: 1 (3 enodes) 1545989145.295 * [exit]simplify: Simplified to (sqrt PI) 1545989145.295 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt PI) (* (pow PI (- (/ k 2))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))))) 1545989145.295 * * * * [misc]progress: [ 116 / 133 ] simplifiying candidate # 1545989145.296 * [enter]simplify: Simplifying (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) 1545989145.296 * * [misc]simplify: iters left: 6 (9 enodes) 1545989145.298 * * [misc]simplify: iters left: 5 (11 enodes) 1545989145.302 * * [misc]simplify: iters left: 4 (14 enodes) 1545989145.306 * [exit]simplify: Simplified to (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) 1545989145.306 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) (* (cbrt (pow PI (- 1/2 (/ k 2)))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))))) 1545989145.306 * * * * [misc]progress: [ 117 / 133 ] simplifiying candidate # 1545989145.307 * [enter]simplify: Simplifying (sqrt (pow PI (- 1/2 (/ k 2)))) 1545989145.307 * * [misc]simplify: iters left: 6 (8 enodes) 1545989145.309 * * [misc]simplify: iters left: 5 (10 enodes) 1545989145.312 * * [misc]simplify: iters left: 4 (13 enodes) 1545989145.316 * [exit]simplify: Simplified to (sqrt (pow PI (- 1/2 (/ k 2)))) 1545989145.316 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (pow PI (- 1/2 (/ k 2)))) (* (sqrt (pow PI (- 1/2 (/ k 2)))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))))) 1545989145.316 * * * * [misc]progress: [ 118 / 133 ] simplifiying candidate # 1545989145.316 * * * * [misc]progress: [ 119 / 133 ] simplifiying candidate # 1545989145.316 * [enter]simplify: Simplifying (sqrt k) 1545989145.316 * * [misc]simplify: iters left: 1 (2 enodes) 1545989145.317 * [exit]simplify: Simplified to (sqrt k) 1545989145.317 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (* (pow PI (- 1/2 (/ k 2))) (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt k))) 1545989145.317 * * * * [misc]progress: [ 120 / 133 ] simplifiying candidate # 1545989145.317 * [enter]simplify: Simplifying (* (pow PI 1/2) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))) 1545989145.317 * * [misc]simplify: iters left: 6 (13 enodes) 1545989145.322 * * [misc]simplify: iters left: 5 (20 enodes) 1545989145.327 * * [misc]simplify: iters left: 4 (27 enodes) 1545989145.334 * * [misc]simplify: iters left: 3 (29 enodes) 1545989145.340 * * [misc]simplify: iters left: 2 (31 enodes) 1545989145.343 * * [misc]simplify: iters left: 1 (32 enodes) 1545989145.347 * [exit]simplify: Simplified to (* (/ (sqrt PI) (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))) 1545989145.347 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (* (/ (sqrt PI) (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))) (pow PI (/ k 2)))) 1545989145.347 * * * * [misc]progress: [ 121 / 133 ] simplifiying candidate # 1545989145.347 * * * * [misc]progress: [ 122 / 133 ] simplifiying candidate # 1545989145.348 * [enter]simplify: Simplifying (- (+ (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (* (pow (log 2) 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (pow k 2)))) (+ (* 1/4 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) (pow k 2))))) (* 1/8 (* (exp (* 1/2 (+ (log 2) (log n)))) (* (pow (log n) 2) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) k))) (* 1/2 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) k))))) 1545989145.348 * * [misc]simplify: iters left: 6 (35 enodes) 1545989145.355 * * [misc]simplify: iters left: 5 (99 enodes) 1545989145.375 * * [misc]simplify: iters left: 4 (298 enodes) 1545989145.555 * [exit]simplify: Simplified to (+ (- (* (pow n 1/2) (pow 2 1/2)) (* (* 1/2 k) (* (* (pow n 1/2) (pow 2 1/2)) (+ (log 2) (log n))))) (+ (* (* (log 2) 1/8) (* (* (pow n 1/2) (pow 2 1/2)) (* (* k k) (log 2)))) (* (* (pow n 1/2) (pow 2 1/2)) (+ (* (* 1/4 (log 2)) (* (* k k) (log n))) (* (* 1/8 (log n)) (* (* k k) (log n))))))) 1545989145.556 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (+ (- (* (pow n 1/2) (pow 2 1/2)) (* (* 1/2 k) (* (* (pow n 1/2) (pow 2 1/2)) (+ (log 2) (log n))))) (+ (* (* (log 2) 1/8) (* (* (pow n 1/2) (pow 2 1/2)) (* (* k k) (log 2)))) (* (* (pow n 1/2) (pow 2 1/2)) (+ (* (* 1/4 (log 2)) (* (* k k) (log n))) (* (* 1/8 (log n)) (* (* k k) (log n))))))) (sqrt k)))) 1545989145.556 * * * * [misc]progress: [ 123 / 133 ] simplifiying candidate # 1545989145.556 * [enter]simplify: Simplifying (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) 1545989145.556 * * [misc]simplify: iters left: 6 (13 enodes) 1545989145.561 * * [misc]simplify: iters left: 5 (27 enodes) 1545989145.570 * * [misc]simplify: iters left: 4 (53 enodes) 1545989145.588 * * [misc]simplify: iters left: 3 (116 enodes) 1545989145.651 * * [misc]simplify: iters left: 2 (362 enodes) 1545989145.943 * [exit]simplify: Simplified to (pow (sqrt (* n 2)) (- 1 k)) 1545989145.943 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (pow (sqrt (* n 2)) (- 1 k)) (sqrt k)))) 1545989145.943 * * * * [misc]progress: [ 124 / 133 ] simplifiying candidate # 1545989145.943 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) 1545989145.943 * * [misc]simplify: iters left: 6 (13 enodes) 1545989145.949 * * [misc]simplify: iters left: 5 (24 enodes) 1545989145.963 * * [misc]simplify: iters left: 4 (54 enodes) 1545989145.976 * * [misc]simplify: iters left: 3 (143 enodes) 1545989146.025 * [exit]simplify: Simplified to (pow (exp (- 1/2 (* 1/2 k))) (- (log -2) (log (/ -1 n)))) 1545989146.025 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (pow (exp (- 1/2 (* 1/2 k))) (- (log -2) (log (/ -1 n)))) (sqrt k)))) 1545989146.025 * * * * [misc]progress: [ 125 / 133 ] simplifiying candidate # 1545989146.026 * [enter]simplify: Simplifying (- (+ (pow PI 1/2) (* 1/8 (* (* (pow (log PI) 2) (pow k 2)) (sqrt PI)))) (* 1/2 (* (* (log PI) k) (sqrt PI)))) 1545989146.026 * * [misc]simplify: iters left: 6 (18 enodes) 1545989146.029 * * [misc]simplify: iters left: 5 (39 enodes) 1545989146.036 * * [misc]simplify: iters left: 4 (104 enodes) 1545989146.068 * * [misc]simplify: iters left: 3 (275 enodes) 1545989146.158 * [exit]simplify: Simplified to (+ (* (* (* k (log PI)) (* k (log PI))) (* (sqrt PI) 1/8)) (+ (* (* k (log PI)) (* (sqrt PI) -1/2)) (sqrt PI))) 1545989146.158 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (+ (* (* (* k (log PI)) (* k (log PI))) (* (sqrt PI) 1/8)) (+ (* (* k (log PI)) (* (sqrt PI) -1/2)) (sqrt PI))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1545989146.158 * * * * [misc]progress: [ 126 / 133 ] simplifiying candidate # 1545989146.158 * [enter]simplify: Simplifying (pow PI (- 1/2 (* 1/2 k))) 1545989146.159 * * [misc]simplify: iters left: 5 (6 enodes) 1545989146.159 * * [misc]simplify: iters left: 4 (9 enodes) 1545989146.161 * * [misc]simplify: iters left: 3 (17 enodes) 1545989146.163 * * [misc]simplify: iters left: 2 (20 enodes) 1545989146.166 * * [misc]simplify: iters left: 1 (24 enodes) 1545989146.171 * [exit]simplify: Simplified to (pow PI (- 1/2 (* k 1/2))) 1545989146.171 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (pow PI (- 1/2 (* k 1/2))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1545989146.171 * * * * [misc]progress: [ 127 / 133 ] simplifiying candidate # 1545989146.171 * [enter]simplify: Simplifying (pow PI (- 1/2 (* 1/2 k))) 1545989146.171 * * [misc]simplify: iters left: 5 (6 enodes) 1545989146.172 * * [misc]simplify: iters left: 4 (9 enodes) 1545989146.174 * * [misc]simplify: iters left: 3 (17 enodes) 1545989146.176 * * [misc]simplify: iters left: 2 (20 enodes) 1545989146.178 * * [misc]simplify: iters left: 1 (24 enodes) 1545989146.190 * [exit]simplify: Simplified to (pow PI (- 1/2 (* k 1/2))) 1545989146.190 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (pow PI (- 1/2 (* k 1/2))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1545989146.190 * * * * [misc]progress: [ 128 / 133 ] simplifiying candidate # 1545989146.190 * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) k))) (- (+ (* +nan.0 (* (pow (log 2) 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (pow k 2)))) (- (+ (* +nan.0 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) k)) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (pow k 2)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log 2) (log n))))) (- (+ (* +nan.0 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (pow k 2)))))))))))))))))))))) 1545989146.190 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) +nan.0)) 1545989146.190 * * * * [misc]progress: [ 129 / 133 ] simplifiying candidate # 1545989146.191 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) k)) (- (* +nan.0 (/ (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) (pow k 2)))))))) 1545989146.191 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) +nan.0)) 1545989146.191 * * * * [misc]progress: [ 130 / 133 ] simplifiying candidate # 1545989146.191 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (pow k 2))) (- (+ (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n)))))) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) k))))))) 1545989146.191 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) +nan.0)) 1545989146.191 * * * * [misc]progress: [ 131 / 133 ] simplifiying candidate # 1545989146.191 * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log PI) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))))))))) 1545989146.191 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1545989146.192 * * * * [misc]progress: [ 132 / 133 ] simplifiying candidate # 1545989146.192 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (* (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))) (pow k 2))) (- (+ (* +nan.0 (/ (* (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))) k)) (- (* +nan.0 (/ (* (pow PI (- 1/2 (* 1/2 k))) (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k))))) (pow k 3)))))))) 1545989146.192 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1545989146.192 * * * * [misc]progress: [ 133 / 133 ] simplifiying candidate # 1545989146.192 * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (pow PI (- 1/2 (* 1/2 k))))) (- (+ (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (pow PI (- 1/2 (* 1/2 k)))) k)) (- (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (pow PI (- 1/2 (* 1/2 k)))) (pow k 2)))))))) 1545989146.192 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1545989146.192 * * * [misc]progress: adding candidates to table 1545989148.227 * * [misc]progress: iteration 4 / 4 1545989148.227 * * * [misc]progress: picking best candidate 1545989148.259 * * * * [misc]pick: Picked # 1545989148.259 * * * [misc]progress: localizing error 1545989148.271 * * * [misc]progress: generating rewritten candidates 1545989148.271 * * * * [misc]progress: [ 1 / 4 ] rewriting at (2 2 1) 1545989148.272 * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 2) 1545989148.276 * * * * [misc]progress: [ 3 / 4 ] rewriting at (2) 1545989148.288 * * * * [misc]progress: [ 4 / 4 ] rewriting at (2 1 1) 1545989148.299 * * * [misc]progress: generating series expansions 1545989148.299 * * * * [misc]progress: [ 1 / 4 ] generating series at (2 2 1) 1545989148.299 * [misc]backup-simplify: Simplify (pow (* n 2) (- 1/2 (/ k 2))) into (pow (* 2 n) (- 1/2 (* 1/2 k))) 1545989148.299 * [misc]approximate: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in (n k) around 0 1545989148.299 * [misc]taylor: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in k 1545989148.299 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in k 1545989148.299 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in k 1545989148.299 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1545989148.299 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989148.299 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.299 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1545989148.299 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989148.300 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.300 * [misc]taylor: Taking taylor expansion of k in k 1545989148.300 * [misc]backup-simplify: Simplify 0 into 0 1545989148.300 * [misc]backup-simplify: Simplify 1 into 1 1545989148.300 * [misc]taylor: Taking taylor expansion of (log (* 2 n)) in k 1545989148.300 * [misc]taylor: Taking taylor expansion of (* 2 n) in k 1545989148.300 * [misc]taylor: Taking taylor expansion of 2 in k 1545989148.300 * [misc]backup-simplify: Simplify 2 into 2 1545989148.300 * [misc]taylor: Taking taylor expansion of n in k 1545989148.300 * [misc]backup-simplify: Simplify n into n 1545989148.300 * [misc]backup-simplify: Simplify (* 2 n) into (* 2 n) 1545989148.300 * [misc]backup-simplify: Simplify (log (* 2 n)) into (log (* 2 n)) 1545989148.300 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1545989148.300 * [misc]backup-simplify: Simplify (- 0) into 0 1545989148.301 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545989148.301 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 n))) into (* 1/2 (log (* 2 n))) 1545989148.301 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 n)))) into (pow (* 2 n) 1/2) 1545989148.301 * [misc]taylor: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in n 1545989148.301 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in n 1545989148.301 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in n 1545989148.301 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1545989148.301 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989148.301 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.301 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1545989148.301 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989148.301 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.301 * [misc]taylor: Taking taylor expansion of k in n 1545989148.301 * [misc]backup-simplify: Simplify k into k 1545989148.301 * [misc]taylor: Taking taylor expansion of (log (* 2 n)) in n 1545989148.301 * [misc]taylor: Taking taylor expansion of (* 2 n) in n 1545989148.301 * [misc]taylor: Taking taylor expansion of 2 in n 1545989148.301 * [misc]backup-simplify: Simplify 2 into 2 1545989148.301 * [misc]taylor: Taking taylor expansion of n in n 1545989148.301 * [misc]backup-simplify: Simplify 0 into 0 1545989148.301 * [misc]backup-simplify: Simplify 1 into 1 1545989148.301 * [misc]backup-simplify: Simplify (* 2 0) into 0 1545989148.302 * [misc]backup-simplify: Simplify (+ (* 2 1) (* 0 0)) into 2 1545989148.302 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1545989148.302 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1545989148.302 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1545989148.302 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1545989148.302 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 1545989148.303 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (+ (log 2) (log n))) into (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) 1545989148.303 * [misc]backup-simplify: Simplify (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) into (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) 1545989148.303 * [misc]taylor: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in n 1545989148.303 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in n 1545989148.303 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in n 1545989148.303 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1545989148.303 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989148.303 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.303 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1545989148.303 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989148.303 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.303 * [misc]taylor: Taking taylor expansion of k in n 1545989148.303 * [misc]backup-simplify: Simplify k into k 1545989148.303 * [misc]taylor: Taking taylor expansion of (log (* 2 n)) in n 1545989148.303 * [misc]taylor: Taking taylor expansion of (* 2 n) in n 1545989148.303 * [misc]taylor: Taking taylor expansion of 2 in n 1545989148.303 * [misc]backup-simplify: Simplify 2 into 2 1545989148.303 * [misc]taylor: Taking taylor expansion of n in n 1545989148.303 * [misc]backup-simplify: Simplify 0 into 0 1545989148.304 * [misc]backup-simplify: Simplify 1 into 1 1545989148.304 * [misc]backup-simplify: Simplify (* 2 0) into 0 1545989148.304 * [misc]backup-simplify: Simplify (+ (* 2 1) (* 0 0)) into 2 1545989148.304 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1545989148.304 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1545989148.304 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1545989148.304 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1545989148.305 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 1545989148.305 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (+ (log 2) (log n))) into (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) 1545989148.305 * [misc]backup-simplify: Simplify (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) into (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) 1545989148.305 * [misc]taylor: Taking taylor expansion of (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) in k 1545989148.305 * [misc]taylor: Taking taylor expansion of (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) in k 1545989148.305 * [misc]taylor: Taking taylor expansion of (+ (log 2) (log n)) in k 1545989148.305 * [misc]taylor: Taking taylor expansion of (log 2) in k 1545989148.305 * [misc]taylor: Taking taylor expansion of 2 in k 1545989148.305 * [misc]backup-simplify: Simplify 2 into 2 1545989148.306 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1545989148.306 * [misc]taylor: Taking taylor expansion of (log n) in k 1545989148.306 * [misc]taylor: Taking taylor expansion of n in k 1545989148.306 * [misc]backup-simplify: Simplify n into n 1545989148.306 * [misc]backup-simplify: Simplify (log n) into (log n) 1545989148.306 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1545989148.306 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989148.306 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.306 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1545989148.306 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989148.306 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.306 * [misc]taylor: Taking taylor expansion of k in k 1545989148.306 * [misc]backup-simplify: Simplify 0 into 0 1545989148.306 * [misc]backup-simplify: Simplify 1 into 1 1545989148.306 * [misc]backup-simplify: Simplify (+ (log 2) (log n)) into (+ (log 2) (log n)) 1545989148.306 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1545989148.307 * [misc]backup-simplify: Simplify (- 0) into 0 1545989148.307 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545989148.307 * [misc]backup-simplify: Simplify (* (+ (log 2) (log n)) 1/2) into (* 1/2 (+ (log 2) (log n))) 1545989148.307 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log 2) (log n)))) into (exp (* 1/2 (+ (log 2) (log n)))) 1545989148.308 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log 2) (log n)))) into (exp (* 1/2 (+ (log 2) (log n)))) 1545989148.308 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 1) (* 0 0))) into 0 1545989148.310 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 1545989148.311 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1545989148.311 * [misc]backup-simplify: Simplify (- 0) into 0 1545989148.311 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989148.311 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 1545989148.312 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log 2) (log n)))) into 0 1545989148.313 * [misc]backup-simplify: Simplify (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (+ (* (/ (pow 0 1) 1)))) into 0 1545989148.313 * [misc]taylor: Taking taylor expansion of 0 in k 1545989148.313 * [misc]backup-simplify: Simplify 0 into 0 1545989148.313 * [misc]backup-simplify: Simplify 0 into 0 1545989148.313 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1545989148.314 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1545989148.314 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1545989148.316 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 1545989148.317 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1545989148.317 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989148.318 * [misc]backup-simplify: Simplify (+ (* (+ (log 2) (log n)) -1/2) (* 0 1/2)) into (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 1545989148.318 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) 1545989148.319 * [misc]backup-simplify: Simplify (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) into (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) 1545989148.319 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1545989148.329 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 1545989148.329 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1545989148.329 * [misc]backup-simplify: Simplify (- 0) into 0 1545989148.330 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989148.330 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 1545989148.331 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log 2) (log n))))) into 0 1545989148.332 * [misc]backup-simplify: Simplify (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1545989148.332 * [misc]taylor: Taking taylor expansion of 0 in k 1545989148.332 * [misc]backup-simplify: Simplify 0 into 0 1545989148.332 * [misc]backup-simplify: Simplify 0 into 0 1545989148.332 * [misc]backup-simplify: Simplify 0 into 0 1545989148.332 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1545989148.333 * [misc]backup-simplify: Simplify (- 0) into 0 1545989148.333 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989148.335 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 1545989148.336 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1545989148.336 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989148.337 * [misc]backup-simplify: Simplify (+ (* (+ (log 2) (log n)) 0) (+ (* 0 -1/2) (* 0 1/2))) into 0 1545989148.338 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))) 1545989148.339 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))) into (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))) 1545989148.341 * [misc]backup-simplify: Simplify (+ (* (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) (* k 1)) (exp (* 1/2 (+ (log 2) (log n)))))) into (- (+ (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (* (pow (log 2) 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (pow k 2)))) (+ (* 1/4 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) (pow k 2))))) (* 1/8 (* (exp (* 1/2 (+ (log 2) (log n)))) (* (pow (log n) 2) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) k))) (* 1/2 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) k))))) 1545989148.341 * [misc]backup-simplify: Simplify (pow (* (/ 1 n) 2) (- 1/2 (/ (/ 1 k) 2))) into (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) 1545989148.341 * [misc]approximate: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 1545989148.341 * [misc]taylor: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in k 1545989148.341 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in k 1545989148.341 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in k 1545989148.341 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1545989148.341 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989148.341 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.341 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545989148.341 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989148.341 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.341 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989148.341 * [misc]taylor: Taking taylor expansion of k in k 1545989148.341 * [misc]backup-simplify: Simplify 0 into 0 1545989148.341 * [misc]backup-simplify: Simplify 1 into 1 1545989148.341 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989148.341 * [misc]taylor: Taking taylor expansion of (log (/ 2 n)) in k 1545989148.341 * [misc]taylor: Taking taylor expansion of (/ 2 n) in k 1545989148.341 * [misc]taylor: Taking taylor expansion of 2 in k 1545989148.341 * [misc]backup-simplify: Simplify 2 into 2 1545989148.341 * [misc]taylor: Taking taylor expansion of n in k 1545989148.341 * [misc]backup-simplify: Simplify n into n 1545989148.341 * [misc]backup-simplify: Simplify (/ 2 n) into (/ 2 n) 1545989148.341 * [misc]backup-simplify: Simplify (log (/ 2 n)) into (log (/ 2 n)) 1545989148.341 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545989148.342 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1545989148.342 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1545989148.342 * [misc]backup-simplify: Simplify (* -1/2 (log (/ 2 n))) into (* -1/2 (log (/ 2 n))) 1545989148.342 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) into (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) 1545989148.342 * [misc]taylor: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 1545989148.342 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 1545989148.342 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 1545989148.342 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1545989148.342 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989148.342 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.342 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989148.342 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989148.342 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.342 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989148.342 * [misc]taylor: Taking taylor expansion of k in n 1545989148.342 * [misc]backup-simplify: Simplify k into k 1545989148.342 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989148.342 * [misc]taylor: Taking taylor expansion of (log (/ 2 n)) in n 1545989148.342 * [misc]taylor: Taking taylor expansion of (/ 2 n) in n 1545989148.342 * [misc]taylor: Taking taylor expansion of 2 in n 1545989148.342 * [misc]backup-simplify: Simplify 2 into 2 1545989148.342 * [misc]taylor: Taking taylor expansion of n in n 1545989148.342 * [misc]backup-simplify: Simplify 0 into 0 1545989148.342 * [misc]backup-simplify: Simplify 1 into 1 1545989148.342 * [misc]backup-simplify: Simplify (/ 2 1) into 2 1545989148.342 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1545989148.342 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989148.342 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1545989148.343 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1545989148.343 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 1545989148.343 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 1545989148.343 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 1545989148.343 * [misc]taylor: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 1545989148.343 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 1545989148.343 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 1545989148.343 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1545989148.343 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989148.343 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.343 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989148.343 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989148.343 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.343 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989148.343 * [misc]taylor: Taking taylor expansion of k in n 1545989148.343 * [misc]backup-simplify: Simplify k into k 1545989148.343 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989148.343 * [misc]taylor: Taking taylor expansion of (log (/ 2 n)) in n 1545989148.343 * [misc]taylor: Taking taylor expansion of (/ 2 n) in n 1545989148.343 * [misc]taylor: Taking taylor expansion of 2 in n 1545989148.344 * [misc]backup-simplify: Simplify 2 into 2 1545989148.344 * [misc]taylor: Taking taylor expansion of n in n 1545989148.344 * [misc]backup-simplify: Simplify 0 into 0 1545989148.344 * [misc]backup-simplify: Simplify 1 into 1 1545989148.344 * [misc]backup-simplify: Simplify (/ 2 1) into 2 1545989148.344 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1545989148.344 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989148.344 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1545989148.344 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1545989148.344 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 1545989148.344 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 1545989148.345 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 1545989148.345 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) in k 1545989148.345 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) in k 1545989148.345 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1545989148.345 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989148.345 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.345 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545989148.345 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989148.345 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.345 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989148.345 * [misc]taylor: Taking taylor expansion of k in k 1545989148.345 * [misc]backup-simplify: Simplify 0 into 0 1545989148.345 * [misc]backup-simplify: Simplify 1 into 1 1545989148.345 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989148.345 * [misc]taylor: Taking taylor expansion of (- (log 2) (log n)) in k 1545989148.345 * [misc]taylor: Taking taylor expansion of (log 2) in k 1545989148.345 * [misc]taylor: Taking taylor expansion of 2 in k 1545989148.345 * [misc]backup-simplify: Simplify 2 into 2 1545989148.345 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1545989148.345 * [misc]taylor: Taking taylor expansion of (log n) in k 1545989148.345 * [misc]taylor: Taking taylor expansion of n in k 1545989148.345 * [misc]backup-simplify: Simplify n into n 1545989148.345 * [misc]backup-simplify: Simplify (log n) into (log n) 1545989148.345 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545989148.345 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1545989148.346 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1545989148.346 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1545989148.346 * [misc]backup-simplify: Simplify (+ (log 2) (- (log n))) into (- (log 2) (log n)) 1545989148.346 * [misc]backup-simplify: Simplify (* -1/2 (- (log 2) (log n))) into (* -1/2 (- (log 2) (log n))) 1545989148.346 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 1545989148.346 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 1545989148.346 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)))) into 0 1545989148.348 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 1545989148.348 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1545989148.348 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1545989148.348 * [misc]backup-simplify: Simplify (- 0) into 0 1545989148.348 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989148.349 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 1545989148.349 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log 2) (log n)))) into 0 1545989148.350 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1545989148.350 * [misc]taylor: Taking taylor expansion of 0 in k 1545989148.350 * [misc]backup-simplify: Simplify 0 into 0 1545989148.350 * [misc]backup-simplify: Simplify 0 into 0 1545989148.350 * [misc]backup-simplify: Simplify 0 into 0 1545989148.350 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989148.353 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 1545989148.353 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545989148.353 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1545989148.353 * [misc]backup-simplify: Simplify (- 0) into 0 1545989148.353 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989148.353 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 1545989148.354 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log 2) (log n))))) into 0 1545989148.355 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1545989148.355 * [misc]taylor: Taking taylor expansion of 0 in k 1545989148.355 * [misc]backup-simplify: Simplify 0 into 0 1545989148.355 * [misc]backup-simplify: Simplify 0 into 0 1545989148.355 * [misc]backup-simplify: Simplify 0 into 0 1545989148.355 * [misc]backup-simplify: Simplify 0 into 0 1545989148.355 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989148.359 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 1545989148.359 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545989148.360 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1545989148.360 * [misc]backup-simplify: Simplify (- 0) into 0 1545989148.360 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989148.361 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 1545989148.362 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log 2) (log n)))))) into 0 1545989148.366 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1545989148.366 * [misc]taylor: Taking taylor expansion of 0 in k 1545989148.366 * [misc]backup-simplify: Simplify 0 into 0 1545989148.366 * [misc]backup-simplify: Simplify 0 into 0 1545989148.366 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log 2) (log (/ 1 n))))) into (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) 1545989148.366 * [misc]backup-simplify: Simplify (pow (* (/ 1 (- n)) 2) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) 1545989148.367 * [misc]approximate: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 1545989148.367 * [misc]taylor: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1545989148.367 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in k 1545989148.367 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in k 1545989148.367 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1545989148.367 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545989148.367 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989148.367 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.367 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989148.367 * [misc]taylor: Taking taylor expansion of k in k 1545989148.367 * [misc]backup-simplify: Simplify 0 into 0 1545989148.367 * [misc]backup-simplify: Simplify 1 into 1 1545989148.367 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989148.367 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989148.367 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.367 * [misc]taylor: Taking taylor expansion of (log (/ -2 n)) in k 1545989148.367 * [misc]taylor: Taking taylor expansion of (/ -2 n) in k 1545989148.367 * [misc]taylor: Taking taylor expansion of -2 in k 1545989148.367 * [misc]backup-simplify: Simplify -2 into -2 1545989148.367 * [misc]taylor: Taking taylor expansion of n in k 1545989148.367 * [misc]backup-simplify: Simplify n into n 1545989148.367 * [misc]backup-simplify: Simplify (/ -2 n) into (/ -2 n) 1545989148.367 * [misc]backup-simplify: Simplify (log (/ -2 n)) into (log (/ -2 n)) 1545989148.368 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545989148.368 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545989148.368 * [misc]backup-simplify: Simplify (* 1/2 (log (/ -2 n))) into (* 1/2 (log (/ -2 n))) 1545989148.368 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) into (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) 1545989148.368 * [misc]taylor: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1545989148.368 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 1545989148.368 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 1545989148.368 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1545989148.368 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989148.368 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989148.368 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.368 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989148.368 * [misc]taylor: Taking taylor expansion of k in n 1545989148.368 * [misc]backup-simplify: Simplify k into k 1545989148.369 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989148.369 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989148.369 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.369 * [misc]taylor: Taking taylor expansion of (log (/ -2 n)) in n 1545989148.369 * [misc]taylor: Taking taylor expansion of (/ -2 n) in n 1545989148.369 * [misc]taylor: Taking taylor expansion of -2 in n 1545989148.369 * [misc]backup-simplify: Simplify -2 into -2 1545989148.369 * [misc]taylor: Taking taylor expansion of n in n 1545989148.369 * [misc]backup-simplify: Simplify 0 into 0 1545989148.369 * [misc]backup-simplify: Simplify 1 into 1 1545989148.369 * [misc]backup-simplify: Simplify (/ -2 1) into -2 1545989148.369 * [misc]backup-simplify: Simplify (log -2) into (log -2) 1545989148.369 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989148.369 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1545989148.370 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 1545989148.370 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 1545989148.370 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 1545989148.370 * [misc]taylor: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1545989148.370 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 1545989148.370 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 1545989148.371 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1545989148.371 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989148.371 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989148.371 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.371 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989148.371 * [misc]taylor: Taking taylor expansion of k in n 1545989148.371 * [misc]backup-simplify: Simplify k into k 1545989148.371 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989148.371 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989148.371 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.371 * [misc]taylor: Taking taylor expansion of (log (/ -2 n)) in n 1545989148.371 * [misc]taylor: Taking taylor expansion of (/ -2 n) in n 1545989148.371 * [misc]taylor: Taking taylor expansion of -2 in n 1545989148.371 * [misc]backup-simplify: Simplify -2 into -2 1545989148.371 * [misc]taylor: Taking taylor expansion of n in n 1545989148.371 * [misc]backup-simplify: Simplify 0 into 0 1545989148.371 * [misc]backup-simplify: Simplify 1 into 1 1545989148.371 * [misc]backup-simplify: Simplify (/ -2 1) into -2 1545989148.371 * [misc]backup-simplify: Simplify (log -2) into (log -2) 1545989148.371 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989148.372 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1545989148.372 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 1545989148.372 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 1545989148.373 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 1545989148.373 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) in k 1545989148.373 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) in k 1545989148.373 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1545989148.373 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545989148.373 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989148.373 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.373 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989148.373 * [misc]taylor: Taking taylor expansion of k in k 1545989148.373 * [misc]backup-simplify: Simplify 0 into 0 1545989148.373 * [misc]backup-simplify: Simplify 1 into 1 1545989148.373 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989148.373 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989148.373 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.373 * [misc]taylor: Taking taylor expansion of (- (log -2) (log n)) in k 1545989148.373 * [misc]taylor: Taking taylor expansion of (log -2) in k 1545989148.373 * [misc]taylor: Taking taylor expansion of -2 in k 1545989148.373 * [misc]backup-simplify: Simplify -2 into -2 1545989148.374 * [misc]backup-simplify: Simplify (log -2) into (log -2) 1545989148.374 * [misc]taylor: Taking taylor expansion of (log n) in k 1545989148.374 * [misc]taylor: Taking taylor expansion of n in k 1545989148.374 * [misc]backup-simplify: Simplify n into n 1545989148.374 * [misc]backup-simplify: Simplify (log n) into (log n) 1545989148.374 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545989148.374 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545989148.374 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1545989148.374 * [misc]backup-simplify: Simplify (+ (log -2) (- (log n))) into (- (log -2) (log n)) 1545989148.375 * [misc]backup-simplify: Simplify (* 1/2 (- (log -2) (log n))) into (* 1/2 (- (log -2) (log n))) 1545989148.375 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 1545989148.375 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 1545989148.376 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -2 (/ 0 1)))) into 0 1545989148.378 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -2 1)))) 1) into 0 1545989148.378 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1545989148.379 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1545989148.379 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989148.379 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 1545989148.379 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log -2) (log n)))) into 0 1545989148.381 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1545989148.381 * [misc]taylor: Taking taylor expansion of 0 in k 1545989148.381 * [misc]backup-simplify: Simplify 0 into 0 1545989148.381 * [misc]backup-simplify: Simplify 0 into 0 1545989148.381 * [misc]backup-simplify: Simplify 0 into 0 1545989148.381 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -2 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989148.386 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -2 1)))) 2) into 0 1545989148.386 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545989148.387 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1545989148.387 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989148.387 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 1545989148.388 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log -2) (log n))))) into 0 1545989148.390 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1545989148.390 * [misc]taylor: Taking taylor expansion of 0 in k 1545989148.390 * [misc]backup-simplify: Simplify 0 into 0 1545989148.390 * [misc]backup-simplify: Simplify 0 into 0 1545989148.390 * [misc]backup-simplify: Simplify 0 into 0 1545989148.390 * [misc]backup-simplify: Simplify 0 into 0 1545989148.391 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -2 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989148.398 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow -2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow -2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow -2 1)))) 6) into 0 1545989148.398 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545989148.399 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1545989148.399 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989148.399 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 1545989148.400 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log -2) (log n)))))) into 0 1545989148.402 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1545989148.402 * [misc]taylor: Taking taylor expansion of 0 in k 1545989148.402 * [misc]backup-simplify: Simplify 0 into 0 1545989148.402 * [misc]backup-simplify: Simplify 0 into 0 1545989148.402 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -2) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) 1545989148.402 * * * * [misc]progress: [ 2 / 4 ] generating series at (2 2) 1545989148.402 * [misc]backup-simplify: Simplify (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)) into (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) 1545989148.402 * [misc]approximate: Taking taylor expansion of (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in (n k) around 0 1545989148.402 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in k 1545989148.402 * [misc]taylor: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in k 1545989148.402 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in k 1545989148.402 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in k 1545989148.402 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1545989148.402 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989148.402 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.402 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1545989148.402 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989148.402 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.402 * [misc]taylor: Taking taylor expansion of k in k 1545989148.402 * [misc]backup-simplify: Simplify 0 into 0 1545989148.402 * [misc]backup-simplify: Simplify 1 into 1 1545989148.402 * [misc]taylor: Taking taylor expansion of (log (* 2 n)) in k 1545989148.402 * [misc]taylor: Taking taylor expansion of (* 2 n) in k 1545989148.402 * [misc]taylor: Taking taylor expansion of 2 in k 1545989148.402 * [misc]backup-simplify: Simplify 2 into 2 1545989148.402 * [misc]taylor: Taking taylor expansion of n in k 1545989148.402 * [misc]backup-simplify: Simplify n into n 1545989148.403 * [misc]backup-simplify: Simplify (* 2 n) into (* 2 n) 1545989148.403 * [misc]backup-simplify: Simplify (log (* 2 n)) into (log (* 2 n)) 1545989148.403 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1545989148.403 * [misc]backup-simplify: Simplify (- 0) into 0 1545989148.403 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545989148.403 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 n))) into (* 1/2 (log (* 2 n))) 1545989148.403 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 n)))) into (pow (* 2 n) 1/2) 1545989148.403 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1545989148.403 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989148.403 * [misc]taylor: Taking taylor expansion of k in k 1545989148.403 * [misc]backup-simplify: Simplify 0 into 0 1545989148.403 * [misc]backup-simplify: Simplify 1 into 1 1545989148.403 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989148.403 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545989148.404 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1545989148.404 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in n 1545989148.404 * [misc]taylor: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in n 1545989148.404 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in n 1545989148.404 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in n 1545989148.404 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1545989148.404 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989148.404 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.404 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1545989148.404 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989148.404 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.404 * [misc]taylor: Taking taylor expansion of k in n 1545989148.404 * [misc]backup-simplify: Simplify k into k 1545989148.404 * [misc]taylor: Taking taylor expansion of (log (* 2 n)) in n 1545989148.404 * [misc]taylor: Taking taylor expansion of (* 2 n) in n 1545989148.404 * [misc]taylor: Taking taylor expansion of 2 in n 1545989148.404 * [misc]backup-simplify: Simplify 2 into 2 1545989148.404 * [misc]taylor: Taking taylor expansion of n in n 1545989148.404 * [misc]backup-simplify: Simplify 0 into 0 1545989148.404 * [misc]backup-simplify: Simplify 1 into 1 1545989148.404 * [misc]backup-simplify: Simplify (* 2 0) into 0 1545989148.404 * [misc]backup-simplify: Simplify (+ (* 2 1) (* 0 0)) into 2 1545989148.404 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1545989148.404 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1545989148.404 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1545989148.404 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1545989148.405 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 1545989148.405 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (+ (log 2) (log n))) into (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) 1545989148.405 * [misc]backup-simplify: Simplify (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) into (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) 1545989148.405 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1545989148.405 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989148.405 * [misc]taylor: Taking taylor expansion of k in n 1545989148.405 * [misc]backup-simplify: Simplify k into k 1545989148.405 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989148.405 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1545989148.405 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1545989148.405 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1545989148.405 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in n 1545989148.405 * [misc]taylor: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in n 1545989148.405 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in n 1545989148.405 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in n 1545989148.405 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1545989148.405 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989148.405 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.405 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1545989148.405 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989148.406 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.406 * [misc]taylor: Taking taylor expansion of k in n 1545989148.406 * [misc]backup-simplify: Simplify k into k 1545989148.406 * [misc]taylor: Taking taylor expansion of (log (* 2 n)) in n 1545989148.406 * [misc]taylor: Taking taylor expansion of (* 2 n) in n 1545989148.406 * [misc]taylor: Taking taylor expansion of 2 in n 1545989148.406 * [misc]backup-simplify: Simplify 2 into 2 1545989148.406 * [misc]taylor: Taking taylor expansion of n in n 1545989148.406 * [misc]backup-simplify: Simplify 0 into 0 1545989148.406 * [misc]backup-simplify: Simplify 1 into 1 1545989148.406 * [misc]backup-simplify: Simplify (* 2 0) into 0 1545989148.406 * [misc]backup-simplify: Simplify (+ (* 2 1) (* 0 0)) into 2 1545989148.406 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1545989148.406 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1545989148.406 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1545989148.406 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1545989148.406 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 1545989148.407 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (+ (log 2) (log n))) into (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) 1545989148.407 * [misc]backup-simplify: Simplify (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) into (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) 1545989148.407 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1545989148.407 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989148.407 * [misc]taylor: Taking taylor expansion of k in n 1545989148.407 * [misc]backup-simplify: Simplify k into k 1545989148.407 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989148.407 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1545989148.407 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1545989148.407 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1545989148.407 * [misc]backup-simplify: Simplify (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) into (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) 1545989148.407 * [misc]taylor: Taking taylor expansion of (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in k 1545989148.407 * [misc]taylor: Taking taylor expansion of (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) in k 1545989148.407 * [misc]taylor: Taking taylor expansion of (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) in k 1545989148.407 * [misc]taylor: Taking taylor expansion of (+ (log 2) (log n)) in k 1545989148.407 * [misc]taylor: Taking taylor expansion of (log 2) in k 1545989148.407 * [misc]taylor: Taking taylor expansion of 2 in k 1545989148.407 * [misc]backup-simplify: Simplify 2 into 2 1545989148.408 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1545989148.408 * [misc]taylor: Taking taylor expansion of (log n) in k 1545989148.408 * [misc]taylor: Taking taylor expansion of n in k 1545989148.408 * [misc]backup-simplify: Simplify n into n 1545989148.408 * [misc]backup-simplify: Simplify (log n) into (log n) 1545989148.408 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1545989148.408 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989148.408 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.408 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1545989148.408 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989148.408 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.408 * [misc]taylor: Taking taylor expansion of k in k 1545989148.408 * [misc]backup-simplify: Simplify 0 into 0 1545989148.408 * [misc]backup-simplify: Simplify 1 into 1 1545989148.408 * [misc]backup-simplify: Simplify (+ (log 2) (log n)) into (+ (log 2) (log n)) 1545989148.408 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1545989148.408 * [misc]backup-simplify: Simplify (- 0) into 0 1545989148.408 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545989148.408 * [misc]backup-simplify: Simplify (* (+ (log 2) (log n)) 1/2) into (* 1/2 (+ (log 2) (log n))) 1545989148.408 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log 2) (log n)))) into (exp (* 1/2 (+ (log 2) (log n)))) 1545989148.408 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1545989148.409 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989148.409 * [misc]taylor: Taking taylor expansion of k in k 1545989148.409 * [misc]backup-simplify: Simplify 0 into 0 1545989148.409 * [misc]backup-simplify: Simplify 1 into 1 1545989148.409 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989148.409 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545989148.409 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1545989148.409 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) 0) into 0 1545989148.409 * [misc]backup-simplify: Simplify 0 into 0 1545989148.409 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 1) (* 0 0))) into 0 1545989148.411 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 1545989148.411 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1545989148.411 * [misc]backup-simplify: Simplify (- 0) into 0 1545989148.411 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989148.411 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 1545989148.412 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log 2) (log n)))) into 0 1545989148.412 * [misc]backup-simplify: Simplify (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (+ (* (/ (pow 0 1) 1)))) into 0 1545989148.413 * [misc]backup-simplify: Simplify (+ (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) 0) (* 0 (sqrt (/ 1 k)))) into 0 1545989148.413 * [misc]taylor: Taking taylor expansion of 0 in k 1545989148.413 * [misc]backup-simplify: Simplify 0 into 0 1545989148.413 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1545989148.413 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1545989148.413 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1545989148.414 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 1545989148.415 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1545989148.415 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989148.415 * [misc]backup-simplify: Simplify (+ (* (+ (log 2) (log n)) -1/2) (* 0 1/2)) into (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 1545989148.416 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) 1545989148.416 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log 2) (log n)))) +nan.0) (* (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) 0)) into (- (* +nan.0 (exp (* 1/2 (+ (log 2) (log n)))))) 1545989148.416 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (+ (log 2) (log n)))))) into (- (* +nan.0 (exp (* 1/2 (+ (log 2) (log n)))))) 1545989148.416 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545989148.417 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 1545989148.417 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1545989148.420 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 1545989148.420 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1545989148.420 * [misc]backup-simplify: Simplify (- 0) into 0 1545989148.420 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989148.420 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 1545989148.421 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log 2) (log n))))) into 0 1545989148.422 * [misc]backup-simplify: Simplify (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1545989148.422 * [misc]backup-simplify: Simplify (+ (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k))))) into 0 1545989148.422 * [misc]taylor: Taking taylor expansion of 0 in k 1545989148.422 * [misc]backup-simplify: Simplify 0 into 0 1545989148.422 * [misc]backup-simplify: Simplify 0 into 0 1545989148.422 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1545989148.423 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1545989148.423 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1545989148.423 * [misc]backup-simplify: Simplify (- 0) into 0 1545989148.423 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989148.426 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 1545989148.427 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1545989148.427 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989148.427 * [misc]backup-simplify: Simplify (+ (* (+ (log 2) (log n)) 0) (+ (* 0 -1/2) (* 0 1/2))) into 0 1545989148.429 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))) 1545989148.432 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log 2) (log n)))) +nan.0) (+ (* (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) +nan.0) (* (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))) 0))) into (- (+ (* +nan.0 (* (log 2) (exp (* 1/2 (+ (log 2) (log n)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (- (* +nan.0 (exp (* 1/2 (+ (log 2) (log n)))))))))) 1545989148.433 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (log 2) (exp (* 1/2 (+ (log 2) (log n)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (- (* +nan.0 (exp (* 1/2 (+ (log 2) (log n)))))))))) into (- (+ (* +nan.0 (* (log 2) (exp (* 1/2 (+ (log 2) (log n)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (- (* +nan.0 (exp (* 1/2 (+ (log 2) (log n)))))))))) 1545989148.433 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545989148.433 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 1545989148.434 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))) into 0 1545989148.441 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 1545989148.441 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 1545989148.441 * [misc]backup-simplify: Simplify (- 0) into 0 1545989148.442 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989148.442 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 1545989148.443 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log 2) (log n)))))) into 0 1545989148.446 * [misc]backup-simplify: Simplify (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1545989148.447 * [misc]backup-simplify: Simplify (+ (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k)))))) into 0 1545989148.447 * [misc]taylor: Taking taylor expansion of 0 in k 1545989148.447 * [misc]backup-simplify: Simplify 0 into 0 1545989148.447 * [misc]backup-simplify: Simplify 0 into 0 1545989148.447 * [misc]backup-simplify: Simplify 0 into 0 1545989148.447 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989148.448 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1545989148.449 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1545989148.449 * [misc]backup-simplify: Simplify (- 0) into 0 1545989148.449 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989148.457 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 1545989148.460 * [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 1545989148.460 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989148.460 * [misc]backup-simplify: Simplify (+ (* (+ (log 2) (log n)) 0) (+ (* 0 0) (+ (* 0 -1/2) (* 0 1/2)))) into 0 1545989148.462 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 3) 6)) (* (/ (pow (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (log 2) (pow (log n) 2))) (+ (* 1/16 (* (pow (log 2) 2) (log n))) (* 1/48 (pow (log 2) 3))))) (exp (* 1/2 (+ (log 2) (log n)))))) 1545989148.465 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log 2) (log n)))) +nan.0) (+ (* (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) +nan.0) (+ (* (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))) +nan.0) (* (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (log 2) (pow (log n) 2))) (+ (* 1/16 (* (pow (log 2) 2) (log n))) (* 1/48 (pow (log 2) 3))))) (exp (* 1/2 (+ (log 2) (log n)))))) 0)))) into (- (+ (* +nan.0 (* (log 2) (exp (* 1/2 (+ (log 2) (log n)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log 2) (log n))))) (- (+ (* +nan.0 (* (pow (log 2) 2) (exp (* 1/2 (+ (log 2) (log n)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2))) (- (* +nan.0 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))))))))))))))) 1545989148.467 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (log 2) (exp (* 1/2 (+ (log 2) (log n)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log 2) (log n))))) (- (+ (* +nan.0 (* (pow (log 2) 2) (exp (* 1/2 (+ (log 2) (log n)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2))) (- (* +nan.0 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))))))))))))))) into (- (+ (* +nan.0 (* (log 2) (exp (* 1/2 (+ (log 2) (log n)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log 2) (log n))))) (- (+ (* +nan.0 (* (pow (log 2) 2) (exp (* 1/2 (+ (log 2) (log n)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2))) (- (* +nan.0 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))))))))))))))) 1545989148.471 * [misc]backup-simplify: Simplify (+ (* (- (+ (* +nan.0 (* (log 2) (exp (* 1/2 (+ (log 2) (log n)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log 2) (log n))))) (- (+ (* +nan.0 (* (pow (log 2) 2) (exp (* 1/2 (+ (log 2) (log n)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2))) (- (* +nan.0 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (log 2) (exp (* 1/2 (+ (log 2) (log n)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (- (* +nan.0 (exp (* 1/2 (+ (log 2) (log n)))))))))) (* k 1)) (- (* +nan.0 (exp (* 1/2 (+ (log 2) (log n)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) k))) (- (+ (* +nan.0 (* (pow (log 2) 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (pow k 2)))) (- (+ (* +nan.0 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) k)) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (pow k 2)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log 2) (log n))))) (- (+ (* +nan.0 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (pow k 2)))))))))))))))))))))) 1545989148.471 * [misc]backup-simplify: Simplify (/ (pow (* (/ 1 n) 2) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) into (* (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) 1545989148.471 * [misc]approximate: Taking taylor expansion of (* (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in (n k) around 0 1545989148.471 * [misc]taylor: Taking taylor expansion of (* (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in k 1545989148.471 * [misc]taylor: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in k 1545989148.471 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in k 1545989148.471 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in k 1545989148.471 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1545989148.471 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989148.471 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.471 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545989148.471 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989148.472 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.472 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989148.472 * [misc]taylor: Taking taylor expansion of k in k 1545989148.472 * [misc]backup-simplify: Simplify 0 into 0 1545989148.472 * [misc]backup-simplify: Simplify 1 into 1 1545989148.472 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989148.472 * [misc]taylor: Taking taylor expansion of (log (/ 2 n)) in k 1545989148.472 * [misc]taylor: Taking taylor expansion of (/ 2 n) in k 1545989148.472 * [misc]taylor: Taking taylor expansion of 2 in k 1545989148.472 * [misc]backup-simplify: Simplify 2 into 2 1545989148.472 * [misc]taylor: Taking taylor expansion of n in k 1545989148.472 * [misc]backup-simplify: Simplify n into n 1545989148.472 * [misc]backup-simplify: Simplify (/ 2 n) into (/ 2 n) 1545989148.472 * [misc]backup-simplify: Simplify (log (/ 2 n)) into (log (/ 2 n)) 1545989148.472 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545989148.472 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1545989148.472 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1545989148.472 * [misc]backup-simplify: Simplify (* -1/2 (log (/ 2 n))) into (* -1/2 (log (/ 2 n))) 1545989148.472 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) into (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) 1545989148.472 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1545989148.472 * [misc]taylor: Taking taylor expansion of k in k 1545989148.472 * [misc]backup-simplify: Simplify 0 into 0 1545989148.472 * [misc]backup-simplify: Simplify 1 into 1 1545989148.473 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545989148.473 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1545989148.473 * [misc]taylor: Taking taylor expansion of (* (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in n 1545989148.473 * [misc]taylor: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 1545989148.473 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 1545989148.473 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 1545989148.473 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1545989148.473 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989148.473 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.473 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989148.473 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989148.473 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.473 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989148.473 * [misc]taylor: Taking taylor expansion of k in n 1545989148.473 * [misc]backup-simplify: Simplify k into k 1545989148.473 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989148.473 * [misc]taylor: Taking taylor expansion of (log (/ 2 n)) in n 1545989148.473 * [misc]taylor: Taking taylor expansion of (/ 2 n) in n 1545989148.473 * [misc]taylor: Taking taylor expansion of 2 in n 1545989148.473 * [misc]backup-simplify: Simplify 2 into 2 1545989148.473 * [misc]taylor: Taking taylor expansion of n in n 1545989148.473 * [misc]backup-simplify: Simplify 0 into 0 1545989148.473 * [misc]backup-simplify: Simplify 1 into 1 1545989148.473 * [misc]backup-simplify: Simplify (/ 2 1) into 2 1545989148.474 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1545989148.474 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989148.474 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1545989148.474 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1545989148.474 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 1545989148.474 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 1545989148.474 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 1545989148.474 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1545989148.474 * [misc]taylor: Taking taylor expansion of k in n 1545989148.474 * [misc]backup-simplify: Simplify k into k 1545989148.474 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1545989148.474 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1545989148.474 * [misc]taylor: Taking taylor expansion of (* (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in n 1545989148.474 * [misc]taylor: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 1545989148.474 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 1545989148.475 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 1545989148.475 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1545989148.475 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989148.475 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.475 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989148.475 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989148.475 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.475 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989148.475 * [misc]taylor: Taking taylor expansion of k in n 1545989148.475 * [misc]backup-simplify: Simplify k into k 1545989148.475 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989148.475 * [misc]taylor: Taking taylor expansion of (log (/ 2 n)) in n 1545989148.475 * [misc]taylor: Taking taylor expansion of (/ 2 n) in n 1545989148.475 * [misc]taylor: Taking taylor expansion of 2 in n 1545989148.475 * [misc]backup-simplify: Simplify 2 into 2 1545989148.475 * [misc]taylor: Taking taylor expansion of n in n 1545989148.475 * [misc]backup-simplify: Simplify 0 into 0 1545989148.475 * [misc]backup-simplify: Simplify 1 into 1 1545989148.475 * [misc]backup-simplify: Simplify (/ 2 1) into 2 1545989148.475 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1545989148.475 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989148.475 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1545989148.475 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1545989148.475 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 1545989148.476 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 1545989148.476 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 1545989148.476 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1545989148.476 * [misc]taylor: Taking taylor expansion of k in n 1545989148.476 * [misc]backup-simplify: Simplify k into k 1545989148.476 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1545989148.476 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1545989148.476 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (sqrt k)) into (* (sqrt k) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) 1545989148.476 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) in k 1545989148.476 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1545989148.476 * [misc]taylor: Taking taylor expansion of k in k 1545989148.476 * [misc]backup-simplify: Simplify 0 into 0 1545989148.476 * [misc]backup-simplify: Simplify 1 into 1 1545989148.476 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545989148.477 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1545989148.477 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) in k 1545989148.477 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) in k 1545989148.477 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1545989148.477 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989148.477 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.477 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545989148.477 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989148.477 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.477 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989148.477 * [misc]taylor: Taking taylor expansion of k in k 1545989148.477 * [misc]backup-simplify: Simplify 0 into 0 1545989148.477 * [misc]backup-simplify: Simplify 1 into 1 1545989148.477 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989148.477 * [misc]taylor: Taking taylor expansion of (- (log 2) (log n)) in k 1545989148.477 * [misc]taylor: Taking taylor expansion of (log 2) in k 1545989148.477 * [misc]taylor: Taking taylor expansion of 2 in k 1545989148.477 * [misc]backup-simplify: Simplify 2 into 2 1545989148.477 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1545989148.477 * [misc]taylor: Taking taylor expansion of (log n) in k 1545989148.477 * [misc]taylor: Taking taylor expansion of n in k 1545989148.477 * [misc]backup-simplify: Simplify n into n 1545989148.477 * [misc]backup-simplify: Simplify (log n) into (log n) 1545989148.477 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545989148.477 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1545989148.478 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1545989148.478 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1545989148.478 * [misc]backup-simplify: Simplify (+ (log 2) (- (log n))) into (- (log 2) (log n)) 1545989148.478 * [misc]backup-simplify: Simplify (* -1/2 (- (log 2) (log n))) into (* -1/2 (- (log 2) (log n))) 1545989148.478 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 1545989148.478 * [misc]backup-simplify: Simplify (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) into 0 1545989148.478 * [misc]backup-simplify: Simplify 0 into 0 1545989148.478 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)))) into 0 1545989148.480 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 1545989148.480 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1545989148.480 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1545989148.480 * [misc]backup-simplify: Simplify (- 0) into 0 1545989148.480 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989148.481 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 1545989148.481 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log 2) (log n)))) into 0 1545989148.482 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1545989148.482 * [misc]backup-simplify: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 0) (* 0 (sqrt k))) into 0 1545989148.482 * [misc]taylor: Taking taylor expansion of 0 in k 1545989148.482 * [misc]backup-simplify: Simplify 0 into 0 1545989148.482 * [misc]backup-simplify: Simplify 0 into 0 1545989148.482 * [misc]backup-simplify: Simplify (+ (* 0 0) (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) 1545989148.482 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) 1545989148.483 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 1545989148.483 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989148.486 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 1545989148.486 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545989148.486 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1545989148.486 * [misc]backup-simplify: Simplify (- 0) into 0 1545989148.486 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989148.486 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 1545989148.487 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log 2) (log n))))) into 0 1545989148.488 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1545989148.489 * [misc]backup-simplify: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 0) (+ (* 0 0) (* 0 (sqrt k)))) into 0 1545989148.489 * [misc]taylor: Taking taylor expansion of 0 in k 1545989148.489 * [misc]backup-simplify: Simplify 0 into 0 1545989148.489 * [misc]backup-simplify: Simplify 0 into 0 1545989148.489 * [misc]backup-simplify: Simplify 0 into 0 1545989148.490 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1545989148.491 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) 1545989148.491 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) 1545989148.492 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 1545989148.492 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989148.500 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 1545989148.500 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545989148.500 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1545989148.500 * [misc]backup-simplify: Simplify (- 0) into 0 1545989148.501 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989148.501 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 1545989148.502 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log 2) (log n)))))) into 0 1545989148.505 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1545989148.506 * [misc]backup-simplify: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt k))))) into 0 1545989148.506 * [misc]taylor: Taking taylor expansion of 0 in k 1545989148.506 * [misc]backup-simplify: Simplify 0 into 0 1545989148.506 * [misc]backup-simplify: Simplify 0 into 0 1545989148.506 * [misc]backup-simplify: Simplify 0 into 0 1545989148.506 * [misc]backup-simplify: Simplify 0 into 0 1545989148.508 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1545989148.509 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* +nan.0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) 1545989148.509 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) 1545989148.511 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log 2) (log (/ 1 n))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log 2) (log (/ 1 n))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log 2) (log (/ 1 n))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) k)) (- (* +nan.0 (/ (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) (pow k 2)))))))) 1545989148.511 * [misc]backup-simplify: Simplify (/ (pow (* (/ 1 (- n)) 2) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) into (/ (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) 1545989148.511 * [misc]approximate: Taking taylor expansion of (/ (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (n k) around 0 1545989148.511 * [misc]taylor: Taking taylor expansion of (/ (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 1545989148.511 * [misc]taylor: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1545989148.511 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in k 1545989148.511 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in k 1545989148.511 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1545989148.511 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545989148.511 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989148.512 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.512 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989148.512 * [misc]taylor: Taking taylor expansion of k in k 1545989148.512 * [misc]backup-simplify: Simplify 0 into 0 1545989148.512 * [misc]backup-simplify: Simplify 1 into 1 1545989148.512 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989148.512 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989148.512 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.512 * [misc]taylor: Taking taylor expansion of (log (/ -2 n)) in k 1545989148.512 * [misc]taylor: Taking taylor expansion of (/ -2 n) in k 1545989148.512 * [misc]taylor: Taking taylor expansion of -2 in k 1545989148.512 * [misc]backup-simplify: Simplify -2 into -2 1545989148.512 * [misc]taylor: Taking taylor expansion of n in k 1545989148.512 * [misc]backup-simplify: Simplify n into n 1545989148.512 * [misc]backup-simplify: Simplify (/ -2 n) into (/ -2 n) 1545989148.512 * [misc]backup-simplify: Simplify (log (/ -2 n)) into (log (/ -2 n)) 1545989148.512 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545989148.513 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545989148.513 * [misc]backup-simplify: Simplify (* 1/2 (log (/ -2 n))) into (* 1/2 (log (/ -2 n))) 1545989148.513 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) into (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) 1545989148.513 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1545989148.513 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1545989148.513 * [misc]taylor: Taking taylor expansion of -1 in k 1545989148.513 * [misc]backup-simplify: Simplify -1 into -1 1545989148.513 * [misc]taylor: Taking taylor expansion of k in k 1545989148.513 * [misc]backup-simplify: Simplify 0 into 0 1545989148.513 * [misc]backup-simplify: Simplify 1 into 1 1545989148.513 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1545989148.513 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545989148.514 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1545989148.514 * [misc]backup-simplify: Simplify (/ (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) +nan.0) into (* +nan.0 (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2))) 1545989148.514 * [misc]taylor: Taking taylor expansion of (/ (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 1545989148.514 * [misc]taylor: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1545989148.514 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 1545989148.514 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 1545989148.514 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1545989148.514 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989148.514 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989148.515 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.515 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989148.515 * [misc]taylor: Taking taylor expansion of k in n 1545989148.515 * [misc]backup-simplify: Simplify k into k 1545989148.515 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989148.515 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989148.515 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.515 * [misc]taylor: Taking taylor expansion of (log (/ -2 n)) in n 1545989148.515 * [misc]taylor: Taking taylor expansion of (/ -2 n) in n 1545989148.515 * [misc]taylor: Taking taylor expansion of -2 in n 1545989148.515 * [misc]backup-simplify: Simplify -2 into -2 1545989148.515 * [misc]taylor: Taking taylor expansion of n in n 1545989148.515 * [misc]backup-simplify: Simplify 0 into 0 1545989148.515 * [misc]backup-simplify: Simplify 1 into 1 1545989148.515 * [misc]backup-simplify: Simplify (/ -2 1) into -2 1545989148.515 * [misc]backup-simplify: Simplify (log -2) into (log -2) 1545989148.515 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989148.515 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1545989148.516 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 1545989148.516 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 1545989148.517 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 1545989148.517 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1545989148.517 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1545989148.517 * [misc]taylor: Taking taylor expansion of -1 in n 1545989148.517 * [misc]backup-simplify: Simplify -1 into -1 1545989148.517 * [misc]taylor: Taking taylor expansion of k in n 1545989148.517 * [misc]backup-simplify: Simplify k into k 1545989148.517 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1545989148.517 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1545989148.517 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1545989148.517 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1545989148.518 * [misc]backup-simplify: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt (/ -1 k))) 1545989148.518 * [misc]taylor: Taking taylor expansion of (/ (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 1545989148.518 * [misc]taylor: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1545989148.518 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 1545989148.518 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 1545989148.518 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1545989148.518 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989148.518 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989148.518 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.518 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989148.518 * [misc]taylor: Taking taylor expansion of k in n 1545989148.518 * [misc]backup-simplify: Simplify k into k 1545989148.518 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989148.518 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989148.518 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.518 * [misc]taylor: Taking taylor expansion of (log (/ -2 n)) in n 1545989148.518 * [misc]taylor: Taking taylor expansion of (/ -2 n) in n 1545989148.518 * [misc]taylor: Taking taylor expansion of -2 in n 1545989148.518 * [misc]backup-simplify: Simplify -2 into -2 1545989148.518 * [misc]taylor: Taking taylor expansion of n in n 1545989148.518 * [misc]backup-simplify: Simplify 0 into 0 1545989148.518 * [misc]backup-simplify: Simplify 1 into 1 1545989148.519 * [misc]backup-simplify: Simplify (/ -2 1) into -2 1545989148.519 * [misc]backup-simplify: Simplify (log -2) into (log -2) 1545989148.519 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989148.519 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1545989148.519 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 1545989148.519 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 1545989148.520 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 1545989148.520 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1545989148.520 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1545989148.520 * [misc]taylor: Taking taylor expansion of -1 in n 1545989148.520 * [misc]backup-simplify: Simplify -1 into -1 1545989148.520 * [misc]taylor: Taking taylor expansion of k in n 1545989148.520 * [misc]backup-simplify: Simplify k into k 1545989148.520 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1545989148.520 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1545989148.520 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1545989148.520 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1545989148.520 * [misc]backup-simplify: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt (/ -1 k))) 1545989148.520 * [misc]taylor: Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt (/ -1 k))) in k 1545989148.520 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) in k 1545989148.520 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) in k 1545989148.520 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1545989148.520 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545989148.520 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989148.520 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.520 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989148.520 * [misc]taylor: Taking taylor expansion of k in k 1545989148.520 * [misc]backup-simplify: Simplify 0 into 0 1545989148.520 * [misc]backup-simplify: Simplify 1 into 1 1545989148.521 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989148.521 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989148.521 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.521 * [misc]taylor: Taking taylor expansion of (- (log -2) (log n)) in k 1545989148.521 * [misc]taylor: Taking taylor expansion of (log -2) in k 1545989148.521 * [misc]taylor: Taking taylor expansion of -2 in k 1545989148.521 * [misc]backup-simplify: Simplify -2 into -2 1545989148.521 * [misc]backup-simplify: Simplify (log -2) into (log -2) 1545989148.521 * [misc]taylor: Taking taylor expansion of (log n) in k 1545989148.521 * [misc]taylor: Taking taylor expansion of n in k 1545989148.521 * [misc]backup-simplify: Simplify n into n 1545989148.521 * [misc]backup-simplify: Simplify (log n) into (log n) 1545989148.521 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545989148.521 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545989148.521 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1545989148.521 * [misc]backup-simplify: Simplify (+ (log -2) (- (log n))) into (- (log -2) (log n)) 1545989148.521 * [misc]backup-simplify: Simplify (* 1/2 (- (log -2) (log n))) into (* 1/2 (- (log -2) (log n))) 1545989148.522 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 1545989148.522 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1545989148.522 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1545989148.522 * [misc]taylor: Taking taylor expansion of -1 in k 1545989148.522 * [misc]backup-simplify: Simplify -1 into -1 1545989148.522 * [misc]taylor: Taking taylor expansion of k in k 1545989148.522 * [misc]backup-simplify: Simplify 0 into 0 1545989148.522 * [misc]backup-simplify: Simplify 1 into 1 1545989148.522 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1545989148.522 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545989148.522 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1545989148.522 * [misc]backup-simplify: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) +nan.0) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))) 1545989148.523 * [misc]backup-simplify: Simplify (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))) 1545989148.523 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -2 (/ 0 1)))) into 0 1545989148.524 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -2 1)))) 1) into 0 1545989148.524 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1545989148.525 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1545989148.525 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989148.525 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 1545989148.525 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log -2) (log n)))) into 0 1545989148.526 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1545989148.527 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0 1545989148.527 * [misc]taylor: Taking taylor expansion of 0 in k 1545989148.527 * [misc]backup-simplify: Simplify 0 into 0 1545989148.527 * [misc]backup-simplify: Simplify 0 into 0 1545989148.527 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1545989148.528 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1545989148.528 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))))) 1545989148.528 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))))) 1545989148.529 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -2 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989148.531 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -2 1)))) 2) into 0 1545989148.531 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545989148.532 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1545989148.532 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989148.532 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 1545989148.532 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log -2) (log n))))) into 0 1545989148.534 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1545989148.534 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1545989148.534 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 1545989148.534 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0 1545989148.534 * [misc]taylor: Taking taylor expansion of 0 in k 1545989148.534 * [misc]backup-simplify: Simplify 0 into 0 1545989148.535 * [misc]backup-simplify: Simplify 0 into 0 1545989148.535 * [misc]backup-simplify: Simplify 0 into 0 1545989148.535 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989148.535 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1545989148.536 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))))) 1545989148.536 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))))) 1545989148.537 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -2) (log (/ 1 (- n)))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -2) (log (/ 1 (- n)))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -2) (log (/ 1 (- n))))))))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (pow k 2))) (- (+ (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n)))))) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) k))))))) 1545989148.537 * * * * [misc]progress: [ 3 / 4 ] generating series at (2) 1545989148.538 * [misc]backup-simplify: Simplify (* (exp (* (log PI) (- 1/2 (/ k 2)))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))) into (* (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) 1545989148.538 * [misc]approximate: Taking taylor expansion of (* (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in (k n) around 0 1545989148.538 * [misc]taylor: Taking taylor expansion of (* (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in n 1545989148.538 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) in n 1545989148.538 * [misc]taylor: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in n 1545989148.538 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in n 1545989148.538 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in n 1545989148.538 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1545989148.538 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989148.538 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.538 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1545989148.538 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989148.538 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.538 * [misc]taylor: Taking taylor expansion of k in n 1545989148.538 * [misc]backup-simplify: Simplify k into k 1545989148.538 * [misc]taylor: Taking taylor expansion of (log (* 2 n)) in n 1545989148.538 * [misc]taylor: Taking taylor expansion of (* 2 n) in n 1545989148.538 * [misc]taylor: Taking taylor expansion of 2 in n 1545989148.538 * [misc]backup-simplify: Simplify 2 into 2 1545989148.538 * [misc]taylor: Taking taylor expansion of n in n 1545989148.538 * [misc]backup-simplify: Simplify 0 into 0 1545989148.538 * [misc]backup-simplify: Simplify 1 into 1 1545989148.538 * [misc]backup-simplify: Simplify (* 2 0) into 0 1545989148.538 * [misc]backup-simplify: Simplify (+ (* 2 1) (* 0 0)) into 2 1545989148.539 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1545989148.539 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1545989148.539 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1545989148.539 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1545989148.539 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 1545989148.539 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (+ (log 2) (log n))) into (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) 1545989148.539 * [misc]backup-simplify: Simplify (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) into (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) 1545989148.539 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in n 1545989148.539 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in n 1545989148.539 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in n 1545989148.539 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1545989148.539 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989148.539 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.539 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1545989148.539 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989148.539 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.539 * [misc]taylor: Taking taylor expansion of k in n 1545989148.539 * [misc]backup-simplify: Simplify k into k 1545989148.540 * [misc]taylor: Taking taylor expansion of (log PI) in n 1545989148.540 * [misc]taylor: Taking taylor expansion of PI in n 1545989148.540 * [misc]backup-simplify: Simplify PI into PI 1545989148.540 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1545989148.540 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1545989148.540 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1545989148.540 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1545989148.540 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (log PI)) into (* (- 1/2 (* 1/2 k)) (log PI)) 1545989148.540 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 k)) (log PI))) into (pow PI (- 1/2 (* 1/2 k))) 1545989148.540 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1545989148.540 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989148.540 * [misc]taylor: Taking taylor expansion of k in n 1545989148.540 * [misc]backup-simplify: Simplify k into k 1545989148.540 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989148.540 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1545989148.540 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1545989148.541 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1545989148.541 * [misc]taylor: Taking taylor expansion of (* (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in k 1545989148.541 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) in k 1545989148.541 * [misc]taylor: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in k 1545989148.541 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in k 1545989148.541 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in k 1545989148.541 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1545989148.541 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989148.541 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.541 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1545989148.541 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989148.541 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.541 * [misc]taylor: Taking taylor expansion of k in k 1545989148.541 * [misc]backup-simplify: Simplify 0 into 0 1545989148.541 * [misc]backup-simplify: Simplify 1 into 1 1545989148.541 * [misc]taylor: Taking taylor expansion of (log (* 2 n)) in k 1545989148.541 * [misc]taylor: Taking taylor expansion of (* 2 n) in k 1545989148.541 * [misc]taylor: Taking taylor expansion of 2 in k 1545989148.541 * [misc]backup-simplify: Simplify 2 into 2 1545989148.541 * [misc]taylor: Taking taylor expansion of n in k 1545989148.541 * [misc]backup-simplify: Simplify n into n 1545989148.541 * [misc]backup-simplify: Simplify (* 2 n) into (* 2 n) 1545989148.541 * [misc]backup-simplify: Simplify (log (* 2 n)) into (log (* 2 n)) 1545989148.541 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1545989148.541 * [misc]backup-simplify: Simplify (- 0) into 0 1545989148.541 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545989148.541 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 n))) into (* 1/2 (log (* 2 n))) 1545989148.541 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 n)))) into (pow (* 2 n) 1/2) 1545989148.541 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 1545989148.541 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 1545989148.541 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 1545989148.541 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1545989148.541 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989148.541 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.541 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1545989148.542 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989148.542 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.542 * [misc]taylor: Taking taylor expansion of k in k 1545989148.542 * [misc]backup-simplify: Simplify 0 into 0 1545989148.542 * [misc]backup-simplify: Simplify 1 into 1 1545989148.542 * [misc]taylor: Taking taylor expansion of (log PI) in k 1545989148.542 * [misc]taylor: Taking taylor expansion of PI in k 1545989148.542 * [misc]backup-simplify: Simplify PI into PI 1545989148.542 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1545989148.542 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1545989148.542 * [misc]backup-simplify: Simplify (- 0) into 0 1545989148.542 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545989148.542 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1545989148.543 * [misc]backup-simplify: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 1545989148.543 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1545989148.543 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989148.543 * [misc]taylor: Taking taylor expansion of k in k 1545989148.543 * [misc]backup-simplify: Simplify 0 into 0 1545989148.543 * [misc]backup-simplify: Simplify 1 into 1 1545989148.543 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989148.543 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545989148.543 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1545989148.543 * [misc]taylor: Taking taylor expansion of (* (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in k 1545989148.543 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) in k 1545989148.543 * [misc]taylor: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in k 1545989148.543 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in k 1545989148.544 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in k 1545989148.544 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1545989148.544 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989148.544 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.544 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1545989148.544 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989148.544 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.544 * [misc]taylor: Taking taylor expansion of k in k 1545989148.544 * [misc]backup-simplify: Simplify 0 into 0 1545989148.544 * [misc]backup-simplify: Simplify 1 into 1 1545989148.544 * [misc]taylor: Taking taylor expansion of (log (* 2 n)) in k 1545989148.544 * [misc]taylor: Taking taylor expansion of (* 2 n) in k 1545989148.544 * [misc]taylor: Taking taylor expansion of 2 in k 1545989148.544 * [misc]backup-simplify: Simplify 2 into 2 1545989148.544 * [misc]taylor: Taking taylor expansion of n in k 1545989148.544 * [misc]backup-simplify: Simplify n into n 1545989148.544 * [misc]backup-simplify: Simplify (* 2 n) into (* 2 n) 1545989148.544 * [misc]backup-simplify: Simplify (log (* 2 n)) into (log (* 2 n)) 1545989148.544 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1545989148.544 * [misc]backup-simplify: Simplify (- 0) into 0 1545989148.544 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545989148.544 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 n))) into (* 1/2 (log (* 2 n))) 1545989148.544 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 n)))) into (pow (* 2 n) 1/2) 1545989148.544 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 1545989148.544 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 1545989148.544 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 1545989148.544 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1545989148.544 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989148.544 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.544 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1545989148.544 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989148.544 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.544 * [misc]taylor: Taking taylor expansion of k in k 1545989148.544 * [misc]backup-simplify: Simplify 0 into 0 1545989148.544 * [misc]backup-simplify: Simplify 1 into 1 1545989148.544 * [misc]taylor: Taking taylor expansion of (log PI) in k 1545989148.544 * [misc]taylor: Taking taylor expansion of PI in k 1545989148.544 * [misc]backup-simplify: Simplify PI into PI 1545989148.545 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1545989148.545 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1545989148.545 * [misc]backup-simplify: Simplify (- 0) into 0 1545989148.545 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545989148.545 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1545989148.546 * [misc]backup-simplify: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 1545989148.546 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1545989148.546 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989148.546 * [misc]taylor: Taking taylor expansion of k in k 1545989148.546 * [misc]backup-simplify: Simplify 0 into 0 1545989148.546 * [misc]backup-simplify: Simplify 1 into 1 1545989148.546 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989148.546 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545989148.546 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1545989148.547 * [misc]backup-simplify: Simplify (* (pow (* 2 n) 1/2) (pow PI 1/2)) into (sqrt (* PI (* n 2))) 1545989148.547 * [misc]backup-simplify: Simplify (* (sqrt (* PI (* n 2))) 0) into 0 1545989148.547 * [misc]taylor: Taking taylor expansion of 0 in n 1545989148.547 * [misc]backup-simplify: Simplify 0 into 0 1545989148.547 * [misc]backup-simplify: Simplify 0 into 0 1545989148.548 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 1545989148.549 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1545989148.549 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1545989148.549 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1545989148.549 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (log PI))) into (- (* 1/2 (log PI))) 1545989148.551 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 1) 1)))) into (* -1/2 (* (log PI) (sqrt PI))) 1545989148.551 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 n)) into 0 1545989148.552 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 n) 1)))) 1) into 0 1545989148.552 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1545989148.552 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1545989148.552 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1545989148.552 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 n)))) into (- (* 1/2 (log (* 2 n)))) 1545989148.553 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 n)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 n)))) 1) 1)))) into (* -1/2 (* (sqrt (* n 2)) (log (* 2 n)))) 1545989148.553 * [misc]backup-simplify: Simplify (+ (* (pow (* 2 n) 1/2) (* -1/2 (* (log PI) (sqrt PI)))) (* (* -1/2 (* (sqrt (* n 2)) (log (* 2 n)))) (pow PI 1/2))) into (- (+ (* 1/2 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (* 1/2 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n)))))) 1545989148.554 * [misc]backup-simplify: Simplify (+ (* (sqrt (* PI (* n 2))) +nan.0) (* (- (+ (* 1/2 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (* 1/2 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n)))))) 0)) into (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) 1545989148.554 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 1545989148.554 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 1545989148.554 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1545989148.554 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545989148.555 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1545989148.555 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1545989148.555 * [misc]taylor: Taking taylor expansion of 2 in n 1545989148.555 * [misc]backup-simplify: Simplify 2 into 2 1545989148.555 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1545989148.555 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1545989148.555 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1545989148.555 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545989148.555 * [misc]taylor: Taking taylor expansion of n in n 1545989148.555 * [misc]backup-simplify: Simplify 0 into 0 1545989148.555 * [misc]backup-simplify: Simplify 1 into 1 1545989148.555 * [misc]taylor: Taking taylor expansion of PI in n 1545989148.555 * [misc]backup-simplify: Simplify PI into PI 1545989148.555 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1545989148.555 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1545989148.556 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545989148.556 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1545989148.556 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1545989148.556 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1545989148.556 * [misc]backup-simplify: Simplify (- 0) into 0 1545989148.556 * [misc]backup-simplify: Simplify 0 into 0 1545989148.556 * [misc]backup-simplify: Simplify 0 into 0 1545989148.556 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1545989148.557 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1545989148.560 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 1545989148.560 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1545989148.560 * [misc]backup-simplify: Simplify (- 0) into 0 1545989148.560 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989148.561 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log PI)))) into 0 1545989148.564 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI))) 1545989148.564 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 n))) into 0 1545989148.565 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 n) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 n) 1)))) 2) into 0 1545989148.566 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1545989148.566 * [misc]backup-simplify: Simplify (- 0) into 0 1545989148.566 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989148.566 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 n))))) into 0 1545989148.569 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 n)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* n 2)) (pow (log (* 2 n)) 2))) 1545989148.572 * [misc]backup-simplify: Simplify (+ (* (pow (* 2 n) 1/2) (* 1/8 (* (pow (log PI) 2) (sqrt PI)))) (+ (* (* -1/2 (* (sqrt (* n 2)) (log (* 2 n)))) (* -1/2 (* (log PI) (sqrt PI)))) (* (* 1/8 (* (sqrt (* n 2)) (pow (log (* 2 n)) 2))) (pow PI 1/2)))) into (+ (* 1/8 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (+ (* 1/8 (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (sqrt (* PI n)))) (* 1/4 (* (sqrt (* PI n)) (* (sqrt 2) (* (log (* 2 n)) (log PI))))))) 1545989148.576 * [misc]backup-simplify: Simplify (+ (* (sqrt (* PI (* n 2))) +nan.0) (+ (* (- (+ (* 1/2 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (* 1/2 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n)))))) +nan.0) (* (+ (* 1/8 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (+ (* 1/8 (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (sqrt (* PI n)))) (* 1/4 (* (sqrt (* PI n)) (* (sqrt 2) (* (log (* 2 n)) (log PI))))))) 0))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n))))))))) 1545989148.577 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n))))))))) in n 1545989148.577 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n)))))))) in n 1545989148.577 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) in n 1545989148.577 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1545989148.577 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545989148.577 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (log PI)) (sqrt (* PI n))) in n 1545989148.577 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log PI)) in n 1545989148.577 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1545989148.577 * [misc]taylor: Taking taylor expansion of 2 in n 1545989148.577 * [misc]backup-simplify: Simplify 2 into 2 1545989148.577 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1545989148.577 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1545989148.577 * [misc]taylor: Taking taylor expansion of (log PI) in n 1545989148.577 * [misc]taylor: Taking taylor expansion of PI in n 1545989148.577 * [misc]backup-simplify: Simplify PI into PI 1545989148.578 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1545989148.578 * [misc]taylor: Taking taylor expansion of (sqrt (* PI n)) in n 1545989148.578 * [misc]taylor: Taking taylor expansion of (* PI n) in n 1545989148.578 * [misc]taylor: Taking taylor expansion of PI in n 1545989148.578 * [misc]backup-simplify: Simplify PI into PI 1545989148.578 * [misc]taylor: Taking taylor expansion of n in n 1545989148.578 * [misc]backup-simplify: Simplify 0 into 0 1545989148.578 * [misc]backup-simplify: Simplify 1 into 1 1545989148.578 * [misc]backup-simplify: Simplify (* PI 0) into 0 1545989148.579 * [misc]backup-simplify: Simplify (+ (* PI 1) (* 0 0)) into PI 1545989148.579 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545989148.580 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1545989148.580 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n))))))) in n 1545989148.580 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n)))))) in n 1545989148.580 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 1545989148.580 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1545989148.580 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545989148.580 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1545989148.580 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1545989148.580 * [misc]taylor: Taking taylor expansion of 2 in n 1545989148.580 * [misc]backup-simplify: Simplify 2 into 2 1545989148.580 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1545989148.580 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1545989148.580 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1545989148.580 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545989148.580 * [misc]taylor: Taking taylor expansion of n in n 1545989148.580 * [misc]backup-simplify: Simplify 0 into 0 1545989148.580 * [misc]backup-simplify: Simplify 1 into 1 1545989148.580 * [misc]taylor: Taking taylor expansion of PI in n 1545989148.580 * [misc]backup-simplify: Simplify PI into PI 1545989148.581 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1545989148.581 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1545989148.582 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545989148.582 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1545989148.582 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n))))) in n 1545989148.582 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n)))) in n 1545989148.582 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1545989148.582 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545989148.582 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n))) in n 1545989148.582 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log (* 2 n))) in n 1545989148.582 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1545989148.582 * [misc]taylor: Taking taylor expansion of 2 in n 1545989148.582 * [misc]backup-simplify: Simplify 2 into 2 1545989148.582 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1545989148.583 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1545989148.583 * [misc]taylor: Taking taylor expansion of (log (* 2 n)) in n 1545989148.583 * [misc]taylor: Taking taylor expansion of (* 2 n) in n 1545989148.583 * [misc]taylor: Taking taylor expansion of 2 in n 1545989148.583 * [misc]backup-simplify: Simplify 2 into 2 1545989148.583 * [misc]taylor: Taking taylor expansion of n in n 1545989148.583 * [misc]backup-simplify: Simplify 0 into 0 1545989148.583 * [misc]backup-simplify: Simplify 1 into 1 1545989148.583 * [misc]backup-simplify: Simplify (* 2 0) into 0 1545989148.583 * [misc]backup-simplify: Simplify (+ (* 2 1) (* 0 0)) into 2 1545989148.583 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1545989148.584 * [misc]taylor: Taking taylor expansion of (sqrt (* PI n)) in n 1545989148.584 * [misc]taylor: Taking taylor expansion of (* PI n) in n 1545989148.584 * [misc]taylor: Taking taylor expansion of PI in n 1545989148.584 * [misc]backup-simplify: Simplify PI into PI 1545989148.584 * [misc]taylor: Taking taylor expansion of n in n 1545989148.584 * [misc]backup-simplify: Simplify 0 into 0 1545989148.584 * [misc]backup-simplify: Simplify 1 into 1 1545989148.584 * [misc]backup-simplify: Simplify (* PI 0) into 0 1545989148.585 * [misc]backup-simplify: Simplify (+ (* PI 1) (* 0 0)) into PI 1545989148.585 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545989148.585 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1545989148.586 * [misc]backup-simplify: Simplify (* (sqrt 2) (log PI)) into (* (sqrt 2) (log PI)) 1545989148.587 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (log PI)) 0) into 0 1545989148.587 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1545989148.587 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1545989148.587 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1545989148.588 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 1545989148.588 * [misc]backup-simplify: Simplify (* (sqrt 2) (+ (log 2) (log n))) into (* (+ (log 2) (log n)) (sqrt 2)) 1545989148.588 * [misc]backup-simplify: Simplify (* (* (+ (log 2) (log n)) (sqrt 2)) 0) into 0 1545989148.589 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1545989148.589 * [misc]backup-simplify: Simplify (- 0) into 0 1545989148.589 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989148.589 * [misc]backup-simplify: Simplify (- 0) into 0 1545989148.589 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989148.589 * [misc]backup-simplify: Simplify (- 0) into 0 1545989148.589 * [misc]backup-simplify: Simplify 0 into 0 1545989148.591 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1545989148.593 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1545989148.594 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 1545989148.595 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI))) 1545989148.595 * [misc]backup-simplify: Simplify 0 into 0 1545989148.595 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989148.597 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1545989148.604 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0 1545989148.604 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1545989148.604 * [misc]backup-simplify: Simplify (- 0) into 0 1545989148.604 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989148.605 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log PI))))) into 0 1545989148.609 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 3) 6)) (* (/ (pow (- (* 1/2 (log PI))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (pow (log PI) 3) (sqrt PI))) 1545989148.610 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 n)))) into 0 1545989148.611 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 n) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 n) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 n) 1)))) 6) into 0 1545989148.611 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1545989148.611 * [misc]backup-simplify: Simplify (- 0) into 0 1545989148.612 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989148.612 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log (* 2 n)))))) into 0 1545989148.613 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 n)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 n)))) 3) 6)) (* (/ (pow (- (* 1/2 (log (* 2 n)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (sqrt (* n 2)) (pow (log (* 2 n)) 3))) 1545989148.616 * [misc]backup-simplify: Simplify (+ (* (pow (* 2 n) 1/2) (* -1/48 (* (pow (log PI) 3) (sqrt PI)))) (+ (* (* -1/2 (* (sqrt (* n 2)) (log (* 2 n)))) (* 1/8 (* (pow (log PI) 2) (sqrt PI)))) (+ (* (* 1/8 (* (sqrt (* n 2)) (pow (log (* 2 n)) 2))) (* -1/2 (* (log PI) (sqrt PI)))) (* (* -1/48 (* (sqrt (* n 2)) (pow (log (* 2 n)) 3))) (pow PI 1/2))))) into (- (+ (* 1/48 (* (* (sqrt 2) (pow (log (* 2 n)) 3)) (sqrt (* PI n)))) (+ (* 1/16 (* (sqrt (* PI n)) (* (sqrt 2) (* (log (* 2 n)) (pow (log PI) 2))))) (+ (* 1/48 (* (* (sqrt 2) (pow (log PI) 3)) (sqrt (* PI n)))) (* 1/16 (* (sqrt (* PI n)) (* (sqrt 2) (* (pow (log (* 2 n)) 2) (log PI))))))))) 1545989148.622 * [misc]backup-simplify: Simplify (+ (* (sqrt (* PI (* n 2))) +nan.0) (+ (* (- (+ (* 1/2 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (* 1/2 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n)))))) +nan.0) (+ (* (+ (* 1/8 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (+ (* 1/8 (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (sqrt (* PI n)))) (* 1/4 (* (sqrt (* PI n)) (* (sqrt 2) (* (log (* 2 n)) (log PI))))))) +nan.0) (* (- (+ (* 1/48 (* (* (sqrt 2) (pow (log (* 2 n)) 3)) (sqrt (* PI n)))) (+ (* 1/16 (* (sqrt (* PI n)) (* (sqrt 2) (* (log (* 2 n)) (pow (log PI) 2))))) (+ (* 1/48 (* (* (sqrt 2) (pow (log PI) 3)) (sqrt (* PI n)))) (* 1/16 (* (sqrt (* PI n)) (* (sqrt 2) (* (pow (log (* 2 n)) 2) (log PI))))))))) 0)))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 n)) (log PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n))))))))))))))) 1545989148.622 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 n)) (log PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n))))))))))))))) in n 1545989148.622 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 n)) (log PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n)))))))))))))) in n 1545989148.622 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) in n 1545989148.622 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1545989148.622 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545989148.622 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (log PI)) (sqrt (* PI n))) in n 1545989148.622 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log PI)) in n 1545989148.622 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1545989148.622 * [misc]taylor: Taking taylor expansion of 2 in n 1545989148.622 * [misc]backup-simplify: Simplify 2 into 2 1545989148.622 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1545989148.622 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1545989148.622 * [misc]taylor: Taking taylor expansion of (log PI) in n 1545989148.622 * [misc]taylor: Taking taylor expansion of PI in n 1545989148.622 * [misc]backup-simplify: Simplify PI into PI 1545989148.623 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1545989148.623 * [misc]taylor: Taking taylor expansion of (sqrt (* PI n)) in n 1545989148.623 * [misc]taylor: Taking taylor expansion of (* PI n) in n 1545989148.623 * [misc]taylor: Taking taylor expansion of PI in n 1545989148.623 * [misc]backup-simplify: Simplify PI into PI 1545989148.623 * [misc]taylor: Taking taylor expansion of n in n 1545989148.623 * [misc]backup-simplify: Simplify 0 into 0 1545989148.623 * [misc]backup-simplify: Simplify 1 into 1 1545989148.623 * [misc]backup-simplify: Simplify (* PI 0) into 0 1545989148.623 * [misc]backup-simplify: Simplify (+ (* PI 1) (* 0 0)) into PI 1545989148.623 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545989148.624 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1545989148.624 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 n)) (log PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n))))))))))))) in n 1545989148.624 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 n)) (log PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n)))))))))))) in n 1545989148.624 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) in n 1545989148.624 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1545989148.624 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545989148.624 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n))) in n 1545989148.624 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (log PI) 2)) in n 1545989148.624 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1545989148.624 * [misc]taylor: Taking taylor expansion of 2 in n 1545989148.624 * [misc]backup-simplify: Simplify 2 into 2 1545989148.624 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1545989148.624 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1545989148.624 * [misc]taylor: Taking taylor expansion of (pow (log PI) 2) in n 1545989148.624 * [misc]taylor: Taking taylor expansion of (log PI) in n 1545989148.624 * [misc]taylor: Taking taylor expansion of PI in n 1545989148.624 * [misc]backup-simplify: Simplify PI into PI 1545989148.624 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1545989148.624 * [misc]taylor: Taking taylor expansion of (sqrt (* PI n)) in n 1545989148.624 * [misc]taylor: Taking taylor expansion of (* PI n) in n 1545989148.624 * [misc]taylor: Taking taylor expansion of PI in n 1545989148.624 * [misc]backup-simplify: Simplify PI into PI 1545989148.624 * [misc]taylor: Taking taylor expansion of n in n 1545989148.624 * [misc]backup-simplify: Simplify 0 into 0 1545989148.624 * [misc]backup-simplify: Simplify 1 into 1 1545989148.625 * [misc]backup-simplify: Simplify (* PI 0) into 0 1545989148.625 * [misc]backup-simplify: Simplify (+ (* PI 1) (* 0 0)) into PI 1545989148.625 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545989148.625 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1545989148.625 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 n)) (log PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n))))))))))) in n 1545989148.625 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 n)) (log PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n)))))))))) in n 1545989148.625 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (sqrt (* PI n)))) in n 1545989148.625 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1545989148.625 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545989148.626 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (sqrt (* PI n))) in n 1545989148.626 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (log (* 2 n)) 2)) in n 1545989148.626 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1545989148.626 * [misc]taylor: Taking taylor expansion of 2 in n 1545989148.626 * [misc]backup-simplify: Simplify 2 into 2 1545989148.626 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1545989148.626 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1545989148.626 * [misc]taylor: Taking taylor expansion of (pow (log (* 2 n)) 2) in n 1545989148.626 * [misc]taylor: Taking taylor expansion of (log (* 2 n)) in n 1545989148.626 * [misc]taylor: Taking taylor expansion of (* 2 n) in n 1545989148.626 * [misc]taylor: Taking taylor expansion of 2 in n 1545989148.626 * [misc]backup-simplify: Simplify 2 into 2 1545989148.626 * [misc]taylor: Taking taylor expansion of n in n 1545989148.626 * [misc]backup-simplify: Simplify 0 into 0 1545989148.626 * [misc]backup-simplify: Simplify 1 into 1 1545989148.626 * [misc]backup-simplify: Simplify (* 2 0) into 0 1545989148.626 * [misc]backup-simplify: Simplify (+ (* 2 1) (* 0 0)) into 2 1545989148.626 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1545989148.626 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 1545989148.627 * [misc]taylor: Taking taylor expansion of (sqrt (* PI n)) in n 1545989148.627 * [misc]taylor: Taking taylor expansion of (* PI n) in n 1545989148.627 * [misc]taylor: Taking taylor expansion of PI in n 1545989148.627 * [misc]backup-simplify: Simplify PI into PI 1545989148.627 * [misc]taylor: Taking taylor expansion of n in n 1545989148.627 * [misc]backup-simplify: Simplify 0 into 0 1545989148.627 * [misc]backup-simplify: Simplify 1 into 1 1545989148.627 * [misc]backup-simplify: Simplify (* PI 0) into 0 1545989148.627 * [misc]backup-simplify: Simplify (+ (* PI 1) (* 0 0)) into PI 1545989148.627 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545989148.628 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1545989148.628 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 n)) (log PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n))))))))) in n 1545989148.628 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 n)) (log PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n)))))))) in n 1545989148.628 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (* (log (* 2 n)) (log PI))) (sqrt (* n PI)))) in n 1545989148.628 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1545989148.628 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545989148.628 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (* (log (* 2 n)) (log PI))) (sqrt (* n PI))) in n 1545989148.628 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* (log (* 2 n)) (log PI))) in n 1545989148.628 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1545989148.628 * [misc]taylor: Taking taylor expansion of 2 in n 1545989148.628 * [misc]backup-simplify: Simplify 2 into 2 1545989148.628 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1545989148.628 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1545989148.628 * [misc]taylor: Taking taylor expansion of (* (log (* 2 n)) (log PI)) in n 1545989148.628 * [misc]taylor: Taking taylor expansion of (log (* 2 n)) in n 1545989148.628 * [misc]taylor: Taking taylor expansion of (* 2 n) in n 1545989148.628 * [misc]taylor: Taking taylor expansion of 2 in n 1545989148.628 * [misc]backup-simplify: Simplify 2 into 2 1545989148.628 * [misc]taylor: Taking taylor expansion of n in n 1545989148.628 * [misc]backup-simplify: Simplify 0 into 0 1545989148.628 * [misc]backup-simplify: Simplify 1 into 1 1545989148.628 * [misc]backup-simplify: Simplify (* 2 0) into 0 1545989148.628 * [misc]backup-simplify: Simplify (+ (* 2 1) (* 0 0)) into 2 1545989148.628 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1545989148.628 * [misc]taylor: Taking taylor expansion of (log PI) in n 1545989148.628 * [misc]taylor: Taking taylor expansion of PI in n 1545989148.628 * [misc]backup-simplify: Simplify PI into PI 1545989148.629 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1545989148.629 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1545989148.629 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545989148.629 * [misc]taylor: Taking taylor expansion of n in n 1545989148.629 * [misc]backup-simplify: Simplify 0 into 0 1545989148.629 * [misc]backup-simplify: Simplify 1 into 1 1545989148.629 * [misc]taylor: Taking taylor expansion of PI in n 1545989148.629 * [misc]backup-simplify: Simplify PI into PI 1545989148.629 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1545989148.629 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1545989148.630 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545989148.630 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1545989148.630 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n))))))) in n 1545989148.630 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n)))))) in n 1545989148.630 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 1545989148.630 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1545989148.630 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545989148.630 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1545989148.630 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1545989148.630 * [misc]taylor: Taking taylor expansion of 2 in n 1545989148.630 * [misc]backup-simplify: Simplify 2 into 2 1545989148.630 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1545989148.630 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1545989148.630 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1545989148.630 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1545989148.630 * [misc]taylor: Taking taylor expansion of n in n 1545989148.630 * [misc]backup-simplify: Simplify 0 into 0 1545989148.630 * [misc]backup-simplify: Simplify 1 into 1 1545989148.630 * [misc]taylor: Taking taylor expansion of PI in n 1545989148.630 * [misc]backup-simplify: Simplify PI into PI 1545989148.630 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1545989148.631 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1545989148.631 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545989148.631 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1545989148.631 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n))))) in n 1545989148.631 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n)))) in n 1545989148.631 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1545989148.631 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545989148.631 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n))) in n 1545989148.631 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log (* 2 n))) in n 1545989148.632 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1545989148.632 * [misc]taylor: Taking taylor expansion of 2 in n 1545989148.632 * [misc]backup-simplify: Simplify 2 into 2 1545989148.632 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1545989148.632 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1545989148.632 * [misc]taylor: Taking taylor expansion of (log (* 2 n)) in n 1545989148.632 * [misc]taylor: Taking taylor expansion of (* 2 n) in n 1545989148.632 * [misc]taylor: Taking taylor expansion of 2 in n 1545989148.632 * [misc]backup-simplify: Simplify 2 into 2 1545989148.632 * [misc]taylor: Taking taylor expansion of n in n 1545989148.632 * [misc]backup-simplify: Simplify 0 into 0 1545989148.632 * [misc]backup-simplify: Simplify 1 into 1 1545989148.632 * [misc]backup-simplify: Simplify (* 2 0) into 0 1545989148.633 * [misc]backup-simplify: Simplify (+ (* 2 1) (* 0 0)) into 2 1545989148.633 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1545989148.633 * [misc]taylor: Taking taylor expansion of (sqrt (* PI n)) in n 1545989148.633 * [misc]taylor: Taking taylor expansion of (* PI n) in n 1545989148.633 * [misc]taylor: Taking taylor expansion of PI in n 1545989148.633 * [misc]backup-simplify: Simplify PI into PI 1545989148.633 * [misc]taylor: Taking taylor expansion of n in n 1545989148.633 * [misc]backup-simplify: Simplify 0 into 0 1545989148.633 * [misc]backup-simplify: Simplify 1 into 1 1545989148.633 * [misc]backup-simplify: Simplify (* PI 0) into 0 1545989148.634 * [misc]backup-simplify: Simplify (+ (* PI 1) (* 0 0)) into PI 1545989148.634 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545989148.635 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1545989148.635 * [misc]backup-simplify: Simplify (* (sqrt 2) (log PI)) into (* (sqrt 2) (log PI)) 1545989148.636 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (log PI)) 0) into 0 1545989148.637 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1545989148.637 * [misc]backup-simplify: Simplify (* (log PI) (log PI)) into (pow (log PI) 2) 1545989148.638 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow (log PI) 2)) into (* (sqrt 2) (pow (log PI) 2)) 1545989148.639 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (pow (log PI) 2)) 0) into 0 1545989148.640 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1545989148.640 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 1545989148.640 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 1545989148.641 * [misc]backup-simplify: Simplify (* (+ (log 2) (log n)) (+ (log 2) (log n))) into (pow (+ (log 2) (log n)) 2) 1545989148.641 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow (+ (log 2) (log n)) 2)) into (* (pow (+ (log 2) (log n)) 2) (sqrt 2)) 1545989148.642 * [misc]backup-simplify: Simplify (* (* (pow (+ (log 2) (log n)) 2) (sqrt 2)) 0) into 0 1545989148.642 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1545989148.642 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 1545989148.643 * [misc]backup-simplify: Simplify (* (+ (log 2) (log n)) (log PI)) into (* (+ (log 2) (log n)) (log PI)) 1545989148.643 * [misc]backup-simplify: Simplify (* (sqrt 2) (* (+ (log 2) (log n)) (log PI))) into (* (+ (log 2) (log n)) (* (sqrt 2) (log PI))) 1545989148.644 * [misc]backup-simplify: Simplify (* (* (+ (log 2) (log n)) (* (sqrt 2) (log PI))) 0) into 0 1545989148.644 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1545989148.645 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1545989148.645 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1545989148.645 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 1545989148.645 * [misc]backup-simplify: Simplify (* (sqrt 2) (+ (log 2) (log n))) into (* (+ (log 2) (log n)) (sqrt 2)) 1545989148.646 * [misc]backup-simplify: Simplify (* (* (+ (log 2) (log n)) (sqrt 2)) 0) into 0 1545989148.646 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1545989148.646 * [misc]backup-simplify: Simplify (- 0) into 0 1545989148.646 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989148.646 * [misc]backup-simplify: Simplify (- 0) into 0 1545989148.647 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989148.647 * [misc]backup-simplify: Simplify (- 0) into 0 1545989148.647 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989148.647 * [misc]backup-simplify: Simplify (- 0) into 0 1545989148.647 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989148.647 * [misc]backup-simplify: Simplify (- 0) into 0 1545989148.647 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989148.648 * [misc]backup-simplify: Simplify (- 0) into 0 1545989148.648 * [misc]backup-simplify: Simplify 0 into 0 1545989148.650 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 1545989148.651 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (log PI))) into 0 1545989148.653 * [misc]backup-simplify: Simplify (+ (* (* (sqrt 2) (log PI)) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) (* (log PI) PI)))) 1545989148.655 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) (* (log PI) PI))))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) (* (log PI) PI)))) 1545989148.656 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1545989148.657 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1545989148.657 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 1) (* 0 0))) into 0 1545989148.659 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 1545989148.659 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 1545989148.659 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log 2) (log n)))) into 0 1545989148.660 * [misc]backup-simplify: Simplify (+ (* (* (+ (log 2) (log n)) (sqrt 2)) (* +nan.0 PI)) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (log 2) (* (sqrt 2) PI)))))) 1545989148.661 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (log 2) (* (sqrt 2) PI))))))) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (log 2) (* (sqrt 2) PI)))))) 1545989148.662 * [misc]backup-simplify: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (log 2) (* (sqrt 2) PI))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (log 2) (* (sqrt 2) PI)))))) 1545989148.664 * [misc]backup-simplify: Simplify (+ (- (* +nan.0 (* (sqrt 2) PI))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (log 2) (* (sqrt 2) PI))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))) 1545989148.666 * [misc]backup-simplify: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI)))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))) 1545989148.669 * [misc]backup-simplify: Simplify (+ (- (* +nan.0 (* (sqrt 2) (* (log PI) PI)))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI)))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))))) 1545989148.673 * [misc]backup-simplify: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI)))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))))) 1545989148.677 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))))) 1545989148.678 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1545989148.679 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 1545989148.680 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1545989148.681 * [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)))) 1545989148.684 * [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)))) 1545989148.686 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 1545989148.688 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 1545989148.699 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) (pow (* n 1) 2)) (+ (* (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))))) (* n k)) (* (- (* +nan.0 (* (sqrt 2) PI))) (* n 1)))) into (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log PI) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))))))))) 1545989148.700 * [misc]backup-simplify: Simplify (* (exp (* (log PI) (- 1/2 (/ (/ 1 k) 2)))) (/ (pow (* (/ 1 n) 2) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k)))) into (* (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) 1545989148.700 * [misc]approximate: Taking taylor expansion of (* (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in (k n) around 0 1545989148.700 * [misc]taylor: Taking taylor expansion of (* (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in n 1545989148.700 * [misc]taylor: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) in n 1545989148.700 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in n 1545989148.700 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in n 1545989148.701 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in n 1545989148.701 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1545989148.701 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989148.701 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.701 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989148.701 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989148.701 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.701 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989148.701 * [misc]taylor: Taking taylor expansion of k in n 1545989148.701 * [misc]backup-simplify: Simplify k into k 1545989148.701 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989148.701 * [misc]taylor: Taking taylor expansion of (log PI) in n 1545989148.701 * [misc]taylor: Taking taylor expansion of PI in n 1545989148.701 * [misc]backup-simplify: Simplify PI into PI 1545989148.701 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1545989148.701 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989148.701 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1545989148.702 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1545989148.702 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) into (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) 1545989148.702 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1545989148.702 * [misc]taylor: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 1545989148.702 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 1545989148.702 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 1545989148.702 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1545989148.702 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989148.702 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.702 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989148.702 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989148.703 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.703 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989148.703 * [misc]taylor: Taking taylor expansion of k in n 1545989148.703 * [misc]backup-simplify: Simplify k into k 1545989148.703 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989148.703 * [misc]taylor: Taking taylor expansion of (log (/ 2 n)) in n 1545989148.703 * [misc]taylor: Taking taylor expansion of (/ 2 n) in n 1545989148.703 * [misc]taylor: Taking taylor expansion of 2 in n 1545989148.703 * [misc]backup-simplify: Simplify 2 into 2 1545989148.703 * [misc]taylor: Taking taylor expansion of n in n 1545989148.703 * [misc]backup-simplify: Simplify 0 into 0 1545989148.703 * [misc]backup-simplify: Simplify 1 into 1 1545989148.703 * [misc]backup-simplify: Simplify (/ 2 1) into 2 1545989148.703 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1545989148.703 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989148.703 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1545989148.704 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1545989148.704 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 1545989148.704 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 1545989148.705 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 1545989148.705 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1545989148.705 * [misc]taylor: Taking taylor expansion of k in n 1545989148.705 * [misc]backup-simplify: Simplify k into k 1545989148.705 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1545989148.705 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1545989148.705 * [misc]taylor: Taking taylor expansion of (* (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in k 1545989148.705 * [misc]taylor: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) in k 1545989148.705 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 1545989148.705 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 1545989148.705 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 1545989148.705 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1545989148.705 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989148.705 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.705 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545989148.705 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989148.705 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.705 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989148.705 * [misc]taylor: Taking taylor expansion of k in k 1545989148.705 * [misc]backup-simplify: Simplify 0 into 0 1545989148.705 * [misc]backup-simplify: Simplify 1 into 1 1545989148.705 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989148.706 * [misc]taylor: Taking taylor expansion of (log PI) in k 1545989148.706 * [misc]taylor: Taking taylor expansion of PI in k 1545989148.706 * [misc]backup-simplify: Simplify PI into PI 1545989148.706 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1545989148.706 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545989148.706 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1545989148.706 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1545989148.707 * [misc]backup-simplify: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 1545989148.707 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1545989148.707 * [misc]taylor: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in k 1545989148.707 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in k 1545989148.707 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in k 1545989148.707 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1545989148.707 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989148.707 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.707 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545989148.707 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989148.707 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.707 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989148.708 * [misc]taylor: Taking taylor expansion of k in k 1545989148.708 * [misc]backup-simplify: Simplify 0 into 0 1545989148.708 * [misc]backup-simplify: Simplify 1 into 1 1545989148.708 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989148.708 * [misc]taylor: Taking taylor expansion of (log (/ 2 n)) in k 1545989148.708 * [misc]taylor: Taking taylor expansion of (/ 2 n) in k 1545989148.708 * [misc]taylor: Taking taylor expansion of 2 in k 1545989148.708 * [misc]backup-simplify: Simplify 2 into 2 1545989148.708 * [misc]taylor: Taking taylor expansion of n in k 1545989148.708 * [misc]backup-simplify: Simplify n into n 1545989148.708 * [misc]backup-simplify: Simplify (/ 2 n) into (/ 2 n) 1545989148.708 * [misc]backup-simplify: Simplify (log (/ 2 n)) into (log (/ 2 n)) 1545989148.708 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545989148.708 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1545989148.709 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1545989148.709 * [misc]backup-simplify: Simplify (* -1/2 (log (/ 2 n))) into (* -1/2 (log (/ 2 n))) 1545989148.709 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) into (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) 1545989148.709 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1545989148.709 * [misc]taylor: Taking taylor expansion of k in k 1545989148.709 * [misc]backup-simplify: Simplify 0 into 0 1545989148.709 * [misc]backup-simplify: Simplify 1 into 1 1545989148.709 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545989148.710 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1545989148.710 * [misc]taylor: Taking taylor expansion of (* (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in k 1545989148.710 * [misc]taylor: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) in k 1545989148.710 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 1545989148.710 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 1545989148.710 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 1545989148.710 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1545989148.710 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989148.710 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.710 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545989148.710 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989148.710 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.710 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989148.710 * [misc]taylor: Taking taylor expansion of k in k 1545989148.710 * [misc]backup-simplify: Simplify 0 into 0 1545989148.710 * [misc]backup-simplify: Simplify 1 into 1 1545989148.710 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989148.710 * [misc]taylor: Taking taylor expansion of (log PI) in k 1545989148.710 * [misc]taylor: Taking taylor expansion of PI in k 1545989148.710 * [misc]backup-simplify: Simplify PI into PI 1545989148.711 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1545989148.711 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545989148.711 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1545989148.711 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1545989148.712 * [misc]backup-simplify: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 1545989148.712 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1545989148.712 * [misc]taylor: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in k 1545989148.712 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in k 1545989148.712 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in k 1545989148.712 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1545989148.712 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989148.712 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.712 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545989148.712 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989148.712 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.712 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989148.712 * [misc]taylor: Taking taylor expansion of k in k 1545989148.712 * [misc]backup-simplify: Simplify 0 into 0 1545989148.712 * [misc]backup-simplify: Simplify 1 into 1 1545989148.713 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989148.713 * [misc]taylor: Taking taylor expansion of (log (/ 2 n)) in k 1545989148.713 * [misc]taylor: Taking taylor expansion of (/ 2 n) in k 1545989148.713 * [misc]taylor: Taking taylor expansion of 2 in k 1545989148.713 * [misc]backup-simplify: Simplify 2 into 2 1545989148.713 * [misc]taylor: Taking taylor expansion of n in k 1545989148.713 * [misc]backup-simplify: Simplify n into n 1545989148.713 * [misc]backup-simplify: Simplify (/ 2 n) into (/ 2 n) 1545989148.713 * [misc]backup-simplify: Simplify (log (/ 2 n)) into (log (/ 2 n)) 1545989148.713 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545989148.713 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1545989148.713 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1545989148.714 * [misc]backup-simplify: Simplify (* -1/2 (log (/ 2 n))) into (* -1/2 (log (/ 2 n))) 1545989148.714 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) into (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) 1545989148.714 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1545989148.714 * [misc]taylor: Taking taylor expansion of k in k 1545989148.714 * [misc]backup-simplify: Simplify 0 into 0 1545989148.714 * [misc]backup-simplify: Simplify 1 into 1 1545989148.714 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545989148.714 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1545989148.715 * [misc]backup-simplify: Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) into (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) 1545989148.715 * [misc]backup-simplify: Simplify (* (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) 0) into 0 1545989148.715 * [misc]taylor: Taking taylor expansion of 0 in n 1545989148.715 * [misc]backup-simplify: Simplify 0 into 0 1545989148.715 * [misc]backup-simplify: Simplify 0 into 0 1545989148.716 * [misc]backup-simplify: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (* 0 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))) into 0 1545989148.716 * [misc]backup-simplify: Simplify (+ (* (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (* 0 0)) into (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))))) 1545989148.716 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))))) in n 1545989148.716 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))) in n 1545989148.716 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1545989148.716 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545989148.716 * [misc]taylor: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) in n 1545989148.716 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in n 1545989148.716 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in n 1545989148.716 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in n 1545989148.716 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1545989148.716 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989148.716 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.716 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989148.717 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989148.717 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.717 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989148.717 * [misc]taylor: Taking taylor expansion of k in n 1545989148.717 * [misc]backup-simplify: Simplify k into k 1545989148.717 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989148.717 * [misc]taylor: Taking taylor expansion of (log PI) in n 1545989148.717 * [misc]taylor: Taking taylor expansion of PI in n 1545989148.717 * [misc]backup-simplify: Simplify PI into PI 1545989148.717 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1545989148.717 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989148.717 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1545989148.717 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1545989148.718 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) into (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) 1545989148.718 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1545989148.718 * [misc]taylor: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 1545989148.718 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 1545989148.718 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 1545989148.718 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1545989148.718 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989148.718 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.718 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989148.718 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989148.718 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.718 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989148.718 * [misc]taylor: Taking taylor expansion of k in n 1545989148.718 * [misc]backup-simplify: Simplify k into k 1545989148.718 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989148.719 * [misc]taylor: Taking taylor expansion of (log (/ 2 n)) in n 1545989148.719 * [misc]taylor: Taking taylor expansion of (/ 2 n) in n 1545989148.719 * [misc]taylor: Taking taylor expansion of 2 in n 1545989148.719 * [misc]backup-simplify: Simplify 2 into 2 1545989148.719 * [misc]taylor: Taking taylor expansion of n in n 1545989148.719 * [misc]backup-simplify: Simplify 0 into 0 1545989148.719 * [misc]backup-simplify: Simplify 1 into 1 1545989148.719 * [misc]backup-simplify: Simplify (/ 2 1) into 2 1545989148.719 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1545989148.719 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989148.719 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1545989148.719 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1545989148.719 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 1545989148.720 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 1545989148.720 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 1545989148.720 * [misc]backup-simplify: Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) into (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) 1545989148.720 * [misc]backup-simplify: Simplify (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) into (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) 1545989148.721 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) into (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) 1545989148.721 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) into (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) 1545989148.721 * [misc]backup-simplify: Simplify 0 into 0 1545989148.722 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1545989148.722 * [misc]backup-simplify: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (* 0 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))))) into 0 1545989148.722 * [misc]backup-simplify: Simplify (+ (* (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))))) 1545989148.722 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))))) in n 1545989148.722 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))) in n 1545989148.722 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1545989148.722 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545989148.722 * [misc]taylor: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) in n 1545989148.722 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in n 1545989148.722 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in n 1545989148.723 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in n 1545989148.723 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1545989148.723 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989148.723 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.723 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989148.723 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989148.723 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.723 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989148.723 * [misc]taylor: Taking taylor expansion of k in n 1545989148.723 * [misc]backup-simplify: Simplify k into k 1545989148.723 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989148.723 * [misc]taylor: Taking taylor expansion of (log PI) in n 1545989148.723 * [misc]taylor: Taking taylor expansion of PI in n 1545989148.723 * [misc]backup-simplify: Simplify PI into PI 1545989148.723 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1545989148.723 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989148.723 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1545989148.723 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1545989148.723 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) into (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) 1545989148.724 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1545989148.724 * [misc]taylor: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 1545989148.724 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 1545989148.724 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 1545989148.724 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1545989148.724 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989148.724 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.724 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989148.724 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989148.724 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.724 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989148.724 * [misc]taylor: Taking taylor expansion of k in n 1545989148.724 * [misc]backup-simplify: Simplify k into k 1545989148.724 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989148.724 * [misc]taylor: Taking taylor expansion of (log (/ 2 n)) in n 1545989148.724 * [misc]taylor: Taking taylor expansion of (/ 2 n) in n 1545989148.724 * [misc]taylor: Taking taylor expansion of 2 in n 1545989148.724 * [misc]backup-simplify: Simplify 2 into 2 1545989148.724 * [misc]taylor: Taking taylor expansion of n in n 1545989148.724 * [misc]backup-simplify: Simplify 0 into 0 1545989148.724 * [misc]backup-simplify: Simplify 1 into 1 1545989148.724 * [misc]backup-simplify: Simplify (/ 2 1) into 2 1545989148.724 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1545989148.724 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989148.724 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1545989148.724 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1545989148.724 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 1545989148.725 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 1545989148.725 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 1545989148.725 * [misc]backup-simplify: Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) into (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) 1545989148.725 * [misc]backup-simplify: Simplify (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) into (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) 1545989148.726 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) into (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) 1545989148.726 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) into (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) 1545989148.726 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)))) into 0 1545989148.728 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 1545989148.728 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1545989148.728 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1545989148.728 * [misc]backup-simplify: Simplify (- 0) into 0 1545989148.728 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989148.728 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 1545989148.728 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log 2) (log n)))) into 0 1545989148.729 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1545989148.731 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 1545989148.731 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1545989148.731 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1545989148.731 * [misc]backup-simplify: Simplify (- 0) into 0 1545989148.731 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989148.731 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (log PI))) into 0 1545989148.732 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 1545989148.732 * [misc]backup-simplify: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) into 0 1545989148.733 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) into 0 1545989148.733 * [misc]backup-simplify: Simplify (- 0) into 0 1545989148.733 * [misc]backup-simplify: Simplify 0 into 0 1545989148.733 * [misc]backup-simplify: Simplify 0 into 0 1545989148.734 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1545989148.734 * [misc]backup-simplify: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 1545989148.734 * [misc]backup-simplify: Simplify (+ (* (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))))) 1545989148.734 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))))) in n 1545989148.734 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))) in n 1545989148.734 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1545989148.734 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545989148.734 * [misc]taylor: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) in n 1545989148.735 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in n 1545989148.735 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in n 1545989148.735 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in n 1545989148.735 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1545989148.735 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989148.735 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.735 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989148.735 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989148.735 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.735 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989148.735 * [misc]taylor: Taking taylor expansion of k in n 1545989148.735 * [misc]backup-simplify: Simplify k into k 1545989148.735 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989148.735 * [misc]taylor: Taking taylor expansion of (log PI) in n 1545989148.735 * [misc]taylor: Taking taylor expansion of PI in n 1545989148.735 * [misc]backup-simplify: Simplify PI into PI 1545989148.735 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1545989148.735 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989148.735 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1545989148.735 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1545989148.735 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) into (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) 1545989148.736 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1545989148.736 * [misc]taylor: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 1545989148.736 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 1545989148.736 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 1545989148.736 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1545989148.736 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989148.736 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.736 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989148.736 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989148.736 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.736 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989148.736 * [misc]taylor: Taking taylor expansion of k in n 1545989148.736 * [misc]backup-simplify: Simplify k into k 1545989148.736 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989148.736 * [misc]taylor: Taking taylor expansion of (log (/ 2 n)) in n 1545989148.736 * [misc]taylor: Taking taylor expansion of (/ 2 n) in n 1545989148.736 * [misc]taylor: Taking taylor expansion of 2 in n 1545989148.736 * [misc]backup-simplify: Simplify 2 into 2 1545989148.736 * [misc]taylor: Taking taylor expansion of n in n 1545989148.736 * [misc]backup-simplify: Simplify 0 into 0 1545989148.736 * [misc]backup-simplify: Simplify 1 into 1 1545989148.736 * [misc]backup-simplify: Simplify (/ 2 1) into 2 1545989148.736 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1545989148.736 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989148.736 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1545989148.736 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1545989148.737 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 1545989148.737 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 1545989148.737 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 1545989148.737 * [misc]backup-simplify: Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) into (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) 1545989148.737 * [misc]backup-simplify: Simplify (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) into (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) 1545989148.738 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) into (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) 1545989148.738 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) into (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) 1545989148.739 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k))))) (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log 2) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k))))) (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log 2) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k))))) (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log 2) (log (/ 1 n)))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (* (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))) (pow k 2))) (- (+ (* +nan.0 (/ (* (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))) k)) (- (* +nan.0 (/ (* (pow PI (- 1/2 (* 1/2 k))) (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k))))) (pow k 3)))))))) 1545989148.740 * [misc]backup-simplify: Simplify (* (exp (* (log PI) (- 1/2 (/ (/ 1 (- k)) 2)))) (/ (pow (* (/ 1 (- n)) 2) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k))))) into (/ (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) 1545989148.740 * [misc]approximate: Taking taylor expansion of (/ (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) in (k n) around 0 1545989148.740 * [misc]taylor: Taking taylor expansion of (/ (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) in n 1545989148.740 * [misc]taylor: Taking taylor expansion of (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in n 1545989148.740 * [misc]taylor: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1545989148.740 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 1545989148.740 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 1545989148.740 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1545989148.740 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989148.740 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989148.740 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.740 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989148.740 * [misc]taylor: Taking taylor expansion of k in n 1545989148.740 * [misc]backup-simplify: Simplify k into k 1545989148.740 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989148.740 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989148.740 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.740 * [misc]taylor: Taking taylor expansion of (log (/ -2 n)) in n 1545989148.740 * [misc]taylor: Taking taylor expansion of (/ -2 n) in n 1545989148.740 * [misc]taylor: Taking taylor expansion of -2 in n 1545989148.740 * [misc]backup-simplify: Simplify -2 into -2 1545989148.740 * [misc]taylor: Taking taylor expansion of n in n 1545989148.740 * [misc]backup-simplify: Simplify 0 into 0 1545989148.740 * [misc]backup-simplify: Simplify 1 into 1 1545989148.740 * [misc]backup-simplify: Simplify (/ -2 1) into -2 1545989148.740 * [misc]backup-simplify: Simplify (log -2) into (log -2) 1545989148.740 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989148.741 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1545989148.741 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 1545989148.741 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 1545989148.741 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 1545989148.741 * [misc]taylor: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in n 1545989148.741 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in n 1545989148.741 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in n 1545989148.741 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1545989148.741 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989148.741 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989148.741 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.741 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989148.741 * [misc]taylor: Taking taylor expansion of k in n 1545989148.741 * [misc]backup-simplify: Simplify k into k 1545989148.741 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989148.741 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989148.741 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.741 * [misc]taylor: Taking taylor expansion of (log PI) in n 1545989148.741 * [misc]taylor: Taking taylor expansion of PI in n 1545989148.741 * [misc]backup-simplify: Simplify PI into PI 1545989148.742 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1545989148.742 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989148.742 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1545989148.742 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) 1545989148.742 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1545989148.742 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1545989148.742 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1545989148.742 * [misc]taylor: Taking taylor expansion of -1 in n 1545989148.742 * [misc]backup-simplify: Simplify -1 into -1 1545989148.742 * [misc]taylor: Taking taylor expansion of k in n 1545989148.742 * [misc]backup-simplify: Simplify k into k 1545989148.742 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1545989148.742 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1545989148.742 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1545989148.742 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1545989148.743 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 1545989148.743 * [misc]backup-simplify: Simplify (/ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) into (/ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) 1545989148.743 * [misc]taylor: Taking taylor expansion of (/ (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) in k 1545989148.743 * [misc]taylor: Taking taylor expansion of (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in k 1545989148.743 * [misc]taylor: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1545989148.743 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in k 1545989148.743 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in k 1545989148.743 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1545989148.743 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545989148.743 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989148.743 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.743 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989148.743 * [misc]taylor: Taking taylor expansion of k in k 1545989148.743 * [misc]backup-simplify: Simplify 0 into 0 1545989148.743 * [misc]backup-simplify: Simplify 1 into 1 1545989148.743 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989148.743 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989148.743 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.743 * [misc]taylor: Taking taylor expansion of (log (/ -2 n)) in k 1545989148.743 * [misc]taylor: Taking taylor expansion of (/ -2 n) in k 1545989148.743 * [misc]taylor: Taking taylor expansion of -2 in k 1545989148.743 * [misc]backup-simplify: Simplify -2 into -2 1545989148.743 * [misc]taylor: Taking taylor expansion of n in k 1545989148.744 * [misc]backup-simplify: Simplify n into n 1545989148.744 * [misc]backup-simplify: Simplify (/ -2 n) into (/ -2 n) 1545989148.744 * [misc]backup-simplify: Simplify (log (/ -2 n)) into (log (/ -2 n)) 1545989148.744 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545989148.744 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545989148.744 * [misc]backup-simplify: Simplify (* 1/2 (log (/ -2 n))) into (* 1/2 (log (/ -2 n))) 1545989148.744 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) into (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) 1545989148.744 * [misc]taylor: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 1545989148.744 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 1545989148.744 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 1545989148.744 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1545989148.744 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545989148.744 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989148.744 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.744 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989148.744 * [misc]taylor: Taking taylor expansion of k in k 1545989148.744 * [misc]backup-simplify: Simplify 0 into 0 1545989148.744 * [misc]backup-simplify: Simplify 1 into 1 1545989148.744 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989148.744 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989148.744 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.744 * [misc]taylor: Taking taylor expansion of (log PI) in k 1545989148.744 * [misc]taylor: Taking taylor expansion of PI in k 1545989148.744 * [misc]backup-simplify: Simplify PI into PI 1545989148.745 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1545989148.745 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545989148.745 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545989148.745 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1545989148.745 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1545989148.745 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1545989148.745 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1545989148.745 * [misc]taylor: Taking taylor expansion of -1 in k 1545989148.745 * [misc]backup-simplify: Simplify -1 into -1 1545989148.745 * [misc]taylor: Taking taylor expansion of k in k 1545989148.745 * [misc]backup-simplify: Simplify 0 into 0 1545989148.745 * [misc]backup-simplify: Simplify 1 into 1 1545989148.745 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1545989148.746 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545989148.746 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1545989148.746 * [misc]backup-simplify: Simplify (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 1545989148.746 * [misc]backup-simplify: Simplify (/ (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) +nan.0) into (* +nan.0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 1545989148.746 * [misc]taylor: Taking taylor expansion of (/ (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) in k 1545989148.746 * [misc]taylor: Taking taylor expansion of (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in k 1545989148.746 * [misc]taylor: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1545989148.746 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in k 1545989148.746 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in k 1545989148.746 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1545989148.746 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545989148.746 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989148.746 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.746 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989148.746 * [misc]taylor: Taking taylor expansion of k in k 1545989148.746 * [misc]backup-simplify: Simplify 0 into 0 1545989148.746 * [misc]backup-simplify: Simplify 1 into 1 1545989148.747 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989148.747 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989148.747 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.747 * [misc]taylor: Taking taylor expansion of (log (/ -2 n)) in k 1545989148.747 * [misc]taylor: Taking taylor expansion of (/ -2 n) in k 1545989148.747 * [misc]taylor: Taking taylor expansion of -2 in k 1545989148.747 * [misc]backup-simplify: Simplify -2 into -2 1545989148.747 * [misc]taylor: Taking taylor expansion of n in k 1545989148.747 * [misc]backup-simplify: Simplify n into n 1545989148.747 * [misc]backup-simplify: Simplify (/ -2 n) into (/ -2 n) 1545989148.747 * [misc]backup-simplify: Simplify (log (/ -2 n)) into (log (/ -2 n)) 1545989148.747 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545989148.747 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545989148.747 * [misc]backup-simplify: Simplify (* 1/2 (log (/ -2 n))) into (* 1/2 (log (/ -2 n))) 1545989148.747 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) into (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) 1545989148.747 * [misc]taylor: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 1545989148.747 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 1545989148.747 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 1545989148.747 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1545989148.747 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545989148.747 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989148.747 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.747 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989148.747 * [misc]taylor: Taking taylor expansion of k in k 1545989148.747 * [misc]backup-simplify: Simplify 0 into 0 1545989148.747 * [misc]backup-simplify: Simplify 1 into 1 1545989148.748 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989148.748 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989148.748 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.748 * [misc]taylor: Taking taylor expansion of (log PI) in k 1545989148.748 * [misc]taylor: Taking taylor expansion of PI in k 1545989148.748 * [misc]backup-simplify: Simplify PI into PI 1545989148.748 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1545989148.748 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545989148.748 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545989148.749 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1545989148.749 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1545989148.749 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1545989148.749 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1545989148.749 * [misc]taylor: Taking taylor expansion of -1 in k 1545989148.749 * [misc]backup-simplify: Simplify -1 into -1 1545989148.749 * [misc]taylor: Taking taylor expansion of k in k 1545989148.749 * [misc]backup-simplify: Simplify 0 into 0 1545989148.749 * [misc]backup-simplify: Simplify 1 into 1 1545989148.749 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1545989148.750 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1545989148.750 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1545989148.751 * [misc]backup-simplify: Simplify (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 1545989148.751 * [misc]backup-simplify: Simplify (/ (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) +nan.0) into (* +nan.0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 1545989148.751 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1545989148.751 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1545989148.751 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545989148.751 * [misc]taylor: Taking taylor expansion of (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in n 1545989148.751 * [misc]taylor: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1545989148.751 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 1545989148.751 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 1545989148.751 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1545989148.751 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989148.751 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989148.751 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.752 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989148.752 * [misc]taylor: Taking taylor expansion of k in n 1545989148.752 * [misc]backup-simplify: Simplify k into k 1545989148.752 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989148.752 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989148.752 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.752 * [misc]taylor: Taking taylor expansion of (log (/ -2 n)) in n 1545989148.752 * [misc]taylor: Taking taylor expansion of (/ -2 n) in n 1545989148.752 * [misc]taylor: Taking taylor expansion of -2 in n 1545989148.752 * [misc]backup-simplify: Simplify -2 into -2 1545989148.752 * [misc]taylor: Taking taylor expansion of n in n 1545989148.752 * [misc]backup-simplify: Simplify 0 into 0 1545989148.752 * [misc]backup-simplify: Simplify 1 into 1 1545989148.752 * [misc]backup-simplify: Simplify (/ -2 1) into -2 1545989148.752 * [misc]backup-simplify: Simplify (log -2) into (log -2) 1545989148.752 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989148.752 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1545989148.753 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 1545989148.753 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 1545989148.753 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 1545989148.753 * [misc]taylor: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in n 1545989148.753 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in n 1545989148.753 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in n 1545989148.754 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1545989148.754 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989148.754 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989148.754 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.754 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989148.754 * [misc]taylor: Taking taylor expansion of k in n 1545989148.754 * [misc]backup-simplify: Simplify k into k 1545989148.754 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989148.754 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989148.754 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.754 * [misc]taylor: Taking taylor expansion of (log PI) in n 1545989148.754 * [misc]taylor: Taking taylor expansion of PI in n 1545989148.754 * [misc]backup-simplify: Simplify PI into PI 1545989148.754 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1545989148.754 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989148.754 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1545989148.755 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) 1545989148.755 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1545989148.756 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 1545989148.756 * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 1545989148.757 * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 1545989148.757 * [misc]backup-simplify: Simplify (+ (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) 0) (* 0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into 0 1545989148.757 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1545989148.758 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1545989148.759 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 1545989148.759 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) in n 1545989148.759 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1545989148.759 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1545989148.759 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545989148.759 * [misc]taylor: Taking taylor expansion of (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in n 1545989148.759 * [misc]taylor: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1545989148.759 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 1545989148.759 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 1545989148.759 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1545989148.759 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989148.759 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989148.760 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.760 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989148.760 * [misc]taylor: Taking taylor expansion of k in n 1545989148.760 * [misc]backup-simplify: Simplify k into k 1545989148.760 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989148.760 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989148.760 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.760 * [misc]taylor: Taking taylor expansion of (log (/ -2 n)) in n 1545989148.760 * [misc]taylor: Taking taylor expansion of (/ -2 n) in n 1545989148.760 * [misc]taylor: Taking taylor expansion of -2 in n 1545989148.760 * [misc]backup-simplify: Simplify -2 into -2 1545989148.760 * [misc]taylor: Taking taylor expansion of n in n 1545989148.760 * [misc]backup-simplify: Simplify 0 into 0 1545989148.760 * [misc]backup-simplify: Simplify 1 into 1 1545989148.760 * [misc]backup-simplify: Simplify (/ -2 1) into -2 1545989148.760 * [misc]backup-simplify: Simplify (log -2) into (log -2) 1545989148.760 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989148.760 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1545989148.761 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 1545989148.761 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 1545989148.761 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 1545989148.761 * [misc]taylor: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in n 1545989148.762 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in n 1545989148.762 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in n 1545989148.762 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1545989148.762 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989148.762 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989148.762 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.762 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989148.762 * [misc]taylor: Taking taylor expansion of k in n 1545989148.762 * [misc]backup-simplify: Simplify k into k 1545989148.762 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989148.762 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989148.762 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.762 * [misc]taylor: Taking taylor expansion of (log PI) in n 1545989148.762 * [misc]taylor: Taking taylor expansion of PI in n 1545989148.762 * [misc]backup-simplify: Simplify PI into PI 1545989148.762 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1545989148.762 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989148.762 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1545989148.763 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) 1545989148.763 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1545989148.764 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 1545989148.765 * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 1545989148.766 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 1545989148.766 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 1545989148.769 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 1545989148.769 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1545989148.769 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1545989148.769 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989148.770 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (log PI))) into 0 1545989148.771 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 1545989148.771 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -2 (/ 0 1)))) into 0 1545989148.774 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -2 1)))) 1) into 0 1545989148.774 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1545989148.774 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1545989148.774 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989148.775 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 1545989148.775 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log -2) (log n)))) into 0 1545989148.776 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1545989148.777 * [misc]backup-simplify: Simplify (+ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 0) (* 0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into 0 1545989148.777 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into 0 1545989148.777 * [misc]backup-simplify: Simplify 0 into 0 1545989148.778 * [misc]backup-simplify: Simplify (+ (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (* 0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into 0 1545989148.778 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989148.779 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1545989148.780 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 1545989148.780 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) in n 1545989148.780 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1545989148.780 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1545989148.780 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1545989148.780 * [misc]taylor: Taking taylor expansion of (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in n 1545989148.780 * [misc]taylor: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1545989148.780 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 1545989148.780 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 1545989148.780 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1545989148.780 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989148.780 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989148.780 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.780 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989148.780 * [misc]taylor: Taking taylor expansion of k in n 1545989148.780 * [misc]backup-simplify: Simplify k into k 1545989148.780 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989148.780 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989148.781 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.781 * [misc]taylor: Taking taylor expansion of (log (/ -2 n)) in n 1545989148.781 * [misc]taylor: Taking taylor expansion of (/ -2 n) in n 1545989148.781 * [misc]taylor: Taking taylor expansion of -2 in n 1545989148.781 * [misc]backup-simplify: Simplify -2 into -2 1545989148.781 * [misc]taylor: Taking taylor expansion of n in n 1545989148.781 * [misc]backup-simplify: Simplify 0 into 0 1545989148.781 * [misc]backup-simplify: Simplify 1 into 1 1545989148.781 * [misc]backup-simplify: Simplify (/ -2 1) into -2 1545989148.781 * [misc]backup-simplify: Simplify (log -2) into (log -2) 1545989148.781 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989148.781 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1545989148.781 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 1545989148.781 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 1545989148.782 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 1545989148.782 * [misc]taylor: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in n 1545989148.782 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in n 1545989148.782 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in n 1545989148.782 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1545989148.782 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1545989148.782 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989148.782 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.782 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1545989148.782 * [misc]taylor: Taking taylor expansion of k in n 1545989148.782 * [misc]backup-simplify: Simplify k into k 1545989148.782 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1545989148.782 * [misc]taylor: Taking taylor expansion of 1/2 in n 1545989148.782 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.782 * [misc]taylor: Taking taylor expansion of (log PI) in n 1545989148.782 * [misc]taylor: Taking taylor expansion of PI in n 1545989148.782 * [misc]backup-simplify: Simplify PI into PI 1545989148.782 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1545989148.782 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1545989148.782 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1545989148.782 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) 1545989148.783 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1545989148.783 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 1545989148.783 * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 1545989148.783 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 1545989148.784 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 1545989148.785 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -2) (log (/ 1 (- n)))))) (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -2) (log (/ 1 (- n)))))) (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))))) (* 1 (/ 1 (- k)))) (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -2) (log (/ 1 (- n)))))) (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)))))) into (- (+ (* +nan.0 (* (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (pow PI (- 1/2 (* 1/2 k))))) (- (+ (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (pow PI (- 1/2 (* 1/2 k)))) k)) (- (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (pow PI (- 1/2 (* 1/2 k)))) (pow k 2)))))))) 1545989148.785 * * * * [misc]progress: [ 4 / 4 ] generating series at (2 1 1) 1545989148.785 * [misc]backup-simplify: Simplify (* (log PI) (- 1/2 (/ k 2))) into (* (- 1/2 (* 1/2 k)) (log PI)) 1545989148.785 * [misc]approximate: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in (k) around 0 1545989148.785 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 1545989148.785 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1545989148.785 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989148.785 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.785 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1545989148.785 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989148.785 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.785 * [misc]taylor: Taking taylor expansion of k in k 1545989148.785 * [misc]backup-simplify: Simplify 0 into 0 1545989148.785 * [misc]backup-simplify: Simplify 1 into 1 1545989148.786 * [misc]taylor: Taking taylor expansion of (log PI) in k 1545989148.786 * [misc]taylor: Taking taylor expansion of PI in k 1545989148.786 * [misc]backup-simplify: Simplify PI into PI 1545989148.786 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1545989148.786 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 1545989148.786 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1545989148.786 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989148.786 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.786 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1545989148.786 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989148.786 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.786 * [misc]taylor: Taking taylor expansion of k in k 1545989148.786 * [misc]backup-simplify: Simplify 0 into 0 1545989148.786 * [misc]backup-simplify: Simplify 1 into 1 1545989148.786 * [misc]taylor: Taking taylor expansion of (log PI) in k 1545989148.786 * [misc]taylor: Taking taylor expansion of PI in k 1545989148.786 * [misc]backup-simplify: Simplify PI into PI 1545989148.786 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1545989148.786 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1545989148.786 * [misc]backup-simplify: Simplify (- 0) into 0 1545989148.786 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545989148.787 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1545989148.787 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1545989148.788 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 1545989148.789 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1545989148.789 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1545989148.789 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1545989148.789 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (log PI))) into (- (* 1/2 (log PI))) 1545989148.790 * [misc]backup-simplify: Simplify (- (* 1/2 (log PI))) into (- (* 1/2 (log PI))) 1545989148.792 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 1545989148.792 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1545989148.793 * [misc]backup-simplify: Simplify (- 0) into 0 1545989148.793 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989148.793 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log PI)))) into 0 1545989148.793 * [misc]backup-simplify: Simplify 0 into 0 1545989148.797 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0 1545989148.798 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1545989148.798 * [misc]backup-simplify: Simplify (- 0) into 0 1545989148.798 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989148.799 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log PI))))) into 0 1545989148.799 * [misc]backup-simplify: Simplify 0 into 0 1545989148.806 * [misc]backup-simplify: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow PI 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow PI 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow PI 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow PI 1)))) 24) into 0 1545989148.806 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))) into 0 1545989148.806 * [misc]backup-simplify: Simplify (- 0) into 0 1545989148.806 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989148.808 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log PI)))))) into 0 1545989148.808 * [misc]backup-simplify: Simplify 0 into 0 1545989148.827 * [misc]backup-simplify: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow PI 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow PI 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow PI 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow PI 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow PI 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow PI 1)))) 120) into 0 1545989148.828 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))))) into 0 1545989148.828 * [misc]backup-simplify: Simplify (- 0) into 0 1545989148.828 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989148.831 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log PI))))))) into 0 1545989148.831 * [misc]backup-simplify: Simplify 0 into 0 1545989148.846 * [misc]backup-simplify: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow PI 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow PI 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow PI 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow PI 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow PI 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow PI 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow PI 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow PI 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow PI 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow PI 1)))) 720) into 0 1545989148.847 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))))) into 0 1545989148.847 * [misc]backup-simplify: Simplify (- 0) into 0 1545989148.847 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989148.849 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log PI)))))))) into 0 1545989148.849 * [misc]backup-simplify: Simplify 0 into 0 1545989148.872 * [misc]backup-simplify: Simplify (/ (+ (* 720 (/ (* (pow (* 1 0) 7)) (pow PI 7))) (* -2520 (/ (* (pow (* 1 0) 5) (pow (* 2 0) 1)) (pow PI 6))) (* 2520 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 2)) (pow PI 5))) (* 840 (/ (* (pow (* 1 0) 4) 1 (pow (* 6 0) 1)) (pow PI 5))) (* -630 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 3)) (pow PI 4))) (* -1260 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow PI 4))) (* -210 (/ (* (pow (* 1 0) 3) 1 1 (pow (* 24 0) 1)) (pow PI 4))) (* 210 (/ (* 1 (pow (* 2 0) 2) (pow (* 6 0) 1)) (pow PI 3))) (* 140 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 2)) (pow PI 3))) (* 210 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow PI 3))) (* 42 (/ (* (pow (* 1 0) 2) 1 1 1 (pow (* 120 0) 1)) (pow PI 3))) (* -35 (/ (* 1 1 (pow (* 6 0) 1) (pow (* 24 0) 1)) (pow PI 2))) (* -21 (/ (* 1 (pow (* 2 0) 1) 1 1 (pow (* 120 0) 1)) (pow PI 2))) (* -7 (/ (* (pow (* 1 0) 1) 1 1 1 1 (pow (* 720 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 1 1 1 1 (pow (* 5040 0) 1)) (pow PI 1)))) 5040) into 0 1545989148.873 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))))))) into 0 1545989148.873 * [misc]backup-simplify: Simplify (- 0) into 0 1545989148.873 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989148.875 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log PI))))))))) into 0 1545989148.875 * [misc]backup-simplify: Simplify 0 into 0 1545989148.877 * [misc]backup-simplify: Simplify (+ (* (- (* 1/2 (log PI))) k) (* 1/2 (log PI))) into (- (* 1/2 (log PI)) (* 1/2 (* (log PI) k))) 1545989148.877 * [misc]backup-simplify: Simplify (* (log PI) (- 1/2 (/ (/ 1 k) 2))) into (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) 1545989148.877 * [misc]approximate: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in (k) around 0 1545989148.878 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 1545989148.878 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1545989148.878 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989148.878 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.878 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545989148.878 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989148.878 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.878 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989148.878 * [misc]taylor: Taking taylor expansion of k in k 1545989148.878 * [misc]backup-simplify: Simplify 0 into 0 1545989148.878 * [misc]backup-simplify: Simplify 1 into 1 1545989148.878 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989148.878 * [misc]taylor: Taking taylor expansion of (log PI) in k 1545989148.878 * [misc]taylor: Taking taylor expansion of PI in k 1545989148.878 * [misc]backup-simplify: Simplify PI into PI 1545989148.878 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1545989148.878 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 1545989148.878 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1545989148.878 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989148.878 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.878 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545989148.878 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989148.878 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.878 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989148.879 * [misc]taylor: Taking taylor expansion of k in k 1545989148.879 * [misc]backup-simplify: Simplify 0 into 0 1545989148.879 * [misc]backup-simplify: Simplify 1 into 1 1545989148.879 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989148.879 * [misc]taylor: Taking taylor expansion of (log PI) in k 1545989148.879 * [misc]taylor: Taking taylor expansion of PI in k 1545989148.879 * [misc]backup-simplify: Simplify PI into PI 1545989148.879 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1545989148.879 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545989148.880 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1545989148.880 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1545989148.880 * [misc]backup-simplify: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 1545989148.881 * [misc]backup-simplify: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 1545989148.883 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 1545989148.883 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1545989148.884 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 1)) into 0 1545989148.884 * [misc]backup-simplify: Simplify (- 0) into 0 1545989148.884 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545989148.884 * [misc]backup-simplify: Simplify (+ (* -1/2 0) (* 1/2 (log PI))) into (* 1/2 (log PI)) 1545989148.885 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1545989148.887 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 1545989148.887 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989148.888 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 1))) into 0 1545989148.888 * [misc]backup-simplify: Simplify (- 0) into 0 1545989148.888 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989148.888 * [misc]backup-simplify: Simplify (+ (* -1/2 0) (+ (* 1/2 0) (* 0 (log PI)))) into 0 1545989148.889 * [misc]backup-simplify: Simplify 0 into 0 1545989148.893 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0 1545989148.893 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989148.893 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 1545989148.893 * [misc]backup-simplify: Simplify (- 0) into 0 1545989148.893 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989148.894 * [misc]backup-simplify: Simplify (+ (* -1/2 0) (+ (* 1/2 0) (+ (* 0 0) (* 0 (log PI))))) into 0 1545989148.894 * [misc]backup-simplify: Simplify 0 into 0 1545989148.901 * [misc]backup-simplify: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow PI 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow PI 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow PI 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow PI 1)))) 24) into 0 1545989148.901 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989148.902 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 1545989148.902 * [misc]backup-simplify: Simplify (- 0) into 0 1545989148.902 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989148.903 * [misc]backup-simplify: Simplify (+ (* -1/2 0) (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log PI)))))) into 0 1545989148.903 * [misc]backup-simplify: Simplify 0 into 0 1545989148.915 * [misc]backup-simplify: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow PI 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow PI 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow PI 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow PI 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow PI 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow PI 1)))) 120) into 0 1545989148.916 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989148.917 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))))) into 0 1545989148.917 * [misc]backup-simplify: Simplify (- 0) into 0 1545989148.917 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989148.920 * [misc]backup-simplify: Simplify (+ (* -1/2 0) (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log PI))))))) into 0 1545989148.920 * [misc]backup-simplify: Simplify 0 into 0 1545989148.942 * [misc]backup-simplify: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow PI 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow PI 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow PI 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow PI 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow PI 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow PI 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow PI 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow PI 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow PI 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow PI 1)))) 720) into 0 1545989148.942 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989148.943 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))))) into 0 1545989148.943 * [misc]backup-simplify: Simplify (- 0) into 0 1545989148.943 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989148.945 * [misc]backup-simplify: Simplify (+ (* -1/2 0) (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log PI)))))))) into 0 1545989148.945 * [misc]backup-simplify: Simplify 0 into 0 1545989148.971 * [misc]backup-simplify: Simplify (/ (+ (* 720 (/ (* (pow (* 1 0) 7)) (pow PI 7))) (* -2520 (/ (* (pow (* 1 0) 5) (pow (* 2 0) 1)) (pow PI 6))) (* 2520 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 2)) (pow PI 5))) (* 840 (/ (* (pow (* 1 0) 4) 1 (pow (* 6 0) 1)) (pow PI 5))) (* -630 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 3)) (pow PI 4))) (* -1260 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow PI 4))) (* -210 (/ (* (pow (* 1 0) 3) 1 1 (pow (* 24 0) 1)) (pow PI 4))) (* 210 (/ (* 1 (pow (* 2 0) 2) (pow (* 6 0) 1)) (pow PI 3))) (* 140 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 2)) (pow PI 3))) (* 210 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow PI 3))) (* 42 (/ (* (pow (* 1 0) 2) 1 1 1 (pow (* 120 0) 1)) (pow PI 3))) (* -35 (/ (* 1 1 (pow (* 6 0) 1) (pow (* 24 0) 1)) (pow PI 2))) (* -21 (/ (* 1 (pow (* 2 0) 1) 1 1 (pow (* 120 0) 1)) (pow PI 2))) (* -7 (/ (* (pow (* 1 0) 1) 1 1 1 1 (pow (* 720 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 1 1 1 1 (pow (* 5040 0) 1)) (pow PI 1)))) 5040) into 0 1545989148.971 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989148.972 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))))))) into 0 1545989148.972 * [misc]backup-simplify: Simplify (- 0) into 0 1545989148.972 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989148.974 * [misc]backup-simplify: Simplify (+ (* -1/2 0) (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log PI))))))))) into 0 1545989148.974 * [misc]backup-simplify: Simplify 0 into 0 1545989148.975 * [misc]backup-simplify: Simplify (+ (* 1/2 (log PI)) (* (* -1/2 (log PI)) (/ 1 (/ 1 k)))) into (- (* 1/2 (log PI)) (* 1/2 (* (log PI) k))) 1545989148.975 * [misc]backup-simplify: Simplify (* (log PI) (- 1/2 (/ (/ 1 (- k)) 2))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) 1545989148.975 * [misc]approximate: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in (k) around 0 1545989148.975 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 1545989148.975 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1545989148.975 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545989148.975 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989148.975 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.976 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989148.976 * [misc]taylor: Taking taylor expansion of k in k 1545989148.976 * [misc]backup-simplify: Simplify 0 into 0 1545989148.976 * [misc]backup-simplify: Simplify 1 into 1 1545989148.976 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989148.976 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989148.976 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.976 * [misc]taylor: Taking taylor expansion of (log PI) in k 1545989148.976 * [misc]taylor: Taking taylor expansion of PI in k 1545989148.976 * [misc]backup-simplify: Simplify PI into PI 1545989148.976 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1545989148.976 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 1545989148.976 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1545989148.976 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1545989148.976 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989148.976 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.976 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1545989148.976 * [misc]taylor: Taking taylor expansion of k in k 1545989148.976 * [misc]backup-simplify: Simplify 0 into 0 1545989148.976 * [misc]backup-simplify: Simplify 1 into 1 1545989148.976 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1545989148.976 * [misc]taylor: Taking taylor expansion of 1/2 in k 1545989148.976 * [misc]backup-simplify: Simplify 1/2 into 1/2 1545989148.976 * [misc]taylor: Taking taylor expansion of (log PI) in k 1545989148.976 * [misc]taylor: Taking taylor expansion of PI in k 1545989148.976 * [misc]backup-simplify: Simplify PI into PI 1545989148.976 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1545989148.977 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1545989148.977 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1545989148.977 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1545989148.977 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1545989148.979 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 1545989148.979 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1545989148.979 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 1)) into 0 1545989148.979 * [misc]backup-simplify: Simplify (+ 0 1/2) into 1/2 1545989148.980 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 1/2 (log PI))) into (* 1/2 (log PI)) 1545989148.980 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1545989148.983 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 1545989148.983 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989148.983 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 1))) into 0 1545989148.983 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989148.984 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 1/2 0) (* 0 (log PI)))) into 0 1545989148.984 * [misc]backup-simplify: Simplify 0 into 0 1545989148.988 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0 1545989148.988 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989148.988 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 1545989148.988 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989148.989 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 1/2 0) (+ (* 0 0) (* 0 (log PI))))) into 0 1545989148.989 * [misc]backup-simplify: Simplify 0 into 0 1545989148.996 * [misc]backup-simplify: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow PI 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow PI 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow PI 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow PI 1)))) 24) into 0 1545989148.996 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989148.997 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 1545989148.997 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989148.998 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log PI)))))) into 0 1545989148.998 * [misc]backup-simplify: Simplify 0 into 0 1545989149.015 * [misc]backup-simplify: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow PI 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow PI 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow PI 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow PI 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow PI 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow PI 1)))) 120) into 0 1545989149.016 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989149.016 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))))) into 0 1545989149.017 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989149.020 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log PI))))))) into 0 1545989149.020 * [misc]backup-simplify: Simplify 0 into 0 1545989149.049 * [misc]backup-simplify: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow PI 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow PI 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow PI 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow PI 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow PI 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow PI 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow PI 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow PI 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow PI 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow PI 1)))) 720) into 0 1545989149.049 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989149.050 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))))) into 0 1545989149.050 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989149.054 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log PI)))))))) into 0 1545989149.054 * [misc]backup-simplify: Simplify 0 into 0 1545989149.095 * [misc]backup-simplify: Simplify (/ (+ (* 720 (/ (* (pow (* 1 0) 7)) (pow PI 7))) (* -2520 (/ (* (pow (* 1 0) 5) (pow (* 2 0) 1)) (pow PI 6))) (* 2520 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 2)) (pow PI 5))) (* 840 (/ (* (pow (* 1 0) 4) 1 (pow (* 6 0) 1)) (pow PI 5))) (* -630 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 3)) (pow PI 4))) (* -1260 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow PI 4))) (* -210 (/ (* (pow (* 1 0) 3) 1 1 (pow (* 24 0) 1)) (pow PI 4))) (* 210 (/ (* 1 (pow (* 2 0) 2) (pow (* 6 0) 1)) (pow PI 3))) (* 140 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 2)) (pow PI 3))) (* 210 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow PI 3))) (* 42 (/ (* (pow (* 1 0) 2) 1 1 1 (pow (* 120 0) 1)) (pow PI 3))) (* -35 (/ (* 1 1 (pow (* 6 0) 1) (pow (* 24 0) 1)) (pow PI 2))) (* -21 (/ (* 1 (pow (* 2 0) 1) 1 1 (pow (* 120 0) 1)) (pow PI 2))) (* -7 (/ (* (pow (* 1 0) 1) 1 1 1 1 (pow (* 720 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 1 1 1 1 (pow (* 5040 0) 1)) (pow PI 1)))) 5040) into 0 1545989149.095 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1545989149.096 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))))))) into 0 1545989149.096 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1545989149.101 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log PI))))))))) into 0 1545989149.101 * [misc]backup-simplify: Simplify 0 into 0 1545989149.103 * [misc]backup-simplify: Simplify (+ (* 1/2 (log PI)) (* (* 1/2 (log PI)) (/ 1 (/ 1 (- k))))) into (- (* 1/2 (log PI)) (* 1/2 (* (log PI) k))) 1545989149.103 * * * [misc]progress: simplifying candidates 1545989149.103 * * * * [misc]progress: [ 1 / 139 ] simplifiying candidate # 1545989149.103 * [enter]simplify: Simplifying (* (log (* n 2)) (- 1/2 (/ k 2))) 1545989149.103 * * [misc]simplify: iters left: 6 (9 enodes) 1545989149.107 * * [misc]simplify: iters left: 5 (16 enodes) 1545989149.113 * * [misc]simplify: iters left: 4 (32 enodes) 1545989149.122 * * [misc]simplify: iters left: 3 (68 enodes) 1545989149.137 * * [misc]simplify: iters left: 2 (171 enodes) 1545989149.185 * * [misc]simplify: iters left: 1 (342 enodes) 1545989149.287 * [exit]simplify: Simplified to (* (log (* n 2)) (- 1/2 (/ k 2))) 1545989149.287 * [misc]simplify: Simplified (2 2 1 1) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (/ (exp (* (log (* n 2)) (- 1/2 (/ k 2)))) (sqrt k)))) 1545989149.287 * * * * [misc]progress: [ 2 / 139 ] simplifiying candidate # 1545989149.287 * * * * [misc]progress: [ 3 / 139 ] simplifiying candidate # 1545989149.287 * [enter]simplify: Simplifying (* n 2) 1545989149.287 * * [misc]simplify: iters left: 2 (3 enodes) 1545989149.288 * * [misc]simplify: iters left: 1 (4 enodes) 1545989149.288 * [exit]simplify: Simplified to (* n 2) 1545989149.288 * [misc]simplify: Simplified (2 2 1 1) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (/ (pow (* n 2) (* 1 (- 1/2 (/ k 2)))) (sqrt k)))) 1545989149.288 * * * * [misc]progress: [ 4 / 139 ] simplifiying candidate # 1545989149.288 * [enter]simplify: Simplifying (pow (* n 2) (/ k 2)) 1545989149.288 * * [misc]simplify: iters left: 3 (6 enodes) 1545989149.289 * * [misc]simplify: iters left: 2 (7 enodes) 1545989149.290 * [exit]simplify: Simplified to (pow (* n 2) (/ k 2)) 1545989149.290 * [misc]simplify: Simplified (2 2 1 2) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (/ (/ (pow (* n 2) 1/2) (pow (* n 2) (/ k 2))) (sqrt k)))) 1545989149.290 * * * * [misc]progress: [ 5 / 139 ] simplifiying candidate # 1545989149.290 * [enter]simplify: Simplifying (cbrt (- 1/2 (/ k 2))) 1545989149.290 * * [misc]simplify: iters left: 5 (6 enodes) 1545989149.291 * * [misc]simplify: iters left: 4 (8 enodes) 1545989149.292 * * [misc]simplify: iters left: 3 (11 enodes) 1545989149.295 * [exit]simplify: Simplified to (cbrt (- 1/2 (/ k 2))) 1545989149.295 * [misc]simplify: Simplified (2 2 1 2) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (/ (pow (pow (* n 2) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))) (sqrt k)))) 1545989149.295 * * * * [misc]progress: [ 6 / 139 ] simplifiying candidate # 1545989149.295 * [enter]simplify: Simplifying (sqrt (- 1/2 (/ k 2))) 1545989149.296 * * [misc]simplify: iters left: 5 (6 enodes) 1545989149.296 * * [misc]simplify: iters left: 4 (8 enodes) 1545989149.297 * * [misc]simplify: iters left: 3 (11 enodes) 1545989149.299 * [exit]simplify: Simplified to (sqrt (- 1/2 (/ k 2))) 1545989149.299 * [misc]simplify: Simplified (2 2 1 2) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (/ (pow (pow (* n 2) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))) (sqrt k)))) 1545989149.299 * * * * [misc]progress: [ 7 / 139 ] simplifiying candidate # 1545989149.299 * [enter]simplify: Simplifying (- 1/2 (/ k 2)) 1545989149.299 * * [misc]simplify: iters left: 4 (5 enodes) 1545989149.300 * * [misc]simplify: iters left: 3 (7 enodes) 1545989149.301 * * [misc]simplify: iters left: 2 (10 enodes) 1545989149.302 * [exit]simplify: Simplified to (- 1/2 (/ k 2)) 1545989149.302 * [misc]simplify: Simplified (2 2 1 2) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (/ (pow (pow (* n 2) 1) (- 1/2 (/ k 2))) (sqrt k)))) 1545989149.302 * * * * [misc]progress: [ 8 / 139 ] simplifiying candidate # 1545989149.302 * [enter]simplify: Simplifying (pow (* n 2) (- (/ k 2))) 1545989149.302 * * [misc]simplify: iters left: 5 (7 enodes) 1545989149.303 * * [misc]simplify: iters left: 4 (10 enodes) 1545989149.305 * [exit]simplify: Simplified to (pow (* n 2) (- (/ k 2))) 1545989149.305 * [misc]simplify: Simplified (2 2 1 2) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (/ (* (pow (* n 2) 1/2) (pow (* n 2) (- (/ k 2)))) (sqrt k)))) 1545989149.305 * * * * [misc]progress: [ 9 / 139 ] simplifiying candidate # 1545989149.305 * [enter]simplify: Simplifying (pow (* n 2) (- (/ k 2))) 1545989149.305 * * [misc]simplify: iters left: 5 (7 enodes) 1545989149.306 * * [misc]simplify: iters left: 4 (10 enodes) 1545989149.307 * [exit]simplify: Simplified to (pow (* n 2) (- (/ k 2))) 1545989149.307 * [misc]simplify: Simplified (2 2 1 2) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (/ (* (pow (* n 2) 1/2) (pow (* n 2) (- (/ k 2)))) (sqrt k)))) 1545989149.307 * * * * [misc]progress: [ 10 / 139 ] simplifiying candidate # 1545989149.307 * [enter]simplify: Simplifying (pow n (- 1/2 (/ k 2))) 1545989149.307 * * [misc]simplify: iters left: 5 (7 enodes) 1545989149.308 * * [misc]simplify: iters left: 4 (9 enodes) 1545989149.309 * * [misc]simplify: iters left: 3 (12 enodes) 1545989149.311 * [exit]simplify: Simplified to (pow n (- 1/2 (/ k 2))) 1545989149.311 * [misc]simplify: Simplified (2 2 1 1) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (/ (* (pow n (- 1/2 (/ k 2))) (pow 2 (- 1/2 (/ k 2)))) (sqrt k)))) 1545989149.311 * * * * [misc]progress: [ 11 / 139 ] simplifiying candidate # 1545989149.311 * * * * [misc]progress: [ 12 / 139 ] simplifiying candidate # 1545989149.311 * * * * [misc]progress: [ 13 / 139 ] simplifiying candidate # 1545989149.311 * * * * [misc]progress: [ 14 / 139 ] simplifiying candidate # 1545989149.311 * * * * [misc]progress: [ 15 / 139 ] simplifiying candidate # 1545989149.311 * * * * [misc]progress: [ 16 / 139 ] simplifiying candidate # 1545989149.311 * * * * [misc]progress: [ 17 / 139 ] simplifiying candidate # 1545989149.311 * * * * [misc]progress: [ 18 / 139 ] simplifiying candidate # 1545989149.311 * * * * [misc]progress: [ 19 / 139 ] simplifiying candidate # 1545989149.311 * [enter]simplify: Simplifying (- (* (log (* n 2)) (- 1/2 (/ k 2))) (log (sqrt k))) 1545989149.312 * * [misc]simplify: iters left: 6 (12 enodes) 1545989149.314 * * [misc]simplify: iters left: 5 (21 enodes) 1545989149.317 * * [misc]simplify: iters left: 4 (38 enodes) 1545989149.325 * * [misc]simplify: iters left: 3 (98 enodes) 1545989149.357 * * [misc]simplify: iters left: 2 (325 enodes) 1545989149.563 * [exit]simplify: Simplified to (- (* (log (* n 2)) (- 1/2 (/ k 2))) (log (sqrt k))) 1545989149.563 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (exp (- (* (log (* n 2)) (- 1/2 (/ k 2))) (log (sqrt k)))))) 1545989149.563 * * * * [misc]progress: [ 20 / 139 ] simplifiying candidate # 1545989149.563 * [enter]simplify: Simplifying (- (* (log (* n 2)) (- 1/2 (/ k 2))) (log (sqrt k))) 1545989149.563 * * [misc]simplify: iters left: 6 (12 enodes) 1545989149.568 * * [misc]simplify: iters left: 5 (21 enodes) 1545989149.574 * * [misc]simplify: iters left: 4 (38 enodes) 1545989149.588 * * [misc]simplify: iters left: 3 (98 enodes) 1545989149.627 * * [misc]simplify: iters left: 2 (325 enodes) 1545989149.804 * [exit]simplify: Simplified to (- (* (log (* n 2)) (- 1/2 (/ k 2))) (log (sqrt k))) 1545989149.804 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (exp (- (* (log (* n 2)) (- 1/2 (/ k 2))) (log (sqrt k)))))) 1545989149.804 * * * * [misc]progress: [ 21 / 139 ] simplifiying candidate # 1545989149.804 * [enter]simplify: Simplifying (- (log (pow (* n 2) (- 1/2 (/ k 2)))) (log (sqrt k))) 1545989149.804 * * [misc]simplify: iters left: 6 (12 enodes) 1545989149.807 * * [misc]simplify: iters left: 5 (19 enodes) 1545989149.818 * * [misc]simplify: iters left: 4 (28 enodes) 1545989149.826 * * [misc]simplify: iters left: 3 (44 enodes) 1545989149.845 * * [misc]simplify: iters left: 2 (124 enodes) 1545989149.926 * * [misc]simplify: iters left: 1 (453 enodes) 1545989150.209 * [exit]simplify: Simplified to (- (* (log (* n 2)) (- 1/2 (/ k 2))) (log (sqrt k))) 1545989150.209 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (exp (- (* (log (* n 2)) (- 1/2 (/ k 2))) (log (sqrt k)))))) 1545989150.209 * * * * [misc]progress: [ 22 / 139 ] simplifiying candidate # 1545989150.210 * * * * [misc]progress: [ 23 / 139 ] simplifiying candidate # 1545989150.210 * * * * [misc]progress: [ 24 / 139 ] simplifiying candidate # 1545989150.210 * [enter]simplify: Simplifying (/ (* (* (pow (* n 2) (- 1/2 (/ k 2))) (pow (* n 2) (- 1/2 (/ k 2)))) (pow (* n 2) (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k))) 1545989150.210 * * [misc]simplify: iters left: 6 (14 enodes) 1545989150.214 * * [misc]simplify: iters left: 5 (26 enodes) 1545989150.221 * * [misc]simplify: iters left: 4 (57 enodes) 1545989150.239 * * [misc]simplify: iters left: 3 (112 enodes) 1545989150.262 * * [misc]simplify: iters left: 2 (189 enodes) 1545989150.334 * * [misc]simplify: iters left: 1 (316 enodes) 1545989150.532 * [exit]simplify: Simplified to (* (/ (pow (* n 2) (- 1/2 (/ k 2))) (* k (sqrt k))) (* (pow (* n 2) (- 1/2 (/ k 2))) (pow (* n 2) (- 1/2 (/ k 2))))) 1545989150.532 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (cbrt (* (/ (pow (* n 2) (- 1/2 (/ k 2))) (* k (sqrt k))) (* (pow (* n 2) (- 1/2 (/ k 2))) (pow (* n 2) (- 1/2 (/ k 2)))))))) 1545989150.533 * * * * [misc]progress: [ 25 / 139 ] simplifiying candidate # 1545989150.533 * * * * [misc]progress: [ 26 / 139 ] simplifiying candidate # 1545989150.533 * * * * [misc]progress: [ 27 / 139 ] simplifiying candidate # 1545989150.533 * * * * [misc]progress: [ 28 / 139 ] simplifiying candidate # 1545989150.533 * * * * [misc]progress: [ 29 / 139 ] simplifiying candidate # 1545989150.533 * [enter]simplify: Simplifying (/ (pow (* n 2) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1545989150.533 * * [misc]simplify: iters left: 6 (10 enodes) 1545989150.536 * * [misc]simplify: iters left: 5 (14 enodes) 1545989150.540 * [exit]simplify: Simplified to (/ (sqrt (* n 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1545989150.540 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (* (/ (sqrt (* n 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n 2) (- (/ k 2))) (cbrt (sqrt k)))))) 1545989150.540 * [enter]simplify: Simplifying (/ (pow (* n 2) (- (/ k 2))) (cbrt (sqrt k))) 1545989150.540 * * [misc]simplify: iters left: 6 (10 enodes) 1545989150.543 * * [misc]simplify: iters left: 5 (13 enodes) 1545989150.546 * [exit]simplify: Simplified to (/ (pow (* n 2) (/ (- k) 2)) (cbrt (sqrt k))) 1545989150.547 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (* (/ (sqrt (* n 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n 2) (/ (- k) 2)) (cbrt (sqrt k)))))) 1545989150.547 * * * * [misc]progress: [ 30 / 139 ] simplifiying candidate # 1545989150.547 * [enter]simplify: Simplifying (/ (pow (* n 2) 1/2) (sqrt (sqrt k))) 1545989150.547 * * [misc]simplify: iters left: 5 (9 enodes) 1545989150.550 * * [misc]simplify: iters left: 4 (11 enodes) 1545989150.552 * [exit]simplify: Simplified to (/ (sqrt (* n 2)) (sqrt (sqrt k))) 1545989150.552 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (* (/ (sqrt (* n 2)) (sqrt (sqrt k))) (/ (pow (* n 2) (- (/ k 2))) (sqrt (sqrt k)))))) 1545989150.553 * [enter]simplify: Simplifying (/ (pow (* n 2) (- (/ k 2))) (sqrt (sqrt k))) 1545989150.553 * * [misc]simplify: iters left: 6 (10 enodes) 1545989150.556 * * [misc]simplify: iters left: 5 (13 enodes) 1545989150.559 * [exit]simplify: Simplified to (/ (pow (* n 2) (/ (- k) 2)) (sqrt (sqrt k))) 1545989150.559 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (* (/ (sqrt (* n 2)) (sqrt (sqrt k))) (/ (pow (* n 2) (/ (- k) 2)) (sqrt (sqrt k)))))) 1545989150.559 * * * * [misc]progress: [ 31 / 139 ] simplifiying candidate # 1545989150.560 * [enter]simplify: Simplifying (/ (pow (* n 2) 1/2) 1) 1545989150.560 * * [misc]simplify: iters left: 5 (7 enodes) 1545989150.563 * * [misc]simplify: iters left: 4 (11 enodes) 1545989150.567 * * [misc]simplify: iters left: 3 (13 enodes) 1545989150.569 * [exit]simplify: Simplified to (sqrt (* n 2)) 1545989150.570 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (* (sqrt (* n 2)) (/ (pow (* n 2) (- (/ k 2))) (sqrt k))))) 1545989150.570 * [enter]simplify: Simplifying (/ (pow (* n 2) (- (/ k 2))) (sqrt k)) 1545989150.570 * * [misc]simplify: iters left: 6 (9 enodes) 1545989150.573 * * [misc]simplify: iters left: 5 (12 enodes) 1545989150.577 * [exit]simplify: Simplified to (/ (pow (* n 2) (- (/ k 2))) (sqrt k)) 1545989150.577 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (* (sqrt (* n 2)) (/ (pow (* n 2) (- (/ k 2))) (sqrt k))))) 1545989150.577 * * * * [misc]progress: [ 32 / 139 ] simplifiying candidate # 1545989150.577 * [enter]simplify: Simplifying (/ (pow (* n 2) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1545989150.577 * * [misc]simplify: iters left: 6 (10 enodes) 1545989150.580 * * [misc]simplify: iters left: 5 (14 enodes) 1545989150.584 * [exit]simplify: Simplified to (/ (sqrt (* n 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1545989150.584 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (* (/ (sqrt (* n 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n 2) (- (/ k 2))) (cbrt (sqrt k)))))) 1545989150.584 * [enter]simplify: Simplifying (/ (pow (* n 2) (- (/ k 2))) (cbrt (sqrt k))) 1545989150.584 * * [misc]simplify: iters left: 6 (10 enodes) 1545989150.587 * * [misc]simplify: iters left: 5 (13 enodes) 1545989150.590 * [exit]simplify: Simplified to (/ (pow (* n 2) (/ (- k) 2)) (cbrt (sqrt k))) 1545989150.590 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (* (/ (sqrt (* n 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n 2) (/ (- k) 2)) (cbrt (sqrt k)))))) 1545989150.590 * * * * [misc]progress: [ 33 / 139 ] simplifiying candidate # 1545989150.591 * [enter]simplify: Simplifying (/ (pow (* n 2) 1/2) (sqrt (sqrt k))) 1545989150.591 * * [misc]simplify: iters left: 5 (9 enodes) 1545989150.593 * * [misc]simplify: iters left: 4 (11 enodes) 1545989150.596 * [exit]simplify: Simplified to (/ (sqrt (* n 2)) (sqrt (sqrt k))) 1545989150.596 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (* (/ (sqrt (* n 2)) (sqrt (sqrt k))) (/ (pow (* n 2) (- (/ k 2))) (sqrt (sqrt k)))))) 1545989150.596 * [enter]simplify: Simplifying (/ (pow (* n 2) (- (/ k 2))) (sqrt (sqrt k))) 1545989150.596 * * [misc]simplify: iters left: 6 (10 enodes) 1545989150.599 * * [misc]simplify: iters left: 5 (13 enodes) 1545989150.603 * [exit]simplify: Simplified to (/ (pow (* n 2) (/ (- k) 2)) (sqrt (sqrt k))) 1545989150.603 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (* (/ (sqrt (* n 2)) (sqrt (sqrt k))) (/ (pow (* n 2) (/ (- k) 2)) (sqrt (sqrt k)))))) 1545989150.603 * * * * [misc]progress: [ 34 / 139 ] simplifiying candidate # 1545989150.603 * [enter]simplify: Simplifying (/ (pow (* n 2) 1/2) 1) 1545989150.604 * * [misc]simplify: iters left: 5 (7 enodes) 1545989150.606 * * [misc]simplify: iters left: 4 (11 enodes) 1545989150.609 * * [misc]simplify: iters left: 3 (13 enodes) 1545989150.611 * [exit]simplify: Simplified to (sqrt (* n 2)) 1545989150.611 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (* (sqrt (* n 2)) (/ (pow (* n 2) (- (/ k 2))) (sqrt k))))) 1545989150.612 * [enter]simplify: Simplifying (/ (pow (* n 2) (- (/ k 2))) (sqrt k)) 1545989150.612 * * [misc]simplify: iters left: 6 (9 enodes) 1545989150.614 * * [misc]simplify: iters left: 5 (12 enodes) 1545989150.618 * [exit]simplify: Simplified to (/ (pow (* n 2) (- (/ k 2))) (sqrt k)) 1545989150.618 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (* (sqrt (* n 2)) (/ (pow (* n 2) (- (/ k 2))) (sqrt k))))) 1545989150.618 * * * * [misc]progress: [ 35 / 139 ] simplifiying candidate # 1545989150.618 * [enter]simplify: Simplifying (/ (pow n (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1545989150.618 * * [misc]simplify: iters left: 6 (11 enodes) 1545989150.621 * * [misc]simplify: iters left: 5 (15 enodes) 1545989150.626 * * [misc]simplify: iters left: 4 (18 enodes) 1545989150.631 * [exit]simplify: Simplified to (/ (pow n (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1545989150.631 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (* (/ (pow n (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow 2 (- 1/2 (/ k 2))) (cbrt (sqrt k)))))) 1545989150.631 * [enter]simplify: Simplifying (/ (pow 2 (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1545989150.631 * * [misc]simplify: iters left: 6 (9 enodes) 1545989150.634 * * [misc]simplify: iters left: 5 (11 enodes) 1545989150.636 * * [misc]simplify: iters left: 4 (14 enodes) 1545989150.638 * [exit]simplify: Simplified to (/ (pow 2 (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1545989150.638 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (* (/ (pow n (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow 2 (- 1/2 (/ k 2))) (cbrt (sqrt k)))))) 1545989150.638 * * * * [misc]progress: [ 36 / 139 ] simplifiying candidate # 1545989150.638 * [enter]simplify: Simplifying (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1545989150.638 * * [misc]simplify: iters left: 6 (10 enodes) 1545989150.640 * * [misc]simplify: iters left: 5 (12 enodes) 1545989150.641 * * [misc]simplify: iters left: 4 (15 enodes) 1545989150.643 * [exit]simplify: Simplified to (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1545989150.643 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (* (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow 2 (- 1/2 (/ k 2))) (sqrt (sqrt k)))))) 1545989150.643 * [enter]simplify: Simplifying (/ (pow 2 (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1545989150.643 * * [misc]simplify: iters left: 6 (9 enodes) 1545989150.645 * * [misc]simplify: iters left: 5 (11 enodes) 1545989150.646 * * [misc]simplify: iters left: 4 (14 enodes) 1545989150.648 * [exit]simplify: Simplified to (/ (pow 2 (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1545989150.648 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (* (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow 2 (- 1/2 (/ k 2))) (sqrt (sqrt k)))))) 1545989150.648 * * * * [misc]progress: [ 37 / 139 ] simplifiying candidate # 1545989150.648 * [enter]simplify: Simplifying (/ (pow n (- 1/2 (/ k 2))) 1) 1545989150.648 * * [misc]simplify: iters left: 6 (9 enodes) 1545989150.650 * * [misc]simplify: iters left: 5 (13 enodes) 1545989150.652 * * [misc]simplify: iters left: 4 (18 enodes) 1545989150.654 * [exit]simplify: Simplified to (pow n (- 1/2 (/ k 2))) 1545989150.654 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (* (pow n (- 1/2 (/ k 2))) (/ (pow 2 (- 1/2 (/ k 2))) (sqrt k))))) 1545989150.654 * [enter]simplify: Simplifying (/ (pow 2 (- 1/2 (/ k 2))) (sqrt k)) 1545989150.654 * * [misc]simplify: iters left: 6 (8 enodes) 1545989150.655 * * [misc]simplify: iters left: 5 (10 enodes) 1545989150.656 * * [misc]simplify: iters left: 4 (13 enodes) 1545989150.658 * [exit]simplify: Simplified to (/ (pow 2 (- 1/2 (/ k 2))) (sqrt k)) 1545989150.658 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (* (pow n (- 1/2 (/ k 2))) (/ (pow 2 (- 1/2 (/ k 2))) (sqrt k))))) 1545989150.658 * * * * [misc]progress: [ 38 / 139 ] simplifiying candidate # 1545989150.658 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (pow (* n 2) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1545989150.658 * * [misc]simplify: iters left: 6 (14 enodes) 1545989150.660 * * [misc]simplify: iters left: 5 (23 enodes) 1545989150.664 * * [misc]simplify: iters left: 4 (35 enodes) 1545989150.670 * * [misc]simplify: iters left: 3 (38 enodes) 1545989150.681 * * [misc]simplify: iters left: 2 (41 enodes) 1545989150.691 * [exit]simplify: Simplified to (* (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))) 1545989150.691 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (* (* (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))) (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))) 1545989150.692 * [enter]simplify: Simplifying (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1545989150.692 * * [misc]simplify: iters left: 6 (12 enodes) 1545989150.695 * * [misc]simplify: iters left: 5 (15 enodes) 1545989150.700 * * [misc]simplify: iters left: 4 (18 enodes) 1545989150.704 * [exit]simplify: Simplified to (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1545989150.704 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (* (/ (* (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (pow (* n 2) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))) 1545989150.704 * * * * [misc]progress: [ 39 / 139 ] simplifiying candidate # 1545989150.705 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (pow (* n 2) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) 1545989150.705 * * [misc]simplify: iters left: 6 (13 enodes) 1545989150.709 * * [misc]simplify: iters left: 5 (18 enodes) 1545989150.714 * * [misc]simplify: iters left: 4 (23 enodes) 1545989150.720 * * [misc]simplify: iters left: 3 (24 enodes) 1545989150.727 * [exit]simplify: Simplified to (* (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (cbrt (pow (* n 2) (- 1/2 (/ k 2))))) 1545989150.727 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (* (* (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (cbrt (pow (* n 2) (- 1/2 (/ k 2))))) (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))) 1545989150.727 * [enter]simplify: Simplifying (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1545989150.727 * * [misc]simplify: iters left: 6 (12 enodes) 1545989150.730 * * [misc]simplify: iters left: 5 (15 enodes) 1545989150.735 * * [misc]simplify: iters left: 4 (18 enodes) 1545989150.739 * [exit]simplify: Simplified to (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1545989150.740 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (* (/ (* (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (pow (* n 2) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))) 1545989150.740 * * * * [misc]progress: [ 40 / 139 ] simplifiying candidate # 1545989150.740 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (pow (* n 2) (- 1/2 (/ k 2))))) 1) 1545989150.740 * * [misc]simplify: iters left: 6 (12 enodes) 1545989150.744 * * [misc]simplify: iters left: 5 (19 enodes) 1545989150.750 * * [misc]simplify: iters left: 4 (28 enodes) 1545989150.757 * * [misc]simplify: iters left: 3 (42 enodes) 1545989150.769 * * [misc]simplify: iters left: 2 (68 enodes) 1545989150.786 * [exit]simplify: Simplified to (* (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (pow (* n 2) (- 1/2 (/ k 2))))) 1545989150.786 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (* (* (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (pow (* n 2) (- 1/2 (/ k 2))))) (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt k))))) 1545989150.786 * [enter]simplify: Simplifying (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt k)) 1545989150.786 * * [misc]simplify: iters left: 6 (11 enodes) 1545989150.790 * * [misc]simplify: iters left: 5 (14 enodes) 1545989150.793 * * [misc]simplify: iters left: 4 (17 enodes) 1545989150.798 * [exit]simplify: Simplified to (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt k)) 1545989150.798 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (* (* (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (pow (* n 2) (- 1/2 (/ k 2))))) (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt k))))) 1545989150.798 * * * * [misc]progress: [ 41 / 139 ] simplifiying candidate # 1545989150.799 * [enter]simplify: Simplifying (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1545989150.799 * * [misc]simplify: iters left: 6 (13 enodes) 1545989150.803 * * [misc]simplify: iters left: 5 (18 enodes) 1545989150.808 * * [misc]simplify: iters left: 4 (21 enodes) 1545989150.813 * [exit]simplify: Simplified to (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1545989150.813 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (* (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))) 1545989150.813 * [enter]simplify: Simplifying (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1545989150.813 * * [misc]simplify: iters left: 6 (12 enodes) 1545989150.815 * * [misc]simplify: iters left: 5 (15 enodes) 1545989150.816 * * [misc]simplify: iters left: 4 (18 enodes) 1545989150.819 * [exit]simplify: Simplified to (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1545989150.819 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (* (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))) 1545989150.819 * * * * [misc]progress: [ 42 / 139 ] simplifiying candidate # 1545989150.819 * [enter]simplify: Simplifying (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1545989150.819 * * [misc]simplify: iters left: 6 (12 enodes) 1545989150.822 * * [misc]simplify: iters left: 5 (15 enodes) 1545989150.824 * * [misc]simplify: iters left: 4 (18 enodes) 1545989150.826 * [exit]simplify: Simplified to (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1545989150.826 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (* (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))) 1545989150.826 * [enter]simplify: Simplifying (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1545989150.826 * * [misc]simplify: iters left: 6 (12 enodes) 1545989150.828 * * [misc]simplify: iters left: 5 (15 enodes) 1545989150.830 * * [misc]simplify: iters left: 4 (18 enodes) 1545989150.832 * [exit]simplify: Simplified to (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1545989150.832 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (* (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))) 1545989150.832 * * * * [misc]progress: [ 43 / 139 ] simplifiying candidate # 1545989150.832 * [enter]simplify: Simplifying (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) 1) 1545989150.832 * * [misc]simplify: iters left: 6 (11 enodes) 1545989150.834 * * [misc]simplify: iters left: 5 (16 enodes) 1545989150.836 * * [misc]simplify: iters left: 4 (21 enodes) 1545989150.838 * [exit]simplify: Simplified to (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) 1545989150.839 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (* (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt k))))) 1545989150.839 * [enter]simplify: Simplifying (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt k)) 1545989150.839 * * [misc]simplify: iters left: 6 (11 enodes) 1545989150.840 * * [misc]simplify: iters left: 5 (14 enodes) 1545989150.842 * * [misc]simplify: iters left: 4 (17 enodes) 1545989150.844 * [exit]simplify: Simplified to (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt k)) 1545989150.844 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (* (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt k))))) 1545989150.845 * * * * [misc]progress: [ 44 / 139 ] simplifiying candidate # 1545989150.845 * [enter]simplify: Simplifying (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1545989150.845 * * [misc]simplify: iters left: 6 (6 enodes) 1545989150.846 * * [misc]simplify: iters left: 5 (10 enodes) 1545989150.847 * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) 1545989150.847 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (* (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k)))))) 1545989150.847 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1545989150.847 * * [misc]simplify: iters left: 6 (11 enodes) 1545989150.850 * * [misc]simplify: iters left: 5 (14 enodes) 1545989150.854 * * [misc]simplify: iters left: 4 (17 enodes) 1545989150.859 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1545989150.859 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k)))))) 1545989150.859 * * * * [misc]progress: [ 45 / 139 ] simplifiying candidate # 1545989150.859 * [enter]simplify: Simplifying (/ 1 (sqrt (sqrt k))) 1545989150.860 * * [misc]simplify: iters left: 4 (5 enodes) 1545989150.861 * * [misc]simplify: iters left: 3 (7 enodes) 1545989150.863 * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt k))) 1545989150.863 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))) 1545989150.863 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1545989150.863 * * [misc]simplify: iters left: 6 (11 enodes) 1545989150.866 * * [misc]simplify: iters left: 5 (14 enodes) 1545989150.870 * * [misc]simplify: iters left: 4 (17 enodes) 1545989150.875 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1545989150.875 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))) 1545989150.875 * * * * [misc]progress: [ 46 / 139 ] simplifiying candidate # 1545989150.875 * [enter]simplify: Simplifying (/ 1 1) 1545989150.875 * * [misc]simplify: iters left: 2 (2 enodes) 1545989150.876 * * [misc]simplify: iters left: 1 (4 enodes) 1545989150.876 * [exit]simplify: Simplified to 1 1545989150.877 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (* 1 (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))))) 1545989150.877 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)) 1545989150.877 * * [misc]simplify: iters left: 6 (10 enodes) 1545989150.880 * * [misc]simplify: iters left: 5 (13 enodes) 1545989150.883 * * [misc]simplify: iters left: 4 (16 enodes) 1545989150.888 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)) 1545989150.888 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (* 1 (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))))) 1545989150.888 * * * * [misc]progress: [ 47 / 139 ] simplifiying candidate # 1545989150.888 * * * * [misc]progress: [ 48 / 139 ] simplifiying candidate # 1545989150.888 * * * * [misc]progress: [ 49 / 139 ] simplifiying candidate # 1545989150.888 * * * * [misc]progress: [ 50 / 139 ] simplifiying candidate # 1545989150.888 * [enter]simplify: Simplifying (cbrt (sqrt k)) 1545989150.888 * * [misc]simplify: iters left: 2 (3 enodes) 1545989150.889 * [exit]simplify: Simplified to (cbrt (sqrt k)) 1545989150.889 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (/ (/ (pow (* n 2) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k))))) 1545989150.889 * * * * [misc]progress: [ 51 / 139 ] simplifiying candidate # 1545989150.890 * [enter]simplify: Simplifying (sqrt (sqrt k)) 1545989150.890 * * [misc]simplify: iters left: 2 (3 enodes) 1545989150.890 * [exit]simplify: Simplified to (sqrt (sqrt k)) 1545989150.891 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (/ (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k))))) 1545989150.891 * * * * [misc]progress: [ 52 / 139 ] simplifiying candidate # 1545989150.891 * [enter]simplify: Simplifying (sqrt k) 1545989150.891 * * [misc]simplify: iters left: 1 (2 enodes) 1545989150.891 * [exit]simplify: Simplified to (sqrt k) 1545989150.892 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (/ (/ (pow (* n 2) (- 1/2 (/ k 2))) 1) (sqrt k)))) 1545989150.892 * * * * [misc]progress: [ 53 / 139 ] simplifiying candidate # 1545989150.892 * [enter]simplify: Simplifying (pow (* n 2) 1/2) 1545989150.892 * * [misc]simplify: iters left: 3 (5 enodes) 1545989150.893 * * [misc]simplify: iters left: 2 (7 enodes) 1545989150.895 * [exit]simplify: Simplified to (sqrt (* n 2)) 1545989150.895 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (/ (sqrt (* n 2)) (/ (sqrt k) (pow (* n 2) (- (/ k 2))))))) 1545989150.895 * * * * [misc]progress: [ 54 / 139 ] simplifiying candidate # 1545989150.896 * [enter]simplify: Simplifying (pow (* n 2) 1/2) 1545989150.896 * * [misc]simplify: iters left: 3 (5 enodes) 1545989150.897 * * [misc]simplify: iters left: 2 (7 enodes) 1545989150.899 * [exit]simplify: Simplified to (sqrt (* n 2)) 1545989150.899 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (/ (sqrt (* n 2)) (/ (sqrt k) (pow (* n 2) (- (/ k 2))))))) 1545989150.899 * * * * [misc]progress: [ 55 / 139 ] simplifiying candidate # 1545989150.900 * [enter]simplify: Simplifying (pow n (- 1/2 (/ k 2))) 1545989150.900 * * [misc]simplify: iters left: 5 (7 enodes) 1545989150.902 * * [misc]simplify: iters left: 4 (9 enodes) 1545989150.905 * * [misc]simplify: iters left: 3 (12 enodes) 1545989150.907 * [exit]simplify: Simplified to (pow n (- 1/2 (/ k 2))) 1545989150.908 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (/ (pow n (- 1/2 (/ k 2))) (/ (sqrt k) (pow 2 (- 1/2 (/ k 2))))))) 1545989150.908 * * * * [misc]progress: [ 56 / 139 ] simplifiying candidate # 1545989150.908 * [enter]simplify: Simplifying (* (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (pow (* n 2) (- 1/2 (/ k 2))))) 1545989150.908 * * [misc]simplify: iters left: 6 (10 enodes) 1545989150.909 * * [misc]simplify: iters left: 5 (13 enodes) 1545989150.911 * * [misc]simplify: iters left: 4 (16 enodes) 1545989150.913 * [exit]simplify: Simplified to (* (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (pow (* n 2) (- 1/2 (/ k 2))))) 1545989150.913 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (/ (* (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (pow (* n 2) (- 1/2 (/ k 2))))) (/ (sqrt k) (cbrt (pow (* n 2) (- 1/2 (/ k 2)))))))) 1545989150.913 * * * * [misc]progress: [ 57 / 139 ] simplifiying candidate # 1545989150.913 * [enter]simplify: Simplifying (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) 1545989150.913 * * [misc]simplify: iters left: 6 (9 enodes) 1545989150.914 * * [misc]simplify: iters left: 5 (12 enodes) 1545989150.916 * * [misc]simplify: iters left: 4 (15 enodes) 1545989150.918 * [exit]simplify: Simplified to (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) 1545989150.918 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* n 2) (- 1/2 (/ k 2)))))))) 1545989150.918 * * * * [misc]progress: [ 58 / 139 ] simplifiying candidate # 1545989150.918 * * * * [misc]progress: [ 59 / 139 ] simplifiying candidate # 1545989150.918 * [enter]simplify: Simplifying (pow (* n 2) 1/2) 1545989150.918 * * [misc]simplify: iters left: 3 (5 enodes) 1545989150.919 * * [misc]simplify: iters left: 2 (7 enodes) 1545989150.920 * [exit]simplify: Simplified to (sqrt (* n 2)) 1545989150.920 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (/ (sqrt (* n 2)) (* (sqrt k) (pow (* n 2) (/ k 2)))))) 1545989150.920 * * * * [misc]progress: [ 60 / 139 ] simplifiying candidate # 1545989150.920 * [enter]simplify: Simplifying (* (exp (* (log PI) (- 1/2 (/ k 2)))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))) 1545989150.920 * * [misc]simplify: iters left: 6 (15 enodes) 1545989150.922 * * [misc]simplify: iters left: 5 (25 enodes) 1545989150.927 * * [misc]simplify: iters left: 4 (38 enodes) 1545989150.932 * * [misc]simplify: iters left: 3 (56 enodes) 1545989150.940 * * [misc]simplify: iters left: 2 (109 enodes) 1545989150.975 * * [misc]simplify: iters left: 1 (181 enodes) 1545989151.027 * [exit]simplify: Simplified to (* (/ (/ (sqrt PI) (sqrt k)) (sqrt (pow PI k))) (pow (* 2 n) (- 1/2 (/ k 2)))) 1545989151.027 * [misc]simplify: Simplified (2 1) to (λ (k n) (pow (* (/ (/ (sqrt PI) (sqrt k)) (sqrt (pow PI k))) (pow (* 2 n) (- 1/2 (/ k 2)))) 1)) 1545989151.028 * * * * [misc]progress: [ 61 / 139 ] simplifiying candidate # 1545989151.028 * * * * [misc]progress: [ 62 / 139 ] simplifiying candidate # 1545989151.028 * [enter]simplify: Simplifying (+ (* (log PI) (- 1/2 (/ k 2))) (- (* (log (* n 2)) (- 1/2 (/ k 2))) (log (sqrt k)))) 1545989151.028 * * [misc]simplify: iters left: 6 (16 enodes) 1545989151.031 * * [misc]simplify: iters left: 5 (29 enodes) 1545989151.035 * * [misc]simplify: iters left: 4 (60 enodes) 1545989151.052 * * [misc]simplify: iters left: 3 (191 enodes) 1545989151.159 * [exit]simplify: Simplified to (- (* (+ (log PI) (log (* 2 n))) (- 1/2 (/ k 2))) (log (sqrt k))) 1545989151.159 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (+ (log PI) (log (* 2 n))) (- 1/2 (/ k 2))) (log (sqrt k))))) 1545989151.159 * * * * [misc]progress: [ 63 / 139 ] simplifiying candidate # 1545989151.159 * [enter]simplify: Simplifying (+ (* (log PI) (- 1/2 (/ k 2))) (- (* (log (* n 2)) (- 1/2 (/ k 2))) (log (sqrt k)))) 1545989151.159 * * [misc]simplify: iters left: 6 (16 enodes) 1545989151.162 * * [misc]simplify: iters left: 5 (29 enodes) 1545989151.167 * * [misc]simplify: iters left: 4 (60 enodes) 1545989151.181 * * [misc]simplify: iters left: 3 (191 enodes) 1545989151.300 * [exit]simplify: Simplified to (- (* (+ (log PI) (log (* 2 n))) (- 1/2 (/ k 2))) (log (sqrt k))) 1545989151.300 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (+ (log PI) (log (* 2 n))) (- 1/2 (/ k 2))) (log (sqrt k))))) 1545989151.300 * * * * [misc]progress: [ 64 / 139 ] simplifiying candidate # 1545989151.301 * [enter]simplify: Simplifying (+ (* (log PI) (- 1/2 (/ k 2))) (- (log (pow (* n 2) (- 1/2 (/ k 2)))) (log (sqrt k)))) 1545989151.301 * * [misc]simplify: iters left: 6 (16 enodes) 1545989151.306 * * [misc]simplify: iters left: 5 (27 enodes) 1545989151.315 * * [misc]simplify: iters left: 4 (50 enodes) 1545989151.333 * * [misc]simplify: iters left: 3 (114 enodes) 1545989151.408 * * [misc]simplify: iters left: 2 (426 enodes) 1545989151.927 * [exit]simplify: Simplified to (- (* (+ (log PI) (log (* 2 n))) (- 1/2 (/ k 2))) (log (sqrt k))) 1545989151.927 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (+ (log PI) (log (* 2 n))) (- 1/2 (/ k 2))) (log (sqrt k))))) 1545989151.927 * * * * [misc]progress: [ 65 / 139 ] simplifiying candidate # 1545989151.928 * [enter]simplify: Simplifying (+ (* (log PI) (- 1/2 (/ k 2))) (log (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1545989151.928 * * [misc]simplify: iters left: 6 (15 enodes) 1545989151.932 * * [misc]simplify: iters left: 5 (23 enodes) 1545989151.939 * * [misc]simplify: iters left: 4 (40 enodes) 1545989151.953 * * [misc]simplify: iters left: 3 (82 enodes) 1545989151.981 * * [misc]simplify: iters left: 2 (187 enodes) 1545989152.106 * [exit]simplify: Simplified to (- (* (+ (log PI) (log (* 2 n))) (- 1/2 (/ k 2))) (log (sqrt k))) 1545989152.106 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (+ (log PI) (log (* 2 n))) (- 1/2 (/ k 2))) (log (sqrt k))))) 1545989152.106 * * * * [misc]progress: [ 66 / 139 ] simplifiying candidate # 1545989152.106 * * * * [misc]progress: [ 67 / 139 ] simplifiying candidate # 1545989152.106 * * * * [misc]progress: [ 68 / 139 ] simplifiying candidate # 1545989152.106 * [enter]simplify: Simplifying (* (* (* (exp (* (log PI) (- 1/2 (/ k 2)))) (exp (* (log PI) (- 1/2 (/ k 2))))) (exp (* (log PI) (- 1/2 (/ k 2))))) (/ (* (* (pow (* n 2) (- 1/2 (/ k 2))) (pow (* n 2) (- 1/2 (/ k 2)))) (pow (* n 2) (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))) 1545989152.107 * * [misc]simplify: iters left: 6 (21 enodes) 1545989152.114 * * [misc]simplify: iters left: 5 (45 enodes) 1545989152.131 * * [misc]simplify: iters left: 4 (136 enodes) 1545989152.229 * [exit]simplify: Simplified to (* (/ (pow (pow PI (- 1/2 (/ k 2))) 3) (sqrt k)) (/ (* (pow (* n 2) (- 1/2 (/ k 2))) (pow (* n 2) (- 1/2 (/ k 2)))) (/ k (pow (* n 2) (- 1/2 (/ k 2)))))) 1545989152.229 * [misc]simplify: Simplified (2 1) to (λ (k n) (cbrt (* (/ (pow (pow PI (- 1/2 (/ k 2))) 3) (sqrt k)) (/ (* (pow (* n 2) (- 1/2 (/ k 2))) (pow (* n 2) (- 1/2 (/ k 2)))) (/ k (pow (* n 2) (- 1/2 (/ k 2)))))))) 1545989152.229 * * * * [misc]progress: [ 69 / 139 ] simplifiying candidate # 1545989152.230 * [enter]simplify: Simplifying (* (* (* (exp (* (log PI) (- 1/2 (/ k 2)))) (exp (* (log PI) (- 1/2 (/ k 2))))) (exp (* (log PI) (- 1/2 (/ k 2))))) (* (* (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1545989152.230 * * [misc]simplify: iters left: 6 (19 enodes) 1545989152.234 * * [misc]simplify: iters left: 5 (41 enodes) 1545989152.241 * * [misc]simplify: iters left: 4 (113 enodes) 1545989152.275 * * [misc]simplify: iters left: 3 (312 enodes) 1545989152.426 * [exit]simplify: Simplified to (* (/ (/ (pow (* n 2) (- 1/2 (/ k 2))) k) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (* (pow (pow PI (- 1/2 (/ k 2))) 3) (pow (* n 2) (- 1/2 (/ k 2))))) 1545989152.426 * [misc]simplify: Simplified (2 1) to (λ (k n) (cbrt (* (/ (/ (pow (* n 2) (- 1/2 (/ k 2))) k) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (* (pow (pow PI (- 1/2 (/ k 2))) 3) (pow (* n 2) (- 1/2 (/ k 2))))))) 1545989152.426 * * * * [misc]progress: [ 70 / 139 ] simplifiying candidate # 1545989152.426 * * * * [misc]progress: [ 71 / 139 ] simplifiying candidate # 1545989152.426 * * * * [misc]progress: [ 72 / 139 ] simplifiying candidate # 1545989152.426 * * * * [misc]progress: [ 73 / 139 ] simplifiying candidate # 1545989152.426 * * * * [misc]progress: [ 74 / 139 ] simplifiying candidate # 1545989152.426 * [enter]simplify: Simplifying (cbrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))) 1545989152.426 * * [misc]simplify: iters left: 6 (11 enodes) 1545989152.428 * * [misc]simplify: iters left: 5 (14 enodes) 1545989152.430 * * [misc]simplify: iters left: 4 (17 enodes) 1545989152.433 * [exit]simplify: Simplified to (cbrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))) 1545989152.433 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (exp (* (log PI) (- 1/2 (/ k 2)))) (* (cbrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))))) (cbrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))))) 1545989152.433 * * * * [misc]progress: [ 75 / 139 ] simplifiying candidate # 1545989152.433 * [enter]simplify: Simplifying (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))) 1545989152.433 * * [misc]simplify: iters left: 6 (11 enodes) 1545989152.437 * * [misc]simplify: iters left: 5 (14 enodes) 1545989152.441 * * [misc]simplify: iters left: 4 (17 enodes) 1545989152.446 * [exit]simplify: Simplified to (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))) 1545989152.446 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (exp (* (log PI) (- 1/2 (/ k 2)))) (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))))) 1545989152.446 * * * * [misc]progress: [ 76 / 139 ] simplifiying candidate # 1545989152.446 * [enter]simplify: Simplifying (/ (pow (* n 2) (- (/ k 2))) (cbrt (sqrt k))) 1545989152.446 * * [misc]simplify: iters left: 6 (10 enodes) 1545989152.449 * * [misc]simplify: iters left: 5 (13 enodes) 1545989152.453 * [exit]simplify: Simplified to (/ (pow (* n 2) (/ (- k) 2)) (cbrt (sqrt k))) 1545989152.453 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (exp (* (log PI) (- 1/2 (/ k 2)))) (/ (pow (* n 2) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow (* n 2) (/ (- k) 2)) (cbrt (sqrt k))))) 1545989152.453 * * * * [misc]progress: [ 77 / 139 ] simplifiying candidate # 1545989152.453 * [enter]simplify: Simplifying (/ (pow (* n 2) (- (/ k 2))) (sqrt (sqrt k))) 1545989152.453 * * [misc]simplify: iters left: 6 (10 enodes) 1545989152.456 * * [misc]simplify: iters left: 5 (13 enodes) 1545989152.460 * [exit]simplify: Simplified to (/ (pow (* n 2) (/ (- k) 2)) (sqrt (sqrt k))) 1545989152.460 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (exp (* (log PI) (- 1/2 (/ k 2)))) (/ (pow (* n 2) 1/2) (sqrt (sqrt k)))) (/ (pow (* n 2) (/ (- k) 2)) (sqrt (sqrt k))))) 1545989152.460 * * * * [misc]progress: [ 78 / 139 ] simplifiying candidate # 1545989152.460 * [enter]simplify: Simplifying (/ (pow (* n 2) (- (/ k 2))) (sqrt k)) 1545989152.460 * * [misc]simplify: iters left: 6 (9 enodes) 1545989152.463 * * [misc]simplify: iters left: 5 (12 enodes) 1545989152.466 * [exit]simplify: Simplified to (/ (pow (* n 2) (- (/ k 2))) (sqrt k)) 1545989152.466 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (exp (* (log PI) (- 1/2 (/ k 2)))) (/ (pow (* n 2) 1/2) 1)) (/ (pow (* n 2) (- (/ k 2))) (sqrt k)))) 1545989152.466 * * * * [misc]progress: [ 79 / 139 ] simplifiying candidate # 1545989152.466 * [enter]simplify: Simplifying (/ (pow (* n 2) (- (/ k 2))) (cbrt (sqrt k))) 1545989152.466 * * [misc]simplify: iters left: 6 (10 enodes) 1545989152.469 * * [misc]simplify: iters left: 5 (13 enodes) 1545989152.473 * [exit]simplify: Simplified to (/ (pow (* n 2) (/ (- k) 2)) (cbrt (sqrt k))) 1545989152.473 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (exp (* (log PI) (- 1/2 (/ k 2)))) (/ (pow (* n 2) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow (* n 2) (/ (- k) 2)) (cbrt (sqrt k))))) 1545989152.473 * * * * [misc]progress: [ 80 / 139 ] simplifiying candidate # 1545989152.473 * [enter]simplify: Simplifying (/ (pow (* n 2) (- (/ k 2))) (sqrt (sqrt k))) 1545989152.473 * * [misc]simplify: iters left: 6 (10 enodes) 1545989152.476 * * [misc]simplify: iters left: 5 (13 enodes) 1545989152.480 * [exit]simplify: Simplified to (/ (pow (* n 2) (/ (- k) 2)) (sqrt (sqrt k))) 1545989152.480 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (exp (* (log PI) (- 1/2 (/ k 2)))) (/ (pow (* n 2) 1/2) (sqrt (sqrt k)))) (/ (pow (* n 2) (/ (- k) 2)) (sqrt (sqrt k))))) 1545989152.480 * * * * [misc]progress: [ 81 / 139 ] simplifiying candidate # 1545989152.480 * [enter]simplify: Simplifying (/ (pow (* n 2) (- (/ k 2))) (sqrt k)) 1545989152.480 * * [misc]simplify: iters left: 6 (9 enodes) 1545989152.483 * * [misc]simplify: iters left: 5 (12 enodes) 1545989152.486 * [exit]simplify: Simplified to (/ (pow (* n 2) (- (/ k 2))) (sqrt k)) 1545989152.486 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (exp (* (log PI) (- 1/2 (/ k 2)))) (/ (pow (* n 2) 1/2) 1)) (/ (pow (* n 2) (- (/ k 2))) (sqrt k)))) 1545989152.486 * * * * [misc]progress: [ 82 / 139 ] simplifiying candidate # 1545989152.487 * [enter]simplify: Simplifying (/ (pow 2 (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1545989152.487 * * [misc]simplify: iters left: 6 (9 enodes) 1545989152.488 * * [misc]simplify: iters left: 5 (11 enodes) 1545989152.490 * * [misc]simplify: iters left: 4 (14 enodes) 1545989152.492 * [exit]simplify: Simplified to (/ (pow 2 (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1545989152.492 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (exp (* (log PI) (- 1/2 (/ k 2)))) (/ (pow n (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow 2 (- 1/2 (/ k 2))) (cbrt (sqrt k))))) 1545989152.492 * * * * [misc]progress: [ 83 / 139 ] simplifiying candidate # 1545989152.492 * [enter]simplify: Simplifying (/ (pow 2 (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1545989152.492 * * [misc]simplify: iters left: 6 (9 enodes) 1545989152.493 * * [misc]simplify: iters left: 5 (11 enodes) 1545989152.495 * * [misc]simplify: iters left: 4 (14 enodes) 1545989152.497 * [exit]simplify: Simplified to (/ (pow 2 (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1545989152.497 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (exp (* (log PI) (- 1/2 (/ k 2)))) (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (/ (pow 2 (- 1/2 (/ k 2))) (sqrt (sqrt k))))) 1545989152.497 * * * * [misc]progress: [ 84 / 139 ] simplifiying candidate # 1545989152.497 * [enter]simplify: Simplifying (/ (pow 2 (- 1/2 (/ k 2))) (sqrt k)) 1545989152.497 * * [misc]simplify: iters left: 6 (8 enodes) 1545989152.498 * * [misc]simplify: iters left: 5 (10 enodes) 1545989152.499 * * [misc]simplify: iters left: 4 (13 enodes) 1545989152.501 * [exit]simplify: Simplified to (/ (pow 2 (- 1/2 (/ k 2))) (sqrt k)) 1545989152.501 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (exp (* (log PI) (- 1/2 (/ k 2)))) (/ (pow n (- 1/2 (/ k 2))) 1)) (/ (pow 2 (- 1/2 (/ k 2))) (sqrt k)))) 1545989152.501 * * * * [misc]progress: [ 85 / 139 ] simplifiying candidate # 1545989152.501 * [enter]simplify: Simplifying (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1545989152.501 * * [misc]simplify: iters left: 6 (12 enodes) 1545989152.503 * * [misc]simplify: iters left: 5 (15 enodes) 1545989152.505 * * [misc]simplify: iters left: 4 (18 enodes) 1545989152.507 * [exit]simplify: Simplified to (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1545989152.507 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (exp (* (log PI) (- 1/2 (/ k 2)))) (/ (* (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (pow (* n 2) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))) 1545989152.507 * * * * [misc]progress: [ 86 / 139 ] simplifiying candidate # 1545989152.507 * [enter]simplify: Simplifying (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1545989152.507 * * [misc]simplify: iters left: 6 (12 enodes) 1545989152.511 * * [misc]simplify: iters left: 5 (15 enodes) 1545989152.517 * * [misc]simplify: iters left: 4 (18 enodes) 1545989152.522 * [exit]simplify: Simplified to (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1545989152.522 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (exp (* (log PI) (- 1/2 (/ k 2)))) (/ (* (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (pow (* n 2) (- 1/2 (/ k 2))))) (sqrt (sqrt k)))) (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) 1545989152.522 * * * * [misc]progress: [ 87 / 139 ] simplifiying candidate # 1545989152.523 * [enter]simplify: Simplifying (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt k)) 1545989152.523 * * [misc]simplify: iters left: 6 (11 enodes) 1545989152.526 * * [misc]simplify: iters left: 5 (14 enodes) 1545989152.530 * * [misc]simplify: iters left: 4 (17 enodes) 1545989152.534 * [exit]simplify: Simplified to (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt k)) 1545989152.534 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (exp (* (log PI) (- 1/2 (/ k 2)))) (/ (* (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (pow (* n 2) (- 1/2 (/ k 2))))) 1)) (/ (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt k)))) 1545989152.534 * * * * [misc]progress: [ 88 / 139 ] simplifiying candidate # 1545989152.535 * [enter]simplify: Simplifying (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1545989152.535 * * [misc]simplify: iters left: 6 (12 enodes) 1545989152.538 * * [misc]simplify: iters left: 5 (15 enodes) 1545989152.542 * * [misc]simplify: iters left: 4 (18 enodes) 1545989152.549 * [exit]simplify: Simplified to (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1545989152.549 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (exp (* (log PI) (- 1/2 (/ k 2)))) (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))) 1545989152.549 * * * * [misc]progress: [ 89 / 139 ] simplifiying candidate # 1545989152.549 * [enter]simplify: Simplifying (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1545989152.550 * * [misc]simplify: iters left: 6 (12 enodes) 1545989152.553 * * [misc]simplify: iters left: 5 (15 enodes) 1545989152.557 * * [misc]simplify: iters left: 4 (18 enodes) 1545989152.562 * [exit]simplify: Simplified to (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1545989152.562 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (exp (* (log PI) (- 1/2 (/ k 2)))) (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) 1545989152.562 * * * * [misc]progress: [ 90 / 139 ] simplifiying candidate # 1545989152.563 * [enter]simplify: Simplifying (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt k)) 1545989152.563 * * [misc]simplify: iters left: 6 (11 enodes) 1545989152.566 * * [misc]simplify: iters left: 5 (14 enodes) 1545989152.570 * * [misc]simplify: iters left: 4 (17 enodes) 1545989152.574 * [exit]simplify: Simplified to (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt k)) 1545989152.575 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (exp (* (log PI) (- 1/2 (/ k 2)))) (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) 1)) (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt k)))) 1545989152.575 * * * * [misc]progress: [ 91 / 139 ] simplifiying candidate # 1545989152.575 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1545989152.575 * * [misc]simplify: iters left: 6 (11 enodes) 1545989152.577 * * [misc]simplify: iters left: 5 (14 enodes) 1545989152.578 * * [misc]simplify: iters left: 4 (17 enodes) 1545989152.581 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1545989152.581 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (exp (* (log PI) (- 1/2 (/ k 2)))) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))))) 1545989152.581 * * * * [misc]progress: [ 92 / 139 ] simplifiying candidate # 1545989152.581 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1545989152.581 * * [misc]simplify: iters left: 6 (11 enodes) 1545989152.583 * * [misc]simplify: iters left: 5 (14 enodes) 1545989152.584 * * [misc]simplify: iters left: 4 (17 enodes) 1545989152.587 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1545989152.587 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (exp (* (log PI) (- 1/2 (/ k 2)))) (/ 1 (sqrt (sqrt k)))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) 1545989152.587 * * * * [misc]progress: [ 93 / 139 ] simplifiying candidate # 1545989152.587 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)) 1545989152.587 * * [misc]simplify: iters left: 6 (10 enodes) 1545989152.588 * * [misc]simplify: iters left: 5 (13 enodes) 1545989152.590 * * [misc]simplify: iters left: 4 (16 enodes) 1545989152.592 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)) 1545989152.592 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (exp (* (log PI) (- 1/2 (/ k 2)))) (/ 1 1)) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1545989152.592 * * * * [misc]progress: [ 94 / 139 ] simplifiying candidate # 1545989152.592 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)) 1545989152.592 * * [misc]simplify: iters left: 6 (10 enodes) 1545989152.594 * * [misc]simplify: iters left: 5 (13 enodes) 1545989152.596 * * [misc]simplify: iters left: 4 (16 enodes) 1545989152.598 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)) 1545989152.598 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (exp (* (log PI) (- 1/2 (/ k 2)))) 1) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1545989152.598 * * * * [misc]progress: [ 95 / 139 ] simplifiying candidate # 1545989152.598 * [enter]simplify: Simplifying (/ 1 (sqrt k)) 1545989152.598 * * [misc]simplify: iters left: 3 (4 enodes) 1545989152.598 * * [misc]simplify: iters left: 2 (6 enodes) 1545989152.599 * [exit]simplify: Simplified to (/ 1 (sqrt k)) 1545989152.599 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (exp (* (log PI) (- 1/2 (/ k 2)))) (pow (* n 2) (- 1/2 (/ k 2)))) (/ 1 (sqrt k)))) 1545989152.599 * * * * [misc]progress: [ 96 / 139 ] simplifiying candidate # 1545989152.600 * [enter]simplify: Simplifying (exp (* (log PI) 1/2)) 1545989152.600 * * [misc]simplify: iters left: 4 (5 enodes) 1545989152.600 * * [misc]simplify: iters left: 3 (9 enodes) 1545989152.602 * * [misc]simplify: iters left: 2 (11 enodes) 1545989152.603 * * [misc]simplify: iters left: 1 (13 enodes) 1545989152.605 * [exit]simplify: Simplified to (sqrt PI) 1545989152.605 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt PI) (* (exp (* (log PI) (- (/ k 2)))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))))) 1545989152.605 * * * * [misc]progress: [ 97 / 139 ] simplifiying candidate # 1545989152.605 * [enter]simplify: Simplifying (exp (* (log PI) 1/2)) 1545989152.605 * * [misc]simplify: iters left: 4 (5 enodes) 1545989152.606 * * [misc]simplify: iters left: 3 (9 enodes) 1545989152.607 * * [misc]simplify: iters left: 2 (11 enodes) 1545989152.609 * * [misc]simplify: iters left: 1 (13 enodes) 1545989152.612 * [exit]simplify: Simplified to (sqrt PI) 1545989152.612 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt PI) (* (exp (* (log PI) (- (/ k 2)))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))))) 1545989152.612 * * * * [misc]progress: [ 98 / 139 ] simplifiying candidate # 1545989152.613 * [enter]simplify: Simplifying (exp (* 1/2 (log PI))) 1545989152.613 * * [misc]simplify: iters left: 4 (5 enodes) 1545989152.615 * * [misc]simplify: iters left: 3 (8 enodes) 1545989152.617 * * [misc]simplify: iters left: 2 (9 enodes) 1545989152.620 * * [misc]simplify: iters left: 1 (12 enodes) 1545989152.623 * [exit]simplify: Simplified to (sqrt PI) 1545989152.623 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt PI) (* (exp (* (- (/ k 2)) (log PI))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))))) 1545989152.623 * * * * [misc]progress: [ 99 / 139 ] simplifiying candidate # 1545989152.624 * [enter]simplify: Simplifying (exp (* 1/2 (log PI))) 1545989152.624 * * [misc]simplify: iters left: 4 (5 enodes) 1545989152.625 * * [misc]simplify: iters left: 3 (8 enodes) 1545989152.626 * * [misc]simplify: iters left: 2 (9 enodes) 1545989152.627 * * [misc]simplify: iters left: 1 (12 enodes) 1545989152.629 * [exit]simplify: Simplified to (sqrt PI) 1545989152.629 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt PI) (* (exp (* (- (/ k 2)) (log PI))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))))) 1545989152.629 * * * * [misc]progress: [ 100 / 139 ] simplifiying candidate # 1545989152.629 * [enter]simplify: Simplifying (* (cbrt (exp (* (log PI) (- 1/2 (/ k 2))))) (cbrt (exp (* (log PI) (- 1/2 (/ k 2)))))) 1545989152.629 * * [misc]simplify: iters left: 6 (11 enodes) 1545989152.631 * * [misc]simplify: iters left: 5 (17 enodes) 1545989152.633 * * [misc]simplify: iters left: 4 (26 enodes) 1545989152.637 * * [misc]simplify: iters left: 3 (42 enodes) 1545989152.643 * * [misc]simplify: iters left: 2 (81 enodes) 1545989152.655 * * [misc]simplify: iters left: 1 (119 enodes) 1545989152.680 * [exit]simplify: Simplified to (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) 1545989152.680 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) (* (cbrt (exp (* (log PI) (- 1/2 (/ k 2))))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))))) 1545989152.680 * * * * [misc]progress: [ 101 / 139 ] simplifiying candidate # 1545989152.680 * [enter]simplify: Simplifying (sqrt (exp (* (log PI) (- 1/2 (/ k 2))))) 1545989152.681 * * [misc]simplify: iters left: 6 (10 enodes) 1545989152.683 * * [misc]simplify: iters left: 5 (16 enodes) 1545989152.688 * * [misc]simplify: iters left: 4 (25 enodes) 1545989152.695 * * [misc]simplify: iters left: 3 (41 enodes) 1545989152.707 * * [misc]simplify: iters left: 2 (80 enodes) 1545989152.729 * * [misc]simplify: iters left: 1 (118 enodes) 1545989152.754 * [exit]simplify: Simplified to (sqrt (pow PI (- 1/2 (/ k 2)))) 1545989152.754 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (pow PI (- 1/2 (/ k 2)))) (* (sqrt (exp (* (log PI) (- 1/2 (/ k 2))))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))))) 1545989152.754 * * * * [misc]progress: [ 102 / 139 ] simplifiying candidate # 1545989152.755 * * * * [misc]progress: [ 103 / 139 ] simplifiying candidate # 1545989152.755 * [enter]simplify: Simplifying (sqrt k) 1545989152.755 * * [misc]simplify: iters left: 1 (2 enodes) 1545989152.755 * [exit]simplify: Simplified to (sqrt k) 1545989152.755 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (* (exp (* (log PI) (- 1/2 (/ k 2)))) (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt k))) 1545989152.756 * * * * [misc]progress: [ 104 / 139 ] simplifiying candidate # 1545989152.756 * * * * [misc]progress: [ 105 / 139 ] simplifiying candidate # 1545989152.756 * [enter]simplify: Simplifying (* (log PI) (- 1/2 (/ k 2))) 1545989152.756 * * [misc]simplify: iters left: 6 (8 enodes) 1545989152.758 * * [misc]simplify: iters left: 5 (11 enodes) 1545989152.762 * * [misc]simplify: iters left: 4 (20 enodes) 1545989152.768 * * [misc]simplify: iters left: 3 (30 enodes) 1545989152.776 * * [misc]simplify: iters left: 2 (45 enodes) 1545989152.790 * * [misc]simplify: iters left: 1 (53 enodes) 1545989152.799 * [exit]simplify: Simplified to (* (- 1/2 (/ k 2)) (log PI)) 1545989152.799 * [misc]simplify: Simplified (2 1 1 1) to (λ (k n) (* (exp (pow (* (- 1/2 (/ k 2)) (log PI)) 1)) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1545989152.799 * * * * [misc]progress: [ 106 / 139 ] simplifiying candidate # 1545989152.799 * * * * [misc]progress: [ 107 / 139 ] simplifiying candidate # 1545989152.799 * [enter]simplify: Simplifying (+ (log (log PI)) (log (- 1/2 (/ k 2)))) 1545989152.799 * * [misc]simplify: iters left: 6 (10 enodes) 1545989152.801 * * [misc]simplify: iters left: 5 (13 enodes) 1545989152.802 * * [misc]simplify: iters left: 4 (16 enodes) 1545989152.804 * [exit]simplify: Simplified to (+ (log (- 1/2 (/ k 2))) (log (log PI))) 1545989152.805 * [misc]simplify: Simplified (2 1 1 1) to (λ (k n) (* (exp (exp (+ (log (- 1/2 (/ k 2))) (log (log PI))))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1545989152.805 * * * * [misc]progress: [ 108 / 139 ] simplifiying candidate # 1545989152.805 * * * * [misc]progress: [ 109 / 139 ] simplifiying candidate # 1545989152.805 * * * * [misc]progress: [ 110 / 139 ] simplifiying candidate # 1545989152.805 * [enter]simplify: Simplifying (* (* (* (log PI) (log PI)) (log PI)) (* (* (- 1/2 (/ k 2)) (- 1/2 (/ k 2))) (- 1/2 (/ k 2)))) 1545989152.805 * * [misc]simplify: iters left: 6 (12 enodes) 1545989152.807 * * [misc]simplify: iters left: 5 (21 enodes) 1545989152.811 * * [misc]simplify: iters left: 4 (67 enodes) 1545989152.833 * * [misc]simplify: iters left: 3 (321 enodes) 1545989153.246 * [exit]simplify: Simplified to (* (* (- 1/2 (/ k 2)) (pow (log PI) 3)) (* (- 1/2 (/ k 2)) (- 1/2 (/ k 2)))) 1545989153.246 * [misc]simplify: Simplified (2 1 1 1) to (λ (k n) (* (exp (cbrt (* (* (- 1/2 (/ k 2)) (pow (log PI) 3)) (* (- 1/2 (/ k 2)) (- 1/2 (/ k 2)))))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1545989153.246 * * * * [misc]progress: [ 111 / 139 ] simplifiying candidate # 1545989153.246 * * * * [misc]progress: [ 112 / 139 ] simplifiying candidate # 1545989153.246 * * * * [misc]progress: [ 113 / 139 ] simplifiying candidate # 1545989153.246 * * * * [misc]progress: [ 114 / 139 ] simplifiying candidate # 1545989153.246 * * * * [misc]progress: [ 115 / 139 ] simplifiying candidate # 1545989153.247 * [enter]simplify: Simplifying (* (log PI) (- (/ k 2))) 1545989153.247 * * [misc]simplify: iters left: 6 (7 enodes) 1545989153.249 * * [misc]simplify: iters left: 5 (12 enodes) 1545989153.253 * * [misc]simplify: iters left: 4 (22 enodes) 1545989153.259 * * [misc]simplify: iters left: 3 (35 enodes) 1545989153.268 * * [misc]simplify: iters left: 2 (42 enodes) 1545989153.278 * * [misc]simplify: iters left: 1 (47 enodes) 1545989153.290 * [exit]simplify: Simplified to (* (- k) (/ (log PI) 2)) 1545989153.290 * [misc]simplify: Simplified (2 1 1 2) to (λ (k n) (* (exp (+ (* (log PI) 1/2) (* (- k) (/ (log PI) 2)))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1545989153.290 * * * * [misc]progress: [ 116 / 139 ] simplifiying candidate # 1545989153.290 * [enter]simplify: Simplifying (* (log PI) (- (/ k 2))) 1545989153.291 * * [misc]simplify: iters left: 6 (7 enodes) 1545989153.293 * * [misc]simplify: iters left: 5 (12 enodes) 1545989153.296 * * [misc]simplify: iters left: 4 (22 enodes) 1545989153.307 * * [misc]simplify: iters left: 3 (35 enodes) 1545989153.315 * * [misc]simplify: iters left: 2 (42 enodes) 1545989153.325 * * [misc]simplify: iters left: 1 (47 enodes) 1545989153.337 * [exit]simplify: Simplified to (* (- k) (/ (log PI) 2)) 1545989153.337 * [misc]simplify: Simplified (2 1 1 2) to (λ (k n) (* (exp (+ (* (log PI) 1/2) (* (- k) (/ (log PI) 2)))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1545989153.337 * * * * [misc]progress: [ 117 / 139 ] simplifiying candidate # 1545989153.337 * [enter]simplify: Simplifying (* (- (/ k 2)) (log PI)) 1545989153.337 * * [misc]simplify: iters left: 6 (7 enodes) 1545989153.339 * * [misc]simplify: iters left: 5 (12 enodes) 1545989153.343 * * [misc]simplify: iters left: 4 (22 enodes) 1545989153.349 * * [misc]simplify: iters left: 3 (32 enodes) 1545989153.356 * * [misc]simplify: iters left: 2 (36 enodes) 1545989153.364 * * [misc]simplify: iters left: 1 (43 enodes) 1545989153.375 * [exit]simplify: Simplified to (* (- (/ k 2)) (log PI)) 1545989153.375 * [misc]simplify: Simplified (2 1 1 2) to (λ (k n) (* (exp (+ (* 1/2 (log PI)) (* (- (/ k 2)) (log PI)))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1545989153.375 * * * * [misc]progress: [ 118 / 139 ] simplifiying candidate # 1545989153.375 * [enter]simplify: Simplifying (* (- (/ k 2)) (log PI)) 1545989153.376 * * [misc]simplify: iters left: 6 (7 enodes) 1545989153.378 * * [misc]simplify: iters left: 5 (12 enodes) 1545989153.381 * * [misc]simplify: iters left: 4 (22 enodes) 1545989153.387 * * [misc]simplify: iters left: 3 (32 enodes) 1545989153.394 * * [misc]simplify: iters left: 2 (36 enodes) 1545989153.402 * * [misc]simplify: iters left: 1 (43 enodes) 1545989153.414 * [exit]simplify: Simplified to (* (- (/ k 2)) (log PI)) 1545989153.414 * [misc]simplify: Simplified (2 1 1 2) to (λ (k n) (* (exp (+ (* 1/2 (log PI)) (* (- (/ k 2)) (log PI)))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1545989153.414 * * * * [misc]progress: [ 119 / 139 ] simplifiying candidate # 1545989153.414 * [enter]simplify: Simplifying (cbrt (- 1/2 (/ k 2))) 1545989153.414 * * [misc]simplify: iters left: 5 (6 enodes) 1545989153.416 * * [misc]simplify: iters left: 4 (8 enodes) 1545989153.418 * * [misc]simplify: iters left: 3 (11 enodes) 1545989153.421 * [exit]simplify: Simplified to (cbrt (- 1/2 (/ k 2))) 1545989153.421 * [misc]simplify: Simplified (2 1 1 2) to (λ (k n) (* (exp (* (* (log PI) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2))))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1545989153.421 * * * * [misc]progress: [ 120 / 139 ] simplifiying candidate # 1545989153.422 * [enter]simplify: Simplifying (sqrt (- 1/2 (/ k 2))) 1545989153.422 * * [misc]simplify: iters left: 5 (6 enodes) 1545989153.424 * * [misc]simplify: iters left: 4 (8 enodes) 1545989153.426 * * [misc]simplify: iters left: 3 (11 enodes) 1545989153.429 * [exit]simplify: Simplified to (sqrt (- 1/2 (/ k 2))) 1545989153.429 * [misc]simplify: Simplified (2 1 1 2) to (λ (k n) (* (exp (* (* (log PI) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2))))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1545989153.429 * * * * [misc]progress: [ 121 / 139 ] simplifiying candidate # 1545989153.429 * [enter]simplify: Simplifying (- 1/2 (/ k 2)) 1545989153.429 * * [misc]simplify: iters left: 4 (5 enodes) 1545989153.430 * * [misc]simplify: iters left: 3 (7 enodes) 1545989153.432 * * [misc]simplify: iters left: 2 (10 enodes) 1545989153.435 * [exit]simplify: Simplified to (- 1/2 (/ k 2)) 1545989153.435 * [misc]simplify: Simplified (2 1 1 2) to (λ (k n) (* (exp (* (* (log PI) 1) (- 1/2 (/ k 2)))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1545989153.435 * * * * [misc]progress: [ 122 / 139 ] simplifiying candidate # 1545989153.435 * [enter]simplify: Simplifying (* (cbrt (log PI)) (cbrt (log PI))) 1545989153.435 * * [misc]simplify: iters left: 4 (4 enodes) 1545989153.437 * [exit]simplify: Simplified to (* (cbrt (log PI)) (cbrt (log PI))) 1545989153.437 * [misc]simplify: Simplified (2 1 1 1) to (λ (k n) (* (exp (* (* (cbrt (log PI)) (cbrt (log PI))) (* (cbrt (log PI)) (- 1/2 (/ k 2))))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1545989153.437 * * * * [misc]progress: [ 123 / 139 ] simplifiying candidate # 1545989153.437 * [enter]simplify: Simplifying (sqrt (log PI)) 1545989153.437 * * [misc]simplify: iters left: 2 (3 enodes) 1545989153.438 * [exit]simplify: Simplified to (sqrt (log PI)) 1545989153.438 * [misc]simplify: Simplified (2 1 1 1) to (λ (k n) (* (exp (* (sqrt (log PI)) (* (sqrt (log PI)) (- 1/2 (/ k 2))))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1545989153.438 * * * * [misc]progress: [ 124 / 139 ] simplifiying candidate # 1545989153.438 * * * * [misc]progress: [ 125 / 139 ] simplifiying candidate # 1545989153.438 * [enter]simplify: Simplifying (+ (* 1/2 1/2) (+ (* (/ k 2) (/ k 2)) (* 1/2 (/ k 2)))) 1545989153.438 * * [misc]simplify: iters left: 6 (9 enodes) 1545989153.442 * * [misc]simplify: iters left: 5 (23 enodes) 1545989153.451 * * [misc]simplify: iters left: 4 (47 enodes) 1545989153.461 * * [misc]simplify: iters left: 3 (69 enodes) 1545989153.470 * * [misc]simplify: iters left: 2 (82 enodes) 1545989153.478 * * [misc]simplify: iters left: 1 (105 enodes) 1545989153.503 * [exit]simplify: Simplified to (+ (+ 1/4 (* k 1/4)) (/ (* k k) 4)) 1545989153.503 * [misc]simplify: Simplified (2 1 1 2) to (λ (k n) (* (exp (/ (* (log PI) (- (pow 1/2 3) (pow (/ k 2) 3))) (+ (+ 1/4 (* k 1/4)) (/ (* k k) 4)))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1545989153.504 * * * * [misc]progress: [ 126 / 139 ] simplifiying candidate # 1545989153.504 * [enter]simplify: Simplifying (+ 1/2 (/ k 2)) 1545989153.504 * * [misc]simplify: iters left: 4 (5 enodes) 1545989153.505 * * [misc]simplify: iters left: 3 (6 enodes) 1545989153.505 * [exit]simplify: Simplified to (+ (/ k 2) 1/2) 1545989153.505 * [misc]simplify: Simplified (2 1 1 2) to (λ (k n) (* (exp (/ (* (log PI) (- (* 1/2 1/2) (* (/ k 2) (/ k 2)))) (+ (/ k 2) 1/2))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1545989153.505 * * * * [misc]progress: [ 127 / 139 ] simplifiying candidate # 1545989153.505 * * * * [misc]progress: [ 128 / 139 ] simplifiying candidate # 1545989153.506 * [enter]simplify: Simplifying (- (+ (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (* (pow (log 2) 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (pow k 2)))) (+ (* 1/4 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) (pow k 2))))) (* 1/8 (* (exp (* 1/2 (+ (log 2) (log n)))) (* (pow (log n) 2) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) k))) (* 1/2 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) k))))) 1545989153.506 * * [misc]simplify: iters left: 6 (35 enodes) 1545989153.513 * * [misc]simplify: iters left: 5 (99 enodes) 1545989153.542 * * [misc]simplify: iters left: 4 (298 enodes) 1545989153.692 * [exit]simplify: Simplified to (+ (- (* (pow n 1/2) (pow 2 1/2)) (* (* 1/2 k) (* (* (pow n 1/2) (pow 2 1/2)) (+ (log 2) (log n))))) (+ (* (* (log 2) 1/8) (* (* (pow n 1/2) (pow 2 1/2)) (* (* k k) (log 2)))) (* (* (pow n 1/2) (pow 2 1/2)) (+ (* (* 1/4 (log 2)) (* (* k k) (log n))) (* (* 1/8 (log n)) (* (* k k) (log n))))))) 1545989153.692 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (/ (+ (- (* (pow n 1/2) (pow 2 1/2)) (* (* 1/2 k) (* (* (pow n 1/2) (pow 2 1/2)) (+ (log 2) (log n))))) (+ (* (* (log 2) 1/8) (* (* (pow n 1/2) (pow 2 1/2)) (* (* k k) (log 2)))) (* (* (pow n 1/2) (pow 2 1/2)) (+ (* (* 1/4 (log 2)) (* (* k k) (log n))) (* (* 1/8 (log n)) (* (* k k) (log n))))))) (sqrt k)))) 1545989153.693 * * * * [misc]progress: [ 129 / 139 ] simplifiying candidate # 1545989153.693 * [enter]simplify: Simplifying (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) 1545989153.693 * * [misc]simplify: iters left: 6 (13 enodes) 1545989153.696 * * [misc]simplify: iters left: 5 (27 enodes) 1545989153.700 * * [misc]simplify: iters left: 4 (53 enodes) 1545989153.709 * * [misc]simplify: iters left: 3 (116 enodes) 1545989153.749 * * [misc]simplify: iters left: 2 (362 enodes) 1545989154.029 * [exit]simplify: Simplified to (pow (sqrt (* n 2)) (- 1 k)) 1545989154.029 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (/ (pow (sqrt (* n 2)) (- 1 k)) (sqrt k)))) 1545989154.029 * * * * [misc]progress: [ 130 / 139 ] simplifiying candidate # 1545989154.029 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) 1545989154.029 * * [misc]simplify: iters left: 6 (13 enodes) 1545989154.032 * * [misc]simplify: iters left: 5 (24 enodes) 1545989154.037 * * [misc]simplify: iters left: 4 (54 enodes) 1545989154.057 * * [misc]simplify: iters left: 3 (143 enodes) 1545989154.123 * [exit]simplify: Simplified to (pow (exp (- 1/2 (* 1/2 k))) (- (log -2) (log (/ -1 n)))) 1545989154.123 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) (/ (pow (exp (- 1/2 (* 1/2 k))) (- (log -2) (log (/ -1 n)))) (sqrt k)))) 1545989154.123 * * * * [misc]progress: [ 131 / 139 ] simplifiying candidate # 1545989154.123 * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) k))) (- (+ (* +nan.0 (* (pow (log 2) 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (pow k 2)))) (- (+ (* +nan.0 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) k)) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (pow k 2)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log 2) (log n))))) (- (+ (* +nan.0 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (pow k 2)))))))))))))))))))))) 1545989154.123 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) +nan.0)) 1545989154.123 * * * * [misc]progress: [ 132 / 139 ] simplifiying candidate # 1545989154.123 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) k)) (- (* +nan.0 (/ (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) (pow k 2)))))))) 1545989154.123 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) +nan.0)) 1545989154.123 * * * * [misc]progress: [ 133 / 139 ] simplifiying candidate # 1545989154.124 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (pow k 2))) (- (+ (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n)))))) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) k))))))) 1545989154.124 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (exp (* (log PI) (- 1/2 (/ k 2)))) +nan.0)) 1545989154.124 * * * * [misc]progress: [ 134 / 139 ] simplifiying candidate # 1545989154.124 * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log PI) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))))))))) 1545989154.124 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1545989154.124 * * * * [misc]progress: [ 135 / 139 ] simplifiying candidate # 1545989154.124 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (* (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))) (pow k 2))) (- (+ (* +nan.0 (/ (* (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))) k)) (- (* +nan.0 (/ (* (pow PI (- 1/2 (* 1/2 k))) (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k))))) (pow k 3)))))))) 1545989154.124 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1545989154.124 * * * * [misc]progress: [ 136 / 139 ] simplifiying candidate # 1545989154.124 * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (pow PI (- 1/2 (* 1/2 k))))) (- (+ (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (pow PI (- 1/2 (* 1/2 k)))) k)) (- (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (pow PI (- 1/2 (* 1/2 k)))) (pow k 2)))))))) 1545989154.124 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1545989154.124 * * * * [misc]progress: [ 137 / 139 ] simplifiying candidate # 1545989154.124 * [enter]simplify: Simplifying (- (* 1/2 (log PI)) (* 1/2 (* (log PI) k))) 1545989154.124 * * [misc]simplify: iters left: 6 (8 enodes) 1545989154.127 * * [misc]simplify: iters left: 5 (16 enodes) 1545989154.130 * * [misc]simplify: iters left: 4 (36 enodes) 1545989154.141 * * [misc]simplify: iters left: 3 (60 enodes) 1545989154.157 * * [misc]simplify: iters left: 2 (72 enodes) 1545989154.175 * * [misc]simplify: iters left: 1 (87 enodes) 1545989154.191 * [exit]simplify: Simplified to (* (- 1/2 (* k 1/2)) (log PI)) 1545989154.192 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (exp (* (- 1/2 (* k 1/2)) (log PI))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1545989154.192 * * * * [misc]progress: [ 138 / 139 ] simplifiying candidate # 1545989154.192 * [enter]simplify: Simplifying (- (* 1/2 (log PI)) (* 1/2 (* (log PI) k))) 1545989154.192 * * [misc]simplify: iters left: 6 (8 enodes) 1545989154.193 * * [misc]simplify: iters left: 5 (16 enodes) 1545989154.196 * * [misc]simplify: iters left: 4 (36 enodes) 1545989154.202 * * [misc]simplify: iters left: 3 (60 enodes) 1545989154.210 * * [misc]simplify: iters left: 2 (72 enodes) 1545989154.221 * * [misc]simplify: iters left: 1 (87 enodes) 1545989154.238 * [exit]simplify: Simplified to (* (- 1/2 (* k 1/2)) (log PI)) 1545989154.238 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (exp (* (- 1/2 (* k 1/2)) (log PI))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1545989154.238 * * * * [misc]progress: [ 139 / 139 ] simplifiying candidate # 1545989154.239 * [enter]simplify: Simplifying (- (* 1/2 (log PI)) (* 1/2 (* (log PI) k))) 1545989154.239 * * [misc]simplify: iters left: 6 (8 enodes) 1545989154.242 * * [misc]simplify: iters left: 5 (16 enodes) 1545989154.248 * * [misc]simplify: iters left: 4 (36 enodes) 1545989154.259 * * [misc]simplify: iters left: 3 (60 enodes) 1545989154.276 * * [misc]simplify: iters left: 2 (72 enodes) 1545989154.294 * * [misc]simplify: iters left: 1 (87 enodes) 1545989154.327 * [exit]simplify: Simplified to (* (- 1/2 (* k 1/2)) (log PI)) 1545989154.327 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (exp (* (- 1/2 (* k 1/2)) (log PI))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1545989154.327 * * * [misc]progress: adding candidates to table 1545989156.841 * [misc]progress: [Phase 3 of 3] Extracting. 1545989156.841 * * [misc]regime: Finding splitpoints for: (# # # # # # #) 1545989156.843 * * * [misc]regime-changes: Trying 2 branch expressions: (n k) 1545989156.843 * * * * [misc]regimes: Trying to branch on n from (# # # # # # #) 1545989156.903 * * * * [misc]regimes: Trying to branch on k from (# # # # # # #) 1545989156.957 * * * [misc]regime: Found split indices: #